Automaticity in acute ischemia: bifurcation analysis of a human ventricular model

Acute ischemia (restriction in blood supply to part of the heart as a result of myocardial infarction) induces major changes in the electrophysiological properties of the ventricular tissue. Extracellular potassium concentration ([K(o)(+)]) increases in the ischemic zone, leading to an elevation of the resting membrane potential that creates an "injury current" (I(S)) between the infarcted and the healthy zone. In addition, the lack of oxygen impairs the metabolic activity of the myocytes and decreases ATP production, thereby affecting ATP-sensitive potassium channels (I(Katp)). Frequent complications of myocardial infarction are tachycardia, fibrillation, and sudden cardiac death, but the mechanisms underlying their initiation are still debated. One hypothesis is that these arrhythmias may be triggered by abnormal automaticity. We investigated the effect of ischemia on myocyte automaticity by performing a comprehensive bifurcation analysis (fixed points, cycles, and their stability) of a human ventricular myocyte model [K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 291, H1088 (2006)] as a function of three ischemia-relevant parameters [K(o)(+)], I(S), and I(Katp). In this single-cell model, we found that automatic activity was possible only in the presence of an injury current. Changes in [K(o)(+)] and I(Katp) significantly altered the bifurcation structure of I(S), including the occurrence of early-after depolarization. The results provide a sound basis for studying higher-dimensional tissue structures representing an ischemic heart.