New frequency entrainment scenario in a pair of cardiac cells coupled through a variable resistance

Describe the frequency entrainment behavior of a pair of cardiac cells coupled through a variable resistance (R_j) which is a function of the intracellular calcium concentration and a scaling parameter R_b. R_j is increased with higher firing rates in both cells. If R_b is high enough, R_j reaches a value for which the coupling current is too low to trigger an active response in the follower cell. The missed response causes a shortening of the action potential duration in the paced cell. These two factors force R_j to decrease, thereby removing some of the previous decoupling effect. For a pair of cells with a fixed coupling resistance, the activation ratio of the frequency entrainment responses was found to change abruptly when the value of the coupling resistance was changed. With the variable coupling resistance, using R_b as the bifurcation parameter, the negative feedback effect of the firing rates on R_j makes the transition from one mode to the other more gradual. The resulting rhythm is a succession of stable patterns consisting of a mix of the adjacent activation ratios appearing on the bifurcation map of the fixed resistance system