A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue

In this paper, we study a mathematical model of cardiac tissue based on explicit representation of individual cells. In this EMI model, the extracellular (E) space, the cell membrane (M), and the intracellular (I) space are represented as separate geometrical domains. This representation introduces modeling flexibility needed for detailed representation of the properties of cardiac cells including their membrane. In particular, we will show that the model allows ion channels to be non-uniformly distributed along the membrane of the cell. Such features are difficult to include in classical homogenized models like the monodomain and bidomain models frequently used in computational analyses of cardiac electrophysiology. The EMI model is solved using a finite difference method (FDM) and two variants of the finite element method (FEM). We compare the three schemes numerically, reporting on CPU-efforts and convergence rates. Finally, we illustrate the distinctive capabilities of the EMI model compared to classical models by simulating monolayers of cardiac cells with heterogeneous distributions of ionic channels along the cell membrane. Because of the detailed representation of every cell, the computational problems that result from using the EMI model are much larger than for the classical homogenized models, and thus represent a computational challenge. However, our numerical simulations indicate that the FDM scheme is optimal in the sense that the computational complexity increases proportionally to the number of cardiac cells in the model. Moreover, we present simulations, based on systems of equations involving ~117 million unknowns, representing up to ~16,000 cells. We conclude that collections of cardiac cells can be simulated using the EMI model, and that the EMI model enable greater modeling flexibility than the classical monodomain and bidomain models

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

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An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant—at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest

Metabolically driven maturation of human-induced-pluripotent-stem-cell-derived cardiac microtissues on microfluidic chips

The immature physiology of cardiomyocytes derived from human induced pluripotent stem cells (hiPSCs) limits their utility for drug screening and disease modelling. Here we show that suitable combinations of mechanical stimuli and metabolic cues can enhance the maturation of hiPSC-derived cardiomyocytes, and that the maturation-inducing cues have phenotype-dependent effects on the cells' action-potential morphology and calcium handling. By using microfluidic chips that enhanced the alignment and extracellular-matrix production of cardiac microtissues derived from genetically distinct sources of hiPSC-derived cardiomyocytes, we identified fatty-acid-enriched maturation media that improved the cells' mitochondrial structure and calcium handling, and observed divergent cell-source-dependent effects on action-potential duration (APD). Specifically, in the presence of maturation media, tissues with abnormally prolonged APDs exhibited shorter APDs, and tissues with aberrantly short APDs displayed prolonged APDs. Regardless of cell source, tissue maturation reduced variabilities in spontaneous beat rate and in APD, and led to converging cell phenotypes (with APDs within the 300-450 ms range characteristic of human left ventricular cardiomyocytes) that improved the modelling of the effects of pro-arrhythmic drugs on cardiac tissue