a cell-based framework for numerical modeling of electrical conduction in cardiac tissue

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ID: 225717
2017
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Abstract
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.
Reference Key
tveito2017frontiersa Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Aslak Tveito;Aslak Tveito;Karoline H. Jæger;Miroslav Kuchta;Miroslav Kuchta;Kent-Andre Mardal;Kent-Andre Mardal;Marie E. Rognes
Journal journal of biomaterials science polymer edition
Year 2017
DOI
10.3389/fphy.2017.00048
URL
http://journal.frontiersin.org/article/10.3389/fphy.2017.00048/full
Keywords
Finite Element Method finite difference method

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