Thermoelectric model to study the cardiac action potential and arrhythmias

Abstract

This paper proposes a new thermoelectric model to examine the behavior of the heart in cooling situations. A modified Karma model with temperature-dependence is exploited to describe the ion exchange dynamics at the mesoscopic scale while the propagation of the action potential is governed by a mono-domain equation at the macroscopic scale. In addition to perfusion and heat metabolism, we call the Penne equation coupled to the mono-domain equation by using the Joule effect to depict the temperature behavior in the system. Galerkin’s finite element method is utilized to start solving the partial differential equations governing the action potential and temperature propagations. The incomplete lower–upper decomposition and generalized minimal residual methods are solicited to solve the resulting nonlinear system. The cases of zero temperature and potential gradients are integrated through the scheme of Runge–Kutta, and the results obtained corroborate well with those of the literature. We analyze the contributions of the nonlinear coupling tensor and arterial temperature on the thermal and electrical responses of the system. The established results reveal that when the temperature in the medium augments, the duration of the action potential decreases and the Joule coupling tensor plays a crucial role in the propagation of the potential. Moreover, we show that temperature and action potential are in phase and that propagation of this potential generates thermal energy. Furthermore, we establish the existence of spiral waves in heart cells and show that the effect of global cooling helps to modulate or dampen these spiral waves, leading to control of the cardiac arrhythmia. This work also develops a technique to resolve conduction disorders and cancel them completely. It exhibits an increased added value to the use of hypothermia as therapy during cardiac arrest and makes it possible to anticipate and perhaps avoid this pathology.