A comparison of four common mathematical models to assess baroreflex sensitivity

Different methods have been used to assess baroreflex gain in experiments where changes in the carotid sinus pressure or the arterial blood pressure using different techniques provoke a baroreflex response, usually a rapid variation of heart rate. Four mathematical models are most used in the literature: the linear regression, the piecewise regression, and two different four-parameter logistic equations: equation 1, Y = (A1-D1)/[1 + e^{B1(X - C1)} ] + D1; equation 2, Y = (A2-D2)/[1 + (X/C2)^B2 ] + D2. We compared the four models regarding the best fit to previously published data in all vertebrate classes. The linear regression had the worst fit in all cases. The piecewise regression generally exhibited a better fit than the linear regression, though it returned a similar fit when no breakpoints were found. The logistic equations showed the best fit among the tested models and were similar to each other. We demonstrate that equation 2 is asymmetric and the level of asymmetry is accentuated according to B2. This means that the baroreflex gain calculated when X = C2 is different from the actual maximum gain. Alternatively, the symmetric equation 1 returns the maximum gain when X = C1. Furthermore, the calculation of baroreflex gain using equation 2 disregards that baroreceptors may reset when individuals experience different mean arterial pressures. Finally, the asymmetry from equation 2 is a mathematical artifact inherently skewed to the left of C2, thus bearing no biological meaning. Therefore, we suggest that equation 1 should be used instead of equation 2.