Assessment of threshold and saturation pressure in the baroreflex function curve: a new mathematical analysis

The baroreflex function has been assessed with logistic function analysis, a mathematical model suitable for function curves of sigmoid shape. The nonlinear (sigmoid) relationship between carotid sinus pressure (CSP) and systemic arterial pressure (SAP) reflects threshold and saturation of the SAP responses to CSP changes. The threshold and saturation pressures (TP and SP) are often determined by gross inspection from the experimental recordings. Objective and accurate determination of TP and SP may be achieved by mathematical analysis. Kent et al. (Cardiology, Vol. 57, pp. 295-310, 1972) provided equations that estimated SP and TP to be +/- 1.317/k from the midrange CSP (k, the slope coefficient of a curve). Tan et al. (Circ. Res., Vol. 65, pp. 63-70, 1989) recently used an equation to calculate TP based on the consideration that it is about 95% of the maximal SAP. In this report, we elaborated new equations for the estimation of SP and TP, which approximate midrange pressure +/- 2/k. The accuracy of these new equations compared to other equations was tested using various sets of simulation data. In addition, experiments were conducted in anesthetized dogs with isolated carotid sinus. The open-loop CSP-SAP curves were obtained following various holding pressure (HPs) to demonstrate the phenomenon of baroreflex acute resetting. The effects of using different equations on the values of TP, SP, and delta TP/delta HP (extent of resetting) were analyzed. Both simulation and experimental data revealed that the equations of Kent et al. gave rise to values of TP and SP far different from the realistic values. The values of TP calculated by equation of Tan et al. were dependent on the maximal SAP and the slope of the function curve. The TP and SP (+/- 2/k from the midrange pressure of the sigmoid curve) obtained by our new equations were not significantly affected by the maximal SAP and the curve slope. The mathematical analysis may be particularly useful for comparison among various baroreflex curves with different maximal SAP and/or curve slope.