Cycle-Averaged Models of Cardiovascular Dynamics

Lumped-parameter time-varying electrical circuit analogs for the cardiovascular system are frequently used in medical research and teaching for simulating and analyzing hemodynamic data. Pulsatile models provide details of the intracycle dynamics of each heart beat. In some settings, however, such as when tracking a hospital patient's hemodynamic state over time, it is more useful to dynamically track the beat-to-beat or intercycle dynamics. Rather than introducing heuristic averaging during the model-building step, as is done in existing nonpulsatile models, we apply a short-term, cycle-averaging operation to the differential equations of the underlying pulsatile model to obtain cycle-averaged models. The cycle-averaging method preserves the dependence of the output variables on the model parameters. In this paper, we apply cycle averaging to a simple pulsatile cardiovascular model to derive a cycle-averaged model for cardiovascular dynamics. The resultant model captures the intercycle dynamics with relatively small approximation errors for a large range of perturbations in important system parameters