Mathematical simulation of the Wenckebach phenomenon in Purkinje fibers

We were able to simulate the Wenckebach phenomenon using a model of a one-dimensional cable, consisting of 20 serially connected Purkinje fiber cells represented by the model of McAllister, Noble, and Tsien. The internal resistance between the 10th and 11th cells was modified to five times the normal. To reconstruct the action potential, the derivative equation was solved using a fourth-order Runge-Kutta algorithm. When the first cell of the cable was stimulated, periodically, at an interval of 610 ms, a 9:8 Wenckebach pattern was elicited in the conduction between the tenth and 11th cells. Lower order 5:4, 4:3, 3:2 Wenckebach patterns were observed at pacing cycle length of 605, 600-595, and 590-575 ms, respectively. At a pacing cycle length of 570ms or less, 2:1 block was elicited. In another simulation, only when INa, was 0 could the Wenckebach phenomenon be elicited in a cable model. in which internal cell resistance and membrane capacitance were uniformly set, but in which the INa of the center two cells of the cable were alternated between 1 and 0. A localized increase in internal resistance, a relatively long time constant of deactivation of the delayed rectifier outward current, and a relatively rapid rate of pacing cycle length was necessary to evoke the Wenckebach phenomenon. The conductance of the delayed rectifier current at the end of an action potential increased progressively, except after a dropped beat when it was allowed to decrease. It was concluded that the change of conductance affected the cable property of the fiber and consequently evoked the Wenckebach phenomenon.