Mathematical simulation of the Wenckebach phenomenon in Purkinje fibers

We were able to simulate the Wenckebach phenomenon using a model of a one-d imensional cable, consisting of 20 serially connected Purkinje fiber cells represented by the model of McAllister, Noble, and Tsien. The internal resi stance between the 10th and 11th cells was modified to five times the norma l. To reconstruct the action potential, the derivative equation was solved using a fourth-order Runge-Kutta algorithm. When the first cell of the cabl e 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. Lo wer order 5:4, 4.3, 3:2 Wenckebach patterns were observed at pacing cycle l ength of 605, 600-595, and 590-575 ms, respectively. At a pacing cycle leng th of 570 ms or less, 2:1 block was elicited. In another simulation, only w hen I-Na 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 I-Na of the center two cells of the cable were alter nated between 1 and 0. A localized increase in internal resistance, a relat ively long time constant of deactivation of the delayed rectifier outward c urrent, 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 a fter 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 cons equently evoked the Wenckebach phenomenon.