Modeling transport of interstitial potassium in regional myocardial ischemia: effect on the injury current

Myocardial ischemia leads to an efflux of potassium ions from affected cells. The resulting depolarization of the resting membrane is one of the main features of ischemic myocardium. It has been shown experimentally that a part of the surplus interstitial potassium is transported out of the ischemic zone, even if no coronary blood flow is present in the affected area. We propose to model this transport mechanism mathematically with a diffusion equation. This model explains the measured spatial profiles of extracellular potential and potassium concentration. In addition, it allows a quantitative prediction of the transmembrane current that flows as a result of ischemia-induced depolarization. This current is thought to play a role in arrhythmogenicity, which is an important cause of mortality in acute myocardial infarction. Our model predicts that this current reaches its maximum exactly on the border of the hypoxic area. An important depolarizing current would be present just within the border, where hypoxia is accompanied by a resting membrane potential that is only slightly elevated, due to coupling with the adjacent normal tissue. Still, in the presence of potassium transport the predicted current density is not large enough to explain ectopic activation on the lateral border of the ischemia. This suggests that activation is more likely to occur at the endocardium, where the potassium gradient is steeper.