Logistic Characterization of Left Ventricular Isovolumic Pressure-Time Curve.

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Abstract
Although some investigators have attempted to express the left ventricular pressure-time curve by mathematical functions such as exponential and sinusoidal functions, none of them reasonably fits the left ventricular pressure-time curve. In the present study, we hypothesized that a ventricular isovolumic pressure-time curve could be expressed as the difference between two S-shaped curves for pressure rising and falling, and proposed a new "hybrid logistic" function to express the left ventricular isovolumic pressure-time curve. We investigated how well this hybrid logistic function fits left ventricular isovolumic pressure curves experimentally observed under physiological preload and contractility in the excised cross-circulated left ventricles of 10 dogs. The new function precisely fitted the isovolumic pressure curves regardless of preload and contractility with correlation coefficients above 0.9996, much better than the previously proposed functions. The observed values characterizing the magnitude and time course of the isovolumic pressure curve such as peak +/- dP/dt also closely correlated with the corresponding theoretical values calculated by the present best-fit function. We conclude that our new hybrid logistic function reasonably characterizes the canine left ventricular isovolumic pressure-time curve within physiological ranges of preload and contractility. The present results indicate that this hybrid logistic function is useful to evaluate left ventricular contraction and relaxation comprehensively.

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