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 (θ) 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 (V_rest) in the depolarizing direction and reduces input resistance (R_in) by increasing an inwardly rectifying K⁺ conductance, I_Kl. Our results show that in this model: (1) θ depends on [K⁺]_o in a “biphasic” fashion. Moderate elevations of [K⁺]_o (to less than 8 mM) result in a small increase in θ, whereas at higher [K⁺]_o (8–16 mM) θ is reduced. (2) This biphasic relationship can be attributed to the competing effects of (i) the smaller depolarization needed to reach the excitation threshold (V_thresh – V_rest) and (ii) reduced availability (increased inactivation) of sodium current, I_Na, as the cell depolarizes progressively. (3) Decreasing R_in reduces θ due to the increased electrical load on surrounding cells. (4) The effect on θ 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 effect could be substantial, however, under conditions in which R_in 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.