Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle

Life-threatening arrhythmias such as ventricular tachycardia and fibrillation often occur during acute myocardial ischemia. During the first few minutes following coronary occlusion, there is a gradual rise in the extracellular concentration of potassium ions ${\mathrm{([K}}^{+}{]}_0)$ within ischemic tissue. This elevation of ${\mathrm{[K}}^{+}{]}_0$ is one of the main causes of the electrophysiological changes produced by ischemia, and has been implicated in inducing arrhythmias. We investigate an ionic model of a 3 cm×3 cm sheet of normal ventricular myocardium containing an ischemic zone, simulated by elevating ${\mathrm{[K}}^{+}{]}_0$ within a centrally-placed 1 cm×1 cm area of the sheet. As ${\mathrm{[K}}^{+}{]}_0$ is gradually raised within the ischemic zone from the normal value of 5.4 mM, conduction first slows within the ischemic zone and then, at higher ${\mathrm{[K}}^{+}{]}_0,$ an arc of block develops within that area. The area distal to the arc of block is activated in a delayed fashion by a retrogradely moving wavefront originating from the distal edge of the ischemic zone. With a further increase in ${\mathrm{[K}}^{+}{]}_0,$ the point eventually comes where a very small increase in ${\mathrm{[K}}^{+}{]}_0$ (0.01 mM) results in the abrupt transition from a global period-1 rhythm to a global period-2 rhythm in the sheet. In the peripheral part of the ischemic zone and in the normal area surrounding it, there is an alternation of action potential duration, producing a 2:2 response. Within the core of the ischemic zone, there is an alternation between an action potential and a maintained small-amplitude response (∼30 mV in height). With a further increase of ${\mathrm{[K}}^{+}{]}_0,$ the maintained small-amplitude response turns into a decrementing subthreshold response, so that there is 2:1 block in the central part of the ischemic zone. A still further increase of ${\mathrm{[K}}^{+}{]}_0$ leads to a transition in the sheet from a global period-2 to a period-4 rhythm, and then to period-6 and period-8 rhythms, and finally to a complete block of propagation within the ischemic core. When the size of the sheet is increased to 4 cm×4 cm (with a 2 cm×2 cm ischemic area), one observes essentially the same sequence of rhythms, except that the period-6 rhythm is not seen. Very similar sequences of rhythms are seen as ${\mathrm{[K}}^{+}{]}_0$ is increased in the central region (1 or 2 cm long) of a thin strand of tissue (3 or 4 cm long) in which propagation is essentially one-dimensional and in which retrograde propagation does not occur. While reentrant rhythms resembling tachycardia and fibrillation were not encountered in the above simulations, well-known precursors to such rhythms (e.g., delayed activation, arcs of block, two-component upstrokes, retrograde activation, nascent spiral tips, alternans) were seen. We outline how additional modifications to the ischemic model might result in the emergence of reentrant rhythms following alternans.