Calculation of threshold and saturation points of sigmoidal baroreflex function curves

Abstract

McDowall, Lachlan M., and Roger A. L. Dampney. Calculation of threshold and saturation points of sigmoidal baroreflex function curves. Am J Physiol Heart Circ Physiol 291: H2003-H2007, 2006. First published May 19, 2006 doi:10.1152/ajpheart.00219.2006The logistic sigmoid function curve provides an accurate description of the baroreflex input-output relationship and is the most commonly used equation for this purpose. The threshold (Thr) and saturation (Sat) values for the baroreflex are commonly defined as the values of mean arterial pressure (MAP) at which the reflexly controlled variable (e.g., heart rate or sympathetic nerve activity) is within 5% of the upper or lower plateau, respectively, of the sigmoid function. These values are referred to here as Thr 5% and Sat5%. In many studies, Thr and Sat are calculated with the equations Thr ϭ A3 Ϫ 2.0/A2 and Sat ϭ A3 ϩ 2.0/A2, where A3 is the value of MAP at the point where the reflexly controlled variable is at the midpoint of its range and A2 is the gain coefficient. Although it is commonly stated that the values of Thr and Sat calculated with these equations represent Thr 5% and Sat5%, we show here that instead they are significantly greater and less than Thr5% and Sat5%, respectively. Furthermore, the operating range (difference between Thr and Sat) calculated with these equations is 32% less than the difference between Thr5% and Sat5%. We further show that the equations that provide correct values of Thr5% and Sat5% are Thr5% ϭ A3 Ϫ 2.944/A2 and Sat5% ϭ A3 ϩ 2.944/A2. We propose that these be used as the standard equations for calculating threshold and saturation values when a logistic sigmoid function is used to model the open-loop baroreflex function curve. mathematical modeling; input-output relationship; baroreflex operating range; regression analysis THE BARORECEPTOR REFLEX is the major feedback control system regulating arterial blood pressure in the short term (5, 14), and possibly also in the longer term (15,27). Numerous studies in humans and animals have demonstrated that the baroreceptor reflex can be reset under physiological conditions such as exercise (6 -8, 12, 17, 19 -24, 26, 28), sleep (18), heat stress (3), or pregnancy (4) and also pathological conditions such as hypertension (9, 11) and cardiovascular deconditioning (10). To quantify the changes in baroreflex function that occur under different conditions, many investigators have used a mathematical equation to describe the relationship between input [e.g., mean arterial pressure (MAP)] and output (e.g., heart rate or sympathetic nerve activity). In some cases, where the carotid sinus pressure can be controlled independently of systemic arterial pressure, the input is carotid sinus pressure and the output is systemic arterial pressure.Kent et al. (13) first proposed that a logistic sigmoid function curve be used to describe baroreflex function, according to the following equation:where Y is the output (dependent) variable (e.g., heart rate, sympathetic nerve activity, or systemic arterial...

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