A linear system of partial differential equations modeling the resting potential of a heart with regional ischemia.

Ischemic ST-segment shift has been modeled using scalar stationary approximations of the bidomain model. Here, we propose an alternative simplification of the bidomain equations: a linear system modeling the resting potential, to be used in determining ischemic TP shift. Results of 2D and 3D simulations show that the linear system model is much more accurate than the scalar model. This improved accuracy is important if the model is to be used for solving the inverse problem of determining the size and location of an ischemic region. Furthermore, the model can provide insight into how the resting potential depends on the variations in the extracellular potassium concentration that characterize ischemic regions.

Simple T-Wave Metrics May Better Predict Early Ischemia as Compared to ST Segment.

There is pressing clinical need to identify developing heart attack (infarction) in patients as early as possible. However, current state-of-the-art tools in clinical practice, underpinned by the evaluation of elevation of the ST segment of the 12-lead electrocardiogram (ECG), do not identify all patients suffering from lack of blood flow to the heart muscle (cardiac ischemia), worsening the risk for further adverse events and patient outcome overall. In this study, we aimed to explore and compare the portions of cardiac repolarization in the ECG that best capture the electrophysiological changes associated with ischemia. We developed three-dimensional electrophysiological models of the human ventricles and torso, incorporating biophysically-based membrane kinetics and realistic activation sequence, to compute simulated ECGs and their alteration with the application of simulated ischemia of differing severity in diverse regions of the heart. Results suggest that metrics based on the T-wave in addition to the ST segment may be more sensitive to detecting ischemia than those using the ST segment alone. Further research into how such simulation-aided risk assessment methods may aid workflows in extant clinical practice, with the ultimate goal of multimodality clinical support, is warranted.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model.

Unstable eigenmodes are possible drivers for cardiac arrhythmias.

The well-organized contraction of each heartbeat is enabled by an electrical wave traversing and exciting the myocardium in a regular manner. Perturbations to this wave, referred to as arrhythmias, can lead to lethal fibrillation if not treated within minutes. One manner in which arrhythmias originate is an ill-fated interaction of the regular electrical signal controlling the heartbeat, the sinus wave, with an ectopic stimulus. It is not fully understood how and when ectopic waves are generated. Based on mathematical models, we show that ectopic beats can be characterized in terms of unstable eigenmodes of the resting state.

Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts.

We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark.

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

A second-order algorithm for solving dynamic cell membrane equations.

This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of nonlinear terms in combination with the analytical solution of linear ordinary differential equations to obtain a second-order accurate numerical scheme. We compare the error and computational load of the second-order scheme to the original Rush-Larsen method and a second-order Runge-Kutta (RK) method. The numerical results indicate that the new method outperforms the original Rush-Larsen scheme for all the test cases. The comparison with the RK solver reveals that the new method is more efficient for stiff problems.