摘要
This work presents the dynamical modelling of cardiac 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 Vm, extracellular potential φe and gating variable w. We implemented the discretized model and 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, Vm, in the normal cardiac tissue was obtained by setting the values of ionic model parameters to 0.2, 0.2, 0.7 and 0.8 for excitation rate constant ε1, recovery rate constant ε2, recovery decay constant γ and excitation decay constant β respectively. Changing the values of ε1, ε2 to 0.04 and 0.28 respectively, the obtained Vm showed a time dilation at 0.04 indicating cardiac arrhythmia but no significant change to Vm was observed at 0.28. Also, changing β to 0.3 and 1.1 and γ to 0.4 and 1.2 sequentially, there was no significant change to the time characteristic of Vm. The obtained results revealed that only decrease in ε1, ε2 impacted significantly on the cardiac wave propagation.
This work presents the dynamical modelling of cardiac 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 Vm, extracellular potential φe and gating variable w. We implemented the discretized model and 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, Vm, in the normal cardiac tissue was obtained by setting the values of ionic model parameters to 0.2, 0.2, 0.7 and 0.8 for excitation rate constant ε1, recovery rate constant ε2, recovery decay constant γ and excitation decay constant β respectively. Changing the values of ε1, ε2 to 0.04 and 0.28 respectively, the obtained Vm showed a time dilation at 0.04 indicating cardiac arrhythmia but no significant change to Vm was observed at 0.28. Also, changing β to 0.3 and 1.1 and γ to 0.4 and 1.2 sequentially, there was no significant change to the time characteristic of Vm. The obtained results revealed that only decrease in ε1, ε2 impacted significantly on the cardiac wave propagation.
