Four-parametric non-linear regression fit of isovolumic relaxation in isolated ejecting rat and guinea pig hearts

Left ventricular isovolumic pressure fall is characterized by the time constant tau obtained by fitting the exponential p(t) = p(infinity) + (p(0)-p(infinity))3exp(-t/tau) to pressure fall. It has been shown that tau, calculated from the first half of pressure fall, differs considerably from that found at late relaxation in normal and pathophysiological conditions. The present study aims at testing for such differences statistically and to quantify tau changes during relaxation. Two improvements of the common regression procedure are introduced for that purpose: the use of the four-parametric regression function, p(t) = p(infinity) + (p(0)-p(infinity))3exp[-t/(tau(0)+b(tau)t)], and an optimal data-dependent split of the isovolumic pressure fall interval. The residual regression errors of the methods are statistically compared in one-hundred isolated working rat and one-hundred guinea pig hearts, additionally including a logistic regression method. Regression error is significantly reduced by introducing that b(tau). b(tau) is negative in most cases, indicating accelerated relaxation during isovolumic pressure fall, but zero and positive b(tau) are occasionally seen. Optimal interval tripartition further improves the regression error in most cases. The statistically proved acceleration of the time constant during isovolumic relaxation justifies factor b(t) as a direct and continuous measure of differences between early and late relaxation. This difference between early and late isovolumic relaxation is probably caused by residually contracted myocardium at the beginning of pressure fall, and is therefore important to describe pathophysiological effects on relaxation phases.