Dynamical modelling of cardiac electrical activity using bidomain approach: The effects of variation of ionic model parameters

Abstract

<p> <span style="font-family:Verdana;">This work presents the dynamical modelling of cardiac</span><span><span style="font-family:Verdana;"> electrical activity using bidomain approach. It focuses on the effects of variation of the ionic model parameters on cardiac wave propagation. Cardiac electrical activity is governed by partial differential equations coupled to a system of ordinary differential equations. Numerical simulation of these equations is computationally expensive due to their non-linearity and stiffness. Nevertheless, we adopted the bidomain model due to its ability to reflect the actual cardiac wave propagation. The derived bidomain equations coupled with FitzHugh-Nagumo’s ionic equations were time-discretized using explicit forward Euler method and space-discretized using 2-D network modelling to obtain linearized equations for transmembrane potential </span><i><span style="font-family:Verdana;">V</span>_{<span style="font-family:Verdana;">m</span>}</i><span style="font-family:Verdana;">, extracellular potential </span></span><i><span style="font-family:Verdana;">φ</span></i><i>_{<span style="font-family:Verdana;">e</span>}</i><span><span style="font-family:Verdana;"> and gating </span><span><span style="font-family:Verdana;">variable </span><i><span style="font-family:Verdana;">w</span></i><span style="font-family:Verdana;">. We implemented the discretized model and</span></span><span style="font-family:Verdana;"> performed simulation experiments to study the effects of variation of ionic model parameters on the propagation of electrical wave across the cardiac tissue. Time characteristic of transmembrane potential, </span><i><span style="font-family:Verdana;">V</span>_{<span style="font-family:Verdana;">m</span>}</i><span style="font-family:Verdana;">, in the normal cardiac tissue </span><span style="font-family:Verdana;">was obtained by setting the values of ionic model parameters to 0.2, 0.2, 0.7 and 0.8 for excitation rate constant </span></span><i><span style="font-family:Verdana;"><i><span style="font-size:10.0pt;font-family:;" "="">ε</span></i></span></i><i>_{<span style="font-family:Verdana;">1</span>}</i><span style="font-family:Verdana;">, recovery rate constant </span><i><span style="font-family:Verdana;"><i><span style="font-size:10.0pt;font-family:;" "="">ε</span></i></span></i><span style="font-family:Verdana;">₂</span><span><span style="font-family:Verdana;">, recovery decay constant </span><i><span style="font-family:Verdana;">γ </span></i><span style="font-family:Verdana;">and excitation decay constant </span><i><span style="font-family:Verdana;">β</span></i><span style="font-family:Verdana;"> respectively. Changing the values of </span></span><i><span style="font-family:Verdana;"><i><span style="font-size:10.0pt;font-family:;" "="">ε</span></i></span></i><span style="font-family:Verdana;">₁</span><i><span style="font-family:Verdana;">, </span></i><span style="font-family:Verdana;"><span style="font-size:10.0pt;font-family:;"...