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