Mathematical modeling of the entrainment of asymmetrical cardiac cell pairs

Complex multidimensional interactions between spatial distributions of Intrinsic cellular electrical properties and intercellular coupling resistances underlie the activation patterns related to sinus node function. In the present study we have used a model of two coupled cardiac cells, a pacemaker and a non pacemaker cell, to investigate the dependence of successful conduction on three components of the system: (1) the intrinsic cellular properties, (2) the intercellular resistance, and (3) the pacemaker: non pacemaker size ratio between the two cells. The use of numerical simulations and continuation — bifurcation techniques demonstrated the presence of period doubling bifurcations and abrupt decreases of the activation ratio similar to sino-atrial exit blocks associated with bi- and even tristabilities. A stable entrainment was obtained with a size ratio as low as 0.1, but this geometrical configuration induced a large early repolarisation in the pacemaker cell during the conduction process due to the loading influence of the large non pacemaker cell.