Nonlinear modelling of renal vasoaction

Abstract

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs. #

Investigation of events in the EEG signal correlated with changes in both oxygen and glucose in the brain

“…They both manifest an inverse exponential-shaped response and represent activation levels for the effects of oxygen and glucose on the EEG signal. Such static nonlinear functions are commonly found in physiological systems [14] and are due to the fact that different concentration levels of one substance result in different corresponding levels of release/uptake of another substance (or in this case they result in different voltage levels). Table 1 Mean squared errors for the linear ARMAX model and the non-linear model shown in Figure 5.…”