Slow oscillations in blood pressure via a nonlinear feedback model

Abstract

Ringwood, John V., and Simon C. Malpas. Slow oscillations in blood pressure via a nonlinear feedback model. Am J Physiol Regulatory Integrative Comp Physiol 280: R1105-R1115, 2001.-Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex 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. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar 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 nonlinearity 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 that it provides for sustained stable oscillations under a wide variety of situations 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 oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback 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 between species. sympathetic nervous system; baroreflex; stability; describing function; artificial neural network IT IS WELL ESTABLISHED that blood pressure in humans can contain a distinct oscillation at 0.1 Hz, often referred to as the Mayer wave (26,38). Experiments in a variety of animal models have shown that this oscillation is due to the action of the sympathetic nervous system on the vasculature. Although the oscillation in blood pressure is shifted to 0.4 Hz in the rat (7) and to 0.3 Hz in the rabbit (22), changes in the strength of this oscillation have been proposed to reflect changes in the mean level of sympathetic nerve activity (SNA) and/or baroreflex gain (6), raising the possibility that measurement of the strength of this oscillation may be used as a diagnostic measure of neural control of the cardiovascular system in humans (1,10,26).Current evidence favors the concept of feedback in the baroreflex loop as the origin for the 0.1-Hz oscillation in blood pressure (5,6,13,25,41). In this model, a change in blood pressure is sensed by the arterial barorece...

Arterial baroreflex function and cardiovascular variability: interactions and implications

“…Simple mathematical models indicate that there is a strong linear coupling between arterial blood pressure and sympathetic nerve activity and/or R-R interval (9,21). However, there is emerging evidence that the R-R and MSNA responses to blood pressure may be modulated in accordance with nonlinear dynamics (97).…”

Phase synchronization of elements of autonomic control in mathematical model of cardiovascular system

“…Для моделирования системы барорефлекторной регуляции тонуса артерий мы отказались от линейных представлений, развиваемых в работах [14,21], и в соответствии с работой [19] использовали уравнения с сигмоидальными нелинейностями для моделиро-вания симпатических контуров.…”

A delay recruitment model of the cardiovascular control system

“…There has also been evidence presented that the sympathetic control of peripheral resistance is more important than sympathetic feedback to the heart muscle or heart rate changes [23,26,31].…”

“…We anticipate (and find) that this natural frequency has a significant effect on the dynamics of the response of the cardiac system to baroreflex feedback. The importance of peripheral resistance has been raised in a number of previous studies [23,26,29,31], so it is useful here to also consider the relative importance of sympathetic control of peripheral resistance and sympathetic control of heart rate.…”