Vol. 13, No. 3, 2020

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Linkages of calcium-induced calcium release in a cardiomyocyte simulated by a system of seven coupled partial differential equations

Gerson C. Kroiz, Carlos Barajas, Matthias K. Gobbert and Bradford E. Peercy

Vol. 13 (2020), No. 3, 399–424
Abstract

Cardiac arrhythmias affect millions of adults in the U.S. each year. This irregularity in the beating of the heart is often caused by dysregulation of calcium in cardiomyocytes, the cardiac muscle cell. Cardiomyocytes function through the interplay between electrical excitation, calcium signaling, and mechanical contraction, an overall process known as calcium-induced calcium release (CICR). A system of seven coupled nonlinear time-dependent partial differential equations (PDEs), which model physiological variables in a cardiac cell, link the processes of cardiomyocytes. Through parameter studies for each component system at a time, we create a set of values for critical parameters that connect the calcium store in the sarcoplasmic reticulum, the effect of electrical excitation, and mechanical contraction in a physiologically reasonable manner. This paper shows the design process of this set of parameters and then shows the possibility to study the influence of a particular problem parameter using the overall model.

Keywords
cardiac arrhythmia, calcium-induced calcium release, reaction diffusion equations, finite-volume method, parallel computing
Mathematical Subject Classification 2010
Primary: 35K57, 65M08, 65Y05, 68U20, 92C30
Secondary: 65L04, 65M20, 68W10, 92C37, 92C50
Milestones
Received: 1 June 2019
Revised: 13 December 2019
Accepted: 6 January 2020
Published: 14 July 2020

Communicated by Suzanne Lenhart
Authors
Gerson C. Kroiz
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Baltimore, MD
United States
Carlos Barajas
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Baltimore, MD
United States
Matthias K. Gobbert
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Baltimore, MD
United States
Bradford E. Peercy
Department of Mathematics and Statistics
University of Maryland, Baltimore County
Baltimore, MD
United States