Complex versus simple models: ion-channel cardiac toxicity prediction.

Science.gov (United States)

Mistry, Hitesh B

2018-01-01

There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model B net was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the B net model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.

Complex versus simple models: ion-channel cardiac toxicity prediction

Directory of Open Access Journals (Sweden)

Hitesh B. Mistry

2018-02-01

Full Text Available There is growing interest in applying detailed mathematical models of the heart for ion-channel related cardiac toxicity prediction. However, a debate as to whether such complex models are required exists. Here an assessment in the predictive performance between two established large-scale biophysical cardiac models and a simple linear model Bnet was conducted. Three ion-channel data-sets were extracted from literature. Each compound was designated a cardiac risk category using two different classification schemes based on information within CredibleMeds. The predictive performance of each model within each data-set for each classification scheme was assessed via a leave-one-out cross validation. Overall the Bnet model performed equally as well as the leading cardiac models in two of the data-sets and outperformed both cardiac models on the latest. These results highlight the importance of benchmarking complex versus simple models but also encourage the development of simple models.

Conditional shape models for cardiac motion estimation

DEFF Research Database (Denmark)

Metz, Coert; Baka, Nora; Kirisli, Hortense

2010-01-01

We propose a conditional statistical shape model to predict patient specific cardiac motion from the 3D end-diastolic CTA scan. The model is built from 4D CTA sequences by combining atlas based segmentation and 4D registration. Cardiac motion estimation is, for example, relevant in the dynamic...

Patient-specific models of cardiac biomechanics

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Krishnamurthy, Adarsh; Villongco, Christopher T.; Chuang, Joyce; Frank, Lawrence R.; Nigam, Vishal; Belezzuoli, Ernest; Stark, Paul; Krummen, David E.; Narayan, Sanjiv; Omens, Jeffrey H.; McCulloch, Andrew D.; Kerckhoffs, Roy C. P.

2013-07-01

Patient-specific models of cardiac function have the potential to improve diagnosis and management of heart disease by integrating medical images with heterogeneous clinical measurements subject to constraints imposed by physical first principles and prior experimental knowledge. We describe new methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart. Three-dimensional bi-ventricular geometry is segmented from cardiac CT images at end-diastole from patients with heart failure. Human myofiber and sheet architecture is modeled using eigenvectors computed from diffusion tensor MR images from an isolated, fixed human organ-donor heart and transformed to the patient-specific geometric model using large deformation diffeomorphic mapping. Semi-automated methods were developed for optimizing the passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Material properties of active cardiac muscle contraction were optimized to match ventricular pressures measured by cardiac catheterization, and parameters of a lumped-parameter closed-loop model of the circulation were estimated with a circulatory adaptation algorithm making use of information derived from echocardiography. These components were then integrated to create a multi-scale model of the patient-specific heart. These methods were tested in five heart failure patients from the San Diego Veteran's Affairs Medical Center who gave informed consent. The simulation results showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study*

Science.gov (United States)

Zhan, He-qing; Xia, Ling; Shou, Guo-fa; Zang, Yun-liang; Liu, Feng; Crozier, Stuart

2014-01-01

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies. PMID:24599687

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology.

Directory of Open Access Journals (Sweden)

Shankarjee Krishnamoorthi

Full Text Available We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology.

Science.gov (United States)

Krishnamoorthi, Shankarjee; Perotti, Luigi E; Borgstrom, Nils P; Ajijola, Olujimi A; Frid, Anna; Ponnaluri, Aditya V; Weiss, James N; Qu, Zhilin; Klug, William S; Ennis, Daniel B; Garfinkel, Alan

2014-01-01

We describe a sequence of methods to produce a partial differential equation model of the electrical activation of the ventricles. In our framework, we incorporate the anatomy and cardiac microstructure obtained from magnetic resonance imaging and diffusion tensor imaging of a New Zealand White rabbit, the Purkinje structure and the Purkinje-muscle junctions, and an electrophysiologically accurate model of the ventricular myocytes and tissue, which includes transmural and apex-to-base gradients of action potential characteristics. We solve the electrophysiology governing equations using the finite element method and compute both a 6-lead precordial electrocardiogram (ECG) and the activation wavefronts over time. We are particularly concerned with the validation of the various methods used in our model and, in this regard, propose a series of validation criteria that we consider essential. These include producing a physiologically accurate ECG, a correct ventricular activation sequence, and the inducibility of ventricular fibrillation. Among other components, we conclude that a Purkinje geometry with a high density of Purkinje muscle junctions covering the right and left ventricular endocardial surfaces as well as transmural and apex-to-base gradients in action potential characteristics are necessary to produce ECGs and time activation plots that agree with physiological observations.

Uncertainty and variability in computational and mathematical models of cardiac physiology.

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Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for

Computational cardiology: the bidomain based modified Hill model incorporating viscous effects for cardiac defibrillation

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Cansız, Barış; Dal, Hüsnü; Kaliske, Michael

2017-10-01

Working mechanisms of the cardiac defibrillation are still in debate due to the limited experimental facilities and one-third of patients even do not respond to cardiac resynchronization therapy. With an aim to develop a milestone towards reaching the unrevealed mechanisms of the defibrillation phenomenon, we propose a bidomain based finite element formulation of cardiac electromechanics by taking into account the viscous effects that are disregarded by many researchers. To do so, the material is deemed as an electro-visco-active material and described by the modified Hill model (Cansız et al. in Comput Methods Appl Mech Eng 315:434-466, 2017). On the numerical side, we utilize a staggered solution method, where the elliptic and parabolic part of the bidomain equations and the mechanical field are solved sequentially. The comparative simulations designate that the viscoelastic and elastic formulations lead to remarkably different outcomes upon an externally applied electric field to the myocardial tissue. Besides, the achieved framework requires significantly less computational time and memory compared to monolithic schemes without loss of stability for the presented examples.

"Just-In-Time" Simulation Training Using 3-D Printed Cardiac Models After Congenital Cardiac Surgery.

Science.gov (United States)

Olivieri, Laura J; Su, Lillian; Hynes, Conor F; Krieger, Axel; Alfares, Fahad A; Ramakrishnan, Karthik; Zurakowski, David; Marshall, M Blair; Kim, Peter C W; Jonas, Richard A; Nath, Dilip S

2016-03-01

High-fidelity simulation using patient-specific three-dimensional (3D) models may be effective in facilitating pediatric cardiac intensive care unit (PCICU) provider training for clinical management of congenital cardiac surgery patients. The 3D-printed heart models were rendered from preoperative cross-sectional cardiac imaging for 10 patients undergoing congenital cardiac surgery. Immediately following surgical repair, a congenital cardiac surgeon and an intensive care physician conducted a simulation training session regarding postoperative care utilizing the patient-specific 3D model for the PCICU team. After the simulation, Likert-type 0 to 10 scale questionnaire assessed participant perception of impact of the training session. Seventy clinicians participated in training sessions, including 22 physicians, 38 nurses, and 10 ancillary care providers. Average response to whether 3D models were more helpful than standard hand off was 8.4 of 10. Questions regarding enhancement of understanding and clinical ability received average responses of 9.0 or greater, and 90% of participants scored 8 of 10 or higher. Nurses scored significantly higher than other clinicians on self-reported familiarity with the surgery (7.1 vs. 5.8; P = .04), clinical management ability (8.6 vs. 7.7; P = .02), and ability enhancement (9.5 vs. 8.7; P = .02). Compared to physicians, nurses and ancillary providers were more likely to consider 3D models more helpful than standard hand off (8.7 vs. 7.7; P = .05). Higher case complexity predicted greater enhancement of understanding of surgery (P = .04). The 3D heart models can be used to enhance congenital cardiac critical care via simulation training of multidisciplinary intensive care teams. Benefit may be dependent on provider type and case complexity. © The Author(s) 2016.

Distributed predictive control of spiral wave in cardiac excitable media

International Nuclear Information System (INIS)

Zheng-Ning, Gan; Xin-Ming, Cheng

2010-01-01

In this paper, we propose the distributed predictive control strategies of spiral wave in cardiac excitable media. The modified FitzHugh–Nagumo model was used to express the cardiac excitable media approximately. Based on the control-Lyapunov theory, we obtained the distributed control equation, which consists of a positive control-Lyapunov function and a positive cost function. Using the equation, we investigate two kinds of robust control strategies: the time-dependent distributed control strategy and the space-time dependent distributed control strategy. The feasibility of the strategies was demonstrated via an illustrative example, in which the spiral wave was prevented to occur, and the possibility for inducing ventricular fibrillation was eliminated. The strategies are helpful in designing various cardiac devices. Since the second strategy is more efficient and robust than the first one, and the response time in the second strategy is far less than that in the first one, the former is suitable for the quick-response control systems. In addition, our spatiotemporal control strategies, especially the second strategy, can be applied to other cardiac models, even to other reaction-diffusion systems. (general)

Relationship between cardiac output and effective renal plasma flow in patients with cardiac disease

Energy Technology Data Exchange (ETDEWEB)

McGriffin, D; Tauxe, W N; Lewis, C; Karp, R; Mantle, J

1984-12-01

The relationship between effective renal plasma flow (ERPF) and cardiac output was examined in 46 patients (22 with congestive heart failure and 24 following cardiac surgical procedures) by simultaneously measuring the global ERPF by the single-injection method and cardiac output by the thermodilution method. Of the patients in the heart-failure group, 21 also had pulmonary artery end diastolic pressure (PAEDP) recorded at the same time. ERPF and cardiac output were found to be related by the regression equations: cardiac output = 2.08 + 0.0065 ERPF (r, 080), with a SE of estimate of 0.81 l/min. ERPF and PAEDP were related by the regression equation: PAEDP = 42.02 - 0.0675 ERPF (r, 0.86), with a SE of estimate of 5.5 mm Hg. ERPF may be a useful noninvasive method of estimating cardiac output if it is known that no intrinsic kidney disease is present, and if the error of 0.81 l/min (1 SE of estimate) is within the range of clinical usefulness. The error is principally attributable to the determination of cardiac output by the thermodilution method.

Model Compaction Equation

African Journals Online (AJOL)

The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

Modern Perspectives on Numerical Modeling of Cardiac Pacemaker Cell

Science.gov (United States)

Maltsev, Victor A.; Yaniv, Yael; Maltsev, Anna V.; Stern, Michael D.; Lakatta, Edward G.

2015-01-01

Cardiac pacemaking is a complex phenomenon that is still not completely understood. Together with experimental studies, numerical modeling has been traditionally used to acquire mechanistic insights in this research area. This review summarizes the present state of numerical modeling of the cardiac pacemaker, including approaches to resolve present paradoxes and controversies. Specifically we discuss the requirement for realistic modeling to consider symmetrical importance of both intracellular and cell membrane processes (within a recent “coupled-clock” theory). Promising future developments of the complex pacemaker system models include the introduction of local calcium control, mitochondria function, and biochemical regulation of protein phosphorylation and cAMP production. Modern numerical and theoretical methods such as multi-parameter sensitivity analyses within extended populations of models and bifurcation analyses are also important for the definition of the most realistic parameters that describe a robust, yet simultaneously flexible operation of the coupled-clock pacemaker cell system. The systems approach to exploring cardiac pacemaker function will guide development of new therapies, such as biological pacemakers for treating insufficient cardiac pacemaker function that becomes especially prevalent with advancing age. PMID:24748434

Cardiac Dysfunction in a Porcine Model of Pediatric Malnutrition

DEFF Research Database (Denmark)

Fabiansen, Christian; Lykke, Mikkel; Hother, Anne-Louise

2015-01-01

BACKGROUND: Half a million children die annually of severe acute malnutrition and cardiac dysfunction may contribute to the mortality. However, cardiac function remains poorly examined in cases of severe acute malnutrition. OBJECTIVE: To determine malnutrition-induced echocardiographic disturbances...... and longitudinal changes in plasma pro-atrial natriuretic peptide and cardiac troponin-T in a pediatric porcine model. METHODS AND RESULTS: Five-week old piglets (Duroc-x-Danish Landrace-x-Yorkshire) were fed a nutritionally inadequate maize-flour diet to induce malnutrition (MAIZE, n = 12) or a reference diet...... groups. The myocardial performance index was 86% higher in MAIZE vs AGE-REF (pMalnutrition associates with cardiac dysfunction in a pediatric porcine model by increased myocardial performance index and pro-atrial natriuretic peptide...

Concise Review: Cardiac Disease Modeling Using Induced Pluripotent Stem Cells.

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Yang, Chunbo; Al-Aama, Jumana; Stojkovic, Miodrag; Keavney, Bernard; Trafford, Andrew; Lako, Majlinda; Armstrong, Lyle

2015-09-01

Genetic cardiac diseases are major causes of morbidity and mortality. Although animal models have been created to provide some useful insights into the pathogenesis of genetic cardiac diseases, the significant species differences and the lack of genetic information for complex genetic diseases markedly attenuate the application values of such data. Generation of induced pluripotent stem cells (iPSCs) from patient-specific specimens and subsequent derivation of cardiomyocytes offer novel avenues to study the mechanisms underlying cardiac diseases, to identify new causative genes, and to provide insights into the disease aetiology. In recent years, the list of human iPSC-based models for genetic cardiac diseases has been expanding rapidly, although there are still remaining concerns on the level of functionality of iPSC-derived cardiomyocytes and their ability to be used for modeling complex cardiac diseases in adults. This review focuses on the development of cardiomyocyte induction from pluripotent stem cells, the recent progress in heart disease modeling using iPSC-derived cardiomyocytes, and the challenges associated with understanding complex genetic diseases. To address these issues, we examine the similarity between iPSC-derived cardiomyocytes and their ex vivo counterparts and how this relates to the method used to differentiate the pluripotent stem cells into a cardiomyocyte phenotype. We progress to examine categories of congenital cardiac abnormalities that are suitable for iPSC-based disease modeling. © AlphaMed Press.

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics.

Science.gov (United States)

Cortassa, Sonia; Aon, Miguel A; Marbán, Eduardo; Winslow, Raimond L; O'Rourke, Brian

2003-04-01

We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an

Cardiac Electromechanical Models: From Cell to Organ

Directory of Open Access Journals (Sweden)

Natalia A Trayanova

2011-08-01

Full Text Available The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computation physiology and medicine. This review focuses on electromechanical (EM models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single cell models and the second half addresses organ models. At the subcelluar level, myofilament models represent actin-myosin interaction and Ca-based activation. Myofilament models and their refinements represent an overview of the development in the field. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered the cellular basis of the Frank-Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction-diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and

Modelling conjugation with stochastic differential equations

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

2010-01-01

Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

Consistent three-equation model for thin films

Science.gov (United States)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.

Science.gov (United States)

Kügler, Philipp; Bulelzai, M A K; Erhardt, André H

2017-04-04

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

A model of survival following pre-hospital cardiac arrest based on the Victorian Ambulance Cardiac Arrest Register.

Science.gov (United States)

Fridman, Masha; Barnes, Vanessa; Whyman, Andrew; Currell, Alex; Bernard, Stephen; Walker, Tony; Smith, Karen L

2007-11-01

This study describes the epidemiology of sudden cardiac arrest patients in Victoria, Australia, as captured via the Victorian Ambulance Cardiac Arrest Register (VACAR). We used the VACAR data to construct a new model of out-of-hospital cardiac arrest (OHCA), which was specified in accordance with observed trends. All cases of cardiac arrest in Victoria that were attended by Victorian ambulance services during the period of 2002-2005. Overall survival to hospital discharge was 3.8% among 18,827 cases of OHCA. Survival was 15.7% among 1726 bystander witnessed, adult cardiac arrests of presumed cardiac aetiology, presenting in ventricular fibrillation or ventricular tachycardia (VF/VT), where resuscitation was attempted. In multivariate logistic regression analysis, bystander CPR, cardiac arrest (CA) location, response time, age and sex were predictors of VF/VT, which, in turn, was a strong predictor of survival. The same factors that affected VF/VT made an additional contribution to survival. However, for bystander CPR, CA location and response time this additional contribution was limited to VF/VT patients only. There was no detectable association between survival and age younger than 60 years or response time over 15min. The new model accounts for relationships among predictors of survival. These relationships indicate that interventions such as reduced response times and bystander CPR act in multiple ways to improve survival.

A cardiac electrical activity model based on a cellular automata system in comparison with neural network model.

Science.gov (United States)

Khan, Muhammad Sadiq Ali; Yousuf, Sidrah

2016-03-01

Cardiac Electrical Activity is commonly distributed into three dimensions of Cardiac Tissue (Myocardium) and evolves with duration of time. The indicator of heart diseases can occur randomly at any time of a day. Heart rate, conduction and each electrical activity during cardiac cycle should be monitor non-invasively for the assessment of "Action Potential" (regular) and "Arrhythmia" (irregular) rhythms. Many heart diseases can easily be examined through Automata model like Cellular Automata concepts. This paper deals with the different states of cardiac rhythms using cellular automata with the comparison of neural network also provides fast and highly effective stimulation for the contraction of cardiac muscles on the Atria in the result of genesis of electrical spark or wave. The specific formulated model named as "States of automaton Proposed Model for CEA (Cardiac Electrical Activity)" by using Cellular Automata Methodology is commonly shows the three states of cardiac tissues conduction phenomena (i) Resting (Relax and Excitable state), (ii) ARP (Excited but Absolutely refractory Phase i.e. Excited but not able to excite neighboring cells) (iii) RRP (Excited but Relatively Refractory Phase i.e. Excited and able to excite neighboring cells). The result indicates most efficient modeling with few burden of computation and it is Action Potential during the pumping of blood in cardiac cycle.

Slave equations for spin models

International Nuclear Information System (INIS)

Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

1992-01-01

We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

Differential Equations Models to Study Quorum Sensing.

Science.gov (United States)

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Microengineered in vitro model of cardiac fibrosis through modulating myofibroblast mechanotransduction

International Nuclear Information System (INIS)

Zhao, Hui; Li, Xiaokang; Zhao, Shan; Zeng, Yang; Ding, Haiyan; Du, Yanan; Zhao, Long; Sun, Wei

2014-01-01

Cardiac fibrosis greatly impairs normal heart function post infarction and there is no effective anti-fibrotic drug developed at present. The current therapies for cardiac infarction mainly take effect by eliminating occlusion in coronary artery by thrombolysis drugs, vascular stent grafting or heart bypass operation, which are capable to provide sufficient blood flow for intact myocardium yet showed subtle efficacy in ameliorating fibrosis condition. The advances of in vitro cell/tissue models open new avenues for drug assessment due to the low cost, good controllability and availability as well as the convenience for operation as compared to the animal models. To our knowledge, no proper biomimetic in vitro cardiac fibrosis model has been reported yet. Here we engineered an in vitro cardiac fibrosis model using heart-derived fibroblasts, and the fibrogenesis was recapitulated by patterning the substrate rigidity which mimicked the mechanical heterogeneity of myocardium post-infarction. Various biomarkers for cardiac fibrosis were assayed to validate the biomimicry of the engineered platform. Subsequent addition of Rho-associated protein kinase (ROCK) pathway inhibitor reduced the ratio of myofibroblasts, indicating the feasibility of applying this platform in screening anti-fibrosis drugs. (paper)

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

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Piero Colli Franzone

2018-04-01

Full Text Available We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1 the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2 the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3 the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4 the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks.

Characterization of Cardiac Patients Based on the Synergy Model

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Tavangar

2014-10-01

Full Text Available Background Cardiac patients need comprehensive support due to the adverse effects of this disease on different aspects of their lives. Synergy intervention is a model that focuses on patients' requirements. Objectives This study aimed to determine the eightfold characteristic of cardiac patients based on the synergy model that represent their clinical requirements. Materials and Methods In this descriptive cross-sectional study, 40 cardiac patients hospitalized at the cardiac care unit (CCU of Yazd Afshar Hospital were randomly selected. The data were collected by using a two-part check-list including demographic characteristics and also by studying eight characteristics of patients through interviewing and reviewing their records. The results were analyzed using descriptive statistics such as frequency (percentage and analytical statistics such as Spearman and Mann-Whitney test with the SPSS software, version 18. Results The results showed that among patients' internal characteristics, reversibility (70.6%, vulnerability (68.6%, and predictability (80.4% at level 1 (the minimum score had the highest frequency and stability (49% and complexity (54.9% were at level 3 (average score. Among external characteristics participation in decision-making (80.4% at level 1 had the highest frequency while care (62.7% and recourses (98% were at level 3. Conclusions Ignoring any of the eightfold characteristics based on the synergy model interferes with comprehensive support of cardiac patients. Therefore, it is necessary for professional health practitioners, especially nurses, to consider patients' eightfold characteristics in order to provide quality care.

Complete cardiac regeneration in a mouse model of myocardial infarction.

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Haubner, Bernhard Johannes; Adamowicz-Brice, Martyna; Khadayate, Sanjay; Tiefenthaler, Viktoria; Metzler, Bernhard; Aitman, Tim; Penninger, Josef M

2012-12-01

Cardiac remodeling and subsequent heart failure remain critical issues after myocardial infarction despite improved treatment and reperfusion strategies. Recently, complete cardiac regeneration has been demonstrated in fish and newborn mice following resection of the cardiac apex. However, it remained entirely unclear whether the mammalian heart can also completely regenerate following a complex cardiac ischemic injury. We established a protocol to induce a severe heart attack in one-day-old mice using left anterior descending artery (LAD) ligation. LAD ligation triggered substantial cardiac injury in the left ventricle defined by Caspase 3 activation and massive cell death. Ischemia-induced cardiomyocyte death was also visible on day 4 after LAD ligation. Remarkably, 7 days after the initial ischemic insult, we observed complete cardiac regeneration without any signs of tissue damage or scarring. This tissue regeneration translated into long-term normal heart functions as assessed by echocardiography. In contrast, LAD ligations in 7-day-old mice resulted in extensive scarring comparable to adult mice, indicating that the regenerative capacity for complete cardiac healing after heart attacks can be traced to the first week after birth. RNAseq analyses of hearts on day 1, day 3, and day 10 and comparing LAD-ligated and sham-operated mice surprisingly revealed a transcriptional programme of major changes in genes mediating mitosis and cell division between days 1, 3 and 10 postnatally and a very limited set of genes, including genes regulating cell cycle and extracellular matrix synthesis, being differentially regulated in the regenerating hearts. We present for the first time a mammalian model of complete cardiac regeneration following a severe ischemic cardiac injury. This novel model system provides the unique opportunity to uncover molecular and cellular pathways that can induce cardiac regeneration after ischemic injury, findings that one day could be translated

Cardiac regeneration using pluripotent stem cells—Progression to large animal models

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James J.H. Chong

2014-11-01

Full Text Available Pluripotent stem cells (PSCs have indisputable cardiomyogenic potential and therefore have been intensively investigated as a potential cardiac regenerative therapy. Current directed differentiation protocols are able to produce high yields of cardiomyocytes from PSCs and studies in small animal models of cardiovascular disease have proven sustained engraftment and functional efficacy. Therefore, the time is ripe for cardiac regenerative therapies using PSC derivatives to be tested in large animal models that more closely resemble the hearts of humans. In this review, we discuss the results of our recent study using human embryonic stem cell derived cardiomyocytes (hESC-CM in a non-human primate model of ischemic cardiac injury. Large scale remuscularization, electromechanical coupling and short-term arrhythmias demonstrated by our hESC-CM grafts are discussed in the context of other studies using adult stem cells for cardiac regeneration.

Pregnancy as a cardiac stress model

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Chung, Eunhee; Leinwand, Leslie A.

2014-01-01

Cardiac hypertrophy occurs during pregnancy as a consequence of both volume overload and hormonal changes. Both pregnancy- and exercise-induced cardiac hypertrophy are generally thought to be similar and physiological. Despite the fact that there are shared transcriptional responses in both forms of cardiac adaptation, pregnancy results in a distinct signature of gene expression in the heart. In some cases, however, pregnancy can induce adverse cardiac events in previously healthy women without any known cardiovascular disease. Peripartum cardiomyopathy is the leading cause of non-obstetric mortality during pregnancy. To understand how pregnancy can cause heart disease, it is first important to understand cardiac adaptation during normal pregnancy. This review provides an overview of the cardiac consequences of pregnancy, including haemodynamic, functional, structural, and morphological adaptations, as well as molecular phenotypes. In addition, this review describes the signalling pathways responsible for pregnancy-induced cardiac hypertrophy and angiogenesis. We also compare and contrast cardiac adaptation in response to disease, exercise, and pregnancy. The comparisons of these settings of cardiac hypertrophy provide insight into pregnancy-associated cardiac adaptation. PMID:24448313

Time series analysis as input for clinical predictive modeling: modeling cardiac arrest in a pediatric ICU.

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Kennedy, Curtis E; Turley, James P

2011-10-24

Thousands of children experience cardiac arrest events every year in pediatric intensive care units. Most of these children die. Cardiac arrest prediction tools are used as part of medical emergency team evaluations to identify patients in standard hospital beds that are at high risk for cardiac arrest. There are no models to predict cardiac arrest in pediatric intensive care units though, where the risk of an arrest is 10 times higher than for standard hospital beds. Current tools are based on a multivariable approach that does not characterize deterioration, which often precedes cardiac arrests. Characterizing deterioration requires a time series approach. The purpose of this study is to propose a method that will allow for time series data to be used in clinical prediction models. Successful implementation of these methods has the potential to bring arrest prediction to the pediatric intensive care environment, possibly allowing for interventions that can save lives and prevent disabilities. We reviewed prediction models from nonclinical domains that employ time series data, and identified the steps that are necessary for building predictive models using time series clinical data. We illustrate the method by applying it to the specific case of building a predictive model for cardiac arrest in a pediatric intensive care unit. Time course analysis studies from genomic analysis provided a modeling template that was compatible with the steps required to develop a model from clinical time series data. The steps include: 1) selecting candidate variables; 2) specifying measurement parameters; 3) defining data format; 4) defining time window duration and resolution; 5) calculating latent variables for candidate variables not directly measured; 6) calculating time series features as latent variables; 7) creating data subsets to measure model performance effects attributable to various classes of candidate variables; 8) reducing the number of candidate features; 9

Nonlinear dynamics, chaos and complex cardiac arrhythmias

Science.gov (United States)

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.

2009-10-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

KAUST Repository

Southern, J.A.; Plank, G.; Vigmond, E.J.; Whiteley, J.P.

2009-01-01

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.

Structural equation modeling methods and applications

CERN Document Server

Wang, Jichuan

2012-01-01

A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a

Small and large animal models in cardiac contraction research: advantages and disadvantages.

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Milani-Nejad, Nima; Janssen, Paul M L

2014-03-01

The mammalian heart is responsible for not only pumping blood throughout the body but also adjusting this pumping activity quickly depending upon sudden changes in the metabolic demands of the body. For the most part, the human heart is capable of performing its duties without complications; however, throughout many decades of use, at some point this system encounters problems. Research into the heart's activities during healthy states and during adverse impacts that occur in disease states is necessary in order to strategize novel treatment options to ultimately prolong and improve patients' lives. Animal models are an important aspect of cardiac research where a variety of cardiac processes and therapeutic targets can be studied. However, there are differences between the heart of a human being and an animal and depending on the specific animal, these differences can become more pronounced and in certain cases limiting. There is no ideal animal model available for cardiac research, the use of each animal model is accompanied with its own set of advantages and disadvantages. In this review, we will discuss these advantages and disadvantages of commonly used laboratory animals including mouse, rat, rabbit, canine, swine, and sheep. Since the goal of cardiac research is to enhance our understanding of human health and disease and help improve clinical outcomes, we will also discuss the role of human cardiac tissue in cardiac research. This review will focus on the cardiac ventricular contractile and relaxation kinetics of humans and animal models in order to illustrate these differences. © 2013.

Bayesian Sensitivity Analysis of a Cardiac Cell Model Using a Gaussian Process Emulator

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Chang, Eugene T Y; Strong, Mark; Clayton, Richard H

2015-01-01

Models of electrical activity in cardiac cells have become important research tools as they can provide a quantitative description of detailed and integrative physiology. However, cardiac cell models have many parameters, and how uncertainties in these parameters affect the model output is difficult to assess without undertaking large numbers of model runs. In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators. Using this approach we examined how eight outputs describing the action potential shape and action potential duration restitution depend on six inputs, which we selected to be the maximum conductances in the Luo-Rudy 1991 model. We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents. We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models. PMID:26114610

Competition model for aperiodic stochastic resonance in a Fitzhugh-Nagumo model of cardiac sensory neurons.

Science.gov (United States)

Kember, G C; Fenton, G A; Armour, J A; Kalyaniwalla, N

2001-04-01

Regional cardiac control depends upon feedback of the status of the heart from afferent neurons responding to chemical and mechanical stimuli as transduced by an array of sensory neurites. Emerging experimental evidence shows that neural control in the heart may be partially exerted using subthreshold inputs that are amplified by noisy mechanical fluctuations. This amplification is known as aperiodic stochastic resonance (ASR). Neural control in the noisy, subthreshold regime is difficult to see since there is a near absence of any correlation between input and the output, the latter being the average firing (spiking) rate of the neuron. This lack of correlation is unresolved by traditional energy models of ASR since these models are unsuitable for identifying "cause and effect" between such inputs and outputs. In this paper, the "competition between averages" model is used to determine what portion of a noisy, subthreshold input is responsible, on average, for the output of sensory neurons as represented by the Fitzhugh-Nagumo equations. A physiologically relevant conclusion of this analysis is that a nearly constant amount of input is responsible for a spike, on average, and this amount is approximately independent of the firing rate. Hence, correlation measures are generally reduced as the firing rate is lowered even though neural control under this model is actually unaffected.

Meta-analysis a structural equation modeling approach

CERN Document Server

Cheung, Mike W-L

2015-01-01

Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo

Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

Energy Technology Data Exchange (ETDEWEB)

Gregoire, O

2008-07-01

In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

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Hong, Sehee; Kim, Soyoung

2018-01-01

There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.

A first course in structural equation modeling

CERN Document Server

Raykov, Tenko

2012-01-01

In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...

Structural Equation Model Trees

Science.gov (United States)

Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

2013-01-01

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

Induced pluripotent stem cell derived cardiomyocytes as models for cardiac arrhythmias

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Maaike eHoekstra

2012-08-01

Full Text Available Cardiac arrhythmias are a major cause of morbidity and mortality. In younger patients, the majority of sudden cardiac deaths have an underlying Mendelian genetic cause. Over the last 15 years, enormous progress has been made in identifying the distinct clinical phenotypes and in studying the basic cellular and genetic mechanisms associated with the primary Mendelian (monogenic arrhythmia syndromes. Investigation of the electrophysiological consequences of an ion channel mutation is ideally done in the native cardiomyocyte environment. However, the majority of such studies so far have relied on heterologous expression systems in which single ion channel genes are expressed in non-cardiac cells. In some cases, transgenic mouse models haven been generated, but these also have significant shortcomings, primarily related to species differences.The discovery that somatic cells can be reprogrammed to pluripotency as induced pluripotent stem cells (iPSC has generated much interest since it presents an opportunity to generate patient- and disease-specific cell lines from which normal and diseased human cardiomyocytes can be obtained These genetically diverse human model systems can be studied in vitro and used to decipher mechanisms of disease and identify strategies and reagents for new therapies. Here we review the present state of the art with respect to cardiac disease models already generated using IPSC technology and which have been (partially characterized.Human iPSC (hiPSC models have been described for the cardiac arrhythmia syndromes, including LQT1, LQT2, LQT3-Brugada Syndrome, LQT8/Timothy syndrome and catecholaminergic polymorphic ventricular tachycardia. In most cases, the hiPSC-derived cardiomyoctes recapitulate the disease phenotype and have already provided opportunities for novel insight into cardiac pathophysiology. It is expected that the lines will be useful in the development of pharmacological agents for the management of these

Quantification of left ventricular volumes from cardiac cine MRI using active contour model combined with gradient vector flow

International Nuclear Information System (INIS)

Tanki, Nobuyoshi; Murase, Kenya; Kumashiro, Masayuki; Momoi, Risa; Yang, Xiaomei; Tabuchi, Takashi; Nagayama, Masako; Watanabe, Yuji

2005-01-01

We investigated the feasibility of combining the active contour model with gradient vector flow (Snakes-GVF) to estimate left ventricular (LV) volumes from cardiac cine magnetic resonance imaging (MRI). MRI data were acquired from 27 patients, including 14 adults (9 men, 5 women, 55.0±23.3 years) and 13 children (10 boys, 3 girls, 2.7±2.1 years) using Gyroscan Intera (1.5 Tesla, Philips Medical Systems). LV volumes were calculated by adding the areas surrounded by the contour extracted by Snakes-GVF and compared with volumes estimated by manual tracing. Those estimated by Snakes-GVF [y (mL)] correlated well with those estimated by manual tracing [x (mL)]. In adult cases, the regression equation and correlation coefficient were y=1.008x-0.517 and 0.996, respectively. In pediatric cases, they were y=1.174x-2.542 and 0.992, respectively. In conclusion, Snakes-GVF is a powerful and useful tool for quantifying LV volumes using cardiac MRI. (author)

Spatiotemporal processing of gated cardiac SPECT images using deformable mesh modeling

International Nuclear Information System (INIS)

Brankov, Jovan G.; Yang Yongyi; Wernick, Miles N.

2005-01-01

In this paper we present a spatiotemporal processing approach, based on deformable mesh modeling, for noise reduction in gated cardiac single-photon emission computed tomography images. Because of the partial volume effect (PVE), clinical cardiac-gated perfusion images exhibit a phenomenon known as brightening--the myocardium appears to become brighter as the heart wall thickens. Although brightening is an artifact, it serves as an important diagnostic feature for assessment of wall thickening in clinical practice. Our proposed processing algorithm aims to preserve this important diagnostic feature while reducing the noise level in the images. The proposed algorithm is based on the use of a deformable mesh for modeling the cardiac motion in a gated cardiac sequence, based on which the images are processed by smoothing along space-time trajectories of object points while taking into account the PVE. Our experiments demonstrate that the proposed algorithm can yield significantly more-accurate results than several existing methods

Is a Three-Dimensional Printing Model Better Than a Traditional Cardiac Model for Medical Education? A Pilot Randomized Controlled Study.

Science.gov (United States)

Wang, Zhongmin; Liu, Yuhao; Luo, Hongxing; Gao, Chuanyu; Zhang, Jing; Dai, Yuya

2017-11-01

Three-dimensional (3D) printing is a newly-emerged technology converting a series of two-dimensional images to a touchable 3D model, but no studies have investigated whether or not a 3D printing model is better than a traditional cardiac model for medical education. A 3D printing cardiac model was generated using multi-slice computed tomography datasets. Thirty-four medical students were randomized to either the 3D Printing Group taught with the aid of a 3D printing cardiac model or the Traditional Model Group with a commonly used plastic cardiac model. Questionnaires with 10 medical questions and 3 evaluative questions were filled in by the students. A 3D printing cardiac model was successfully generated. Students in the 3D Printing Group were slightly quicker to answer all questions when compared with the Traditional Model Group (224.53 ± 44.13 s vs. 238.71 ± 68.46 s, p = 0.09), but the total score was not significantly different (6.24 ± 1.30 vs. 7.18 ± 1.70, p = 0.12). Neither the students'satisfaction (p = 0.48) nor their understanding of cardiac structures (p = 0.24) was significantly different between two groups. More students in the 3D Printing Group believed that they had understood at least 90% of teaching content (6 vs. 1). Both groups had 12 (70.6%) students who preferred a 3D printing model for medical education. A 3D printing model was not significantly superior to a traditional model in teaching cardiac diseases in our pilot randomized controlled study, yet more studies may be conducted to validate the real effect of 3D printing on medical education.

Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling

NARCIS (Netherlands)

Hesan, R.; Ghorbani, A.; Dignum, M.V.

2014-01-01

In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we

Integrative computational models of cardiac arrhythmias -- simulating the structurally realistic heart

Science.gov (United States)

Trayanova, Natalia A; Tice, Brock M

2009-01-01

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease. PMID:20628585

Cardiac CT for planning redo cardiac surgery: effect of knowledge-based iterative model reconstruction on image quality

International Nuclear Information System (INIS)

Oda, Seitaro; Weissman, Gaby; Weigold, W. Guy; Vembar, Mani

2015-01-01

The purpose of this study was to investigate the effects of knowledge-based iterative model reconstruction (IMR) on image quality in cardiac CT performed for the planning of redo cardiac surgery by comparing IMR images with images reconstructed with filtered back-projection (FBP) and hybrid iterative reconstruction (HIR). We studied 31 patients (23 men, 8 women; mean age 65.1 ± 16.5 years) referred for redo cardiac surgery who underwent cardiac CT. Paired image sets were created using three types of reconstruction: FBP, HIR, and IMR. Quantitative parameters including CT attenuation, image noise, and contrast-to-noise ratio (CNR) of each cardiovascular structure were calculated. The visual image quality - graininess, streak artefact, margin sharpness of each cardiovascular structure, and overall image quality - was scored on a five-point scale. The mean image noise of FBP, HIR, and IMR images was 58.3 ± 26.7, 36.0 ± 12.5, and 14.2 ± 5.5 HU, respectively; there were significant differences in all comparison combinations among the three methods. The CNR of IMR images was better than that of FBP and HIR images in all evaluated structures. The visual scores were significantly higher for IMR than for the other images in all evaluated parameters. IMR can provide significantly improved qualitative and quantitative image quality at in cardiac CT for planning of reoperative cardiac surgery. (orig.)

Embryonic cardiac morphometry in Carnegie stages 15-23, from the Complutense University of Madrid Institute of Embryology Human Embryo Collection.

Science.gov (United States)

Arráez-Aybar, L A; Turrero-Nogués, A; Marantos-Gamarra, D G

2008-01-01

We performed a morphometric study of cardiac development on human embryos to complement the scarce data on human embryonic cardiac morphometry and to attempt to establish, from these, algorithms describing cardiac growth during the second month of gestation. Thirty human embryos from Carnegie stages 15-23 were included in the study. Shrinkage and compression effects from fixation and inclusion in paraffin were considered in our calculations. Growth of the cardiac (whole heart) volume and volume of ventricular myocardium through the Carnegie stages were analysed by ANOVA. Linear correlation was used to describe the relationship between the ventricular myocardium and cardiac volumes. Comparisons of models were carried out through the R2 statistic. The relationship volume of ventricular myocardium versus cardiac volume is expressed by the equation: cardiac volume = 0.6266 + 2.4778 volume of ventricular myocardium. The relationship cardiac volume versus crown-rump length is expressed by the equation: cardiac volume = 1.3 e(0.126 CR length), where e is the base of natural logarithms. At a clinical level, these results can contribute towards the establishment of a normogram for cardiac development, useful for the design of strategies for early diagnosis of congenital heart disease. They can also help in the study of embryogenesis, for example in the discussion of ventricular trabeculation. Copyright 2007 S. Karger AG, Basel.

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics.

Science.gov (United States)

Weise, Louis D; Panfilov, Alexander V

2013-01-01

We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006) and tension development (adjusted Niederer, Hunter, Smith, 2006 model) with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material). Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.

A discrete electromechanical model for human cardiac tissue: effects of stretch-activated currents and stretch conditions on restitution properties and spiral wave dynamics.

Directory of Open Access Journals (Sweden)

Louis D Weise

Full Text Available We introduce an electromechanical model for human cardiac tissue which couples a biophysical model of cardiac excitation (Tusscher, Noble, Noble, Panfilov, 2006 and tension development (adjusted Niederer, Hunter, Smith, 2006 model with a discrete elastic mass-lattice model. The equations for the excitation processes are solved with a finite difference approach, and the equations of the mass-lattice model are solved using Verlet integration. This allows the coupled problem to be solved with high numerical resolution. Passive mechanical properties of the mass-lattice model are described by a generalized Hooke's law for finite deformations (Seth material. Active mechanical contraction is initiated by changes of the intracellular calcium concentration, which is a variable of the electrical model. Mechanical deformation feeds back on the electrophysiology via stretch-activated ion channels whose conductivity is controlled by the local stretch of the medium. We apply the model to study how stretch-activated currents affect the action potential shape, restitution properties, and dynamics of spiral waves, under constant stretch, and dynamic stretch caused by active mechanical contraction. We find that stretch conditions substantially affect these properties via stretch-activated currents. In constantly stretched medium, we observe a substantial decrease in conduction velocity, and an increase of action potential duration; whereas, with dynamic stretch, action potential duration is increased only slightly, and the conduction velocity restitution curve becomes biphasic. Moreover, in constantly stretched medium, we find an increase of the core size and period of a spiral wave, but no change in rotation dynamics; in contrast, in the dynamically stretching medium, we observe spiral drift. Our results may be important to understand how altered stretch conditions affect the heart's functioning.

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

Science.gov (United States)

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

Macroscopic balance equations for two-phase flow models

International Nuclear Information System (INIS)

Hughes, E.D.

1979-01-01

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

Introduction to computation and modeling for differential equations

CERN Document Server

Edsberg, Lennart

2008-01-01

An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

Cardiac magnetic source imaging based on current multipole model

International Nuclear Information System (INIS)

Tang Fa-Kuan; Wang Qian; Hua Ning; Lu Hong; Tang Xue-Zheng; Ma Ping

2011-01-01

It is widely accepted that the heart current source can be reduced into a current multipole. By adopting three linear inverse methods, the cardiac magnetic imaging is achieved in this article based on the current multipole model expanded to the first order terms. This magnetic imaging is realized in a reconstruction plane in the centre of human heart, where the current dipole array is employed to represent realistic cardiac current distribution. The current multipole as testing source generates magnetic fields in the measuring plane, serving as inputs of cardiac magnetic inverse problem. In the heart-torso model constructed by boundary element method, the current multipole magnetic field distribution is compared with that in the homogeneous infinite space, and also with the single current dipole magnetic field distribution. Then the minimum-norm least-squares (MNLS) method, the optimal weighted pseudoinverse method (OWPIM), and the optimal constrained linear inverse method (OCLIM) are selected as the algorithms for inverse computation based on current multipole model innovatively, and the imaging effects of these three inverse methods are compared. Besides, two reconstructing parameters, residual and mean residual, are also discussed, and their trends under MNLS, OWPIM and OCLIM each as a function of SNR are obtained and compared. (general)

Differential equation models for sharp threshold dynamics.

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Schramm, Harrison C; Dimitrov, Nedialko B

2014-01-01

We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.

Fitting ARMA Time Series by Structural Equation Models.

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van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

The reservoir model: a differential equation model of psychological regulation.

Science.gov (United States)

Deboeck, Pascal R; Bergeman, C S

2013-06-01

Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

Mathematical cardiac electrophysiology

CERN Document Server

Colli Franzone, Piero; Scacchi, Simone

2014-01-01

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematica...

Linear causal modeling with structural equations

CERN Document Server

Mulaik, Stanley A

2009-01-01

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

Modeling and Prediction Using Stochastic Differential Equations

DEFF Research Database (Denmark)

Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

2016-01-01

Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...

Isostable reduction with applications to time-dependent partial differential equations.

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Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Stability results for the parameter identification inverse problem in cardiac electrophysiology

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Lassoued, Jamila; Mahjoub, Moncef; Zemzemi, Néjib

2016-11-01

In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation (ODE). We are interested in proving the stability of the identification of the parameter {τ }{in}, which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both partial differential equation (PDE) and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter {τ }{in} giving some observations of both state variables at a given time t 0 in the whole domain and in the PDE variable in a non empty open subset w 0 of the domain.

Partial Differential Equations Modeling and Numerical Simulation

CERN Document Server

Glowinski, Roland

2008-01-01

This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...

A priori motion models for four-dimensional reconstruction in gated cardiac SPECT

International Nuclear Information System (INIS)

Lalush, D.S.; Tsui, B.M.W.; Cui, Lin

1996-01-01

We investigate the benefit of incorporating a priori assumptions about cardiac motion in a fully four-dimensional (4D) reconstruction algorithm for gated cardiac SPECT. Previous work has shown that non-motion-specific 4D Gibbs priors enforcing smoothing in time and space can control noise while preserving resolution. In this paper, we evaluate methods for incorporating known heart motion in the Gibbs prior model. The new model is derived by assigning motion vectors to each 4D voxel, defining the movement of that volume of activity into the neighboring time frames. Weights for the Gibbs cliques are computed based on these open-quotes most likelyclose quotes motion vectors. To evaluate, we employ the mathematical cardiac-torso (MCAT) phantom with a new dynamic heart model that simulates the beating and twisting motion of the heart. Sixteen realistically-simulated gated datasets were generated, with noise simulated to emulate a real Tl-201 gated SPECT study. Reconstructions were performed using several different reconstruction algorithms, all modeling nonuniform attenuation and three-dimensional detector response. These include ML-EM with 4D filtering, 4D MAP-EM without prior motion assumption, and 4D MAP-EM with prior motion assumptions. The prior motion assumptions included both the correct motion model and incorrect models. Results show that reconstructions using the 4D prior model can smooth noise and preserve time-domain resolution more effectively than 4D linear filters. We conclude that modeling of motion in 4D reconstruction algorithms can be a powerful tool for smoothing noise and preserving temporal resolution in gated cardiac studies

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2014-01-01

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

Generalized latent variable modeling multilevel, longitudinal, and structural equation models

CERN Document Server

Skrondal, Anders; Rabe-Hesketh, Sophia

2004-01-01

This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.

Model Servqual Dengan Pendekatan Structural Equation Modeling (Studi Pada Mahasiswa Sistem Informasi)

OpenAIRE

Nurfaizal, Yusmedi

2015-01-01

Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...

A discrete model of a modified Burgers' partial differential equation

Science.gov (United States)

Mickens, R. E.; Shoosmith, J. N.

1990-01-01

A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

Methods of mathematical modelling continuous systems and differential equations

CERN Document Server

Witelski, Thomas

2015-01-01

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

Directory of Open Access Journals (Sweden)

Olaniyi Samuel Iyiola

2014-09-01

Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Dynamic data analysis modeling data with differential equations

CERN Document Server

Ramsay, James

2017-01-01

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

Combining computer modelling and cardiac imaging to understand right ventricular pump function.

Science.gov (United States)

Walmsley, John; van Everdingen, Wouter; Cramer, Maarten J; Prinzen, Frits W; Delhaas, Tammo; Lumens, Joost

2017-10-01

Right ventricular (RV) dysfunction is a strong predictor of outcome in heart failure and is a key determinant of exercise capacity. Despite these crucial findings, the RV remains understudied in the clinical, experimental, and computer modelling literature. This review outlines how recent advances in using computer modelling and cardiac imaging synergistically help to understand RV function in health and disease. We begin by highlighting the complexity of interactions that make modelling the RV both challenging and necessary, and then summarize the multiscale modelling approaches used to date to simulate RV pump function in the context of these interactions. We go on to demonstrate how these modelling approaches in combination with cardiac imaging have improved understanding of RV pump function in pulmonary arterial hypertension, arrhythmogenic right ventricular cardiomyopathy, dyssynchronous heart failure and cardiac resynchronization therapy, hypoplastic left heart syndrome, and repaired tetralogy of Fallot. We conclude with a perspective on key issues to be addressed by computational models of the RV in the near future. Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2017. For permissions, please email: journals.permissions@oup.com.

ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES

Directory of Open Access Journals (Sweden)

Josip Arnerić

2010-12-01

Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.

Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

Energy Technology Data Exchange (ETDEWEB)

Smith, H.L. (Arizona State Univ., Tempe (United States))

1993-01-01

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

Stochastic differential equation model to Prendiville processes

International Nuclear Information System (INIS)

Granita; Bahar, Arifah

2015-01-01

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

Stochastic differential equation model to Prendiville processes

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

2015-10-22

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

Energy Technology Data Exchange (ETDEWEB)

Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

1996-12-31

Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

The dispersionless Lax equations and topological minimal models

International Nuclear Information System (INIS)

Krichever, I.

1992-01-01

It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)

Development and Validation of Predictive Models of Cardiac Mortality and Transplantation in Resynchronization Therapy

Directory of Open Access Journals (Sweden)

Eduardo Arrais Rocha

2015-01-01

Full Text Available Abstract Background: 30-40% of cardiac resynchronization therapy cases do not achieve favorable outcomes. Objective: This study aimed to develop predictive models for the combined endpoint of cardiac death and transplantation (Tx at different stages of cardiac resynchronization therapy (CRT. Methods: Prospective observational study of 116 patients aged 64.8 ± 11.1 years, 68.1% of whom had functional class (FC III and 31.9% had ambulatory class IV. Clinical, electrocardiographic and echocardiographic variables were assessed by using Cox regression and Kaplan-Meier curves. Results: The cardiac mortality/Tx rate was 16.3% during the follow-up period of 34.0 ± 17.9 months. Prior to implantation, right ventricular dysfunction (RVD, ejection fraction < 25% and use of high doses of diuretics (HDD increased the risk of cardiac death and Tx by 3.9-, 4.8-, and 5.9-fold, respectively. In the first year after CRT, RVD, HDD and hospitalization due to congestive heart failure increased the risk of death at hazard ratios of 3.5, 5.3, and 12.5, respectively. In the second year after CRT, RVD and FC III/IV were significant risk factors of mortality in the multivariate Cox model. The accuracy rates of the models were 84.6% at preimplantation, 93% in the first year after CRT, and 90.5% in the second year after CRT. The models were validated by bootstrapping. Conclusion: We developed predictive models of cardiac death and Tx at different stages of CRT based on the analysis of simple and easily obtainable clinical and echocardiographic variables. The models showed good accuracy and adjustment, were validated internally, and are useful in the selection, monitoring and counseling of patients indicated for CRT.

Integrative Modeling of Electrical Properties of Pacemaker Cardiac Cells

Science.gov (United States)

Grigoriev, M.; Babich, L.

2016-06-01

This work represents modeling of electrical properties of pacemaker (sinus) cardiac cells. Special attention is paid to electrical potential arising from transmembrane current of Na+, K+ and Ca2+ ions. This potential is calculated using the NaCaX model. In this respect, molar concentration of ions in the intercellular space which is calculated on the basis of the GENTEX model is essential. Combined use of two different models allows referring this approach to integrative modeling.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

Science.gov (United States)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

Science.gov (United States)

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Bogomolny equations in certain generalized baby BPS Skyrme models

Science.gov (United States)

Stępień, Ł. T.

2018-01-01

By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi-Prasad-Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model: the nonminimal coupling to the gauge field and the k-deformed ungauged model. In particular, we study how the Bogomolny equations and the equation for the potential reflect these two modifications. In both examples, the CSNC method appears to be a very useful tool. We also find certain localized solutions of these Bogomolny equations.

A practical course in differential equations and mathematical modeling

CERN Document Server

Ibragimov , Nail H

2009-01-01

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

Revised predictive equations for salt intrusion modelling in estuaries

NARCIS (Netherlands)

Gisen, J.I.A.; Savenije, H.H.G.; Nijzink, R.C.

2015-01-01

For one-dimensional salt intrusion models to be predictive, we need predictive equations to link model parameters to observable hydraulic and geometric variables. The one-dimensional model of Savenije (1993b) made use of predictive equations for the Van der Burgh coefficient $K$ and the dispersion

Modeling animal movements using stochastic differential equations

Science.gov (United States)

Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie

2004-01-01

We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...

Multiplicity Control in Structural Equation Modeling

Science.gov (United States)

Cribbie, Robert A.

2007-01-01

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…

Parameter Estimates in Differential Equation Models for Chemical Kinetics

Science.gov (United States)

Winkel, Brian

2011-01-01

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

Cardiac spheroids as promising in vitro models to study the human heart microenvironment

DEFF Research Database (Denmark)

Polonchuk, Liudmila; Chabria, Mamta; Badi, Laura

2017-01-01

Three-dimensional in vitro cell systems are a promising alternative to animals to study cardiac biology and disease. We have generated three-dimensional in vitro models of the human heart ("cardiac spheroids", CSs) by co-culturing human primary or iPSC-derived cardiomyocytes, endothelial cells an...

Structural Equation Modeling of Multivariate Time Series

Science.gov (United States)

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

Non-Equilibrium Turbulence and Two-Equation Modeling

Science.gov (United States)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Eight equation model for arbitrary shaped pipe conveying fluid

International Nuclear Information System (INIS)

Gale, J.; Tiselj, I.

2006-01-01

Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)

[Measurement of cardiac output by thermodilution with a diode as a temperature sensor].

Science.gov (United States)

Díaz Fernández, A; Benítez, D; Sánchez Tello, G; Márquez, L A

1979-01-01

An area integrator for the thermodilution curve in cardiac output measurement is described. A new temperature sensor is used, a diode with some advantages over the thermistor normally used. The main advantages are: easy calibration and replacement, and broad range of linearity. The cardiac output values obtained in dog with the integrator follow a linear relationship with those of the flowmeter. In simultaneous measurements the correlation is R = 0.96. Using a diode as temperature sensor a modification of the Steward Hamilton equation (used for thermistor) is necessary. With this new equation a monogram is performed to calculate the cardiac output from the area given by the numerical integrator.

Handbook of structural equation modeling

CERN Document Server

Hoyle, Rick H

2012-01-01

The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu

Cardiac remodeling in the mouse model of Marfan syndrome develops into two distinctive phenotypes.

Science.gov (United States)

Tae, Hyun-Jin; Petrashevskaya, Natalia; Marshall, Shannon; Krawczyk, Melissa; Talan, Mark

2016-01-15

Marfan syndrome (MFS) is a systemic disorder of connective tissue caused by mutations in fibrillin-1. Cardiac dysfunction in MFS has not been characterized halting the development of therapies of cardiac complication in MFS. We aimed to study the age-dependent cardiac remodeling in the mouse model of MFS FbnC1039G+/- mouse [Marfan heterozygous (HT) mouse] and its association with valvular regurgitation. Marfan HT mice of 2-4 mo demonstrated a mild hypertrophic cardiac remodeling with predominant decline of diastolic function and increased transforming growth factor-β canonical (p-SMAD2/3) and noncanonical (p-ERK1/2 and p-p38 MAPK) signaling and upregulation of hypertrophic markers natriuretic peptides atrium natriuretic peptide and brain natriuretic peptide. Among older HT mice (6-14 mo), cardiac remodeling was associated with two distinct phenotypes, manifesting either dilated or constricted left ventricular chamber. Dilatation of left ventricular chamber was accompanied by biochemical evidence of greater mechanical stress, including elevated ERK1/2 and p38 MAPK phosphorylation and higher brain natriuretic peptide expression. The aortic valve regurgitation was registered in 20% of the constricted group and 60% of the dilated group, whereas mitral insufficiency was observed in 40% of the constricted group and 100% of the dilated group. Cardiac dysfunction was not associated with the increase of interstitial fibrosis and nonmyocyte proliferation. In the mouse model fibrillin-1, haploinsufficiency results in the early onset of nonfibrotic hypertrophic cardiac remodeling and dysfunction, independently from valvular abnormalities. MFS heart is vulnerable to stress-induced cardiac dilatation in the face of valvular regurgitation, and stress-activated MAPK signals represent a potential target for cardiac management in MFS.

Modeling of oxygen transport and cellular energetics explains observations on in vivo cardiac energy metabolism.

Directory of Open Access Journals (Sweden)

Daniel A Beard

2006-09-01

Full Text Available Observations on the relationship between cardiac work rate and the levels of energy metabolites adenosine triphosphate (ATP, adenosine diphosphate (ADP, and phosphocreatine (CrP have not been satisfactorily explained by theoretical models of cardiac energy metabolism. Specifically, the in vivo stability of ATP, ADP, and CrP levels in response to changes in work and respiratory rate has eluded explanation. Here a previously developed model of mitochondrial oxidative phosphorylation, which was developed based on data obtained from isolated cardiac mitochondria, is integrated with a spatially distributed model of oxygen transport in the myocardium to analyze data obtained from several laboratories over the past two decades. The model includes the components of the respiratory chain, the F0F1-ATPase, adenine nucleotide translocase, and the mitochondrial phosphate transporter at the mitochondrial level; adenylate kinase, creatine kinase, and ATP consumption in the cytoplasm; and oxygen transport between capillaries, interstitial fluid, and cardiomyocytes. The integrated model is able to reproduce experimental observations on ATP, ADP, CrP, and inorganic phosphate levels in canine hearts over a range of workload and during coronary hypoperfusion and predicts that cytoplasmic inorganic phosphate level is a key regulator of the rate of mitochondrial respiration at workloads for which the rate of cardiac oxygen consumption is less than or equal to approximately 12 mumol per minute per gram of tissue. At work rates corresponding to oxygen consumption higher than 12 mumol min(-1 g(-1, model predictions deviate from the experimental data, indicating that at high work rates, additional regulatory mechanisms that are not currently incorporated into the model may be important. Nevertheless, the integrated model explains metabolite levels observed at low to moderate workloads and the changes in metabolite levels and tissue oxygenation observed during graded

Cardiac disease and arrhythmogenesis: Mechanistic insights from mouse models

Directory of Open Access Journals (Sweden)

Lois Choy

2016-09-01

Full Text Available The mouse is the second mammalian species, after the human, in which substantial amount of the genomic information has been analyzed. With advances in transgenic technology, mutagenesis is now much easier to carry out in mice. Consequently, an increasing number of transgenic mouse systems have been generated for the study of cardiac arrhythmias in ion channelopathies and cardiomyopathies. Mouse hearts are also amenable to physical manipulation such as coronary artery ligation and transverse aortic constriction to induce heart failure, radiofrequency ablation of the AV node to model complete AV block and even implantation of a miniature pacemaker to induce cardiac dyssynchrony. Last but not least, pharmacological models, despite being simplistic, have enabled us to understand the physiological mechanisms of arrhythmias and evaluate the anti-arrhythmic properties of experimental agents, such as gap junction modulators, that may be exert therapeutic effects in other cardiac diseases. In this article, we examine these in turn, demonstrating that primary inherited arrhythmic syndromes are now recognized to be more complex than abnormality in a particular ion channel, involving alterations in gene expression and structural remodelling. Conversely, in cardiomyopathies and heart failure, mutations in ion channels and proteins have been identified as underlying causes, and electrophysiological remodelling are recognized pathological features. Transgenic techniques causing mutagenesis in mice are extremely powerful in dissecting the relative contributions of different genes play in producing disease phenotypes. Mouse models can serve as useful systems in which to explore how protein defects contribute to arrhythmias and direct future therapy.

Generalized heat-transport equations: parabolic and hyperbolic models

Science.gov (United States)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Towards an integrative computational model of the guinea pig cardiac myocyte

Directory of Open Access Journals (Sweden)

Laura Doyle Gauthier

2012-07-01

Full Text Available The local control theory of excitation-contraction (EC coupling asserts that regulation of calcium (Ca2+ release occurs at the nanodomain level, where openings of single L-type Ca2+ channels (LCCs trigger openings of small clusters of ryanodine receptors (RyRs co-localized within the dyad. A consequence of local control is that the whole-cell Ca2+ transient is a smooth continuous function of influx of Ca2+ through LCCs. While this so-called graded release property has been known for some time, it’s functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically-based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca2+ release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally-observed causal relationship between action potential (AP shape and timing of Ca2+ and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca2+ transients, thus influencing tissue-level electro-mechanical function.

Toward an integrative computational model of the Guinea pig cardiac myocyte.

Science.gov (United States)

Gauthier, Laura Doyle; Greenstein, Joseph L; Winslow, Raimond L

2012-01-01

The local control theory of excitation-contraction (EC) coupling asserts that regulation of calcium (Ca(2+)) release occurs at the nanodomain level, where openings of single L-type Ca(2+) channels (LCCs) trigger openings of small clusters of ryanodine receptors (RyRs) co-localized within the dyad. A consequence of local control is that the whole-cell Ca(2+) transient is a smooth continuous function of influx of Ca(2+) through LCCs. While this so-called graded release property has been known for some time, its functional importance to the integrated behavior of the cardiac ventricular myocyte has not been fully appreciated. We previously formulated a biophysically based model, in which LCCs and RyRs interact via a coarse-grained representation of the dyadic space. The model captures key features of local control using a low-dimensional system of ordinary differential equations. Voltage-dependent gain and graded Ca(2+) release are emergent properties of this model by virtue of the fact that model formulation is closely based on the sub-cellular basis of local control. In this current work, we have incorporated this graded release model into a prior model of guinea pig ventricular myocyte electrophysiology, metabolism, and isometric force production. The resulting integrative model predicts the experimentally observed causal relationship between action potential (AP) shape and timing of Ca(2+) and force transients, a relationship that is not explained by models lacking the graded release property. Model results suggest that even relatively subtle changes in AP morphology that may result, for example, from remodeling of membrane transporter expression in disease or spatial variation in cell properties, may have major impact on the temporal waveform of Ca(2+) transients, thus influencing tissue level electromechanical function.

Stochastic differential equations used to model conjugation

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo

Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...

Relations between the kinetic equation and the Langevin models in two-phase flow modelling

International Nuclear Information System (INIS)

Minier, J.P.; Pozorski, J.

1997-05-01

The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)

Large-deflection statics analysis of active cardiac catheters through co-rotational modelling.

Science.gov (United States)

Peng Qi; Chen Qiu; Mehndiratta, Aadarsh; I-Ming Chen; Haoyong Yu

2016-08-01

This paper presents a co-rotational concept for large-deflection formulation of cardiac catheters. Using this approach, the catheter is first discretized with a number of equal length beam elements and nodes, and the rigid body motions of an individual beam element are separated from its deformations. Therefore, it is adequate for modelling arbitrarily large deflections of a catheter with linear elastic analysis at the local element level. A novel design of active cardiac catheter of 9 Fr in diameter at the beginning of the paper is proposed, which is based on the contra-rotating double helix patterns and is improved from the previous prototypes. The modelling section is followed by MATLAB simulations of various deflections when the catheter is exerted different types of loads. This proves the feasibility of the presented modelling approach. To the best knowledge of the authors, it is the first to utilize this methodology for large-deflection static analysis of the catheter, which will enable more accurate control of robot-assisted cardiac catheterization procedures. Future work would include further experimental validations.

Genetic Dissection of Cardiac Remodeling in an Isoproterenol-Induced Heart Failure Mouse Model.

Directory of Open Access Journals (Sweden)

Jessica Jen-Chu Wang

2016-07-01

Full Text Available We aimed to understand the genetic control of cardiac remodeling using an isoproterenol-induced heart failure model in mice, which allowed control of confounding factors in an experimental setting. We characterized the changes in cardiac structure and function in response to chronic isoproterenol infusion using echocardiography in a panel of 104 inbred mouse strains. We showed that cardiac structure and function, whether under normal or stress conditions, has a strong genetic component, with heritability estimates of left ventricular mass between 61% and 81%. Association analyses of cardiac remodeling traits, corrected for population structure, body size and heart rate, revealed 17 genome-wide significant loci, including several loci containing previously implicated genes. Cardiac tissue gene expression profiling, expression quantitative trait loci, expression-phenotype correlation, and coding sequence variation analyses were performed to prioritize candidate genes and to generate hypotheses for downstream mechanistic studies. Using this approach, we have validated a novel gene, Myh14, as a negative regulator of ISO-induced left ventricular mass hypertrophy in an in vivo mouse model and demonstrated the up-regulation of immediate early gene Myc, fetal gene Nppb, and fibrosis gene Lgals3 in ISO-treated Myh14 deficient hearts compared to controls.

Hybrid automata models of cardiac ventricular electrophysiology for real-time computational applications.

Science.gov (United States)

Andalam, Sidharta; Ramanna, Harshavardhan; Malik, Avinash; Roop, Parthasarathi; Patel, Nitish; Trew, Mark L

2016-08-01

Virtual heart models have been proposed for closed loop validation of safety-critical embedded medical devices, such as pacemakers. These models must react in real-time to off-the-shelf medical devices. Real-time performance can be obtained by implementing models in computer hardware, and methods of compiling classes of Hybrid Automata (HA) onto FPGA have been developed. Models of ventricular cardiac cell electrophysiology have been described using HA which capture the complex nonlinear behavior of biological systems. However, many models that have been used for closed-loop validation of pacemakers are highly abstract and do not capture important characteristics of the dynamic rate response. We developed a new HA model of cardiac cells which captures dynamic behavior and we implemented the model in hardware. This potentially enables modeling the heart with over 1 million dynamic cells, making the approach ideal for closed loop testing of medical devices.

on the properties of solutions and some applications on the TOV differential equation with a model of nuclear equation of state

International Nuclear Information System (INIS)

Esmail, S.F.H.

2006-01-01

the mathematical formulation of numerous physical problems results in differential equations actually non-linear differential equations . in our study we are interested in solutions of differential equations which describe the structure of neutron star in non-relativistic and relativistic cases. the aim of this work is to determine the mass and the radius of a neutron star, by solving the tolmann-oppenheimer-volkoff (TOV) differential equation using different models of the nuclear equation of state (EOS). analytically solutions are obtained for a simple form of the nuclear equation of state of Clayton model and poly trope model. for a more realistic equation of state the TOV differential equation is solved numerically using rung -Kutta method

Factors influencing creep model equation selection

International Nuclear Information System (INIS)

Holdsworth, S.R.; Askins, M.; Baker, A.; Gariboldi, E.; Holmstroem, S.; Klenk, A.; Ringel, M.; Merckling, G.; Sandstrom, R.; Schwienheer, M.; Spigarelli, S.

2008-01-01

During the course of the EU-funded Advanced-Creep Thematic Network, ECCC-WG1 reviewed the applicability and effectiveness of a range of model equations to represent the accumulation of creep strain in various engineering alloys. In addition to considering the experience of network members, the ability of several models to describe the deformation characteristics of large single and multi-cast collations of ε(t,T,σ) creep curves have been evaluated in an intensive assessment inter-comparison activity involving three steels, 21/4 CrMo (P22), 9CrMoVNb (Steel-91) and 18Cr13NiMo (Type-316). The choice of the most appropriate creep model equation for a given application depends not only on the high-temperature deformation characteristics of the material under consideration, but also on the characteristics of the dataset, the number of casts for which creep curves are available and on the strain regime for which an analytical representation is required. The paper focuses on the factors which can influence creep model selection and model-fitting approach for multi-source, multi-cast datasets

Nonlinear integral equations for the sausage model

Science.gov (United States)

Ahn, Changrim; Balog, Janos; Ravanini, Francesco

2017-08-01

The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.

On the Use of Structural Equation Models in Marketing Modeling

NARCIS (Netherlands)

Steenkamp, J.E.B.M.; Baumgartner, H.

2000-01-01

We reflect on the role of structural equation modeling (SEM) in marketing modeling and managerial decision making. We discuss some benefits provided by SEM and alert marketing modelers to several recent developments in SEM in three areas: measurement analysis, analysis of cross-sectional data, and

Cardiac remodelling in a baboon model of intrauterine growth restriction mimics accelerated ageing.

Science.gov (United States)

Kuo, Anderson H; Li, Cun; Li, Jinqi; Huber, Hillary F; Nathanielsz, Peter W; Clarke, Geoffrey D

2017-02-15

Rodent models of intrauterine growth restriction (IUGR) successfully identify mechanisms that can lead to short-term and long-term detrimental cardiomyopathies but differences between rodent and human cardiac physiology and placental-fetal development indicate a need for models in precocial species for translation to human development. We developed a baboon model for IUGR studies using a moderate 30% global calorie restriction of pregnant mothers and used cardiac magnetic resonance imaging to evaluate offspring heart function in early adulthood. Impaired diastolic and systolic cardiac function was observed in IUGR offspring with differences between male and female subjects, compared to their respective controls. Aspects of cardiac impairment found in the IUGR offspring were similar to those found in normal controls in a geriatric cohort. Understanding early cardiac biomarkers of IUGR using non-invasive imaging in this susceptible population, especially taking into account sexual dimorphisms, will aid recognition of the clinical presentation, development of biomarkers suitable for use in humans and management of treatment strategies. Extensive rodent studies have shown that reduced perinatal nutrition programmes chronic cardiovascular disease. To enable translation to humans, we developed baboon offspring cohorts from mothers fed ad libitum (control) or 70% of the control ad libitum diet in pregnancy and lactation, which were growth restricted at birth. We hypothesized that intrauterine growth restriction (IUGR) offspring hearts would show impaired function and a premature ageing phenotype. We studied IUGR baboons (8 male, 8 female, 5.7 years), control offspring (8 male, 8 female, 5.6 years - human equivalent approximately 25 years), and normal elderly (OLD) baboons (6 male, 6 female, mean 15.9 years). Left ventricular (LV) morphology and systolic and diastolic function were evaluated with cardiac MRI and normalized to body surface area. Two-way ANOVA by group

Is the Langevin phase equation an efficient model for oscillating neurons?

Science.gov (United States)

Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru

2009-12-01

The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

Is the Langevin phase equation an efficient model for oscillating neurons?

International Nuclear Information System (INIS)

Ota, Keisuke; Tsunoda, Takamasa; Aonishi, Toru; Omori, Toshiaki; Okada, Masato; Watanabe, Shigeo; Miyakawa, Hiroyoshi

2009-01-01

The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

Memory-induced nonlinear dynamics of excitation in cardiac diseases.

Science.gov (United States)

Landaw, Julian; Qu, Zhilin

2018-04-01

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Optimal harvesting for a predator-prey agent-based model using difference equations.

Science.gov (United States)

Oremland, Matthew; Laubenbacher, Reinhard

2015-03-01

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

Understanding post-operative temperature drop in cardiac surgery: a mathematical model

NARCIS (Netherlands)

Tindall, M. J.; Peletier, M. A.; Severens, N. M. W.; Veldman, D. J.; de Mol, B. A. J. M.

2008-01-01

A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central

Cardiac gated ventilation

International Nuclear Information System (INIS)

Hanson, C.W. III; Hoffman, E.A.

1995-01-01

There are several theoretic advantages to synchronizing positive pressure breaths with the cardiac cycle, including the potential for improving distribution of pulmonary and myocardial blood flow and enhancing cardiac output. The authors evaluated the effects of synchronizing respiration to the cardiac cycle using a programmable ventilator and electron beam CT (EBCT) scanning. The hearts of anesthetized dogs were imaged during cardiac gated respiration with a 50 msec scan aperture. Multi slice, short axis, dynamic image data sets spanning the apex to base of the left ventricle were evaluated to determine the volume of the left ventricular chamber at end-diastole and end-systole during apnea, systolic and diastolic cardiac gating. The authors observed an increase in cardiac output of up to 30% with inspiration gated to the systolic phase of the cardiac cycle in a non-failing model of the heart

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2012-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2011-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Structural equation modeling and natural systems

Science.gov (United States)

Grace, James B.

2006-01-01

This book, first published in 2006, presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems.

Equation-free modeling unravels the behavior of complex ecological systems

Science.gov (United States)

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Evaluation of respiratory and cardiac motion correction schemes in dual gated PET/CT cardiac imaging

Energy Technology Data Exchange (ETDEWEB)

Lamare, F., E-mail: frederic.lamare@chu-bordeaux.fr; Fernandez, P. [Univ. Bordeaux, INCIA, UMR 5287, F-33400 Talence (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Service de Médecine Nucléaire, Hôpital Pellegrin, CHU de Bordeaux, 33076 Bordeaux (France); Le Maitre, A.; Visvikis, D. [INSERM, UMR1101, LaTIM, Université de Bretagne Occidentale, 29609 Brest (France); Dawood, M.; Schäfers, K. P. [European Institute for Molecular Imaging, University of Münster, Mendelstr. 11, 48149 Münster (Germany); Rimoldi, O. E. [Vita-Salute University and Scientific Institute San Raffaele, Milan, Italy and CNR Istituto di Bioimmagini e Fisiologia Molecolare, Milan (Italy)

2014-07-15

Purpose: Cardiac imaging suffers from both respiratory and cardiac motion. One of the proposed solutions involves double gated acquisitions. Although such an approach may lead to both respiratory and cardiac motion compensation there are issues associated with (a) the combination of data from cardiac and respiratory motion bins, and (b) poor statistical quality images as a result of using only part of the acquired data. The main objective of this work was to evaluate different schemes of combining binned data in order to identify the best strategy to reconstruct motion free cardiac images from dual gated positron emission tomography (PET) acquisitions. Methods: A digital phantom study as well as seven human studies were used in this evaluation. PET data were acquired in list mode (LM). A real-time position management system and an electrocardiogram device were used to provide the respiratory and cardiac motion triggers registered within the LM file. Acquired data were subsequently binned considering four and six cardiac gates, or the diastole only in combination with eight respiratory amplitude gates. PET images were corrected for attenuation, but no randoms nor scatter corrections were included. Reconstructed images from each of the bins considered above were subsequently used in combination with an affine or an elastic registration algorithm to derive transformation parameters allowing the combination of all acquired data in a particular position in the cardiac and respiratory cycles. Images were assessed in terms of signal-to-noise ratio (SNR), contrast, image profile, coefficient-of-variation (COV), and relative difference of the recovered activity concentration. Results: Regardless of the considered motion compensation strategy, the nonrigid motion model performed better than the affine model, leading to higher SNR and contrast combined with a lower COV. Nevertheless, when compensating for respiration only, no statistically significant differences were

Illness-death model: statistical perspective and differential equations.

Science.gov (United States)

Brinks, Ralph; Hoyer, Annika

2018-01-27

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

Science.gov (United States)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Generalized Ordinary Differential Equation Models.

Science.gov (United States)

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research

Science.gov (United States)

Cheung, Mike W.-L.; Au, Kevin

2005-01-01

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.; Scacchi, S.; Zampini, Stefano

2015-01-01

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.

2015-07-18

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Model identification using stochastic differential equation grey-box models in diabetes.

Science.gov (United States)

Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

2013-03-01

The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.

The issue of statistical power for overall model fit in evaluating structural equation models

Directory of Open Access Journals (Sweden)

Richard HERMIDA

2015-06-01

Full Text Available Statistical power is an important concept for psychological research. However, examining the power of a structural equation model (SEM is rare in practice. This article provides an accessible review of the concept of statistical power for the Root Mean Square Error of Approximation (RMSEA index of overall model fit in structural equation modeling. By way of example, we examine the current state of power in the literature by reviewing studies in top Industrial-Organizational (I/O Psychology journals using SEMs. Results indicate that in many studies, power is very low, which implies acceptance of invalid models. Additionally, we examined methodological situations which may have an influence on statistical power of SEMs. Results showed that power varies significantly as a function of model type and whether or not the model is the main model for the study. Finally, results indicated that power is significantly related to model fit statistics used in evaluating SEMs. The results from this quantitative review imply that researchers should be more vigilant with respect to power in structural equation modeling. We therefore conclude by offering methodological best practices to increase confidence in the interpretation of structural equation modeling results with respect to statistical power issues.

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

The lattice Boltzmann model for the second-order Benjamin–Ono equations

International Nuclear Information System (INIS)

Lai, Huilin; Ma, Changfeng

2010-01-01

In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin–Ono equation. With the Taylor expansion and the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations

Patient-Specific Induced Pluripotent Stem Cell Models: Generation and Characterization of Cardiac Cells.

Science.gov (United States)

Zanella, Fabian; Sheikh, Farah

2016-01-01

The generation of human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes has been of utmost interest for the study of cardiac development, cardiac disease modeling, and evaluation of cardiotoxic effects of novel candidate drugs. Several protocols have been developed to guide human stem cells toward the cardiogenic path. Pioneering work used serum to promote cardiogenesis; however, low cardiogenic throughputs, lack of chemical definition, and batch-to-batch variability of serum lots constituted a considerable impediment to the implementation of those protocols to large-scale cell biology. Further work focused on the manipulation of pathways that mouse genetics indicated to be fundamental in cardiac development to promote cardiac differentiation in stem cells. Although extremely elegant, those serum-free protocols involved the use of human recombinant cytokines that tend to be quite costly and which can also be variable between lots. The latest generation of cardiogenic protocols aimed for a more cost-effective and reproducible definition of the conditions driving cardiac differentiation, using small molecules to manipulate cardiogenic pathways overriding the need for cytokines. This chapter details methods based on currently available cardiac differentiation protocols for the generation and characterization of robust numbers of hiPSC-derived cardiomyocytes under chemically defined conditions.

Transcriptional profile of isoproterenol-induced cardiomyopathy and comparison to exercise-induced cardiac hypertrophy and human cardiac failure

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McIver Lauren J

2009-12-01

Full Text Available Abstract Background Isoproterenol-induced cardiac hypertrophy in mice has been used in a number of studies to model human cardiac disease. In this study, we compared the transcriptional response of the heart in this model to other animal models of heart failure, as well as to the transcriptional response of human hearts suffering heart failure. Results We performed microarray analyses on RNA from mice with isoproterenol-induced cardiac hypertrophy and mice with exercise-induced physiological hypertrophy and identified 865 and 2,534 genes that were significantly altered in pathological and physiological cardiac hypertrophy models, respectively. We compared our results to 18 different microarray data sets (318 individual arrays representing various other animal models and four human cardiac diseases and identified a canonical set of 64 genes that are generally altered in failing hearts. We also produced a pairwise similarity matrix to illustrate relatedness of animal models with human heart disease and identified ischemia as the human condition that most resembles isoproterenol treatment. Conclusion The overall patterns of gene expression are consistent with observed structural and molecular differences between normal and maladaptive cardiac hypertrophy and support a role for the immune system (or immune cell infiltration in the pathology of stress-induced hypertrophy. Cross-study comparisons such as the results presented here provide targets for further research of cardiac disease that might generally apply to maladaptive cardiac stresses and are also a means of identifying which animal models best recapitulate human disease at the transcriptional level.

Modeling High Frequency Semiconductor Devices Using Maxwell's Equations

National Research Council Canada - National Science Library

El-Ghazaly, Samier

1999-01-01

.... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...

Testing strong factorial invariance using three-level structural equation modeling

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Suzanne eJak

2014-07-01

Full Text Available Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak, Oort and Dolan (2013 showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.

A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling.

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Vijay Vedula

2017-10-01

Full Text Available Blood flow and mechanical forces in the ventricle are implicated in cardiac development and trabeculation. However, the mechanisms of mechanotransduction remain elusive. This is due in part to the challenges associated with accurately quantifying mechanical forces in the developing heart. We present a novel computational framework to simulate cardiac hemodynamics in developing zebrafish embryos by coupling 4-D light sheet imaging with a stabilized finite element flow solver, and extract time-dependent mechanical stimuli data. We employ deformable image registration methods to segment the motion of the ventricle from high resolution 4-D light sheet image data. This results in a robust and efficient workflow, as segmentation need only be performed at one cardiac phase, while wall position in the other cardiac phases is found by image registration. Ventricular hemodynamics are then quantified by numerically solving the Navier-Stokes equations in the moving wall domain with our validated flow solver. We demonstrate the applicability of the workflow in wild type zebrafish and three treated fish types that disrupt trabeculation: (a chemical treatment using AG1478, an ErbB2 signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b injection of gata1a morpholino oligomer (gata1aMO suppressing hematopoiesis and resulting in attenuated trabeculation; (c weak-atriumm58 mutant (wea with inhibited atrial contraction leading to a highly undeveloped ventricle and poor cardiac function. Our simulations reveal elevated wall shear stress (WSS in wild type and AG1478 compared to gata1aMO and wea. High oscillatory shear index (OSI in the grooves between trabeculae, compared to lower values on the ridges, in the wild type suggest oscillatory forces as a possible regulatory mechanism of cardiac trabeculation development. The framework has broad applicability for future cardiac developmental studies focused on quantitatively

Mathematical analysis of partial differential equations modeling electrostatic MEMS

CERN Document Server

Esposito, Pierpaolo; Guo, Yujin

2010-01-01

Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed

A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency

Science.gov (United States)

Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake

2014-01-01

This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…

Design of a hybrid model for cardiac arrhythmia classification based on Daubechies wavelet transform.

Science.gov (United States)

Rajagopal, Rekha; Ranganathan, Vidhyapriya

2018-06-05

Automation in cardiac arrhythmia classification helps medical professionals make accurate decisions about the patient's health. The aim of this work was to design a hybrid classification model to classify cardiac arrhythmias. The design phase of the classification model comprises the following stages: preprocessing of the cardiac signal by eliminating detail coefficients that contain noise, feature extraction through Daubechies wavelet transform, and arrhythmia classification using a collaborative decision from the K nearest neighbor classifier (KNN) and a support vector machine (SVM). The proposed model is able to classify 5 arrhythmia classes as per the ANSI/AAMI EC57: 1998 classification standard. Level 1 of the proposed model involves classification using the KNN and the classifier is trained with examples from all classes. Level 2 involves classification using an SVM and is trained specifically to classify overlapped classes. The final classification of a test heartbeat pertaining to a particular class is done using the proposed KNN/SVM hybrid model. The experimental results demonstrated that the average sensitivity of the proposed model was 92.56%, the average specificity 99.35%, the average positive predictive value 98.13%, the average F-score 94.5%, and the average accuracy 99.78%. The results obtained using the proposed model were compared with the results of discriminant, tree, and KNN classifiers. The proposed model is able to achieve a high classification accuracy.

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

A prediction model for 5-year cardiac mortality in patients with chronic heart failure using {sup 123}I-metaiodobenzylguanidine imaging

Energy Technology Data Exchange (ETDEWEB)

Nakajima, Kenichi; Matsuo, Shinro [Kanazawa University Hospital, Department of Nuclear Medicine, Kanazawa (Japan); Nakata, Tomoaki [Sapporo Medical University School of Medicine, Second Department of Internal Medicine (Cardiology), Sapporo (Japan); Hakodate-Goryoukaku Hospital, Department of Cardiology, Hakodate (Japan); Yamada, Takahisa [Osaka Prefectural General Medical Center, Department of Cardiology, Osaka (Japan); Yamashina, Shohei [Toho University Omori Medical Center, Department of Cardiovascular Medicine, Tokyo (Japan); Momose, Mitsuru [Tokyo Women' s Medical University, Department of Nuclear Medicine, Tokyo (Japan); Kasama, Shu [Cardiovascular Hospital of Central Japan, Department of Cardiology, Shibukawa (Japan); Matsui, Toshiki [Social Insurance Shiga General Hospital, Department of Cardiology, Otsu (Japan); Travin, Mark I. [Albert Einstein Medical College, Department of Cardiology and Nuclear Medicine, Montefiore Medical Center, Bronx, NY (United States); Jacobson, Arnold F. [GE Healthcare, Medical Diagnostics, Princeton, NJ (United States)

2014-09-15

Prediction of mortality risk is important in the management of chronic heart failure (CHF). The aim of this study was to create a prediction model for 5-year cardiac death including assessment of cardiac sympathetic innervation using data from a multicenter cohort study in Japan. The original pooled database consisted of cohort studies from six sites in Japan. A total of 933 CHF patients who underwent {sup 123}I-metaiodobenzylguanidine (MIBG) imaging and whose 5-year outcomes were known were selected from this database. The late MIBG heart-to-mediastinum ratio (HMR) was used for quantification of cardiac uptake. Cox proportional hazard and logistic regression analyses were used to select appropriate variables for predicting 5-year cardiac mortality. The formula for predicting 5-year mortality was created using a logistic regression model. During the 5-year follow-up, 205 patients (22 %) died of a cardiac event including heart failure death, sudden cardiac death and fatal acute myocardial infarction (64 %, 30 % and 6 %, respectively). Multivariate logistic analysis selected four parameters, including New York Heart Association (NYHA) functional class, age, gender and left ventricular ejection fraction, without HMR (model 1) and five parameters with the addition of HMR (model 2). The net reclassification improvement analysis for all subjects was 13.8 % (p < 0.0001) by including HMR and its inclusion was most effective in the downward reclassification of low-risk patients. Nomograms for predicting 5-year cardiac mortality were created from the five-parameter regression model. Cardiac MIBG imaging had a significant additive value for predicting cardiac mortality. The prediction formula and nomograms can be used for risk stratifying in patients with CHF. (orig.)

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

International Nuclear Information System (INIS)

Lind, R.C.

1973-01-01

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

Development of a diagnosis- and procedure-based risk model for 30-day outcome after pediatric cardiac surgery.

Science.gov (United States)

Crowe, Sonya; Brown, Kate L; Pagel, Christina; Muthialu, Nagarajan; Cunningham, David; Gibbs, John; Bull, Catherine; Franklin, Rodney; Utley, Martin; Tsang, Victor T

2013-05-01

The study objective was to develop a risk model incorporating diagnostic information to adjust for case-mix severity during routine monitoring of outcomes for pediatric cardiac surgery. Data from the Central Cardiac Audit Database for all pediatric cardiac surgery procedures performed in the United Kingdom between 2000 and 2010 were included: 70% for model development and 30% for validation. Units of analysis were 30-day episodes after the first surgical procedure. We used logistic regression for 30-day mortality. Risk factors considered included procedural information based on Central Cardiac Audit Database "specific procedures," diagnostic information defined by 24 "primary" cardiac diagnoses and "univentricular" status, and other patient characteristics. Of the 27,140 30-day episodes in the development set, 25,613 were survivals, 834 were deaths, and 693 were of unknown status (mortality, 3.2%). The risk model includes procedure, cardiac diagnosis, univentricular status, age band (neonate, infant, child), continuous age, continuous weight, presence of non-Down syndrome comorbidity, bypass, and year of operation 2007 or later (because of decreasing mortality). A risk score was calculated for 95% of cases in the validation set (weight missing in 5%). The model discriminated well; the C-index for validation set was 0.77 (0.81 for post-2007 data). Removal of all but procedural information gave a reduced C-index of 0.72. The model performed well across the spectrum of predicted risk, but there was evidence of underestimation of mortality risk in neonates undergoing operation from 2007. The risk model performs well. Diagnostic information added useful discriminatory power. A future application is risk adjustment during routine monitoring of outcomes in the United Kingdom to assist quality assurance. Copyright © 2013 The American Association for Thoracic Surgery. Published by Mosby, Inc. All rights reserved.

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2005-01-01

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

Directory of Open Access Journals (Sweden)

Narcisa Apreutesei

2014-05-01

Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2004-01-01

Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

Continuous Time Structural Equation Modeling with R Package ctsem

Directory of Open Access Journals (Sweden)

Charles C. Driver

2017-04-01

Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

Science.gov (United States)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

TBA equations for excited states in the sine-Gordon model

International Nuclear Information System (INIS)

Balog, Janos; Hegedus, Arpad

2004-01-01

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found

Integrable hydrodynamics of Calogero-Sutherland model: bidirectional Benjamin-Ono equation

International Nuclear Information System (INIS)

Abanov, Alexander G; Bettelheim, Eldad; Wiegmann, Paul

2009-01-01

We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin-Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin-Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin-Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin-Ono equations and of the chiral nonlinear equations

Computer modelling for better diagnosis and therapy of patients by cardiac resynchronisation therapy

NARCIS (Netherlands)

Pluijmert, Marieke; Lumens, Joost; Potse, Mark; Delhaas, Tammo; Auricchio, Angelo; Prinzen, Frits W

2015-01-01

Mathematical or computer models have become increasingly popular in biomedical science. Although they are a simplification of reality, computer models are able to link a multitude of processes to each other. In the fields of cardiac physiology and cardiology, models can be used to describe the

Excited TBA equations I: Massive tricritical Ising model

International Nuclear Information System (INIS)

Pearce, Paul A.; Chim, Leung; Ahn, Changrim

2001-01-01

We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II

On the Schroedinger equation for the minisuperspace models

International Nuclear Information System (INIS)

Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

2000-01-01

We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator

Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation

Science.gov (United States)

Hofstrand, A.; Moloney, J. V.

2018-03-01

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

Milrinone ameliorates cardiac mechanical dysfunction after hypothermia in an intact rat model.

Science.gov (United States)

Dietrichs, Erik Sveberg; Kondratiev, Timofei; Tveita, Torkjel

2014-12-01

Rewarming from hypothermia is often complicated by cardiac dysfunction, characterized by substantial reduction in stroke volume. Previously we have reported that inotropic agents, working via cardiac β-receptor agonism may exert serious side effects when applied to treat cardiac contractile dysfunction during rewarming. In this study we tested whether Milrinone, a phosphodiesterase III inhibitor, is able to ameliorate such dysfunction when given during rewarming. A rat model designed for circulatory studies during experimental hypothermia with cooling to a core temperature of 15°C, stable hypothermia at this temperature for 3h and subsequent rewarming was used, with a total of 3 groups: (1) a normothermic group receiving Milrinone, (2) a hypothermic group receiving Milrinone the last hour of hypothermia and during rewarming, and (3) a hypothermic saline control group. Hemodynamic function was monitored using a conductance catheter introduced to the left ventricle. After rewarming from 15°C, stroke volume and cardiac output returned to within baseline values in Milrinone treated animals, while these variables were significantly reduced in saline controls. Milrinone ameliorated cardiac dysfunction during rewarming from 15°C. The present results suggest that at low core temperatures and during rewarming from such temperatures, pharmacologic efforts to support cardiovascular function is better achieved by substances preventing cyclic AMP breakdown rather than increasing its formation via β-receptor stimulation. Copyright © 2014 Elsevier Inc. All rights reserved.

A four-equation friction model for water hammer calculation in quasi-rigid pipelines

International Nuclear Information System (INIS)

Ghodhbani, Abdelaziz; Haj Taïeb, Ezzeddine

2017-01-01

Friction coupling affects water hammer evolution in pipelines according to the initial flow regime. Unsteady friction models are only validated with uncoupled formulation. On the other hand, coupled models such as four-equation model, provide more accurate prediction of water hammer since fluid-structure interaction (FSI) is taken into account, but they are limited to steady-state friction formulation. This paper deals with the creation of the “four-equation friction model” which is based on the incorporation of the unsteady head loss given by an unsteady friction model into the four-equation model. For transient laminar flow cases, the Zielke model is considered. The proposed model is applied to a quasi-rigid pipe with axial moving valve, and then calculated by the method of characteristics (MOC). Damping and shape of the numerical solution are in good agreement with experimental data. Thus, the proposed model can be incorporated into a new computer code. - Highlights: • Both Zielke model and four-equation model are insufficient to predict water hammer. • The four-equation friction model proposed is obtained by incorporating the unsteady head loss in the four-equation model. • The solution obtained by the proposed model is in good agreement with experimental data. • The wave-speed adjustment scheme is more efficient than interpolations schemes.

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Modified two-fluid model for the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.

2003-01-01

This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

A 3D active shape model driven by fuzzy inference : application to cardiac CT and MR

NARCIS (Netherlands)

Assen, van H.C.; Danilouchkine, M.G.; Dirksen, M.S.; Reiber, J.H.C.; Lelieveldt, B.P.F.

2008-01-01

Abstract—Manual quantitative analysis of cardiac left ventricular function using Multislice CT and MR is arduous because of the large data volume. In this paper, we present a 3-D active shape model (ASM) for semiautomatic segmentation of cardiac CT and MRvolumes, without the requirement of

Model-based imaging of cardiac electrical function in human atria

Science.gov (United States)

Modre, Robert; Tilg, Bernhard; Fischer, Gerald; Hanser, Friedrich; Messnarz, Bernd; Schocke, Michael F. H.; Kremser, Christian; Hintringer, Florian; Roithinger, Franz

2003-05-01

Noninvasive imaging of electrical function in the human atria is attained by the combination of data from electrocardiographic (ECG) mapping and magnetic resonance imaging (MRI). An anatomical computer model of the individual patient is the basis for our computer-aided diagnosis of cardiac arrhythmias. Three patients suffering from Wolff-Parkinson-White syndrome, from paroxymal atrial fibrillation, and from atrial flutter underwent an electrophysiological study. After successful treatment of the cardiac arrhythmia with invasive catheter technique, pacing protocols with stimuli at several anatomical sites (coronary sinus, left and right pulmonary vein, posterior site of the right atrium, right atrial appendage) were performed. Reconstructed activation time (AT) maps were validated with catheter-based electroanatomical data, with invasively determined pacing sites, and with pacing at anatomical markers. The individual complex anatomical model of the atria of each patient in combination with a high-quality mesh optimization enables accurate AT imaging, resulting in a localization error for the estimated pacing sites within 1 cm. Our findings may have implications for imaging of atrial activity in patients with focal arrhythmias.

Cardiac fatty acid uptake and metabolism in the rat model of polycystic ovary syndrome.

Science.gov (United States)

Tepavčević, Snežana; Milutinović, Danijela Vojnović; Macut, Djuro; Stojiljković, Mojca; Nikolić, Marina; Božić-Antić, Ivana; Ćulafić, Tijana; Bjekić-Macut, Jelica; Matić, Gordana; Korićanac, Goran

2015-09-01

Polycystic ovary syndrome (PCOS) is associated with an altered plasma lipid profile and increased risk for cardiovascular diseases. We hypothesized that molecular mechanisms underlying cardiac pathology in PCOS involve changes in expression and subcellular localization of several key proteins involved in cardiac lipid transport and metabolism, such as fatty acid transporter CD36, lipin 1, peroxisome proliferator-activated receptor α (PPARα), peroxisome proliferator-activated receptor γ coactivator-1 (PGC1), and carnitine palmitoyltransferase 1 (CPT1). We used the animal model of PCOS obtained by treating female rats with dihydrotestosterone (DHT). Protein levels of CD36, lipin 1, PPARα, PGC1, and antioxidative enzymes were assessed by Western blot in different cardiac cell compartments. Cardiac triglycerides (TG) and lipid peroxidation were also measured. The content of CD36 was decreased in both the cardiac plasma membranes and intracellular pool. On the other hand, total content of cardiac lipin 1 in DHT-treated rats was elevated, in contrast to decreased microsomal lipin 1 content. An increase in nuclear content of lipin 1 was observed together with elevation of nuclear PPARα and PGC1, and an increase in CPT1 expression. However, lipid peroxidation was reduced in the heart, without alterations in antioxidative enzymes expression and cardiac TG content. The results indicate that treatment of female rats with DHT is accompanied by a decrease of fatty acid uptake and a reduction of lipid peroxidation in the heart. The observed elevation of lipin 1, PPARα, PGC1, and CPT1 expression suggests that cardiac fatty acid metabolism is shifted toward mitochondrial beta oxidation.

Calculus for cognitive scientists partial differential equation models

CERN Document Server

Peterson, James K

2016-01-01

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics.  A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

String beta function equations from c=1 matrix model

CERN Document Server

Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R

1995-01-01

We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.

Advanced computer techniques for inverse modeling of electric current in cardiac tissue

Energy Technology Data Exchange (ETDEWEB)

Hutchinson, S.A.; Romero, L.A.; Diegert, C.F.

1996-08-01

For many years, ECG`s and vector cardiograms have been the tools of choice for non-invasive diagnosis of cardiac conduction problems, such as found in reentrant tachycardia or Wolff-Parkinson-White (WPW) syndrome. Through skillful analysis of these skin-surface measurements of cardiac generated electric currents, a physician can deduce the general location of heart conduction irregularities. Using a combination of high-fidelity geometry modeling, advanced mathematical algorithms and massively parallel computing, Sandia`s approach would provide much more accurate information and thus allow the physician to pinpoint the source of an arrhythmia or abnormal conduction pathway.

Functional 3-D cardiac co-culture model using bioactive chitosan nanofiber scaffolds.

Science.gov (United States)

Hussain, Ali; Collins, George; Yip, Derek; Cho, Cheul H

2013-02-01

The in vitro generation of a three-dimensional (3-D) myocardial tissue-like construct employing cells, biomaterials, and biomolecules is a promising strategy in cardiac tissue regeneration, drug testing, and tissue engineering applications. Despite significant progress in this field, current cardiac tissue models are not yet able to stably maintain functional characteristics of cardiomyocytes for long-term culture and therapeutic purposes. The objective of this study was to fabricate bioactive 3-D chitosan nanofiber scaffolds using an electrospinning technique and exploring its potential for long-term cardiac function in the 3-D co-culture model. Chitosan is a natural polysaccharide biomaterial that is biocompatible, biodegradable, non-toxic, and cost effective. Electrospun chitosan was utilized to provide structural scaffolding characterized by scale and architectural resemblance to the extracellular matrix (ECM) in vivo. The chitosan fibers were coated with fibronectin via adsorption in order to enhance cellular adhesion to the fibers and migration into the interfibrous milieu. Ventricular cardiomyocytes were harvested from neonatal rats and studied in various culture conditions (i.e., mono- and co-cultures) for their viability and function. Cellular morphology and functionality were examined using immunofluorescent staining for alpha-sarcomeric actin (SM-actin) and gap junction protein, Connexin-43 (Cx43). Scanning electron microscopy (SEM) and light microscopy were used to investigate cellular morphology, spatial organization, and contractions. Calcium indicator was used to monitor calcium ion flux of beating cardiomyocytes. The results demonstrate that the chitosan nanofibers retained their cylindrical morphology in long-term cell cultures and exhibited good cellular attachment and spreading in the presence of adhesion molecule, fibronectin. Cardiomyocyte mono-cultures resulted in loss of cardiomyocyte polarity and islands of non-coherent contractions. However

Differential equations and integrable models: the SU(3) case

International Nuclear Information System (INIS)

Dorey, Patrick; Tateo, Roberto

2000-01-01

We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz

Modeling biological gradient formation: combining partial differential equations and Petri nets.

Science.gov (United States)

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Modelling equation of knee force during instep kicking using ...

African Journals Online (AJOL)

This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Humanitarian Cardiology and Cardiac Surgery in Sub-Saharan Africa: Can We Reshape the Model?

Science.gov (United States)

Tefera, Endale; Nega, Berhanu; Yadeta, Dejuma; Chanie, Yilkal

2016-11-01

In recent decades, humanitarian cardiology and cardiac surgery have shifted toward sending short-term surgical and catheter missions to treat patients. Although this model has been shown to be effective in bringing cardiovascular care to the patients' environment, its effectiveness in creating sustainable service is questioned. This study reports the barriers to contribution of missions to effective skill transfer and possible improvements needed in the future, from the perspective of both the local and overseas teams. We reviewed the mission-based activities in the Children's Heart Fund Cardiac Center in the past six years. We distributed questionnaires to the local surgeons and the lead surgeons of the overseas teams. Twenty-six missions visited the center 57 times. There were 371 operating days and 605 surgical procedures. Of the procedures performed, 498 were open-heart surgeries. Of the operations, 360 were congenital cases and 204 were rheumatic. Six local surgeons and 18 overseas surgeons responded. Both groups agree the current model of collaboration is not optimal for effective skill transfer. The local surgeons suggested deeper involvement of the universities, governmental institutions, defined training goals and time frame, and communication among the overseas teams themselves as remedies in the future. Majority of the overseas surgeons agree that networking and regular communication among the missions themselves are needed. Some reflected that it would be convenient if the local surgeons are trained by one or two frequently visiting surgeons in their early years and later exposed to multiple teams if needed. The current model of collaboration has brought cardiac care to patients having cardiac diseases. However, the model appears to be suboptimal for skill transfer. The model needs to be reshaped to achieve this complex goal. © The Author(s) 2016.

A lattice Boltzmann model for the Burgers-Fisher equation.

Science.gov (United States)

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

Empiric model for mean generation time adjustment factor for classic point kinetics equations

Energy Technology Data Exchange (ETDEWEB)

Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C., E-mail: david.goes@poli.ufrj.br, E-mail: aquilino@lmp.ufrj.br, E-mail: alessandro@con.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Departamento de Engenharia Nuclear

2017-11-01

Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

Empiric model for mean generation time adjustment factor for classic point kinetics equations

International Nuclear Information System (INIS)

Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C.

2017-01-01

Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

Mechanical perturbation control of cardiac alternans

Science.gov (United States)

Hazim, Azzam; Belhamadia, Youssef; Dubljevic, Stevan

2018-05-01

Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. In this control strategy, cardiac tissue mechanics are perturbed via active tension generated by the heart's electrical activity, which alters the tissue's electric wave profile through mechanoelectric coupling. We analyze the effects of mechanical perturbation on the dynamics of a map model that couples the membrane voltage and active tension systems at the cellular level. Therefore, a two-dimensional iterative map of the heart beat-to-beat dynamics is introduced, and a stability analysis of the system of coupled maps is performed in the presence of a mechanical perturbation algorithm. To this end, a bidirectional coupling between the membrane voltage and active tension systems in a single cardiac cell is provided, and a discrete form of the proposed control algorithm, that can be incorporated in the coupled maps, is derived. In addition, a realistic electromechanical model of cardiac tissue is employed to explore the feasibility of suppressing alternans at cellular and tissue levels. Electrical activity is represented in two detailed ionic models, the Luo-Rudy 1 and the Fox models, while two active contractile tension models, namely a smooth variant of the Nash-Panfilov model and the Niederer-Hunter-Smith model, are used to represent mechanical activity in the heart. The Mooney-Rivlin passive elasticity model is employed to describe passive mechanical behavior of the myocardium.

Structural Equation Modeling with the Smartpls

Directory of Open Access Journals (Sweden)

Christian M. Ringle

2014-05-01

Full Text Available The objective of this article is to present a didactic example of Structural Equation Modeling using the software SmartPLS 2.0 M3. The program mentioned uses the method of Partial Least Squares and seeks to address the following situations frequently observed in marketing research: Absence of symmetric distributions of variables measured by a theory still in its beginning phase or with little “consolidation”, formative models, and/or a limited amount of data. The growing use of SmartPLS has demonstrated its robustness and the applicability of the model in the areas that are being studied. 

THE CONTENT MODEL AND THE EQUATIONS OF MOTION OF ELECTRIC VEHICLE

Directory of Open Access Journals (Sweden)

K. O. Soroka

2015-06-01

Full Text Available Purpose. The calculation methods improvement of the electric vehicle curve movement and the cost of electricity with the aim of performance and accuracy of calculations improving are considered in the paper. Methodology. The method is based upon the general principles of mathematical simulation, when a conceptual model of problem domain is created and then a mathematic model is formulated according to the conceptual model. Development of an improved conceptual model of electric vehicles motion is proposed and a corresponding mathematical model is studied. Findings. The authors proposed model in which the vehicle considers as a system of interacting point-like particles with defined interactions under the influence of external forces. As a mathematical model the Euler-Lagrange equation of the second kind is used. Conservative and dissipative forces affecting the system dynamics are considered. Equations for calculating motion of electric vehicles with taking into account the energy consumption are proposed. Originality. In the paper the conceptual model of motion for electric vehicles with distributed masses has been developed as a system of interacting point-like particles. In the easiest case the system has only one degree of freedom. The mathematical model is based on Lagrange equations. The shown approach allows a detailed and physically based description of the electric vehicles dynamics. The derived motion equations for public electric transport are substantially more precise than the equations recommended in textbooks and the reference documentation. The motion equations and energy consumption calculations for transportation of one passenger with a trolleybus are developed. It is shown that the energy consumption depends on the data of vehicle and can increase when the manload is above the certain level. Practical value. The authors received the equations of motion and labour costs in the calculations focused on the use of computer methods

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

Science.gov (United States)

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Modelling cardiac signal as a confound in EEG-fMRI and its application in focal epilepsy studies

DEFF Research Database (Denmark)

Liston, A. D.; Ellegaard Lund, Torben; Salek-Haddadi, A

2006-01-01

effects to be modelled, as effects of no interest. Our model is based on an over-complete basis set covering a linear relationship between cardiac-related MR signal and the phase of the cardiac cycle or time after pulse (TAP). This method showed that, on average, 24.6 +/- 10.9% of grey matter voxels......Cardiac noise has been shown to reduce the sensitivity of functional Magnetic Resonance Imaging (fMRI) to an experimental effect due to its confounding presence in the blood oxygenation level-dependent (BOLD) signal. Its effect is most severe in particular regions of the brain and a method is yet...... to take it into account in routine fMRI analysis. This paper reports the development of a general and robust technique to improve the reliability of EEG-fMRI studies to BOLD signal correlated with interictal epileptiform discharges (IEDs). In these studies, ECG is routinely recorded, enabling cardiac...

Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans

Energy Technology Data Exchange (ETDEWEB)

Skardal, Per Sebastian, E-mail: skardals@gmail.com [Departament d' Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona (Spain); Restrepo, Juan G., E-mail: juanga@colorado.edu [Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309 (United States)

2014-12-15

The spatiotemporal dynamics of cardiac tissue is an active area of research for biologists, physicists, and mathematicians. Of particular interest is the study of period-doubling bifurcations and chaos due to their link with cardiac arrhythmogenesis. In this paper, we study the spatiotemporal dynamics of a recently developed model for calcium-driven alternans in a one dimensional cable of tissue. In particular, we observe in the cable coexistence of regions with chaotic and multi-periodic dynamics over wide ranges of parameters. We study these dynamics using global and local Lyapunov exponents and spatial trajectory correlations. Interestingly, near nodes—or phase reversals—low-periodic dynamics prevail, while away from the nodes, the dynamics tend to be higher-periodic and eventually chaotic. Finally, we show that similar coexisting multi-periodic and chaotic dynamics can also be observed in a detailed ionic model.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model.

Science.gov (United States)

Krogh-Madsen, Trine; Christini, David J

2017-09-01

Accumulation of intracellular Na + is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na + concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na + concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na + ] i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na + ] i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na + ] i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na + ] i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na + ] i may play complex roles in cellular and tissue-level cardiac dynamics.

Ginzburg-Landau equation as a heuristic model for generating rogue waves

Science.gov (United States)

Lechuga, Antonio

2016-04-01

Envelope equations have many applications in the study of physical systems. Particularly interesting is the case 0f surface water waves. In steady conditions, laboratory experiments are carried out for multiple purposes either for researches or for practical problems. In both cases envelope equations are useful for understanding qualitative and quantitative results. The Ginzburg-Landau equation provides an excellent model for systems of that kind with remarkable patterns. Taking into account the above paragraph the main aim of our work is to generate waves in a water tank with almost a symmetric spectrum according to Akhmediev (2011) and thus, to produce a succession of rogue waves. The envelope of these waves gives us some patterns whose model is a type of Ginzburg-Landau equation, Danilov et al (1988). From a heuristic point of view the link between the experiment and the model is achieved. Further, the next step consists of changing generating parameters on the water tank and also the coefficients of the Ginzburg-Landau equation, Lechuga (2013) in order to reach a sufficient good approach.

Chaotic attractors in tumor growth and decay: a differential equation model.

Science.gov (United States)

Harney, Michael; Yim, Wen-sau

2015-01-01

Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.

The Schroedinger-Newton equation as model of self-gravitating quantum systems

International Nuclear Information System (INIS)

Grossardt, Andre

2013-01-01

The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

Modelling biochemical reaction systems by stochastic differential equations with reflection.

Science.gov (United States)

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

Science.gov (United States)

Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

2012-12-01

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Identifying Variability in Mental Models Within and Between Disciplines Caring for the Cardiac Surgical Patient.

Science.gov (United States)

Brown, Evans K H; Harder, Kathleen A; Apostolidou, Ioanna; Wahr, Joyce A; Shook, Douglas C; Farivar, R Saeid; Perry, Tjorvi E; Konia, Mojca R

2017-07-01

The cardiac operating room is a complex environment requiring efficient and effective communication between multiple disciplines. The objectives of this study were to identify and rank critical time points during the perioperative care of cardiac surgical patients, and to assess variability in responses, as a correlate of a shared mental model, regarding the importance of these time points between and within disciplines. Using Delphi technique methodology, panelists from 3 institutions were tasked with developing a list of critical time points, which were subsequently assigned to pause point (PP) categories. Panelists then rated these PPs on a 100-point visual analog scale. Descriptive statistics were expressed as percentages, medians, and interquartile ranges (IQRs). We defined low response variability between panelists as an IQR ≤ 20, moderate response variability as an IQR > 20 and ≤ 40, and high response variability as an IQR > 40. Panelists identified a total of 12 PPs. The PPs identified by the highest number of panelists were (1) before surgical incision, (2) before aortic cannulation, (3) before cardiopulmonary bypass (CPB) initiation, (4) before CPB separation, and (5) at time of transfer of care from operating room (OR) to intensive care unit (ICU) staff. There was low variability among panelists' ratings of the PP "before surgical incision," moderate response variability for the PPs "before separation from CPB," "before transfer from OR table to bed," and "at time of transfer of care from OR to ICU staff," and high response variability for the remaining 8 PPs. In addition, the perceived importance of each of these PPs varies between disciplines and between institutions. Cardiac surgical providers recognize distinct critical time points during cardiac surgery. However, there is a high degree of variability within and between disciplines as to the importance of these times, suggesting an absence of a shared mental model among disciplines caring for

Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

Science.gov (United States)

Winkel, Brian

2015-01-01

We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

Model reduction of multiscale chemical langevin equations: a numerical case study.

Science.gov (United States)

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

Six Conductivity Values to Use in the Bidomain Model of Cardiac Tissue.

Science.gov (United States)

Johnston, Barbara M

2016-07-01

The aim of this work is to produce a consistent set of six conductivity values for use in the bidomain model of cardiac tissue. Studies in 2007 by Hooks et al. and in 2009 by Caldwell et al. have found that, in the directions longitudinal:transverse:normal (l:t:n) to the cardiac fibers, ratios of bulk conductivities and conduction velocities are each approximately in the ratio 4:2:1. These results are used here as the basis for a method that can find sets of six normalized bidomain conductivity values. It is found that the ratios involving transverse and normal conductivities are quite consistent, allowing new light to be shed on conductivity in the normal direction. For example, it is found that the ratio of transverse to normal conductivity is much greater in the intracellular (i) than the extracellular (e) domain. Using parameter values from experimental studies leads to the proposal of a new nominal six conductivity dataset: gil=2.4, gel=2.4, git=0.35, get=2.0, gin=0.08, and gen=1.1 (all in mS/cm). When it is used to model partial thickness ischaemia, this dataset produces epicardial potential distributions in accord with experimental studies in an animal model. It is, therefore, suggested that the dataset is suitable for use in numerical simulations. Since the bidomain approach is the most commonly used method for modeling cardiac electrophysiological phenomena, new information about conductivity in the normal direction, as well as a consistent set of six conductivity values, is valuable for researchers who perform simulation studies.

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, Johan H. L.; Folmer, Henk

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A structural equation approach to models with spatial dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

A Structural Equation Approach to Models with Spatial Dependence

NARCIS (Netherlands)

Oud, J.H.L.; Folmer, H.

2008-01-01

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it

Integral equation models for image restoration: high accuracy methods and fast algorithms

International Nuclear Information System (INIS)

Lu, Yao; Shen, Lixin; Xu, Yuesheng

2010-01-01

Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of true physical (continuous) models, and hence, inevitably impose bottleneck model errors. We propose to work directly with continuous models for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in this paper for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images

Ising models and soliton equations

International Nuclear Information System (INIS)

Perk, J.H.H.; Au-Yang, H.

1985-01-01

Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained

Modeling imperfectly repaired system data via grey differential equations with unequal-gapped times

International Nuclear Information System (INIS)

Guo Renkuan

2007-01-01

In this paper, we argue that grey differential equation models are useful in repairable system modeling. The arguments starts with the review on GM(1,1) model with equal- and unequal-spaced stopping time sequence. In terms of two-stage GM(1,1) filtering, system stopping time can be partitioned into system intrinsic function and repair effect. Furthermore, we propose an approach to use grey differential equation to specify a semi-statistical membership function for system intrinsic function times. Also, we engage an effort to use GM(1,N) model to model system stopping times and the associated operating covariates and propose an unequal-gapped GM(1,N) model for such analysis. Finally, we investigate the GM(1,1)-embed systematic grey equation system modeling of imperfectly repaired system operating data. Practical examples are given in step-by-step manner to illustrate the grey differential equation modeling of repairable system data

Loop equations for multi-cut matrix models

International Nuclear Information System (INIS)

Akemann, G.

1995-03-01

The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Directory of Open Access Journals (Sweden)

P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

Science.gov (United States)

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

Simulation study of a magnetocardiogram based on a virtual heart model: effect of a cardiac equivalent source and a volume conductor

International Nuclear Information System (INIS)

Shou Guo-Fa; Xia Ling; Dai Ling; Ma Ping; Tang Fa-Kuan

2011-01-01

In this paper, we present a magnetocardiogram (MCG) simulation study using the boundary element method (BEM) and based on the virtual heart model and the realistic human volume conductor model. The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated. The single dipole source model, the multiple dipoles source model and the equivalent double layer (EDL) source model are analysed and compared with the cardiac equivalent source models. Meanwhile, the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated. The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken, while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source. Therefore, the EDL source is suitable for the study of MCG forward and inverse problems, and more attention should be paid to it in future MCG studies. (general)

Development and validation of risk models to predict outcomes following in-hospital cardiac arrest attended by a hospital-based resuscitation team.

Science.gov (United States)

Harrison, David A; Patel, Krishna; Nixon, Edel; Soar, Jasmeet; Smith, Gary B; Gwinnutt, Carl; Nolan, Jerry P; Rowan, Kathryn M

2014-08-01

The National Cardiac Arrest Audit (NCAA) is the UK national clinical audit for in-hospital cardiac arrest. To make fair comparisons among health care providers, clinical indicators require case mix adjustment using a validated risk model. The aim of this study was to develop and validate risk models to predict outcomes following in-hospital cardiac arrest attended by a hospital-based resuscitation team in UK hospitals. Risk models for two outcomes-return of spontaneous circulation (ROSC) for greater than 20min and survival to hospital discharge-were developed and validated using data for in-hospital cardiac arrests between April 2011 and March 2013. For each outcome, a full model was fitted and then simplified by testing for non-linearity, combining categories and stepwise reduction. Finally, interactions between predictors were considered. Models were assessed for discrimination, calibration and accuracy. 22,479 in-hospital cardiac arrests in 143 hospitals were included (14,688 development, 7791 validation). The final risk model for ROSC>20min included: age (non-linear), sex, prior length of stay in hospital, reason for attendance, location of arrest, presenting rhythm, and interactions between presenting rhythm and location of arrest. The model for hospital survival included the same predictors, excluding sex. Both models had acceptable performance across the range of measures, although discrimination for hospital mortality exceeded that for ROSC>20min (c index 0.81 versus 0.72). Validated risk models for ROSC>20min and hospital survival following in-hospital cardiac arrest have been developed. These models will strengthen comparative reporting in NCAA and support local quality improvement. Copyright © 2014 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Development and validation of risk models to predict outcomes following in-hospital cardiac arrest attended by a hospital-based resuscitation team☆

Science.gov (United States)

Harrison, David A.; Patel, Krishna; Nixon, Edel; Soar, Jasmeet; Smith, Gary B.; Gwinnutt, Carl; Nolan, Jerry P.; Rowan, Kathryn M.

2014-01-01

Aim The National Cardiac Arrest Audit (NCAA) is the UK national clinical audit for in-hospital cardiac arrest. To make fair comparisons among health care providers, clinical indicators require case mix adjustment using a validated risk model. The aim of this study was to develop and validate risk models to predict outcomes following in-hospital cardiac arrest attended by a hospital-based resuscitation team in UK hospitals. Methods Risk models for two outcomes—return of spontaneous circulation (ROSC) for greater than 20 min and survival to hospital discharge—were developed and validated using data for in-hospital cardiac arrests between April 2011 and March 2013. For each outcome, a full model was fitted and then simplified by testing for non-linearity, combining categories and stepwise reduction. Finally, interactions between predictors were considered. Models were assessed for discrimination, calibration and accuracy. Results 22,479 in-hospital cardiac arrests in 143 hospitals were included (14,688 development, 7791 validation). The final risk model for ROSC > 20 min included: age (non-linear), sex, prior length of stay in hospital, reason for attendance, location of arrest, presenting rhythm, and interactions between presenting rhythm and location of arrest. The model for hospital survival included the same predictors, excluding sex. Both models had acceptable performance across the range of measures, although discrimination for hospital mortality exceeded that for ROSC > 20 min (c index 0.81 versus 0.72). Conclusions Validated risk models for ROSC > 20 min and hospital survival following in-hospital cardiac arrest have been developed. These models will strengthen comparative reporting in NCAA and support local quality improvement. PMID:24830872

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz

2014-04-24

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.

Annotated bibliography of structural equation modelling: technical work.

Science.gov (United States)

Austin, J T; Wolfle, L M

1991-05-01

Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).

Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

DEFF Research Database (Denmark)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode

2009-01-01

are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...

Real Patient and its Virtual Twin: Application of Quantitative Systems Toxicology Modelling in the Cardiac Safety Assessment of Citalopram.

Science.gov (United States)

Patel, Nikunjkumar; Wiśniowska, Barbara; Jamei, Masoud; Polak, Sebastian

2017-11-27

A quantitative systems toxicology (QST) model for citalopram was established to simulate, in silico, a 'virtual twin' of a real patient to predict the occurrence of cardiotoxic events previously reported in patients under various clinical conditions. The QST model considers the effects of citalopram and its most notable electrophysiologically active primary (desmethylcitalopram) and secondary (didesmethylcitalopram) metabolites, on cardiac electrophysiology. The in vitro cardiac ion channel current inhibition data was coupled with the biophysically detailed model of human cardiac electrophysiology to investigate the impact of (i) the inhibition of multiple ion currents (I Kr , I Ks , I CaL ); (ii) the inclusion of metabolites in the QST model; and (iii) unbound or total plasma as the operating drug concentration, in predicting clinically observed QT prolongation. The inclusion of multiple ion channel current inhibition and metabolites in the simulation with unbound plasma citalopram concentration provided the lowest prediction error. The predictive performance of the model was verified with three additional therapeutic and supra-therapeutic drug exposure clinical cases. The results indicate that considering only the hERG ion channel inhibition of only the parent drug is potentially misleading, and the inclusion of active metabolite data and the influence of other ion channel currents should be considered to improve the prediction of potential cardiac toxicity. Mechanistic modelling can help bridge the gaps existing in the quantitative translation from preclinical cardiac safety assessment to clinical toxicology. Moreover, this study shows that the QST models, in combination with appropriate drug and systems parameters, can pave the way towards personalised safety assessment.

Neuregulin-1/erbB-activation improves cardiac function and survival in models of ischemic, dilated, and viral cardiomyopathy.

Science.gov (United States)

Liu, Xifu; Gu, Xinhua; Li, Zhaoming; Li, Xinyan; Li, Hui; Chang, Jianjie; Chen, Ping; Jin, Jing; Xi, Bing; Chen, Denghong; Lai, Donna; Graham, Robert M; Zhou, Mingdong

2006-10-03

We evaluated the therapeutic potential of a recombinant 61-residue neuregulin-1 (beta2a isoform) receptor-active peptide (rhNRG-1) in multiple animal models of heart disease. Activation of the erbB family of receptor tyrosine kinases by rhNRG-1 could provide a treatment option for heart failure, because neuregulin-stimulated erbB2/erbB4 heterodimerization is not only critical for myocardium formation in early heart development but prevents severe dysfunction of the adult heart and premature death. Disabled erbB-signaling is also implicated in the transition from compensatory hypertrophy to failure, whereas erbB receptor-activation promotes myocardial cell growth and survival and protects against anthracycline-induced cardiomyopathy. rhNRG-1 was administered IV to animal models of ischemic, dilated, and viral cardiomyopathy, and cardiac function and survival were evaluated. Short-term intravenous administration of rhNRG-1 to normal dogs and rats did not alter hemodynamics or cardiac contractility. In contrast, rhNRG-1 improved cardiac performance, attenuated pathological changes, and prolonged survival in rodent models of ischemic, dilated, and viral cardiomyopathy, with the survival benefits in the ischemic model being additive to those of angiotensin-converting enzyme inhibitor therapy. In addition, despite continued pacing, rhNRG-1 produced global improvements in cardiac function in a canine model of pacing-induced heart failure. These beneficial effects make rhNRG-1 promising as a broad-spectrum therapeutic for the treatment of heart failure due to a variety of common cardiac diseases.

Continuum model of the two-component Becker-Döring equations

Directory of Open Access Journals (Sweden)

Ali Reza Soheili

2004-01-01

Full Text Available The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

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Nestler, Steffen

2014-05-01

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

Simulation of a plane wavefront propagating in cardiac tissue using a cellular automata model

International Nuclear Information System (INIS)

Barbosa, Carlos R Hall

2003-01-01

We present a detailed description of a cellular automata model for the propagation of action potential in a planar cardiac tissue, which is very fast and easy to use. The model incorporates anisotropy in the electrical conductivity and a spatial variation of the refractory time. The transmembrane potential distribution is directly derived from the cell states, and the intracellular and extracellular potential distributions are calculated for the particular case of a plane wavefront. Once the potential distributions are known, the associated current densities are calculated by Ohm's law, and the magnetic field is determined at a plane parallel to the cardiac tissue by applying the law of Biot and Savart. The results obtained for propagation speed and for magnetic field amplitude with the cellular automata model are compared with values predicted by the bidomain formulation, for various angles between wavefront propagation and fibre direction, characterizing excellent agreement between the models

Reduction of static field equation of Faddeev model to first order PDE

International Nuclear Information System (INIS)

Hirayama, Minoru; Shi Changguang

2007-01-01

A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations

Mouse models for the study of postnatal cardiac hypertrophy

Directory of Open Access Journals (Sweden)

A. Del Olmo-Turrubiarte

2015-06-01

Full Text Available The main objective of this study was to create a postnatal model for cardiac hypertrophy (CH, in order to explain the mechanisms that are present in childhood cardiac hypertrophy. Five days after implantation, intraperitoneal (IP isoproterenol (ISO was injected for 7 days to pregnant female mice. The fetuses were obtained at 15, 17 and 19 dpc from both groups, also newborns (NB, neonates (7–15 days and young adults (6 weeks of age. Histopathological exams were done on the hearts. Immunohistochemistry and western blot demonstrated GATA4 and PCNA protein expression, qPCR real time the mRNA of adrenergic receptors (α-AR and β-AR, alpha and beta myosins (α-MHC, β-MHC and GATA4. After the administration of ISO, there was no change in the number of offsprings. We observed significant structural changes in the size of the offspring hearts. Morphometric analysis revealed an increase in the size of the left ventricular wall and interventricular septum (IVS. Histopathological analysis demonstrated loss of cellular compaction and presence of left ventricular small fibrous foci after birth. Adrenergic receptors might be responsible for changing a physiological into a pathological hypertrophy. However GATA4 seemed to be the determining factor in the pathology. A new animal model was established for the study of pathologic CH in early postnatal stages.

Epidemiology and Outcomes After In-Hospital Cardiac Arrest After Pediatric Cardiac Surgery

Science.gov (United States)

Gupta, Punkaj; Jacobs, Jeffrey P.; Pasquali, Sara K.; Hill, Kevin D.; Gaynor, J. William; O’Brien, Sean M.; He, Max; Sheng, Shubin; Schexnayder, Stephen M.; Berg, Robert A.; Nadkarni, Vinay M.; Imamura, Michiaki; Jacobs, Marshall L.

2014-01-01

Background Multicenter data regarding cardiac arrest in children undergoing heart operations are limited. We describe epidemiology and outcomes associated with postoperative cardiac arrest in a large multiinstitutional cohort. Methods Patients younger than 18 years in the Society of Thoracic Surgeons Congenital Heart Surgery Database (2007 through 2012) were included. Patient factors, operative characteristics, and outcomes were described for patients with and without postoperative cardiac arrest. Multivariable models were used to evaluate the association of center volume with cardiac arrest rate and mortality after cardiac arrest, adjusting for patient and procedural factors. Results Of 70,270 patients (97 centers), 1,843 (2.6%) had postoperative cardiac arrest. Younger age, lower weight, and presence of preoperative morbidities (all p < 0.0001) were associated with cardiac arrest. Arrest rate increased with procedural complexity across common benchmark operations, ranging from 0.7% (ventricular septal defect repair) to 12.7% (Norwood operation). Cardiac arrest was associated with significant mortality risk across procedures, ranging from 15.4% to 62.3% (all p < 0.0001). In multivariable analysis, arrest rate was not associated with center volume (odds ratio, 1.06; 95% confidence interval, 0.71 to 1.57 in low- versus high-volume centers). However, mortality after cardiac arrest was higher in low-volume centers (odds ratio, 2.00; 95% confidence interval, 1.52 to 2.63). This association was present for both high- and low-complexity operations. Conclusions Cardiac arrest carries a significant mortality risk across the stratum of procedural complexity. Although arrest rates are not associated with center volume, lower-volume centers have increased mortality after cardiac arrest. Further study of mechanisms to prevent cardiac arrest and to reduce mortality in those with an arrest is warranted. PMID:25443018

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Direct Cardiac Reprogramming: Advances in Cardiac Regeneration

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Olivia Chen

2015-01-01

Full Text Available Heart disease is one of the lead causes of death worldwide. Many forms of heart disease, including myocardial infarction and pressure-loading cardiomyopathies, result in irreversible cardiomyocyte death. Activated fibroblasts respond to cardiac injury by forming scar tissue, but ultimately this response fails to restore cardiac function. Unfortunately, the human heart has little regenerative ability and long-term outcomes following acute coronary events often include chronic and end-stage heart failure. Building upon years of research aimed at restoring functional cardiomyocytes, recent advances have been made in the direct reprogramming of fibroblasts toward a cardiomyocyte cell fate both in vitro and in vivo. Several experiments show functional improvements in mouse models of myocardial infarction following in situ generation of cardiomyocyte-like cells from endogenous fibroblasts. Though many of these studies are in an early stage, this nascent technology holds promise for future applications in regenerative medicine. In this review, we discuss the history, progress, methods, challenges, and future directions of direct cardiac reprogramming.

River water quality model no. 1 (RWQM1): II. Biochemical process equations

DEFF Research Database (Denmark)

Reichert, P.; Borchardt, D.; Henze, Mogens

2001-01-01

In this paper, biochemical process equations are presented as a basis for water quality modelling in rivers under aerobic and anoxic conditions. These equations are not new, but they summarise parts of the development over the past 75 years. The primary goals of the presentation are to stimulate...... transformation processes. This paper is part of a series of three papers. In the first paper, the general modelling approach is described; in the present paper, the biochemical process equations of a complex model are presented; and in the third paper, recommendations are given for the selection of a reasonable...

Pharmacokinetic/pharmacodynamic modeling of cardiac toxicity in human acute overdoses: utility and limitations.

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Mégarbane, Bruno; Aslani, Arsia Amir; Deye, Nicolas; Baud, Frédéric J

2008-05-01

Hypotension, cardiac failure, QT interval prolongation, dysrhythmias, and conduction disturbances are common complications of overdoses with cardiotoxicants. Pharmacokinetic/pharmacodynamic (PK/PD) relationships are useful to assess diagnosis, prognosis, and treatment efficacy in acute poisonings. To review the utility and limits of PK/PD studies of cardiac toxicity. Discussion of various models, mainly those obtained in digitalis, cyanide, venlafaxine and citalopram poisonings. A sigmoidal E(max) model appears adequate to represent the PK/PD relationships in cardiotoxic poisonings. PK/PD correlations investigate the discrepancies between the time course of the effect magnitude and its evolving concentrations. They may help in understanding the mechanisms of occurrence as well as disappearance of a cardiotoxic effect. When data are sparse, population-based PK/PD modeling using computer-intensive algorithms is helpful to estimate population mean values of PK parameters as well as their individual variability. Further PK/PD studies are needed in medical toxicology to allow understanding of the meaning of blood toxicant concentration in acute poisonings and thus improve management.

On singularity formation of a 3D model for incompressible Navier–Stokes equations

OpenAIRE

Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu

2012-01-01

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...

A mobile phone-based care model for outpatient cardiac rehabilitation: the care assessment platform (CAP

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Francis Rebecca

2010-01-01

Full Text Available Abstract Background Cardiac rehabilitation programs offer effective means to prevent recurrence of a cardiac event, but poor uptake of current programs have been reported globally. Home based models are considered as a feasible alternative to avoid various barriers related to care centre based programs. This paper sets out the study design for a clinical trial seeking to test the hypothesis that these programs can be better and more efficiently supported with novel Information and Communication Technologies (ICT. Methods/Design We have integrated mobile phones and web services into a comprehensive home- based care model for outpatient cardiac rehabilitation. Mobile phones with a built-in accelerometer sensor are used to measure physical exercise and WellnessDiary software is used to collect information on patients' physiological risk factors and other health information. Video and teleconferencing are used for mentoring sessions aiming at behavioural modifications through goal setting. The mentors use web-portal to facilitate personal goal setting and to assess the progress of each patient in the program. Educational multimedia content are stored or transferred via messaging systems to the patients phone to be viewed on demand. We have designed a randomised controlled trial to compare the health outcomes and cost efficiency of the proposed model with a traditional community based rehabilitation program. The main outcome measure is adherence to physical exercise guidelines. Discussion The study will provide evidence on using mobile phones and web services for mentoring and self management in a home-based care model targeting sustainable behavioural modifications in cardiac rehabilitation patients. Trial registration The trial has been registered in the Australian New Zealand Clinical Trials Registry (ANZCTR with number ACTRN12609000251224.

Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.

Science.gov (United States)

Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J

2017-03-01

Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.

Testing strong factorial invariance using three-level structural equation modeling

NARCIS (Netherlands)

Jak, Suzanne

Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is

Defining the Intrinsic Cardiac Risks of Operations to Improve Preoperative Cardiac Risk Assessments.

Science.gov (United States)

Liu, Jason B; Liu, Yaoming; Cohen, Mark E; Ko, Clifford Y; Sweitzer, Bobbie J

2018-02-01

Current preoperative cardiac risk stratification practices group operations into broad categories, which might inadequately consider the intrinsic cardiac risks of individual operations. We sought to define the intrinsic cardiac risks of individual operations and to demonstrate how grouping operations might lead to imprecise estimates of perioperative cardiac risk. Elective operations (based on Common Procedural Terminology codes) performed from January 1, 2010 to December 31, 2015 at hospitals participating in the American College of Surgeons National Surgical Quality Improvement Program were studied. A composite measure of perioperative adverse cardiac events was defined as either cardiac arrest requiring cardiopulmonary resuscitation or acute myocardial infarction. Operations' intrinsic cardiac risks were derived from mixed-effects models while controlling for patient mix. Resultant risks were sorted into low-, intermediate-, and high-risk categories, and the most commonly performed operations within each category were identified. Intrinsic operative risks were also examined using a representative grouping of operations to portray within-group variation. Sixty-six low, 30 intermediate, and 106 high intrinsic cardiac risk operations were identified. Excisional breast biopsy had the lowest intrinsic cardiac risk (overall rate, 0.01%; odds ratio, 0.11; 95% CI, 0.02 to 0.25) relative to the average, whereas aorto-bifemoral bypass grafting had the highest (overall rate, 4.1%; odds ratio, 6.61; 95% CI, 5.54 to 7.90). There was wide variation in the intrinsic cardiac risks of operations within the representative grouping (median odds ratio, 1.40; interquartile range, 0.88 to 2.17). A continuum of intrinsic cardiac risk exists among operations. Grouping operations into broad categories inadequately accounts for the intrinsic cardiac risk of individual operations.

Preoperative predictive model for acute kidney injury after elective cardiac surgery: a prospective multicentre cohort study.

Science.gov (United States)

Callejas, Raquel; Panadero, Alfredo; Vives, Marc; Duque, Paula; Echarri, Gemma; Monedero, Pablo

2018-05-11

Predictive models of CS-AKI include emergency surgery and patients with haemodynamic instability. Our objective was to evaluate the performance of validated predictive models (Thakar and Demirjian) in elective cardiac surgery and to propose a better score in the case of poor performance. A prospective, multicentre, observational study was designed. Data were collected from 942 patients undergoing cardiac surgery, after excluding emergency surgery and patients with an intraaortic balloon pump. The main outcome measure was CS-AKI defined by the composite of requiring dialysis or doubling baseline creatinine values. Both models showed poor discrimination in elective surgery (Thakar's model, AUROC = 0.57, 95% CI = 0.50-0.64 and Demirjian's model, AUROC= 0.64, 95% CI = 0.58-0.71). We generated a new model whose significant independent predictors were: anaemia, age, hypertension, obesity, congestive heart failure, previous cardiac surgery and type of surgery. It classifies patients with scores 0-3 as low risk ( 8 as high risk (>30%) of developing CS-AKI with a statistically significant correlation (p <0.001). Our model reflects acceptable discriminatory ability (AUC = 0.72, 95% CI = 0.66-0.78) which is significantly better than Thakar and Demirjian's models (p<0.01). We developed a new simple predictive model of CS-AKI in elective surgery based on available preoperative information. Our new model is easy to calculate and can be an effective tool for communicating risk to patients and guiding decision-making in the perioperative period. The study requires external validation.

Parameter Estimates in Differential Equation Models for Population Growth

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Winkel, Brian J.

2011-01-01

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

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Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

Science.gov (United States)

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

DEFF Research Database (Denmark)

Banijamali, Babak

model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

Energy Technology Data Exchange (ETDEWEB)

Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp

2017-02-01

The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.

Self-dual form of Ruijsenaars–Schneider models and ILW equation with discrete Laplacian

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A. Zabrodin

2018-02-01

Full Text Available We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable glN Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Science.gov (United States)

Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

2016-10-01

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

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Weam Alharbi

2018-04-01

Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.

3D/2D model-to-image registration by imitation learning for cardiac procedures.

Science.gov (United States)

Toth, Daniel; Miao, Shun; Kurzendorfer, Tanja; Rinaldi, Christopher A; Liao, Rui; Mansi, Tommaso; Rhode, Kawal; Mountney, Peter

2018-05-12

In cardiac interventions, such as cardiac resynchronization therapy (CRT), image guidance can be enhanced by involving preoperative models. Multimodality 3D/2D registration for image guidance, however, remains a significant research challenge for fundamentally different image data, i.e., MR to X-ray. Registration methods must account for differences in intensity, contrast levels, resolution, dimensionality, field of view. Furthermore, same anatomical structures may not be visible in both modalities. Current approaches have focused on developing modality-specific solutions for individual clinical use cases, by introducing constraints, or identifying cross-modality information manually. Machine learning approaches have the potential to create more general registration platforms. However, training image to image methods would require large multimodal datasets and ground truth for each target application. This paper proposes a model-to-image registration approach instead, because it is common in image-guided interventions to create anatomical models for diagnosis, planning or guidance prior to procedures. An imitation learning-based method, trained on 702 datasets, is used to register preoperative models to intraoperative X-ray images. Accuracy is demonstrated on cardiac models and artificial X-rays generated from CTs. The registration error was [Formula: see text] on 1000 test cases, superior to that of manual ([Formula: see text]) and gradient-based ([Formula: see text]) registration. High robustness is shown in 19 clinical CRT cases. Besides the proposed methods feasibility in a clinical environment, evaluation has shown good accuracy and high robustness indicating that it could be applied in image-guided interventions.

Therapy with mesenchymal stromal cells or conditioned medium reverse cardiac alterations in a high-fat diet-induced obesity model.

Science.gov (United States)

Daltro, P S; Barreto, B C; Silva, P G; Neto, P Chenaud; Sousa Filho, P H F; Santana Neta, D; Carvalho, G B; Silva, D N; Paredes, B D; de Alcantara, A C; Freitas, L A R; Couto, R D; Santos, R R; Souza, B S F; Soares, M B P; Macambira, S G

2017-10-01

Obesity is associated with numerous cardiac complications, including arrhythmias, cardiac fibrosis, remodeling and heart failure. Here we evaluated the therapeutic potential of mesenchymal stromal cells (MSCs) and their conditioned medium (CM) to treat cardiac complications in a mouse model of high-fat diet (HFD)-induced obesity. After obesity induction and HFD withdrawal, obese mice were treated with MSCs, CM or vehicle. Cardiac function was assessed using electrocardiography, echocardiography and treadmill test. Body weight and biochemical parameters were evaluated. Cardiac tissue was used for real time (RT)-polymerase chain reaction (PCR) and histopathologic analysis. Characterization of CM by protein array showed the presence of different cytokines and growth factors, including chemokines, osteopontin, cystatin C, Serpin E1 and Gas 6. HFD-fed mice presented cardiac arrhythmias, altered cardiac gene expression and fibrosis reflected in physical exercise incapacity associated with obesity and diabetes. Administration of MSCs or CM improved arrhythmias and exercise capacity. This functional improvement correlated with normalization of GATA4 gene expression in the hearts of MSC- or CM-treated mice. The gene expression of connexin 43, troponin I, adiponectin, transforming growth factor (TGF) β, peroxisome proliferator activated receptor gamma (PPARγ), insulin-like growth factor 1 (IGF-1), matrix metalloproteinase-9 (MMP9) and tissue inhibitor of metalloproteinases 1 (TIMP1) were significantly reduced in MSCs, but not in CM-treated mice. Moreover, MSC or CM administration reduced the intensity of cardiac fibrosis. Our results suggest that MSCs and CM have a recovery effect on cardiac disturbances due to obesity and corroborate to the paracrine action of MSCs in heart disease models. Copyright © 2017 International Society for Cellular Therapy. Published by Elsevier Inc. All rights reserved.

Application of Fokker-Planck equation in positron diffusion trapping model

International Nuclear Information System (INIS)

Bartosova, I.; Ballo, P.

2015-01-01

This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)

Modelling with Difference Equations Supported by GeoGebra: Exploring the Kepler Problem

Science.gov (United States)

Kovacs, Zoltan

2010-01-01

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

Science.gov (United States)

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

International Nuclear Information System (INIS)

Yotsuji, K.; Tachi, Y.; Nishimaki, Y.

2012-01-01

Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Parametric reduced models for the nonlinear Schrödinger equation.

Science.gov (United States)

Harlim, John; Li, Xiantao

2015-05-01

Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

Meta-analytic structural equation modelling

CERN Document Server

Jak, Suzanne

2015-01-01

This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.

Modeling blowing snow accumulation downwind of an obstruction: The Ohara Eulerian particle distribution equation

Science.gov (United States)

Kinar, N. J.

2017-05-01

An equation was proposed to model the height of blowing snow accumulation downwind of an obstacle such as vegetation, a snow fence, a building, or a topographic feature. The equation does not require aerodynamic flow condition parameters such as wind speed, allowing for the spatial distribution of snow to be determined at locations where meteorological data is not available. However, snow particle diffusion, drift, and erosion coefficients must be estimated for application of the equation. These coefficients can be used to provide insight into the relative magnitude of blowing snow processes at a field location. Further research is required to determine efficient methods for coefficient estimation. The equation could be used with other models of wind-transported snow to predict snow accumulation downwind of an obstacle without the need for wind speed adjustments or correction equations. Applications for this equation include the design of snow fences, and the use of this equation with other hydrological models to predict snow distribution, climate change, drought, flooding, and avalanches.

Homogeneous axisymmetric model with a limitting stiff equation of state

International Nuclear Information System (INIS)

Korkina, M.P.; Martynenko, V.G.

1976-01-01

A solution is obtained for Einstein's equations in which all metric coefficients are time functions for a limiting stiff equation of the substance state. Thr solution describes a homogeneous cosmological model with cylindrical symmetry. It is shown that the same metrics can be induced by a massless scalar only time-dependent field. Analysis of this solution is presented

Structural-equation models of migration: an example from the Upper Midwest USA.

Science.gov (United States)

Cadwallader, M

1985-01-01

"To date, most migration models have been specified in terms of a single equation, whereby a set of regional characteristics are used to predict migration rates for various kinds of spatial units. These models are inadequate in at least two respects. First, they omit any causal links between the explanatory variables, thus ignoring indirect effects between these variables and migration. Second, they ignore the possibility of reciprocal causation, or feedback effects, between migration and the explanatory variables...." The author uses data for State Economic Areas to construct a path model and simultaneous-equation model to identify both indirect and feedback effects on migration in the Upper Midwestern United States. "On the basis of the path model, it is suggested that the direct effects of many variables on migration are at least partially offset by the indirect effects, whereas the simultaneous-equation model emphasizes the reciprocal relationship between income and migration." excerpt

A Comparison of a Machine Learning Model with EuroSCORE II in Predicting Mortality after Elective Cardiac Surgery: A Decision Curve Analysis.

Science.gov (United States)

Allyn, Jérôme; Allou, Nicolas; Augustin, Pascal; Philip, Ivan; Martinet, Olivier; Belghiti, Myriem; Provenchere, Sophie; Montravers, Philippe; Ferdynus, Cyril

2017-01-01

The benefits of cardiac surgery are sometimes difficult to predict and the decision to operate on a given individual is complex. Machine Learning and Decision Curve Analysis (DCA) are recent methods developed to create and evaluate prediction models. We conducted a retrospective cohort study using a prospective collected database from December 2005 to December 2012, from a cardiac surgical center at University Hospital. The different models of prediction of mortality in-hospital after elective cardiac surgery, including EuroSCORE II, a logistic regression model and a machine learning model, were compared by ROC and DCA. Of the 6,520 patients having elective cardiac surgery with cardiopulmonary bypass, 6.3% died. Mean age was 63.4 years old (standard deviation 14.4), and mean EuroSCORE II was 3.7 (4.8) %. The area under ROC curve (IC95%) for the machine learning model (0.795 (0.755-0.834)) was significantly higher than EuroSCORE II or the logistic regression model (respectively, 0.737 (0.691-0.783) and 0.742 (0.698-0.785), p machine learning model, in this monocentric study, has a greater benefit whatever the probability threshold. According to ROC and DCA, machine learning model is more accurate in predicting mortality after elective cardiac surgery than EuroSCORE II. These results confirm the use of machine learning methods in the field of medical prediction.

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

Science.gov (United States)

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

Ordinary Differential Equation Models for Adoptive Immunotherapy.

Science.gov (United States)

Talkington, Anne; Dantoin, Claudia; Durrett, Rick

2018-05-01

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

Multiloop soliton and multibreather solutions of the short pulse model equation

International Nuclear Information System (INIS)

Matsuno, Yoshimasa

2007-01-01

We develop a systematic procedure for constructing the multisoliton solutions of the short pulse (SP) model equation which describes the propagation of ultra-short pulses in nonlinear medica. We first introduce a novel hodograph transformation to convert the SP equation into the sine-Gordon (sG) equation. With the soliton solutions of the sG equation, the system of linear partial differential equations governing the inverse mapping can be integrated analytically to obtain the soliton solutions of the SP equation in the form of the parametric representation. By specifying the soliton parameters, we obtain the multiloop and multibreather solutions. We investigate the asymptotic behavior of both solutions and confirm their solitonic feature. The nonsingular breather solutions may play an important role in studying the propagation of ultra-short pulses in an optical fibre. (author)

Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model

Directory of Open Access Journals (Sweden)

Xiao-Wei Guan

2018-01-01

Full Text Available The parabolic equation method based on digital elevation model (DEM is applied on propagation predictions over irregular terrains. Starting from a parabolic approximation to the Helmholtz equation, a wide-angle parabolic equation is deduced under the assumption of forward propagation and the split-step Fourier transform algorithm is used to solve it. The application of DEM is extended to the Cartesian coordinate system and expected to provide a precise representation of a three-dimensional surface with high efficiency. In order to validate the accuracy, a perfectly conducting Gaussian terrain profile is simulated and the results are compared with the shift map. As a consequence, a good agreement is observed. Besides, another example is given to provide a theoretical basis and reference for DEM selection. The simulation results demonstrate that the prediction errors will be obvious only when the resolution of the DEM used is much larger than the range step in the PE method.

Advanced structural equation modeling issues and techniques

CERN Document Server

Marcoulides, George A

2013-01-01

By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.

The Donders model of the circulation in normo- and pathophysiology

DEFF Research Database (Denmark)

Noordergraaf, Gerrit J.; Ottesen, Johnny T.; Kortsmit, Wil J.P.M.

2006-01-01

the continuum of physiological conditions to cardiopulmonary resuscitation effects within the circulation.   Within the model, Harvey's view of the circulation has been broadened to include impedance-defined flow as a unifying concept. The cardiac function curve, the relation between ventricular filling...... and output, changes during exercise. First, it rotates counterclockwise and stretches along the output axis, second, it shifts along the filling axis. The first is induced by sympathetic control, the second by respiratory control. The model shows that depth of respiration, sympathetic stimulation of cardiac......A model of the closed human cardiovascular loop is developed. This model, using one set of 88 equations, allows variations from normal resting conditions to exercise, as well as to the extreme condition of a circulation following cardiac arrest. The principal purpose of the model is to evaluate...

Airline Sustainability Modeling: A New Framework with Application of Bayesian Structural Equation Modeling

DEFF Research Database (Denmark)

Salarzadeh Jenatabadi, Hashem; Babashamsi, Peyman; Khajeheian, Datis

2016-01-01

There are many factors which could influence the sustainability of airlines. The main purpose of this study is to introduce a framework for a financial sustainability index and model it based on structural equation modeling (SEM) with maximum likelihood and Bayesian predictors. The introduced...

J Waves for Predicting Cardiac Events in Hypertrophic Cardiomyopathy.

Science.gov (United States)

Tsuda, Toyonobu; Hayashi, Kenshi; Konno, Tetsuo; Sakata, Kenji; Fujita, Takashi; Hodatsu, Akihiko; Nagata, Yoji; Teramoto, Ryota; Nomura, Akihiro; Tanaka, Yoshihiro; Furusho, Hiroshi; Takamura, Masayuki; Kawashiri, Masa-Aki; Fujino, Noboru; Yamagishi, Masakazu

2017-10-01

This study sought to investigate whether the presence of J waves was associated with cardiac events in patients with hypertrophic cardiomyopathy (HCM). It has been uncertain whether the presence of J waves predicts life-threatening cardiac events in patients with HCM. This study evaluated consecutive 338 patients with HCM (207 men; age 61 ± 17 years of age). A J-wave was defined as J-point elevation >0.1 mV in at least 2 contiguous inferior and/or lateral leads. Cardiac events were defined as sudden cardiac death, ventricular fibrillation or sustained ventricular tachycardia, or appropriate implantable cardiac defibrillator therapy. The study also investigated whether adding the J-wave in a conventional risk model improved a prediction of cardiac events. J waves were seen in 46 (13.6%) patients at registration. Cardiac events occurred in 31 patients (9.2%) during median follow-up of 4.9 years (interquartile range: 2.6 to 7.1 years). In a Cox proportional hazards model, the presence of J waves was significantly associated with cardiac events (adjusted hazard ratio: 4.01; 95% confidence interval [CI]: 1.78 to 9.05; p = 0.001). Compared with the conventional risk model, the model using J waves in addition to conventional risks better predicted cardiac events (net reclassification improvement, 0.55; 95% CI: 0.20 to 0.90; p = 0.002). The presence of J waves was significantly associated with cardiac events in HCM. Adding J waves to conventional cardiac risk factors improved prediction of cardiac events. Further confirmatory studies are needed before considering J-point elevation as a marker of risk for use in making management decisions regarding risk in patients with HCM. Copyright © 2017 American College of Cardiology Foundation. Published by Elsevier Inc. All rights reserved.

Towards modeling of cardiac micro-structure with catheter-based confocal microscopy: a novel approach for dye delivery and tissue characterization.

Science.gov (United States)

Lasher, Richard A; Hitchcock, Robert W; Sachse, Frank B

2009-08-01

This work presents a methodology for modeling of cardiac tissue micro-structure. The approach is based on catheter-based confocal imaging systems, which are emerging as tools for diagnosis in various clinical disciplines. A limitation of these systems is that a fluorescent marker must be available in sufficient concentration in the imaged region. We introduce a novel method for the local delivery of fluorescent markers to cardiac tissue based on a hydro-gel carrier brought into contact with the tissue surface. The method was tested with living rabbit cardiac tissue and applied to acquire three-dimensional image stacks with a standard inverted confocal microscope and two-dimensional images with a catheter-based confocal microscope. We processed these image stacks to obtain spatial models and quantitative data on tissue microstructure. Volumes of atrial and ventricular myocytes were 4901 +/- 1713 and 10 299 +/-3598 mum (3) (mean+/-sd), respectively. Atrial and ventricular myocyte volume fractions were 72.4 +/-4.7% and 79.7 +/- 2.9% (mean +/-sd), respectively. Atrial and ventricular myocyte density was 165 571 +/- 55 836 and 86 957 +/- 32 280 cells/mm (3) (mean+/-sd), respectively. These statistical data and spatial descriptions of tissue microstructure provide important input for modeling studies of cardiac tissue function. We propose that the described methodology can also be used to characterize diseased tissue and allows for personalized modeling of cardiac tissue.

A Structural Equation Model of Expertise in College Physics

Science.gov (United States)

Taasoobshirazi, Gita; Carr, Martha

2009-01-01

A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…

A Structural Equation Model of Conceptual Change in Physics

Science.gov (United States)

Taasoobshirazi, Gita; Sinatra, Gale M.

2011-01-01

A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…

Principles and practice of structural equation modeling

CERN Document Server

Kline, Rex B

2015-01-01

Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex

Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

Science.gov (United States)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

Science.gov (United States)

Deboeck, Pascal R.; Boker, Steven M.

2010-01-01

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for…

Cardiac re-entry dynamics and self-termination in DT-MRI based model of Human Foetal Heart

Science.gov (United States)

Biktasheva, Irina V.; Anderson, Richard A.; Holden, Arun V.; Pervolaraki, Eleftheria; Wen, Fen Cai

2018-02-01

The effect of human foetal heart geometry and anisotropy on anatomy induced drift and self-termination of cardiac re-entry is studied here in MRI based 2D slice and 3D whole heart computer simulations. Isotropic and anisotropic models of 20 weeks of gestational age human foetal heart obtained from 100μm voxel diffusion tensor MRI data sets were used in the computer simulations. The fiber orientation angles of the heart were obtained from the orientation of the DT-MRI primary eigenvectors. In a spatially homogeneous electrophysiological monodomain model with the DT-MRI based heart geometries, cardiac re-entry was initiated at a prescribed location in a 2D slice, and in the 3D whole heart anatomy models. Excitation was described by simplified FitzHugh-Nagumo kinetics. In a slice of the heart, with propagation velocity twice as fast along the fibres than across the fibers, DT-MRI based fiber anisotropy changes the re-entry dynamics from pinned to an anatomical re-entry. In the 3D whole heart models, the fiber anisotropy changes cardiac re-entry dynamics from a persistent re-entry to the re-entry self-termination. The self-termination time depends on the re-entry’s initial position. In all the simulations with the DT-MRI based cardiac geometry, the anisotropy of the myocardial tissue shortens the time to re-entry self-termination several folds. The numerical simulations depend on the validity of the DT-MRI data set used. The ventricular wall showed the characteristic transmural rotation of the helix angle of the developed mammalian heart, while the fiber orientation in the atria was irregular.

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

Science.gov (United States)

Wang, Chi R.

2005-01-01

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation

Computer models for kinetic equations of magnetically confined plasmas

International Nuclear Information System (INIS)

Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.

1987-01-01

This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method

Modeling Inflation Using a Non-Equilibrium Equation of Exchange

Science.gov (United States)

Chamberlain, Robert G.

2013-01-01

Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project

Validation of an employee satisfaction model: A structural equation model approach

OpenAIRE

Ophillia Ledimo; Nico Martins

2015-01-01

The purpose of this study was to validate an employee satisfaction model and to determine the relationships between the different dimensions of the concept, using the structural equation modelling approach (SEM). A cross-sectional quantitative survey design was used to collect data from a random sample of (n=759) permanent employees of a parastatal organisation. Data was collected using the Employee Satisfaction Survey (ESS) to measure employee satisfaction dimensions. Following the steps of ...

Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory

International Nuclear Information System (INIS)

Sanchez, N.; Whiting, B.

1986-01-01

The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers

Control of Stochastic Master Equation Models of Genetic Regulatory Networks by Approximating Their Average Behavior

Science.gov (United States)

Umut Caglar, Mehmet; Pal, Ranadip

2010-10-01

The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology

Ventricular Fibrillation-Induced Cardiac Arrest Results in Regional Cardiac Injury Preferentially in Left Anterior Descending Coronary Artery Territory in Piglet Model

Directory of Open Access Journals (Sweden)

Giridhar Kaliki Venkata

2016-01-01

Full Text Available Objective. Decreased cardiac function after resuscitation from cardiac arrest (CA results from global ischemia of the myocardium. In the evolution of postarrest myocardial dysfunction, preferential involvement of any coronary arterial territory is not known. We hypothesized that there is no preferential involvement of any coronary artery during electrical induced ventricular fibrillation (VF in piglet model. Design. Prospective, randomized controlled study. Methods. 12 piglets were randomized to baseline and electrical induced VF. After 5 min, the animals were resuscitated according to AHA PALS guidelines. After return of spontaneous circulation (ROSC, animals were observed for an additional 4 hours prior to cardiac MRI. Data (mean ± SD was analyzed using unpaired t-test; p value ≤ 0.05 was considered statistically significant. Results. Segmental wall motion (mm; baseline versus postarrest group in segment 7 (left anterior descending (LAD was 4.68±0.54 versus 3.31±0.64, p=0.0026. In segment 13, it was 3.82±0.96 versus 2.58±0.82, p=0.02. In segment 14, it was 2.42±0.44 versus 1.29±0.99, p=0.028. Conclusion. Postarrest myocardial dysfunction resulted in segmental wall motion defects in the LAD territory. There were no perfusion defects in the involved segments.

Application of flexible model in neutron dynamics equations

International Nuclear Information System (INIS)

Liu Cheng; Zhao Fuyu; Fu Xiangang

2009-01-01

Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)

Generalised and Fractional Langevin Equations-Implications for Energy Balance Models

Science.gov (United States)

Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.

2017-12-01

Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).

Partial differential equation models in the socio-economic sciences

KAUST Repository

Burger, Martin; Caffarelli, Luis; Markowich, Peter A.

2014-01-01

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences

Climate Modeling in the Calculus and Differential Equations Classroom

Science.gov (United States)

Kose, Emek; Kunze, Jennifer

2013-01-01

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Modeling of superconductors based on the timedependent Ginsburg-Landau equations

Science.gov (United States)

Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.

2009-11-01

Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.

Cardiac sodium channel NaV1.5 distribution in myocytes via interacting proteins: the multiple pool model.

Science.gov (United States)

Shy, Diana; Gillet, Ludovic; Abriel, Hugues

2013-04-01

The cardiac sodium current (INa) is responsible for the rapid depolarization of cardiac cells, thus allowing for their contraction. It is also involved in regulating the duration of the cardiac action potential (AP) and propagation of the impulse throughout the myocardium. Cardiac INa is generated by the voltage-gated Na(+) channel, NaV1.5, a 2016-residue protein which forms the pore of the channel. Over the past years, hundreds of mutations in SCN5A, the human gene coding for NaV1.5, have been linked to many cardiac electrical disorders, including the congenital and acquired long QT syndrome, Brugada syndrome, conduction slowing, sick sinus syndrome, atrial fibrillation, and dilated cardiomyopathy. Similar to many membrane proteins, NaV1.5 has been found to be regulated by several interacting proteins. In some cases, these different proteins, which reside in distinct membrane compartments (i.e. lateral membrane vs. intercalated disks), have been shown to interact with the same regulatory domain of NaV1.5, thus suggesting that several pools of NaV1.5 channels may co-exist in cardiac cells. The aim of this review article is to summarize the recent works that demonstrate its interaction with regulatory proteins and illustrate the model that the sodium channel NaV1.5 resides in distinct and different pools in cardiac cells. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Cardiac Pathways of Differentiation, Metabolism and Contraction. Copyright © 2012 Elsevier B.V. All rights reserved.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching.

Science.gov (United States)

Chow, Sy-Miin; Ou, Lu; Ciptadi, Arridhana; Prince, Emily B; You, Dongjun; Hunter, Michael D; Rehg, James M; Rozga, Agata; Messinger, Daniel S

2018-06-01

A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of [Formula: see text] mother-infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children's tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.

Algebraic models for the hierarchy structure of evolution equations at small x

International Nuclear Information System (INIS)

Rembiesa, P.; Stasto, A.M.

2005-01-01

We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit

Glutaredoxin-2 controls cardiac mitochondrial dynamics and energetics in mice, and protects against human cardiac pathologies

Directory of Open Access Journals (Sweden)

Georges N. Kanaan

2018-04-01

Full Text Available Glutaredoxin 2 (GRX2, a mitochondrial glutathione-dependent oxidoreductase, is central to glutathione homeostasis and mitochondrial redox, which is crucial in highly metabolic tissues like the heart. Previous research showed that absence of Grx2, leads to impaired mitochondrial complex I function, hypertension and cardiac hypertrophy in mice but the impact on mitochondrial structure and function in intact cardiomyocytes and in humans has not been explored. We hypothesized that Grx2 controls cardiac mitochondrial dynamics and function in cellular and mouse models, and that low expression is associated with human cardiac dysfunction. Here we show that Grx2 absence impairs mitochondrial fusion, ultrastructure and energetics in primary cardiomyocytes and cardiac tissue. Moreover, provision of the glutathione precursor, N-acetylcysteine (NAC to Grx2-/- mice did not restore glutathione redox or prevent impairments. Using genetic and histopathological data from the human Genotype-Tissue Expression consortium we demonstrate that low GRX2 is associated with fibrosis, hypertrophy, and infarct in the left ventricle. Altogether, GRX2 is important in the control of cardiac mitochondrial structure and function, and protects against human cardiac pathologies. Keywords: Human heart, Mitochondria, Oxidative stress, Redox, Cardiac metabolism, Cardiac hypertrophy

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Evaluation of cerebral-cardiac syndrome using echocardiography in a canine model of acute traumatic brain injury.

Science.gov (United States)

Qian, Rong; Yang, Weizhong; Wang, Xiumei; Xu, Zhen; Liu, Xiaodong; Sun, Bing

2015-01-01

Previous studies have confirmed that traumatic brain injury (TBI) can induce general adaptation syndrome (GAS), which subsequently results in myocardial dysfunction and damage in some patients with acute TBI; this condition is also termed as cerebral-cardiac syndrome. However, most clinicians ignore the detection and treatment of myocardial dysfunction, and instead concentrate only on the serious neural damage that is observed in acute TBI, which is one of the most important fatal factors. Therefore, clarification is urgently needed regarding the relationship between TBI and myocardial dysfunction. In the present study, we evaluated 18 canine models of acute TBI, by using real-time myocardial contrast echocardiography and strain rate imaging to accurately evaluate myocardial function and regional microcirculation, including the strain rate of the different myocardial segments, time-amplitude curves, mean ascending slope of the curve, and local myocardial blood flow. Our results suggest that acute TBI often results in cerebral-cardiac syndrome, which rapidly progresses to the serious stage within 3 days. This study is the first to provide comprehensive ultrasonic characteristics of cerebral-cardiac syndrome in an animal model of TBI.

LR-Spring Mass Model for Cardiac Surgical Simulation

DEFF Research Database (Denmark)

Mosegaard, Jesper

2004-01-01

The purpose of the research conducted was to develop a real-time surgical simulator for preoperative planning of surgery in congenital heart disease. The main problem simulating procedures on cardiac morphology is the need for a large degree of detail and simulation speed. In combination with a d......The purpose of the research conducted was to develop a real-time surgical simulator for preoperative planning of surgery in congenital heart disease. The main problem simulating procedures on cardiac morphology is the need for a large degree of detail and simulation speed. In combination...

Guidelines for a graph-theoretic implementation of structural equation modeling

Science.gov (United States)

Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

2012-01-01

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for

A modified two-fluid model for the application of two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun, X.; Ishii, M.; Kelly, J.

2003-01-01

This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

A one-step method for modelling longitudinal data with differential equations.

Science.gov (United States)

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

Hidden physics models: Machine learning of nonlinear partial differential equations

Science.gov (United States)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Neutron star models with realistic high-density equations of state

International Nuclear Information System (INIS)

Malone, R.C.; Johnson, M.B.; Bethe, H.A.

1975-01-01

We calculate neutron star models using four realistic high-density models of the equation of state. We conclude that the maximum mass of a neutron star is unlikely to exceed 2 M/sub sun/. All of the realistic models are consistent with current estimates of the moment of inertia of the Crab pulsar

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

International Nuclear Information System (INIS)

Fujii, Akira; Kluemper, Andreas

1999-01-01

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

Modelling the heat dynamics of a building using stochastic differential equations

DEFF Research Database (Denmark)

Andersen, Klaus Kaae; Madsen, Henrik; Hansen, Lars Henrik

2000-01-01

estimation and model validation, while physical knowledge is used in forming the model structure. The suggested lumped parameter model is thus based on thermodynamics and formulated as a system of stochastic differential equations. Due to the continuous time formulation the parameters of the model...

Designs that make a difference: the Cardiac Universal Bed model.

Science.gov (United States)

Johnson, Jackie; Brown, Katherine Kay; Neal, Kelly

2003-01-01

Information contained in this article includes some of the findings from a joint research project conducted by Corazon Consulting and Ohio State University Medical Center on national trends in Cardiac Universal Bed (CUB) utilization. This article outlines current findings and "best practice" standards related to the benefits of developing care delivery models to differentiate an organization with a competitive advantage in the highly dynamic marketplace of cardiovascular care. (OSUMC, a Corazon client, is incorporating the CUB into their Ross Heart Hospital slated to open this spring.)

Raf-mediated cardiac hypertrophy in adult Drosophila

Directory of Open Access Journals (Sweden)

Lin Yu

2013-07-01

In response to stress and extracellular signals, the heart undergoes a process called cardiac hypertrophy during which cardiomyocytes increase in size. If untreated, cardiac hypertrophy can progress to overt heart failure that causes significant morbidity and mortality. The identification of molecular signals that cause or modify cardiomyopathies is necessary to understand how the normal heart progresses to cardiac hypertrophy and heart failure. Receptor tyrosine kinase (RTK signaling is essential for normal human cardiac function, and the inhibition of RTKs can cause dilated cardiomyopathies. However, neither investigations of activated RTK signaling pathways nor the characterization of hypertrophic cardiomyopathy in the adult fly heart has been previously described. Therefore, we developed strategies using Drosophila as a model to circumvent some of the complexities associated with mammalian models of cardiovascular disease. Transgenes encoding activated EGFRA887T, Ras85DV12 and Ras85DV12S35, which preferentially signal to Raf, or constitutively active human or fly Raf caused hypertrophic cardiomyopathy as determined by decreased end diastolic lumen dimensions, abnormal cardiomyocyte fiber morphology and increased heart wall thicknesses. There were no changes in cardiomyocyte cell numbers. Additionally, activated Raf also induced an increase in cardiomyocyte ploidy compared with control hearts. However, preventing increases in cardiomyocyte ploidy using fizzy-related (Fzr RNAi did not rescue Raf-mediated cardiac hypertrophy, suggesting that Raf-mediated polyploidization is not required for cardiac hypertrophy. Similar to mammals, the cardiac-specific expression of RNAi directed against MEK or ERK rescued Raf-mediated cardiac hypertrophy. However, the cardiac-specific expression of activated ERKD334N, which promotes hyperplasia in non-cardiac tissues, did not cause myocyte hypertrophy. These results suggest that ERK is necessary, but not sufficient, for Raf

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

Directory of Open Access Journals (Sweden)

Kin Wei Ng

2012-01-01

Full Text Available We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY method and the Liu-Storey-Conjugate-Descent (LS-CD method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

Cardiac regeneration therapy: connections to cardiac physiology.

Science.gov (United States)

Takehara, Naofumi; Matsubara, Hiroaki

2011-12-01

Without heart transplantation, a large number of patients with failing hearts worldwide face poor outcomes. By means of cardiomyocyte regeneration, cardiac regeneration therapy is emerging with great promise as a means for restoring loss of cardiac function. However, the limited success of clinical trials using bone marrow-derived cells and myoblasts with heterogeneous constituents, transplanted at a wide range of cell doses, has led to disagreement on the efficacy of cell therapy. It is therefore essential to reevaluate the evidence for the efficacy of cell-based cardiac regeneration therapy, focusing on targets, materials, and methodologies. Meanwhile, the revolutionary innovation of cardiac regeneration therapy is sorely needed to help the millions of people who suffer heart failure from acquired loss of cardiomyocytes. Cardiac regeneration has been used only in limited species or as a developing process in the rodent heart; now, the possibility of cardiomyocyte turnover in the human heart is being revisited. In the pursuit of this concept, the use of cardiac stem/progenitor stem cells in the cardiac niche must be focused to usher in a second era of cardiac regeneration therapy for the severely injured heart. In addition, tissue engineering and cellular reprogramming will advance the next era of treatment that will enable current cell-based therapy to progress to "real" cardiac regeneration therapy. Although many barriers remain, the prevention of refractory heart failure through cardiac regeneration is now becoming a realistic possibility.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

Science.gov (United States)

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

Mitochondria-Targeted Antioxidant Prevents Cardiac Dysfunction Induced by Tafazzin Gene Knockdown in Cardiac Myocytes

Directory of Open Access Journals (Sweden)

Quan He

2014-01-01

Full Text Available Tafazzin, a mitochondrial acyltransferase, plays an important role in cardiolipin side chain remodeling. Previous studies have shown that dysfunction of tafazzin reduces cardiolipin content, impairs mitochondrial function, and causes dilated cardiomyopathy in Barth syndrome. Reactive oxygen species (ROS have been implicated in the development of cardiomyopathy and are also the obligated byproducts of mitochondria. We hypothesized that tafazzin knockdown increases ROS production from mitochondria, and a mitochondria-targeted antioxidant prevents tafazzin knockdown induced mitochondrial and cardiac dysfunction. We employed cardiac myocytes transduced with an adenovirus containing tafazzin shRNA as a model to investigate the effects of the mitochondrial antioxidant, mito-Tempo. Knocking down tafazzin decreased steady state levels of cardiolipin and increased mitochondrial ROS. Treatment of cardiac myocytes with mito-Tempo normalized tafazzin knockdown enhanced mitochondrial ROS production and cellular ATP decline. Mito-Tempo also significantly abrogated tafazzin knockdown induced cardiac hypertrophy, contractile dysfunction, and cell death. We conclude that mitochondria-targeted antioxidant prevents cardiac dysfunction induced by tafazzin gene knockdown in cardiac myocytes and suggest mito-Tempo as a potential therapeutic for Barth syndrome and other dilated cardiomyopathies resulting from mitochondrial oxidative stress.

Newtonian nudging for a Richards equation-based distributed hydrological model

Science.gov (United States)

Paniconi, Claudio; Marrocu, Marino; Putti, Mario; Verbunt, Mark

The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model's behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation

Role of secondary instability theory and parabolized stability equations in transition modeling

Science.gov (United States)

El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

1993-01-01

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

Model Selection and Risk Estimation with Applications to Nonlinear Ordinary Differential Equation Systems

DEFF Research Database (Denmark)

Mikkelsen, Frederik Vissing

eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...

Equation-based model for the stock market.

Science.gov (United States)

Xavier, Paloma O C; Atman, A P F; de Magalhães, A R Bosco

2017-09-01

We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.

Equation-based model for the stock market

Science.gov (United States)

Xavier, Paloma O. C.; Atman, A. P. F.; de Magalhães, A. R. Bosco

2017-09-01

We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.

Partial differential equation models in macroeconomics.

Science.gov (United States)

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

A single model procedure for estimating tank calibration equations

International Nuclear Information System (INIS)

Liebetrau, A.M.

1997-10-01

A fundamental component of any accountability system for nuclear materials is a tank calibration equation that relates the height of liquid in a tank to its volume. Tank volume calibration equations are typically determined from pairs of height and volume measurements taken in a series of calibration runs. After raw calibration data are standardized to a fixed set of reference conditions, the calibration equation is typically fit by dividing the data into several segments--corresponding to regions in the tank--and independently fitting the data for each segment. The estimates obtained for individual segments must then be combined to obtain an estimate of the entire calibration function. This process is tedious and time-consuming. Moreover, uncertainty estimates may be misleading because it is difficult to properly model run-to-run variability and between-segment correlation. In this paper, the authors describe a model whose parameters can be estimated simultaneously for all segments of the calibration data, thereby eliminating the need for segment-by-segment estimation. The essence of the proposed model is to define a suitable polynomial to fit to each segment and then extend its definition to the domain of the entire calibration function, so that it (the entire calibration function) can be expressed as the sum of these extended polynomials. The model provides defensible estimates of between-run variability and yields a proper treatment of between-segment correlations. A portable software package, called TANCS, has been developed to facilitate the acquisition, standardization, and analysis of tank calibration data. The TANCS package was used for the calculations in an example presented to illustrate the unified modeling approach described in this paper. With TANCS, a trial calibration function can be estimated and evaluated in a matter of minutes

Phenomenological neutron star equations of state. 3-window modeling of QCD matter

Energy Technology Data Exchange (ETDEWEB)

Kojo, Toru [University of Illinois at Urbana-Champaign, Department of Physics, Urbana, Illinois (United States)

2016-03-15

We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n{sub B} equations of state that are constrained by empirical observations at density n{sub B} ∝ n{sub s} and neutron star radii. At high density, n{sub B} >or similar 5n{sub s}, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2 equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, 0 ≤ c{sub s}{sup 2} ≤ 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to n{sub B} ∝ 10n{sub s}. The hyperon puzzle is also briefly discussed in light of quark descriptions. (orig.)

Dynamics of spiral waves in a cardiac electromechanical model with a local electrical inhomogeneity

International Nuclear Information System (INIS)

Mesin, Luca

2012-01-01

Highlights: ► I study spirals in a model of electromechanical coupling in a cardiac tissue. ► The model is anisotropic and includes an electrical heterogeneity. ► Mechanical deformation is described under the active strain hypothesis. ► Joint effect of inhomogeneity and deformation influences spiral dynamics. ► Conductivity of stretch activated current is the parameter most affecting spirals. - Abstract: Joint effect of electrical heterogeneity (e.g. induced by ischemia) and mechanical deformation is investigated for an anisotropic, quasi–incompressible model of cardiac electromechanical coupling (EMC) using the active strain approach and periodic boundary conditions. Three local inhomogeneities with different geometry are simulated. Under a specific stimulation protocol, the heterogeneities are able to induce spirals. The interplay between the dimension of the electrical inhomogeneity, the EMC and the mechano-electrical feedback provided by the stretch activated current (SAC) determines the dynamics of the spiral waves of excitation, which could extinguish (in the case of low SAC), or be stable (with the tip rotating inside the inhomogeneity), or drift and be annihilated (in the case of high SAC).

Working covariance model selection for generalized estimating equations.

Science.gov (United States)

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

A single-equation study of US petroleum consumption: The role of model specificiation

International Nuclear Information System (INIS)

Jones, C.T.

1993-01-01

The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas ampersand electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns

Continuum model of the two-component Becker-Döring equations

OpenAIRE

Soheili, Ali Reza

2004-01-01

The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum m...

FEQinput—An editor for the full equations (FEQ) hydraulic modeling system

Science.gov (United States)

Ancalle, David S.; Ancalle, Pablo J.; Domanski, Marian M.

2017-10-30

IntroductionThe Full Equations Model (FEQ) is a computer program that solves the full, dynamic equations of motion for one-dimensional unsteady hydraulic flow in open channels and through control structures. As a result, hydrologists have used FEQ to design and operate flood-control structures, delineate inundation maps, and analyze peak-flow impacts. To aid in fighting floods, hydrologists are using the software to develop a system that uses flood-plain models to simulate real-time streamflow.Input files for FEQ are composed of text files that contain large amounts of parameters, data, and instructions that are written in a format exclusive to FEQ. Although documentation exists that can aid in the creation and editing of these input files, new users face a steep learning curve in order to understand the specific format and language of the files.FEQinput provides a set of tools to help a new user overcome the steep learning curve associated with creating and modifying input files for the FEQ hydraulic model and the related utility tool, Full Equations Utilities (FEQUTL).

Notes on TQFT wire models and coherence equations for SU(3) triangular cells

CERN Document Server

Coquereaux, R.; Schieber, G.

2010-01-01

After a summary of the TQFT wire model formalism we bridge the gap from Kuperberg equations for SU(3) spiders to Ocneanu coherence equations for systems of triangular cells on fusion graphs that describe modules associated with the fusion category of SU(3) at level k. We show how to solve these equations in a number of examples.

A simplified model for computing equation of state of argon plasma

International Nuclear Information System (INIS)

Wang Caixia; Tian Yangmeng

2006-01-01

The paper present a simplified new model of computing equation of state and ionization degree of Argon plasma, which based on Thomas-Fermi (TF) statistical model: the authors fitted the numerical results of the ionization potential calculated by Thomas-Fermi statistical model and gained the analytical function of the potential versus the degree of ionization, then calculated the ionization potential and the average degree of ionization for Argon versus temperature and density in local thermal equilibrium case at 10-1000 eV. The results calculated of this simplified model are basically in agreement with several sets of theory data and experimental data. This simplified model can be used to calculation of the equation of state of plasmas mixture and is expected to have a more wide use in the field of EML technology involving the strongly ionized plasmas. (authors)

Modeling Blazar Spectra by Solving an Electron Transport Equation

Science.gov (United States)

Lewis, Tiffany; Finke, Justin; Becker, Peter A.

2018-01-01

Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Exploratory structural equation modeling of personality data.

Science.gov (United States)

Booth, Tom; Hughes, David J

2014-06-01

The current article compares the use of exploratory structural equation modeling (ESEM) as an alternative to confirmatory factor analytic (CFA) models in personality research. We compare model fit, factor distinctiveness, and criterion associations of factors derived from ESEM and CFA models. In Sample 1 (n = 336) participants completed the NEO-FFI, the Trait Emotional Intelligence Questionnaire-Short Form, and the Creative Domains Questionnaire. In Sample 2 (n = 425) participants completed the Big Five Inventory and the depression and anxiety scales of the General Health Questionnaire. ESEM models provided better fit than CFA models, but ESEM solutions did not uniformly meet cutoff criteria for model fit. Factor scores derived from ESEM and CFA models correlated highly (.91 to .99), suggesting the additional factor loadings within the ESEM model add little in defining latent factor content. Lastly, criterion associations of each personality factor in CFA and ESEM models were near identical in both inventories. We provide an example of how ESEM and CFA might be used together in improving personality assessment. © The Author(s) 2014.

Implementing a working together model for Aboriginal patients with acute coronary syndrome: an Aboriginal Hospital Liaison Officer and a specialist cardiac nurse working together to improve hospital care.

Science.gov (United States)

Daws, Karen; Punch, Amanda; Winters, Michelle; Posenelli, Sonia; Willis, John; MacIsaac, Andrew; Rahman, Muhammad Aziz; Worrall-Carter, Linda

2014-11-01

Acute coronary syndrome (ACS) contributes to the disparity in life expectancy between Aboriginal and non-Aboriginal Australians. Improving hospital care for Aboriginal patients has been identified as a means of addressing this disparity. This project developed and implemented a working together model of care, comprising an Aboriginal Hospital Liaison Officer and a specialist cardiac nurse, providing care coordination specifically directed at improving attendance at cardiac rehabilitation services for Aboriginal Australians in a large metropolitan hospital in Melbourne. A quality improvement framework using a retrospective case notes audit evaluated Aboriginal patients' admissions to hospital and identified low attendance rates at cardiac rehabilitation services. A working together model of care coordination by an Aboriginal Hospital Liaison Officer and a specialist cardiac nurse was implemented to improve cardiac rehabilitation attendance in Aboriginal patients admitted with ACS to the cardiac wards of the hospital. A retrospective medical records audit showed that there were 68 Aboriginal patients admitted to the cardiac wards with ACS from 1 July 2008 to 30 June 2011. A referral to cardiac rehabilitation was recorded for 42% of these. During the implementation of the model of care, 13 of 15 patients (86%) received a referral to cardiac rehabilitation and eight of the 13 (62%) attended. Implementation of the working together model demonstrated improved referral to and attendance at cardiac rehabilitation services, thereby, has potential to prevent complications and mortality. WHAT IS KNOWN ABOUT THE TOPIC?: Aboriginal Australians experience disparities in access to recommended care for acute coronary syndrome. This may contribute to the life expectancy gap between Aboriginal and non-Aboriginal Australians. WHAT DOES THIS PAPER ADD?: This paper describes a model of care involving an Aboriginal Hospital Liaisons Officer and a specialist cardiac nurse working

The effects of malnutrition on cardiac function in African children.

Science.gov (United States)

Silverman, Jonathan A; Chimalizeni, Yamikani; Hawes, Stephen E; Wolf, Elizabeth R; Batra, Maneesh; Khofi, Harriet; Molyneux, Elizabeth M

2016-02-01

Cardiac dysfunction may contribute to high mortality in severely malnourished children. Our objective was to assess the effect of malnutrition on cardiac function in hospitalised African children. Prospective cross-sectional study. Public referral hospital in Blantyre, Malawi. We enrolled 272 stable, hospitalised children ages 6-59 months, with and without WHO-defined severe acute malnutrition. Cardiac index, heart rate, mean arterial pressure, stroke volume index and systemic vascular resistance index were measured by the ultrasound cardiac output monitor (USCOM, New South Wales, Australia). We used linear regression with generalised estimating equations controlling for age, sex and anaemia. Our primary outcome, cardiac index, was similar between those with and without severe malnutrition: difference=0.22 L/min/m(2) (95% CI -0.08 to 0.51). No difference was found in heart rate or stroke volume index. However, mean arterial pressure and systemic vascular resistance index were lower in children with severe malnutrition: difference=-8.6 mm Hg (95% CI -12.7 to -4.6) and difference=-200 dyne s/cm(5)/m(2) (95% CI -320 to -80), respectively. In this largest study to date, we found no significant difference in cardiac function between hospitalised children with and without severe acute malnutrition. Further study is needed to determine if cardiac function is diminished in unstable malnourished children. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Applied structural equation modelling for researchers and practitioners using R and Stata for behavioural research

CERN Document Server

Ramlall, Indranarain

2016-01-01

This book explains in a rigorous, concise and practical manner all the vital components embedded in structural equation modelling. Focusing on R and stata to implement and perform various structural equation models.

Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

KAUST Repository

Potsepaev, R.

2010-09-06

Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU

Directory of Open Access Journals (Sweden)

Yong Xia

2015-01-01

Full Text Available Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation and the other is the diffusion term of the monodomain model (partial differential equation. Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.

A delay differential equation model of follicle waves in women.

Science.gov (United States)

Panza, Nicole M; Wright, Andrew A; Selgrade, James F

2016-01-01

This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.

A New Transgenic Mouse Model of Heart Failure and Cardiac Cachexia Raised by Sustained Activation of Met Tyrosine Kinase in the Heart

Directory of Open Access Journals (Sweden)

Valentina Sala

2016-01-01

Full Text Available Among other diseases characterized by the onset of cachexia, congestive heart failure takes a place of relevance, considering the high prevalence of this pathology in most European countries and in the United States, and is undergoing a rapid increase in developing countries. Actually, only few models of cardiac cachexia exist. Difficulties in the recruitment and follow-up of clinical trials implicate that new reproducible and well-characterized animal models are pivotal in developing therapeutic strategies for cachexia. We generated a new model of cardiac cachexia: a transgenic mouse expressing Tpr-Met receptor, the activated form of c-Met receptor of hepatocyte growth factor, specifically in the heart. We showed that the cardiac-specific induction of Tpr-Met raises a cardiac hypertrophic remodelling, which progresses into concentric hypertrophy with concomitant increase in Gdf15 mRNA levels. Hypertrophy progresses to congestive heart failure with preserved ejection fraction, characterized by reduced body weight gain and food intake and skeletal muscle wasting. Prevention trial by suppressing Tpr-Met showed that loss of body weight could be prevented. Skeletal muscle wasting was also associated with altered gene expression profiling. We propose transgenic Tpr-Met mice as a new model of cardiac cachexia, which will constitute a powerful tool to understand such complex pathology and test new drugs/approaches at the preclinical level.

Integrable discretizations for the short-wave model of the Camassa-Holm equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

Long-Term Overexpression of Hsp70 Does Not Protect against Cardiac Dysfunction and Adverse Remodeling in a MURC Transgenic Mouse Model with Chronic Heart Failure and Atrial Fibrillation.

Science.gov (United States)

Bernardo, Bianca C; Sapra, Geeta; Patterson, Natalie L; Cemerlang, Nelly; Kiriazis, Helen; Ueyama, Tomomi; Febbraio, Mark A; McMullen, Julie R

2015-01-01

Previous animal studies had shown that increasing heat shock protein 70 (Hsp70) using a transgenic, gene therapy or pharmacological approach provided cardiac protection in models of acute cardiac stress. Furthermore, clinical studies had reported associations between Hsp70 levels and protection against atrial fibrillation (AF). AF is the most common cardiac arrhythmia presenting in cardiology clinics and is associated with increased rates of heart failure and stroke. Improved therapies for AF and heart failure are urgently required. Despite promising observations in animal studies which targeted Hsp70, we recently reported that increasing Hsp70 was unable to attenuate cardiac dysfunction and pathology in a mouse model which develops heart failure and intermittent AF. Given our somewhat unexpected finding and the extensive literature suggesting Hsp70 provides cardiac protection, it was considered important to assess whether Hsp70 could provide protection in another mouse model of heart failure and AF. The aim of the current study was to determine whether increasing Hsp70 could attenuate adverse cardiac remodeling, cardiac dysfunction and episodes of arrhythmia in a mouse model of heart failure and AF due to overexpression of Muscle-Restricted Coiled-Coil (MURC). Cardiac function and pathology were assessed in mice at approximately 12 months of age. We report here, that chronic overexpression of Hsp70 was unable to provide protection against cardiac dysfunction, conduction abnormalities, fibrosis or characteristic molecular markers of the failing heart. In summary, elevated Hsp70 may provide protection in acute cardiac stress settings, but appears insufficient to protect the heart under chronic cardiac disease conditions.

Long-Term Overexpression of Hsp70 Does Not Protect against Cardiac Dysfunction and Adverse Remodeling in a MURC Transgenic Mouse Model with Chronic Heart Failure and Atrial Fibrillation.

Directory of Open Access Journals (Sweden)

Bianca C Bernardo

Full Text Available Previous animal studies had shown that increasing heat shock protein 70 (Hsp70 using a transgenic, gene therapy or pharmacological approach provided cardiac protection in models of acute cardiac stress. Furthermore, clinical studies had reported associations between Hsp70 levels and protection against atrial fibrillation (AF. AF is the most common cardiac arrhythmia presenting in cardiology clinics and is associated with increased rates of heart failure and stroke. Improved therapies for AF and heart failure are urgently required. Despite promising observations in animal studies which targeted Hsp70, we recently reported that increasing Hsp70 was unable to attenuate cardiac dysfunction and pathology in a mouse model which develops heart failure and intermittent AF. Given our somewhat unexpected finding and the extensive literature suggesting Hsp70 provides cardiac protection, it was considered important to assess whether Hsp70 could provide protection in another mouse model of heart failure and AF. The aim of the current study was to determine whether increasing Hsp70 could attenuate adverse cardiac remodeling, cardiac dysfunction and episodes of arrhythmia in a mouse model of heart failure and AF due to overexpression of Muscle-Restricted Coiled-Coil (MURC. Cardiac function and pathology were assessed in mice at approximately 12 months of age. We report here, that chronic overexpression of Hsp70 was unable to provide protection against cardiac dysfunction, conduction abnormalities, fibrosis or characteristic molecular markers of the failing heart. In summary, elevated Hsp70 may provide protection in acute cardiac stress settings, but appears insufficient to protect the heart under chronic cardiac disease conditions.

Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity

International Nuclear Information System (INIS)

Yepez, Jeffrey

2006-01-01

Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory

Mathematical modelling of tissue formation on the basis of ordinary differential equations

Directory of Open Access Journals (Sweden)

Maxim N. Nazarov

2017-10-01

Full Text Available A mathematical model is proposed for describing the population dynamics of cellular clusters on the basis of systems of the first-order ordinary differential equations. The main requirement for the construction of model equations was to obtain a formal biological justification for their derivation, as well as proof of their correctness. In addition, for all the parameters involved in the model equations, the presence of biological meaning was guaranteed, as well as the possibility of evaluating them either during the experiment or by using models of intracellular biochemistry. In the desired model the intercellular exchange of a special signal molecules was chosen as the main mechanism for coordination of the tissue growth and new types selection during cell division. For simplicity, all signalling molecules that can create cells of the same type were not considered separately in the model, but were instead combined in a single complex of molecules: a ‘generalized signal’. Such an approach allows us to eventually assign signals as a functions of cell types and introduce their effects in the form of matrices in the models, where the rows are responsible for the types of cells receiving the signals, and the columns for the types of cells emitting signals.

Analytic solution of boundary-value problems for nonstationary model kinetic equations

International Nuclear Information System (INIS)

Latyshev, A.V.; Yushkanov, A.A.

1993-01-01

A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected

The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth...... by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

Science.gov (United States)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

International Nuclear Information System (INIS)

Eliezer, S.; Falquina, R.; Minguez, E.

1994-01-01

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Halogenated anaesthetics and cardiac protection in cardiac and non-cardiac anaesthesia

Directory of Open Access Journals (Sweden)

Landoni Giovanni

2009-01-01

Full Text Available Volatile anaesthetic agents have direct protective properties against ischemic myocardial damage. The implementation of these properties during clinical anaesthesia can provide an additional tool in the treatment or prevention, or both, of ischemic cardiac dysfunction in the perioperative period. A recent meta-analysis showed that desflurane and sevoflurane reduce postoperative mortality and incidence of myocardial infarction following cardiac surgery, with significant advantages in terms of postoperative cardiac troponin release, need for inotrope support, time on mechanical ventilation, intensive care unit and overall hospital stay. Multicentre, randomised clinical trials had previously demonstrated that the use of desflurane can reduce the postoperative release of cardiac troponin I, the need for inotropic support, and the number of patients requiring prolonged hospitalisation following coronary artery bypass graft surgery either with and without cardiopulmonary bypass. The American College of Cardiology/American Heart Association Guidelines recommend volatile anaesthetic agents during non-cardiac surgery for the maintenance of general anaesthesia in patients at risk for myocardial infarction. Nonetheless, e vidence in non-coronary surgical settings is contradictory and will be reviewed in this paper together with the mechanisms of cardiac protection by volatile agents.

Modelling Evolutionary Algorithms with Stochastic Differential Equations.

Science.gov (United States)

Heredia, Jorge Pérez

2017-11-20

There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

Three-dimensional modelling and three-dimensional printing in pediatric and congenital cardiac surgery.

Science.gov (United States)

Kiraly, Laszlo

2018-04-01

Three-dimensional (3D) modelling and printing methods greatly support advances in individualized medicine and surgery. In pediatric and congenital cardiac surgery, personalized imaging and 3D modelling presents with a range of advantages, e.g., better understanding of complex anatomy, interactivity and hands-on approach, possibility for preoperative surgical planning and virtual surgery, ability to assess expected results, and improved communication within the multidisciplinary team and with patients. 3D virtual and printed models often add important new anatomical findings and prompt alternative operative scenarios. For the lack of critical mass of evidence, controlled randomized trials, however, most of these general benefits remain anecdotal. For an individual surgical case-scenario, prior knowledge, preparedness and possibility of emulation are indispensable in raising patient-safety. It is advocated that added value of 3D printing in healthcare could be raised by establishment of a multidisciplinary centre of excellence (COE). Policymakers, research scientists, clinicians, as well as health care financers and local entrepreneurs should cooperate and communicate along a legal framework and established scientific guidelines for the clinical benefit of patients, and towards financial sustainability. It is expected that besides the proven utility of 3D printed patient-specific anatomical models, 3D printing will have a major role in pediatric and congenital cardiac surgery by providing individually customized implants and prostheses, especially in combination with evolving techniques of bioprinting.

Cardiac Rehabilitation After Heart Valve Surgery

DEFF Research Database (Denmark)

Pollmann, Agathe Gerwina Elena; Frederiksen, Marianne; Prescott, Eva

2017-01-01

PURPOSE: Evidence of the effect of cardiac rehabilitation (CR) after heart valve surgery is scarce, but nevertheless CR is recommended for this group of patients. Therefore, this study assessed the effect of CR on exercise capacity, cardiovascular risk factors, and long-term mortality and morbidity...... ((Equation is included in full-text article.)O2peak) or 6-minute walk test (6MWT). A composite endpoint of all-cause mortality and hospital admission due to myocardial infarction, stroke, heart failure, endocarditis, revascularization, or reoperation was used to assess the hazard ratio between CR attenders...

A quantitative model of the cardiac ventricular cell incorporating the transverse-axial tubular system

Czech Academy of Sciences Publication Activity Database

Pásek, Michal; Christé, G.; Šimurda, J.

2003-01-01

Roč. 22, č. 3 (2003), s. 355-368 ISSN 0231-5882 R&D Projects: GA ČR GP204/02/D129 Institutional research plan: CEZ:AV0Z2076919 Keywords : cardiac cell * tubular system * quantitative modelling Subject RIV: BO - Biophysics Impact factor: 0.794, year: 2003

Interactive differential equations modeling program

International Nuclear Information System (INIS)

Rust, B.W.; Mankin, J.B.

1976-01-01

Due to the recent emphasis on mathematical modeling, many ecologists are using mathematics and computers more than ever, and engineers, mathematicians and physical scientists are now included in ecological projects. However, the individual ecologist, with intuitive knowledge of the system, still requires the means to critically examine and adjust system models. An interactive program was developed with the primary goal of allowing an ecologist with minimal experience in either mathematics or computers to develop a system model. It has also been used successfully by systems ecologists, engineers, and mathematicians. This program was written in FORTRAN for the DEC PDP-10, a remote terminal system at Oak Ridge National Laboratory. However, with relatively minor modifications, it can be implemented on any remote terminal system with a FORTRAN IV compiler, or equivalent. This program may be used to simulate any phenomenon which can be described as a system of ordinary differential equations. The program allows the user to interactively change system parameters and/or initial conditions, to interactively select a set of variables to be plotted, and to model discontinuities in the state variables and/or their derivatives. One of the most useful features to the non-computer specialist is the ability to interactively address the system parameters by name and to interactively adjust their values between simulations. These and other features are described in greater detail

Metabolic and cardiac changes in high cholesterol-fructose-fed rats

DEFF Research Database (Denmark)

Axelsen, Lene N; Pedersen, Henrik D; Petersen, Jørgen S

2010-01-01

Introduction: High cholesterol-fructose (HCF) fed rats have previously been described as an animal model of impaired cardiac insulin signaling and decreased contractile performance. In this study, we evaluated the metabolic and cardiac effects of a HCF diet in rats. Methods: Male Sprague-Dawley r......Introduction: High cholesterol-fructose (HCF) fed rats have previously been described as an animal model of impaired cardiac insulin signaling and decreased contractile performance. In this study, we evaluated the metabolic and cardiac effects of a HCF diet in rats. Methods: Male Sprague...

An overview on development and application of an experimental platform for quantitative cardiac imaging research in rabbit models of myocardial infarction.

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Feng, Yuanbo; Bogaert, Jan; Oyen, Raymond; Ni, Yicheng

2014-10-01

To exploit the advantages of using rabbits for cardiac imaging research and to tackle the technical obstacles, efforts have been made under the framework of a doctoral research program. In this overview article, by cross-referencing the current literature, we summarize how we have developed a preclinical cardiac research platform based on modified models of reperfused myocardial infarction (MI) in rabbits; how the in vivo manifestations of cardiac imaging could be closely matched with those ex vivo macro- and microscopic findings; how these imaging outcomes could be quantitatively analyzed, validated and demonstrated; and how we could apply this cardiac imaging platform to provide possible solutions to certain lingering diagnostic and therapeutic problems in experimental cardiology. In particular, tissue components in acute cardiac ischemia have been stratified and characterized, post-infarct lipomatous metaplasia (LM) as a common but hardly illuminated clinical pathology has been identified in rabbit models, and a necrosis avid tracer as well as an anti-ischemic drug have been successfully assessed for their potential utilities in clinical cardiology. These outcomes may interest the researchers in the related fields and help strengthen translational research in cardiovascular diseases.

Quintom models with an equation of state crossing -1

International Nuclear Information System (INIS)

Zhao Wen; Zhang Yang

2006-01-01

In this paper, we investigate a kind of special quintom model, which is made of a quintessence field φ 1 and a phantom field φ 2 , and the potential function has the form of V(φ 1 2 -φ 2 2 ). This kind of quintom field can be separated into two kinds: the hessence model, which has the state of φ 1 2 >φ 2 2 , and the hantom model with the state φ 1 2 2 2 . We discuss the evolution of these models in the ω-ω ' plane (ω is the state equation of the dark energy, and ω ' is its time derivative in units of Hubble time), and find that according to ω>-1 or ' plane can be divided into four parts. The late time attractor solution, if existing, is always quintessencelike or Λ-like for hessence field, so the big rip does not exist. But for hantom field, its late time attractor solution can be phantomlike or Λ-like, and sometimes, the big rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the ω-ω ' plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation-of-state function ω(z). We apply our method to five kinds of parametrizations of equation-of-state parameter, where ω crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom δ Q and the metric Φ are all finite even at the state of ω=-1 and ω ' ≠0

Discrete ellipsoidal statistical BGK model and Burnett equations

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Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

[Third phase of cardiac rehabilitation: a nurse-based "home-control" model].

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Albertini, Sara; Ciocca, Antonella; Opasich, Cristina; Pinna, Gian Domenico; Cobelli, Franco

2011-12-01

Phase 3 is a critical point for cardiac rehabilitation: many problems don't allow achieving a correct secondary prevention, in particular regarding the relationship between patient and cardiologist. Aiming at ensuring continuity of care of phase 3 cardiac rehabilitation patients, we have developed a telemetric educational program to stimulate in them the will and capacity to become active comanagers of their disease. Nurses specialized in cardiac rehabilitation, with the collaboration of the general practitioners, contact the patients by scheduled phone calls to collect questionnaires about their health status and the result of biochemistry. All the results are analyzed by the nurses and discussed with each patient (educational reinforcement). The effects of this program of comanagement of cardiac disease and secondary prevention are analyzed comparing each patient data at the discharge with data after one year and those coming from our archive (retrospective analysis). The patients enrolled in this study pay much more attention to the amount of food they eat; they tend not to gain weight, and they restart smoking in a reduced proportion compared to patients not enrolled in the study. However, despite having received better information on their cardiac disease, their compliance to physical training, consumption of healthy food, and pharmacological therapy is not improved. This study focuses on the role of a continuous educational program of a cardiac rehabilitation unit after the patient's discharge. This home control program conducted by nurses specialized in cardiac rehabilitation, with the assistance of cardiologists, psychologists and physiotherapists, and in collaboration with the general practitioner, was quite cheap, and helped maximizing the knowledge of the disease and reinforcing correct life style in the patients. The results are not as good as expected, probably because one year does not represent a sufficient time, or because the educational

Dissolution process analysis using model-free Noyes-Whitney integral equation.

Science.gov (United States)

Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto

2013-02-01

Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.

Mechanisms Involved in Secondary Cardiac Dysfunction in Animal Models of Trauma and Hemorrhagic Shock.

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Wilson, Nick M; Wall, Johanna; Naganathar, Veena; Brohi, Karim; De'Ath, Henry D

2017-10-01

Clinical evidence reveals the existence of a trauma-induced secondary cardiac injury (TISCI) that is associated with poor patient outcomes. The mechanisms leading to TISCI in injured patients are uncertain. Conversely, animal models of trauma hemorrhage have repeatedly demonstrated significant cardiac dysfunction following injury, and highlighted mechanisms through which this might occur. The aim of this review was to provide an overview of the animal studies describing TISCI and its pathophysiology.Basic science models of trauma show evidence of innate immune system activation via Toll-like receptors, the exact protagonists of which remain unclear. Shortly following trauma and hemorrhage, cardiomyocytes upregulate gene regulatory protein and inflammatory molecule expression including nuclear factor kappa beta, tumor necrosis factor alpha, and interleukin-6. This is associated with expression of membrane bound adhesion molecules and chemokines leading to marked myocardial leukocyte infiltration. This cell activation and infiltration is linked to a rise in enzymes that cause oxidative and nitrative stress and subsequent protein misfolding within cardiomyocytes. Such protein damage may lead to reduced contractility and myocyte apoptosis. Other molecules have been identified as cardioprotective following injury. These include p38 mitogen-activated protein kinases and heat shock proteins.The balance between increasing damaging mediators and a reduction in cardio-protective molecules appears to define myocardial function following trauma. Exogenous therapeutics have been trialled in rodents with promising abilities to favorably alter this balance, and subsequently lead to improved cardiac function.

Estimating varying coefficients for partial differential equation models.

Science.gov (United States)

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

Eicosapentenoic Acid Attenuates Allograft Rejection in an HLA-B27/EGFP Transgenic Rat Cardiac Transplantation Model.

Science.gov (United States)

Liu, Zhong; Hatayama, Naoyuki; Xie, Lin; Kato, Ken; Zhu, Ping; Ochiya, Takahiro; Nagahara, Yukitoshi; Hu, Xiang; Li, Xiao-Kang

2012-01-01

The development of an animal model bearing definite antigens is important to facilitate the evaluation and modulation of specific allo-antigen responses after transplantation. In the present study, heterotopic cardiac transplantation was performed from F344/EGFPTg and F344/HLA-B27Tg rats to F344 rats. The F344 recipients accepted the F344/EGFPTg transplants, whereas they rejected the cardiac tissue from the F344/HLA-B27Tg rats by 39.4 ± 6.5 days, due to high production of anti-HLA-B27 IgM- and IgG-specific antibodies. In addition, immunization of F344 rats with skin grafts from F344/HLA-B27Tg rats resulted in robust production of anti- HLA-B27 IgM and IgG antibodies and accelerated the rejection of a secondary cardiac allograft (7.4 ± 1.9 days). Of interest, the F344 recipients rejected cardiac grafts from double transgenic F344/HLA-B27&EGFPTg rats within 9.0 ± 3.2 days, and this was associated with a significant increase in the infiltration of lymphocytes by day 7, suggesting a role for cellular immune rejection. Eicosapentenoic acid (EPA), one of the ω-3 polyunsaturated fatty acids in fish oil, could attenuate the production of anti-HLA IgG antibodies and B-cell proliferation, significantly prolonging double transgenic F344HLA-B27&EGFPTg to F344 rat cardiac allograft survival (36.1 ± 13.6 days). Moreover, the mRNA expression in the grafts was assessed by quantitative reverse transcription polymerase chain reaction (qRT-PCR), revealing an increase in the expression of the HO-1, IL-10, TGF-β, IDO, and Foxp3 genes in the EPA-treated group. Hence, our data indicate that HLA-B27 and/or GFP transgenic proteins are useful for establishing a unique animal transplantation model to clarify the mechanism underlying the allogeneic cellular and humoral immune response, in which the transplant antigens are specifically presented. Furthermore, we also demonstrated that EPA was effective in the treatment of rat cardiac allograft rejection and may allow the development of

The Influence of Cardiac Risk Factor Burden on Cardiac Stress Test Outcomes.

Science.gov (United States)

Schrock, Jon W; Li, Morgan; Orazulike, Chidubem; Emerman, Charles L

2011-06-01

Chest pain is the most common admission diagnosis for observation unit patients. These patients often undergo cardiac stress testing to further risk stratify for coronary artery disease (CAD). The decision of whom to stress is currently based on clinical judgment. We sought to determine the influence of cardiac risk factor burden on cardiac stress test outcome for patients tested from an observation unit, inpatient or outpatient setting. We performed a retrospective observational cohort study for all patients undergoing stress testing in our institution from June 2006 through July 2007. Cardiac risk factors were collected at the time of stress testing. Risk factors were evaluated in a summative fashion using multivariate regression adjusting for age and known coronary artery disease. The model was tested for goodness of fit and collinearity and the c statistic was calculated using the receiver operating curve. A total of 4026 subjects were included for analysis of which 22% had known CAD. The rates of positive outcome were 89 (12.0%), 95 (12.6%), and 343 (16.9%) for the OU, outpatients, and hospitalized patients respectively. While the odds of a positive test outcome increased for additional cardiac risk factors, ROC curve analysis indicates that simply adding the number of risk factors does not add significant diagnostic value. Hospitalized patients were more likely to have a positive stress test, OR 1.41 (1.10 - 1.81). Our study does not support basing the decision to perform a stress test on the number of cardiac risk factors.

Prior Sensitivity Analysis in Default Bayesian Structural Equation Modeling.

Science.gov (United States)

van Erp, Sara; Mulder, Joris; Oberski, Daniel L

2017-11-27

Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models and solve some of the issues often encountered in classical maximum likelihood estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of the unknown model parameters. Often, researchers rely on default priors, which are constructed in an automatic fashion without requiring substantive prior information. However, the prior can have a serious influence on the estimation of the model parameters, which affects the mean squared error, bias, coverage rates, and quantiles of the estimates. In this article, we investigate the performance of three different default priors: noninformative improper priors, vague proper priors, and empirical Bayes priors-with the latter being novel in the BSEM literature. Based on a simulation study, we find that these three default BSEM methods may perform very differently, especially with small samples. A careful prior sensitivity analysis is therefore needed when performing a default BSEM analysis. For this purpose, we provide a practical step-by-step guide for practitioners to conducting a prior sensitivity analysis in default BSEM. Our recommendations are illustrated using a well-known case study from the structural equation modeling literature, and all code for conducting the prior sensitivity analysis is available in the online supplemental materials. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Cardiac fusion and complex congenital cardiac defects in thoracopagus twins: diagnostic value of cardiac CT

Energy Technology Data Exchange (ETDEWEB)

Goo, Hyun Woo [University of Ulsan College of Medicine, Asan Medical Center, Department of Radiology and Research Institute of Radiology, Seoul (Korea, Republic of); Park, Jeong-Jun [University of Ulsan College of Medicine, Asan Medical Center, Department of Pediatric Cardiac Surgery, Seoul (Korea, Republic of); Kim, Ellen Ai-Rhan [University of Ulsan College of Medicine, Asan Medical Center, Division of Neonatology, Department of Pediatrics, Seoul (Korea, Republic of); Won, Hye-Sung [University of Ulsan College of Medicine, Asan Medical Center, Department of Obstetrics and Gynecology, Seoul (Korea, Republic of)

2014-09-15

Most thoracopagus twins present with cardiac fusion and associated congenital cardiac defects, and assessment of this anatomy is of critical importance in determining patient care and outcome. Cardiac CT with electrocardiographic triggering provides an accurate and quick morphological assessment of both intracardiac and extracardiac structures in newborns, making it the best imaging modality to assess thoracopagus twins during the neonatal period. In this case report, we highlight the diagnostic value of cardiac CT in thoracopagus twins with an interatrial channel and complex congenital cardiac defects. (orig.)

Mechanisms Regulating the Cardiac Output Response to Cyanide Infusion, a Model of Hypoxia

Science.gov (United States)

Liang, Chang-seng; Huckabee, William E.

1973-01-01

When tissue metabolic changes like those of hypoxia were induced by intra-aortic infusion of cyanide in dogs, cardiac output began to increase after 3 to 5 min, reached a peak (220% of the control value) at 15 min, and returned to control in 40 min. This pattern of cardiac output rise was not altered by vagotomy with or without atropine pretreatment. However, this cardiac output response could be differentiated into three phases by pretreating the animals with agents that block specific activities of the sympatho-adrenal system. First, ganglionic blockade produced by mecamylamine or sympathetic nerve blockade by bretylium abolished the middle phase of the cardiac output seen in the untreated animal, but early and late phases still could be discerned. Second, beta-adrenergic receptor blockade produced by propranolol shortened the total duration of the cardiac output rise by abolishing the late phase. Third, when given together, propranolol and mecamylamine (or bretylium) prevented most of the cardiac output rise that follows the early phase. When cyanide was given to splenectomized dogs, the duration of the cardiac output response was not shortened, but the response became biphasic, resembling that seen after chemical sympathectomy. A similar biphasic response of the cardiac output also resulted from splenic denervation; sham operation or nephrectomy had no effect on the monophasic pattern of the normal response. Splenic venous blood obtained from cyanide-treated dogs, when infused intraportally, caused an increase in cardiac output in recipient dogs; similar infusion of arterial blood had no effects. These results suggest that the cardiac output response to cyanide infusion consists of three components: an early phase, related neither to the autonomic nervous system nor to circulating catecholamines; a middle phase, caused by a nonadrenergic humoral substance released from the spleen by sympathetic stimulation; and a late phase, dependent upon adrenergic receptors

Numerical Cerebrospinal System Modeling in Fluid-Structure Interaction.

Science.gov (United States)

Garnotel, Simon; Salmon, Stéphanie; Balédent, Olivier

2018-01-01

Cerebrospinal fluid (CSF) stroke volume in the aqueduct is widely used to evaluate CSF dynamics disorders. In a healthy population, aqueduct stroke volume represents around 10% of the spinal stroke volume while intracranial subarachnoid space stroke volume represents 90%. The amplitude of the CSF oscillations through the different compartments of the cerebrospinal system is a function of the geometry and the compliances of each compartment, but we suspect that it could also be impacted be the cardiac cycle frequency. To study this CSF distribution, we have developed a numerical model of the cerebrospinal system taking into account cerebral ventricles, intracranial subarachnoid spaces, spinal canal and brain tissue in fluid-structure interactions. A numerical fluid-structure interaction model is implemented using a finite-element method library to model the cerebrospinal system and its interaction with the brain based on fluid mechanics equations and linear elasticity equations coupled in a monolithic formulation. The model geometry, simplified in a first approach, is designed in accordance with realistic volume ratios of the different compartments: a thin tube is used to mimic the high flow resistance of the aqueduct. CSF velocity and pressure and brain displacements are obtained as simulation results, and CSF flow and stroke volume are calculated from these results. Simulation results show a significant variability of aqueduct stroke volume and intracranial subarachnoid space stroke volume in the physiological range of cardiac frequencies. Fluid-structure interactions are numerous in the cerebrospinal system and difficult to understand in the rigid skull. The presented model highlights significant variations of stroke volumes under cardiac frequency variations only.

Approximating a retarded-advanced differential equation that models human phonation

Science.gov (United States)

Teodoro, M. Filomena

2017-11-01

In [1, 2, 3] we have got the numerical solution of a linear mixed type functional differential equation (MTFDE) introduced initially in [4], considering the autonomous and non-autonomous case by collocation, least squares and finite element methods considering B-splines basis set. The present work introduces a numerical scheme using least squares method (LSM) and Gaussian basis functions to solve numerically a nonlinear mixed type equation with symmetric delay and advance which models human phonation. The preliminary results are promising. We obtain an accuracy comparable with the previous results.

Rate equation modelling of the optically pumped spin-exchange source

International Nuclear Information System (INIS)

Stenger, J.; Rith, K.

1995-01-01

Sources for spin polarized hydrogen or deuterium, polarized via spin-exchange of a laser optically pumped alkali metal, can be modelled by rate equations. The rate equations for this type of source, operated either with hydrogen or deuterium, are given explicitly with the intention of providing a useful tool for further source optimization and understanding. Laser optical pumping of alkali metal, spin-exchange collisions of hydrogen or deuterium atoms with each other and with alkali metal atoms are included, as well as depolarization due to flow and wall collisions. (orig.)