Estimation of the left ventricular relaxation time constant tau requires consideration of the pressure asymptote.

The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant tau of the exponential regression p(t)=Pomega+(P0-Pomega)exp(-t/tau). However, several authors prefer to prefix Pomega=0 instead of coestimating the pressure asymptote empirically; others present tau values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the tau estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the tau estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating tau with preset Pomega=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of tau estimates from both methods can therefore proceed in reverse direction if tau and Pomega change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.

Differential laws of left ventricular isovolumic pressure fall.

An attempt has been made to test for a reliable method of characterizing the isovolumic left ventricular pressure fall in isolated ejecting hearts by one or two time constants, tau. Alternative nonlinear regression models (three- and four-parametric exponential, logistic, and power function), based upon the common differential law dp(t)/dt = - [p(t)-P ]/ tau(t) are compared in isolated ejecting rat, guinea pig, and ferret hearts. Intraventricular pressure fall data are taken from an isovolumic standard interval and from a subinterval of the latter, determined data-dependently by a statistical procedure. Extending the three-parametric exponential fitting function to four-parametric models reduces regression errors by about 20-30%. No remarkable advantage of a particular four-parametric model over the other was revealed. Enhanced relaxation, induced by isoprenaline, is more sensitively indicated by the asymptotic logistic time constant than by the usual exponential. If early and late parts of the isovolumic pressure fall are discarded by selecting a subinterval of the isovolumic phase, tau remains fairly constant in that central pressure fall region. Physiological considerations point to the logistic model as an advantageous method to cover lusitropic changes by an early and a late tau. Alternatively, identifying a central isovolumic relaxation interval facilitates the calculation of a single ("central") tau; there is no statistical justification in this case to extend the three-parametric exponential further to reduce regression errors.