Calculation of threshold and saturation points of sigmoidal baroreflex function curves

The 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 Sat(5%). In many studies, Thr and Sat are calculated with the equations Thr = A(3) - 2.0/A(2) and Sat = A(3) + 2.0/A(2), where A(3) is the value of MAP at the point where the reflexly controlled variable is at the midpoint of its range and A(2) is the gain coefficient. Although it is commonly stated that the values of Thr and Sat calculated with these equations represent Thr(5%) and Sat(5%), we show here that instead they are significantly greater and less than Thr(5%) and Sat(5%), respectively. Furthermore, the operating range (difference between Thr and Sat) calculated with these equations is 32% less than the difference between Thr(5%) and Sat(5%). We further show that the equations that provide correct values of Thr(5%) and Sat(5%) are Thr(5%) = A(3) - 2.944/A(2) and Sat(5%) = A(3) + 2.944/A(2). 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.