Mathematical analysis of dynamics of cardiac memory and accommodation: theory and experiment

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Abstract
Decreasing the slope of the dynamic, but not conventional, restitution curves is antifibrillatory. Cardiac memory/accommodation underlies the difference. We measured diastolic interval (DI) and action potential duration (APD) in epicardial, endocardial, and Purkinje tissue from eight dogs. Consecutive 100-stimulus trains were given to study transitions between basic cycle lengths (BCL) ranging from 400 to 1,300 ms. (DI,APD) pairs aligned immediately on the line DI + APD = BCL (64/67) or oscillated (3/67). The shifting effect of up to 10 extrastimuli on restitution curves was also measured. These curves were fit with the equation APD = α + β exp(−DI/τ), where α is asymptote, β is drop, and τ is time constant. Linear regression of the parameters against the number of extrastimuli showed that premature and postmature stimuli decreased and increased α and β and increased and decreased τ, respectively. Analysis of a mathematical model treating memory as an exponentially decreasing shift of restitution curves shows that oscillatory DI,APD is expected with large ΔBCL, steep restitution slope, or increased cardiac accommodation. The model explains phase shifts and suggests a common mechanism for Purkinje and myocardial electrical alternans.