Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation betwe en 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the ba roreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. H owever, although this model can produce oscillations at the required freque ncy, some strict relationships between the controller and vasculature param eters must be true for the oscillations to be stable. We developed a nonlin ear model, containing an amplitude-limiting nonlinearity that allows for si milar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlineari ty in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is t hat it provides for sustained stable oscillations under a wide variety of s ituations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the o scillations can disappear altogether. Such variations are shown to accord w ell with observed experimental data. Additionally, using a nonlinear feedba ck model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times bet ween species.