Long-Time Simulation of Calcium Waves in a Heart Cell to Study the Effects of Calcium Release Flux Density and of Coefficients in the Pump and Leak Mechanisms on Self-Organizing Wave Behavior

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Spontaneous calcium sparks can lead to propagation of a self-initiated calcium wave under certain conditions in a heart cell. A model for diffusion waves of calcium ions in a heart cell is given by a system of coupled, time-dependent reaction- diffusion equations. The key term of the model quantifies the release of calcium at the calcium release units by a flux density. The model also includes pump and leak mechanisms that model the extruding and entering of calcium throughout the cell, respectively. Previous simulations for this model with extreme values of the flux density demonstrate that no wave will self-organize for a small value and that a wave will self-organize for a large value; in the latter case, it also becomes apparent that the total concentration of calcium throughout the cell grows without bound. This report shows that the original conclusions with respect to wave self-organization are correct qualitatively, and it identifies the range of values of the flux density quantitatively for which we can be confident about the observation. Additionally, a range of values for the parameters of the pump mechanism is studied. We can conclude that the growth of the total calcium concentration is affected by the choice of coefficients, but that, for the parameters studied here, the growth cannot be avoided for the cases in which a wave self-organizes.