Abstract
Electrical activity is essential for the cardiac cell to perform its function. Mathematical modeling of cardiac electrical activity is performed from the cell, tissue and organ levels through to the body surface level. The electrical activity of the cardiac as a whole is thus characterized by a complex multiscale structure. The most complete model of such a complex setting is the anisotropic bidomain model that consists of a system of two degenerate parabolic reaction diffusion equations describing the intra and extracellular potentials in the cardiac muscle, coupled with a system of ordinary deferential equations describing the ionic currents flowing through the cellular membrane. This study describes an anatomically realistic 3D Bidomain model of whole-heart electrical activity. The heart was embedded in a human torso, incorporating spontaneous activation with heterogeneous action potential (AP) morphologies throughout the heart. The aim of this study is the development of a geometrically simple and computationally efficient 3D model of heart. In this paper a finite element formulation, model and simulation of Bidomain equation has been conducted. The FitzHugh-Nagumo (FHN) equations were incorporated into Bidomain model of cardiac electrical activity, which was comprised of a simplified geometry of the whole heart with the torso as an extracellular volume conductor. Laplace equation for the torso also considered. Simplified 3D cardiac model was implemented using COMSOL Multiphysics 5.0 finite element software. Electrical potential at different point on torso is measured. Propagation of electrical excitation on heart surface is also observed. This study represents the first stage toward the development of an accurate computer model of heart activation.  Â
Highlights
Mathematical models of electrical activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias
The most complete model of such a complex setting is the anisotropic Bidomain model [4] that consists of a system of two degenerate parabolic reaction diffusion equations describing the intra and extracellular potentials in the cardiac muscle, coupled with a system of ordinary deferential equations describing the ionic currents flowing through the cellular membrane [5]
Models of the electrophysiology of one cell are governed by systems of ordinary differential equations and one or more partial differential equations are governed for modeling the electrophysiology of more than one cell
Summary
Mathematical models of electrical activity in cardiac tissue are becoming increasingly powerful tools in the study of cardiac arrhythmias. The first stage involves the identification of the pertinent problem or problems These problems are described using the language of mathematics, important variables and features are identified, underlying assumptions are stated, and equations are formulated. Once a mathematical solution is obtained, it must be interpreted in the language used to describe the original problem, which again is a translation stage When such a model has been extensively verified it can become a powerful tool for predicting function, including, for instance, the effect of interventions such as medical treatments [6]. The finite element formulation of the problem results in a system of simultaneous algebraic equations for solution, rather than requiring the solution of differential equations These numerical methods yield approximate values of the unknowns at discrete numbers of points in the continuum. In the finite element method, instead of solving the problem for the entire body in one operation, we formulate the equations for each finite element and combine them to obtain the solution of the whole body [7]
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