Three-dimensional simulation of calcium waves and contraction in cardiomyocytes using the finite element method.
J. ichi Okada, S. Sugiura, S. Nishimura, and T. Hisada.
Am. J. Physiol. Cell Physiol. 288 (3): C510--C522 (March 2005)

To investigate the characteristics and underlying mechanisms of Ca$^2+$ wave propagation, we developed a three-dimensional (3-D) simulator of cardiac myocytes, in which the sarcolemma, myofibril, and Z-line structure with Ca$^2+$ release sites were modeled as separate structures using the finite element method. Similarly to previous studies, we assumed that Ca$^2+$ diffusion from one release site to another and Ca$^2+$-induced Ca$^2+$ 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 Ca$^2+$ wave propagation velocity on the sarcoplasmic reticulum Ca$^2+$ content and affinity of troponin C for Ca$^2+$, we were able to evaluate the influence of active shortening on the propagation velocity. Furthermore, if the initial Ca$^2+$ release took place in the proximity of the nucleus, spiral Ca$^2+$ 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 Ca$^2+$ waves and contraction, will serve as a useful tool for studying the mechanism of this complex phenomenon.
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