Date Published: May 3, 2019
Publisher: Public Library of Science
Author(s): Youssef Belhamadia, Justin Grenier, Elena G. Tolkacheva.
Previous experimental evidence has shown the effect of temperature on the action potential duration (APD). It has also been demonstrated that regional cooling of the heart can prolong the APD and promote the termination of ventricular tachycardia. The aim of this study is to demonstrate the effect of hypothermia in suppressing cardiac arrhythmias using numerical modeling. For this purpose, we developed a mathematical model that couples Pennes’ bioheat equation and the bidomain model to simulate the effect of heat on the cardiac action potential. The simplification of the proposed heat–bidomain model to the heat–monodomain model is provided. A suitable numerical scheme for this coupling, based on a time adaptive mesh finite element method, is also presented. First, we performed two-dimensional numerical simulations to study the effect of heat on a regular electrophysiological wave, with the comparison of the calculated and experimental values of Q10. Then, we demonstrated the effect of global hypothermia in suppressing single and multiple spiral waves.
Several experimental studies have demonstrated the significant effect of induced hypothermia on cardiac and neurological outcomes for patients (see  for a review). Hypothermia is now recommended as a therapeutic treatment for cases of spinal cord and brain injuries (see  and ), and it is used as a standard treatment for cardiac arrest . Numerical modeling can provide valuable contribution for the understanding of the role of temperature effects in the cardiac electrical dynamics, which is the main aim of this paper.
The bi and monodomain models are widely used in electrocardiology to simulate the spatial propagation of the transmembrane potential in the myocardium. These classical models do not consider the effect of temperature on the electrical wave; therefore, heat–bidomain and heat–monodomain couplings are required.
In this section, we discuss the performance of the model and the numerical method introduced in the previous sections. First, we present the effect of heat on regular electrophysiological wave. The cardiac transmembrane potential is demonstrated at different temperatures and the results are validated by comparing the calculated and the experimental values of Q10, which is a commonly used quantification in biology to describe the rate of change of a system subjected to a temperature increase of 10 °C. Then, the effect of hypothermia in suppressing cardiac arrhythmias is investigated.
A mathematical model obtained by coupling Pennes’ bioheat equation with the bidomain model is presented to simulate the effects of temperature variations on the cardiac APD. The simplification of the proposed heat–bidomain model to the heat–monodomain model is also presented. Several numerical experiments were performed. We demonstrated the effect of temperature on the APD and the conduction velocity, and the obtained numerical results were compared to the experimental results in the literature. We also investigated the effects of hypothermia and regional cooling in suppressing cardiac arrhythmias. We clearly demonstrated that hypothermia of short duration could terminate the spiral wave breakup. To our knowledge, this is the first study that presents numerical modeling of the effect of hypothermia in cardiac arrhythmias. As mentioned in the introduction, the effect of temperature has been included in studies in the literature via the ionic terms. However, in our approach the effect of spatial temperature on the cardiac electrical activity has been introduced directly. The comparison between the two approaches presented in this paper demonstrates the advantages of the proposed methodology.