Iterative restitution effects from heart rate variability

Action potential duration (APD) in the heart depends on the timing of the stimuli from SA node and the preceding diastolic interval (DI), the time it rested since the previous excitation. Such effects can be described by a random iterative map involving a heart rate dependent restitution function. In a steady state the stimuli form a stationary random process and iterative maps converge to stationary stochastic APD and DI sequences. We derive analytical expressions for major stochastic characteristics of such sequences (mean value, variance, etc). The results reveal a remarkable role of the slope of the restitution curve for the properties of the stationary output sequences. Our tentative computer simulations of the process corroborate our analytical results for relatively small heart rate variability.