Parameter Uncertainty Analysis of a Mathematical Ion Channel Model.

In mathematical modeling of cell physiological processes, measurements required for parameter determination are often available only as aggregated data in the literature. Physiological measurements contain relatively large observation errors due to intrinsic variations in physiological processes, and the errors cause uncertainties in parameter values. This paper reports analyses of the uncertainty in parameter estimates of a simple mathematical model of an ion channel from a set of published experimental data.

A Preliminary Computational Model for Hypoxic Acidosis in Cardiac Myocytes.

Intracellular acidosis induced by hypoxia resulted from myocardial ischemia damages myocardium. However, the detailed mechanisms of hypoxic acidosis are not quantitatively explained. The purpose of this study is to create a novel computational model which can reproduce intracellular acidosis caused by myocardial ischemia.

A computational model of myocardial microcirculation including interstitial flow.

Contributions of interstitial fluid (ISF) flow within the myocardial microcirculation is not well understood despite its importance due to difficulties in measurements. For analysing a contribution of interstitial fluid flow within myocardial microcirculation, we developed a computational model of myocardial microcirculation by introducing convection by the ISF flow into an existing myocardial microcirculation model, and performed simulations with varied ISF flows in normal and hypoperfusion conditions. Simulation results show that the ISF flow has a contribution only with low capillary flow.

Modeling analysis of inositol 1,4,5-trisphosphate receptor-mediated Ca2+ mobilization under the control of glucagon-like peptide-1 in mouse pancreatic β-cells.

Glucagon-like peptide-1 (GLP-1) is an intestinally derived blood glucose-lowering hormone that potentiates glucose-stimulated insulin secretion from pancreatic β-cells. The secretagogue action of GLP-1 is explained, at least in part, by its ability to stimulate cAMP production so that cAMP may facilitate the release of Ca(2+) from inositol trisphosphate receptor (IP3R)-regulated Ca(2+) stores. However, a quantitative model has yet to be provided that explains the molecular mechanisms and dynamic processes linking GLP-1-stimulated cAMP production to Ca(2+) mobilization.

Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models.

Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation.

Application of the Kalman Filter for Faster Strong Coupling of Cardiovascular Simulations.

In this paper, we propose a method for reducing the computational cost of strong coupling for multiscale cardiovascular simulation models. In such a model, individual model modules of myocardial cell, left ventricular structural dynamics, and circulatory hemodynamics are coupled. The strong coupling method enables stable and accurate calculation, but requires iterative calculations which are computationally expensive.

Nonlinear multiscale circulation model reproducable linear end-systolic pressure-volume relationship.

As a well-known property of the heart, many studies has reported that the left ventricular end-systolic pressure-volume relationship (ESPVR) is linear. However, the reason of the linearity is poorly understood. This article presents a multiscale circulation model to be a tool for theoretical analyses on the mechanism of the linearity of ESPVR.

A study on the relationship between electrical transmural heterogeneity and ventricular energetics.

In this study, we use cardiovascular simulation to gain new insights on the correlation between electrical heterogeneity and ventricular energetics. Although there are numerous in vivo and in vitro studies on the electrical heterogeneity within the ventricular myocardium, not much attention has been directed to its correlation to cardiovascular mechanics, because of difficulties in simultaneously observing and analyzing multiple spatial scales (the cell, the organ, and the system). We performed simulations with two cardiovascular simulation models, one which uses different myocardial cell models for the epicardial, endocardial, and mid-myocardial cells, and another which uses a homogeneous model throughout the entire myocardium.

Code generator for distributed parameter biological model simulation with PDE numerical schemes.

The physiological simulation at the tissue and organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and in cases like pharmacokinetics, distributed parameters add to the complexity of the PDE solution. These factors make most PDE solutions and their corresponding program codes tailored for specific problems.

Theoretical analysis on the relationship between left ventricular energetic efficiency and acute infarct size.

Energetic efficiency is an important indicator of cardiac function in acute myocardial infarction. However, the relationship between cardiac energetic efficiency and infarct size is not perfectly elucidated. In this study, the relationship is analysed by means of simulation using a theoretical model of the guinea pig left ventricle.

A program code generator for multiphysics biological simulation using markup languages.

To cope with the complexity of the biological function simulation models, model representation with description language is becoming popular. However, simulation software itself becomes complex in these environment, thus, it is difficult to modify the simulation conditions, target computation resources or calculation methods. In the complex biological function simulation software, there are 1) model equations, 2) boundary conditions and 3) calculation schemes.

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena.

A CellML simulation compiler and code generator using ODE solving schemes.

: Models written in description languages such as CellML are becoming a popular solution to the handling of complex cellular physiological models in biological function simulations. However, in order to fully simulate a model, boundary conditions and ordinary differential equation (ODE) solving schemes have to be combined with it. Though boundary conditions can be described in CellML, it is difficult to explicitly specify ODE solving schemes using existing tools.

A general CellML simulation code generator using ODE solving scheme description.

To cope with the complexity of the biological function simulation models, model representation with description language is becoming popular. However, simulation software itself becomes complex in these environment, thus, it is difficult to modify target computation resources or numerical calculation methods or simulation conditions. Typical biological function simulation software consists of 1) model equation, 2) boundary conditions and 3) ODE solving scheme.

A study on prediction methods for a cardiovascular strong-coupling simulation.

We investigated numerical methods for predictors in a multiscale cardiovascular simulation model. The proposed method predicts initial approximations for the iterative convergence calculations of the strong coupling method using the smoothing spline to remove errors from values of past timesteps and using the linear and second-order extrapolation. The new coupling algorithm was used for coupling a left ventricular finite element model to a myocardial excitation-contraction model.

Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells.

In our companion paper, the physiological functions of pancreatic β cells were analyzed with a new β-cell model by time-based integration of a set of differential equations that describe individual reaction steps or functional components based on experimental studies. In this study, we calculate steady-state solutions of these differential equations to obtain the limit cycles (LCs) as well as the equilibrium points (EPs) to make all of the time derivatives equal to zero. The sequential transitions from quiescence to burst-interburst oscillations and then to continuous firing with an increasing glucose concentration were defined objectively by the EPs or LCs for the whole set of equations.

A novel method to quantify contribution of channels and transporters to membrane potential dynamics.

The action potential, once triggered in ventricular or atrial myocytes, automatically proceeds on its time course or is generated spontaneously in sinoatrial node pacemaker cells. It is induced by complex interactions among such cellular components as ion channels, transporters, intracellular ion concentrations, and signaling molecules. We have developed what is, to our knowledge, a new method using a mathematical model to quantify the contribution of each cellular component to the automatic time courses of the action potential.

A method for analysis of simultaneous equations in cell models.

Some models of cellular physiological functions are formulated as ordinary differential equations that contain multiple systems of simultaneous nonlinear equations. Simulation of such a model described in a declarative representation format requires determination of equations to be simultaneously solved with specification of independent and parameter variables in the model. In this report, a method for extracting systems of simultaneous equations in a cell model is presented.

Evaluation of cardiac oxygen consumption under hypoxia with tissue model integrating microcirculation model and cell model.

Analyzing the microscopic energy balance of cardiac tissue is very important for understanding heart diseases. However, such analysis is difficult with animal experiments. Therefore, the accurate simulation model is expected to be an important tool for such research.

An approximation model of myocardial crossbridge for weak coupling calculation of left ventricle model and circulation model.

It is necessary to use complicated myocardial cell model and heart model to evaluate the regional energy production and consumption which leads to the unrealistic computational time. In this research, a left ventricle (LV) simulation model was constructed which includes accurate myocardial cell model. In order to simulate the model in realistic time, we introduced an approximation model of the crossbridge model which can be calculated with weak coupling calculation.

Infant circulation model based on the electrophysiological cell model.

It is important to use a myocardial cell model to evaluate the effects of the drugs to the hemodynamic parameters. We developed an infant circulation model which incorporates an accurate myocardial cell model including a beta adrenergic system. The beta adrenergic system is essential mechanism for reproducing the response of baroreflex control system.

A generic representation format of physiological experimental protocols for computer simulation using ontology.

For computer simulations of physiological experiments using physiological models, a machine-readable format of experimental protocols is effective. Here, we propose an XML-based language, PEPML (Physiological Experimental Protocol Markup Language). In the PEPML, conditions and procedures of an experimental protocol are procedurally described as a list of events, each of which consists of a condition for execution and an action to be executed.

Computer support for physiological cell modelling using an ontology on cell physiology.

The development of electrophysiological whole cell models to support the understanding of biological mechanisms is increasing rapidly. Due to the complexity of biological systems, comprehensive cell models, which are composed of many imported sub-models of functional elements, can get quite complicated as well, making computer modification difficult. Here, we propose a computer support to enhance structural changes of cell models, employing the markup languages CellML and our original PMSML (physiological model structure markup language), in addition to a new ontology for cell physiological modelling.

Stress distribution in a rotationally symmetric and a measurement based left ventricular shape model.

We evaluated the stress distribution in a geometrical shape model and a shape model obtained from human heart using two different fiber orientations. For both orientation models, the results showed large differences of the stress distributions between the mathematical shape model and the measurement based shape model. These results suggest that stress distribution is highly dependent on the model geometry and the usage of a measurement based shape model is important for the evaluation of the left ventricular (LV) wall stress distribution.

Reproducing nonlinear force velocity relation of myocardial tissue by a nonlinear parallel elastic component.

To realize precise simulation of the left ventricular motion, it is important to utilize an accurate myocardial tissue model which can reproduce various characteristics of myocardial tissue contraction. In this study, we show that the nonlinear characteristics of the passive myocardial tissue property is the essential nature of the nonlinear force-velocity relation and present a formulation for hyperelastic physiological tissue property. Experimental results of our myocardial tissue simulation with the hyperelastic material property proposed are in good agreement with the reported force-velocity relation of real tissue.