On the approximation of static open-loop characteristics of baroreceptor reflex

We investigated the adequacy of three different functions that have been used in the literature to characterize the relationship between mean systemic arterial pressure (SAP) and mean baroreceptor pressure (BP) in open-loop experimental preparations. These curves are the normal cumulative distribution function (CDF), the logistic (or growth) function (LF), and the third-order polynomial (TOP). Ten sets of experimental data from isolated carotid sinus preparations were selected from the literature as being representative of all baroreflex curves. Then, the Levenberg-Marquardt method was used to obtain best least-square approximation to these data and parameter estimates for each of the three approximating curves. The first derivative of each best-fit SAP-BP curve yielded a curve for the open-loop gain (G) as a function of BP. Our analysis indicated that both the CDF and the LF were superior to the TOP in fitting the SAP-BP data and in giving a realistic description of the G-BP curve. The operative range of BP was evaluated by estimating threshold (BPth) and saturation (BPsat) BPs using arbitrary definitions reported in the literature. The TOP did not allow this evaluation. The other two curves showed some disagreement due to different definitions of BPth and BPsat. After modifying the definition of these parameters associated with the LF, we could conclude that the analytical descriptions of SAP-BP and G-BP curves as obtained from the LF and the CDF were practically equivalent. Approximation method using the TOP should be avoided.