Three-dimensional simulation of calcium waves and contraction in cardiomyocytes using the finite element method

Abstract

To investigate the characteristics and underlying mechanisms of Ca2+ wave propagation, we developed a three-dimensional (3-D) simulator of cardiac myocytes, in which the sarcolemma, myofibril, and Z-line structure with Ca2+ release sites were modeled as separate structures using the finite element method. Similarly to previous studies, we assumed that Ca2+ diffusion from one release site to another and Ca2+-induced Ca2+ release were the basic mechanisms, but use of the finite element method enabled us to simulate not only the wave propagation in 3-D space but also the active shortening of the myocytes. Therefore, in addition to the dependence of the Ca2+ wave propagation velocity on the sarcoplasmic reticulum Ca2+ content and affinity of troponin C for Ca2+, we were able to evaluate the influence of active shortening on the propagation velocity. Furthermore, if the initial Ca2+ release took place in the proximity of the nucleus, spiral Ca2+ waves evolved and spread in a complex manner, suggesting that this phenomenon has the potential for arrhythmogenicity. The present 3-D simulator, with its ability to study the interaction between Ca2+ waves and contraction, will serve as a useful tool for studying the mechanism of this complex phenomenon.