Examining the Electrical Excitation, Calcium Signaling, and Mechanical Contraction Cycle in a Heart Cell

Correspondence: Prof. Matthias K. Gobbert, Department of Mathematics and Statistics, University of Maryland, Baltimore County (UMBC), 1000 Hilltop Circle, Baltimore, MD 21250, USA gobbert@umbc.edu Abstract As the leading cause of death in the United States, heart disease has become a principal concern in modern society. Cardiac arrhythmias can be caused by a dysregulation of calcium dynamics in cardiomyocytes. Calcium dysregulation, however, is not yet fully understood and is not easily predicted; this provides motivation for the subsequent research. Excitationcontraction coupling (ECC) is the process through which cardiomyocytes undergo contraction from an action potential. Calcium induced calcium release (CICR) is the mechanism through which electrical excitation is coupled with mechanical contraction through calcium signaling. The study of the interplay between electrical excitation, calcium signaling, and mechanical contraction has the potential to improve our understanding of the regular functioning of the cardiomyocytes and help us understand how any dysregulation can lead to potential cardiac arrhythmias. ECC, of which CICR is an important part, can be modeled using a system of partial differential equations that link the electrical excitation, calcium signaling, and mechanical contraction components of a cardiomyocyte. We extend a previous model [Angeloff, Barajas, et al., Examining the effect of introducing a link from electrical excitation to calcium dynamics in a cardiomyocyte, Spora: A Journal of Biomathematics, 2, 2016] to implement a seven variable model that includes for the first time the mechanical component of the ECC. We study how the interaction of electrical and calcium systems can impact the cardiomyocyte’s levels of contraction.