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.