Mathematical simulation of slowing of cardiac conduction velocity by elevated extracellular [K+] in a human atrial strand

We have studied the dependence of conduction velocity (theta) on extracellu lar potassium concentration ([K+](o)) in a model of one-dimensional conduct ion using an idealized strand of human atrial cells. Elevated [K+](o) in th e 5-20 mM range shifts the resting potential (V-rest) in the depolarizing d irection and reduces input resistance (R-in) by increasing an inwardly rect ifying 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 neede d to reach the excitation threshold (V-thresh-V-rest) and (ii) reduced avai lability (increased inactivation) of sodium current, I-Na, as the cell depo larizes progressively. (3) Decreasing R-in reduces theta due to the increas ed electrical load on surrounding cells. (4) The effect on theta of [K+](o) -induced changes in R-in in the atrium (as well as other high-R-in tissue, such as that of the Purkinje system or nodes) is likely to be small. This e ffect could be substantial, however, under conditions in which R-in is comp arable 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. (C) 2000 Bi omedical Engineering Society. [S0090-6964(00)00308-8].