Assessment of Threshold and Saturation Pressure in the Baroreflex Function Curve:A New Mathematical Analysis.

Abstract

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.

Baroreflex control of renal sympathetic nerve activity during air-jet stress in rats

“…Pthr and Psat are MAP values at the points where the tangent at inflection point of the sigmoid curve intersects with the upper and lower plateaus, respectively. At these points, RSNA lies 11.9% (of the RSNA range) below and above the upper and lower plateaus, respectively (6,19). The operating range indicates the range of MAP over which RSNA is responsive.…”

Baroreflex control of lumbar and renal sympathetic nerve activity in conscious rats

“…A four-parameter logistic function was then fitted to AP-SNA data pairs (SigmaPlot 2000; SPSS, Chicago, IL) by an interactive least-squares procedure: SNA ϭ P 1/{1 ϩ exp[P2(AP-P3)]} ϩ P4, where P1 is the full range of SNA variation, P 2 is a slope coefficient, P3 is AP at one-half the SNA range, and P 4 is the lower plateau of the curve. From these parameters, the upper plateau (P 1 ϩ P4), the threshold AP (P 3 Ϫ 2/P2), the saturation AP (P3 ϩ 2/P2), and the operating range (saturation pressure Ϫ threshold pressure) were derived (6,13). Threshold and saturation AP values lay 11.9% (of the SNA range) below and above the upper and lower plateaus, respectively (18).…”

Re-Parameterization the Logistic Model in Assessing Changes in the Baroreceptor Reflex

“…The saturation (C sat ) is defined as 2 3 2 A A  , the threshold (C thr ) is defined as 2 3 2 A A   , according to Chen and Chang [11]. The operation range (OR), i.e., the difference between the saturation and threshold, is equal to 2 4 A .…”