Ca2+ spiral waves in a spatially discrete and random medium

It is well known that the spatial distribution of the calcium ion channels in the endoplasmic reticulum is discrete. We study the Ca2+ spiral pattern formation based on a model in which ion channels are discretely and randomly distributed. Numerical simulations are performed on different types of media with the Ca2+ release sites uniformly distributed, discretely and uniformly arranged, or discretely and randomly arranged. The comparisons among the different media show that random distribution is necessary for spontaneous initiation of Ca2+ spiral waves, and the discrete and random distribution is of significance for spiral waves under physiologically reasonable conditions. The period and velocity of spiral waves are also calculated, and they are not prominently changed by varying the type of medium.