Abstract
In this paper, a ghost structure (GS) method is proposed to simulate the monodomain model in irregular computational domains using finite difference without regenerating body-fitted grids. In order to verify the validity of the GS method, it is first used to solve the Fitzhugh-Nagumo monodomain model in rectangular and circular regions at different states (the stationary and moving states). Then, the GS method is used to simulate the propagation of the action potential (AP) in transverse and longitudinal sections of a healthy human heart, and with left bundle branch block (LBBB). Finally, we analyze the AP and calcium concentration under healthy and LBBB conditions. Our numerical results show that the GS method can accurately simulate AP propagation with different computational domains either stationary or moving, and we also find that LBBB will cause the left ventricle to contract later than the right ventricle, which in turn affects synchronized contraction of the two ventricles.
Highlights
The heart is a rhythmic pump that maintains blood circulation throughout the body[1]
The voltage-gated ion channels are controlled by the membrane potential, while the membrane potential is influenced by these same ion channels, which causes feedback loops which allow for complex temporal dynamics, including oscillations and regenerative events such as action potential (AP)
Based on the ghost structure (GS) method, we capture the patterns of heterogeneity and complex connectivity of electrophysiological dynamics in biological tissues by solving the Fitzhugh-Nagumo monodomain model in rectangular and circular regions
Summary
The heart is a rhythmic pump that maintains blood circulation throughout the body[1]. Liu[41] further developed a decoupling technique to solve the fractional FitzHugh-Nagumo monodomain model, and proposed a new spatially second-order accurate semi-implicit alternating direction method to solve this model on approximate irregular regions.The model generalized a standard monodomain model that described the propagation of potentials in heterogeneous cardiac tissue. Lange et al.[44] proposed a computational model of human heart that included a false tendons, Purkinje network, and papillary muscles, and investigated effects of different types of false tendons on hearts with electrical conduction abnormality caused by LBBB They found that the false tendons could be visualized as an alternative conduction pathway, and compensates for propagation delay with LBBB. Usyk et al.[47] developed a three-dimensional model of a dilated failing heart with LBBB, and investigated how biventricular pacing could improve systolic mechanical performance and synchrony
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