Ransacking the curve of cardiac isovolumic pressure decay by logistic-and-oscillation regression

The decelerative part of the left ventricular isovolumic pressure decay is an important phase to make the heart ready for diastolic refill (lusitropy). Its widely used characterization by an exponential regression with zero pressure asymptote or coestimated asymptote provides empirically biased time constant estimates because of significant deviations of the pressure decay from exponentiality. We systematically analyzed the regression residua of these pressure decays in isolated ejecting rat, guinea pig, and ferret hearts. A four-parametric logistic (tangens hyperbolicus) function, together with a superimposed acustomechanic oscillation, yields normally distributed residua with standard regression error typically less than one per cent of the initial pressure; this is the first model with proved unbiased and statistically complete regressive extraction of the information provided by the time course of pressure decay. Equal values of the lusitropic parameters (logistic time constant and pressure asymptote) were estimated even after the oscillatory component was removed from the regression model. Reliable estimates of the frequency, but not of the amplitude, can be obtained by fitting the oscillation model to the residua provided by the logistic; this two-step method is statistically weaker than the full one-step model, but it reduces computational effort. In conclusion, the four-parametric logistic, but not a three-parametric exponential or logistic model, suffices to obtain unbiased lusitropic parameters characterizing the left ventricular isovolumic pressure decay of small animal hearts.