Mathematical simulation of slowing of cardiac conduction velocity by elevated extracellular

We have studied the dependence of conduction velocity (theta) on extracellular potassium concentration ([K+]o) in a model of one-dimensional conduction using an idealized strand of human atrial cells. Elevated [K+]o in the 5-20 mM range shifts the resting potential (Vrest) in the depolarizing direction and reduces input resistance (Rin) by increasing an inwardly rectifying K+ conductance, I(Kl). Our results show that in this model: (1) theta depends on [K+]o in a "biphasic" fashion. Moderate elevations of [K+]o (to less than 8 mM) result in a small increase in theta, whereas at higher [K+]o (8-16 mM) theta is reduced. (2) This biphasic relationship can be attributed to the competing effects of (i) the smaller depolarization needed to reach the excitation threshold (Vthresh-Vrest) and (ii) reduced availability (increased inactivation) of sodium current, INa, as the cell depolarizes progressively. (3) Decreasing Rin reduces theta due to the increased electrical load on surrounding cells. (4) The effect on theta of [K+]o-induced changes in Rin in the atrium (as well as other high-Rin tissue, such as that of the Purkinje system or nodes) is likely to be small. This effect could be substantial, however, under conditions in which Rin is comparable in size to gap junction resistance and membrane resistance (inverse slope of the whole-cell current-voltage relationship) when sodium channels are open, which is likely to be the case in ventricular tissue.