Modeling of cardiovascular variability using a differential delay equation

The influence of time delay in the baroreflex control of the heart activity is analyzed by using a simple mathematical model of the short-term pressure regulation. The mean arterial pressure in a Windkessel model is controlled by a nonlinear feedback driving a nonpulsatile model of the cardiac pump in accordance with the steady-state characteristics of the arterial baroreceptor reflex. A pure time delay is placed in the feedback branch to simulate the latent period of the baroreceptor regulation. Because of system nonlinearity model dynamics is found to be highly sensitive to time delay and changes of this parameter within a physiological range cause the model to exhibit different patterns of behavior. For low values of time delay (shorter than 0.5 s) the model remains in a steady state. When time delay is longer than 0.5 s, a Hopf bifurcation is crossed and spontaneous oscillations occur with frequencies in the high-frequency (HF) band. Further increases of time delay above 1.2 s cause the oscillations to become more complex, and following the typical Feigenbaum cascade, the system becomes chaotic. In this condition heart rate, pressure, and how show evident variability. The heart rate power spectrum exhibits a peak whose frequency moves from the HF to LF band depending on whether simulated time delay is as short as the vagal-mediated control or long as the sympathetic one.