Modified Kuramoto Phase Model for Simulating Cardiac Pacemaker Cell Synchronization

Abstract

It has been suggested that sick sinus syndrome, which is due to the dysfunction of the sinus node, may result from the sparser gap junctions and/or lower intrinsic frequencies of pacemaker cells that occur with aging. Hence, in this paper, the synchronization mechanism of pacemaker cells that lie in the sinus node of the heart is examined using a modified Kuramoto phase model. Although each element always interacts with all the others in the Kuramoto phase model, in the proposed model, each element interacts only with the neighbors over a certain time (called the interaction time) during Phase 4 of the action potential. The pacemaker cell elements are arranged on a square lattice, and each element connects with the elements surrounding it. The results indicate that the diversity of intrinsic frequencies of pacemaker cells may be necessary for synchronization. Moreover, increasing the proportion of invalid connections causes the elements to take more time to synchronize until eventually they do not synchronize at all, and decreasing the intrinsic frequencies of the elements prevents them from synchronizing. Probably these elucidate the cause of sick sinus syndrome.