On the Propagation of Calcium Waves in an Inhomogeneous Medium

Although the exact details are disputed, it is well established that propagating waves of increased intracellular free Ca2+ concentration arise from a positive feedback or autocatalytic mechanism whereby Ca2+ stimulates its own release. Most previous modeling of the propagation of Ca2+ waves has assumed that the sites of autocatalytic Ca2+ release, the activation sites, are homogeneously distributed through the cytoplasm. We investigate how the spacing and size of the activation sites affect the existence and speed of propagating calcium waves. We first study the simplest model of an excitable system to obtain analytic estimates of the critical spacing. We then derive analytic expressions for the speed of the advancing wave front in the self-oscillatory case and compare them to numerical results. The theoretical results are illustrated by computed solutions of two similar models for calcium wave propagation.