Intra-and inter-cellular Ca2+ waves play key roles in cellular functions. Focal stimulation triggers Ca2+ wave propagation from the stimulation point to neighboring cells through the cytoplasm, which involves localized metabolism reactions and specific diffusion processes. Briefly, inositol 1,4,5-trisphosphate (IP3) is produced at membranes and diffuses into the cytoplasm, resulting in Ca2+ release from the endoplasmic reticulum (ER). Particu-larly, Ca2+ released from the ER is mediated by two princi-ples, the IP3-induced Ca2+ and Ca2+-induced Ca2+ releases. Ca2+ is diffused through the cytoplasm and, furthermore, transported into neighboring cells through gap junctions. These intra-and inter-cellular Ca2+ waves have been widely investigated using theoretical and experimental methods in various cell types. In this review we summarize the mathematical models used for the numerical simulation of intra-and inter-cellular Ca2+ wave propagations.
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