A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies

Abstract

Baroreceptor reflex curves are usually analyzed using a symmetric four-parameter function. We wished to ascertain the validity of assuming symmetry in the baroreflex curve and also of constraining the curves to pass through the resting blood pressure and heart rate (HR) values. Therefore, we have investigated the suitability of a new five-parameter asymmetric logistic model for analysis of baroreflex curves from rabbits and dogs. The five-parameter model is an extension of the usual four-parameter model and reduces to that model when the fitted data are symmetrical. Using 30 data sets of blood pressure versus renal sympathetic nerve activity (RSNA) and HR from six conscious rabbits, we compared the five-parameter curves with the four-parameter model. We also tested the effect of forcing these baroreflex curves through the resting point. We found that the five-parameter model reduced the unexplained variation and gave small but important improvements to the estimates of plateaus for RSNA and HR and the HR gain. Although forcing the HR curves through the resting values had little effect, this procedure, when applied to RSNA, produced a worse curve fit by increasing the unexplained variation with alteration to most of the estimated curve parameters. The mean arterial pressure-HR baroreflex relationship from six conscious dogs was also analyzed and showed clear evidence of systematic asymmetry. We conclude that the asymmetric model is a valuable extension to the symmetric logistic model when examining baroreceptor reflexes, giving improved estimates of the parameters and a new approach to examining the mechanisms contributing to baroreflex curve asymmetry. Furthermore, forcing the curves through the resting value is a statistically questionable practice when analyzing RSNA, because it affects the parameter estimates.