Control of cardiac alternans in a mapping model with memory

A generic feature of cardiac muscle is that the duration of an action potential depends on the long-term history of previous action potentials, known as cardiac 'memory'. Even though memory is known to be an important physiological response, there have only been limited studies of its effect on cardiac dynamics. Here, we investigate a map-based model of paced myocardium in the presence of closed-loop feedback control. The model relates the duration of an action potential to the preceding diastolic interval as well as the preceding action potential duration and thus has some degree of memory. We find that the range of parameters over which control is effective can be enlarged or reduced by memory, a prediction that is independent of the specific functional form of the map. Our work suggests that modifying the degree of memory (e.g., pharmacological agents) with some form of feedback control may be an effective strategy for the maintenance of normal cardiac function.