First-order differential-delay equation for the baroreflex predicts the 0.4-Hz blood pressure rhythm in rats

Abstract

We have described a 0.4-Hz rhythm in renal sympathetic nerve activity (SNA) that is tightly coupled to 0.4-Hz oscillations in blood pressure in the unanesthetized rat. In previous work, the relationship between SNA and fluctuations in mean arterial blood pressure (MAP) was described by a set of two first-order differential equations. We have now modified our earlier model to test the feasibility that the 0.4-Hz rhythm can be explained by the baroreflex without requiring a neural oscillator. In this baroreflex model, a linear feedback term replaces the sympathetic drive to the cardiovascular system. The time delay in the feedback loop is set equal to the time delay on the efferent side, ∼0.5 s (as determined in the initial model), plus a time delay of 0.2 s on the afferent side for a total time delay of ∼0.7 s. A stability analysis of this new model yields feedback resonant frequencies close to 0.4 Hz. Because of the time delay in the feedback loop, the proportional gain may not exceed a value on the order of 10 to maintain stability. The addition of a derivative feedback term increases the system’s stability for a positive range of derivative gains. We conclude that the known physiological time delay for the sympathetic portion of the baroreflex can account for the observed 0.4-Hz rhythm in rat MAP and that the sensitivity of the baroreceptors to the rate of change in blood pressure, as well as average blood pressure, would enhance the natural stability of the baroreflex.