Theoretical Analysis of a Left-Ventricular Pumping Model Based on the Systolic Time-Varying Pressure/Volume Ratio

Abstract

A left-ventricular pumping model based on a left-ventricular systolic time-varying pressure/volume ratio e(t) has been proposed on the basis of the physiological studies indicating that the parameter e(t) is a function of time in systole, almost independent from left-ventricular volume and the arterial-loading conditions, and is a good index of myocardial inotropism. The model has been formulated by the following two equations: \begin{equation} p(t) = e(t) { v(0)- ∫ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t&lt;\sup&gt;₀ - i(t)dt} \end{equation} \begin{equation}p(t) = f{i(t)} \end{equation} where p(t) is the systolic left-ventricular pressure, v(o) is the left-ventricular end-diastolic volume (at the onset of systole), i(t) is the blood-flow rate ejected from the left ventricle, t is the time from the onset of systole, and f is a function of the hydraulic impedance of the load against the ventricular ejection (including the aortic valve). Some theoretical analyses of this model are attempted, first analytically with simplifications of the time course of e(t) and the hydraulic impedance of the load, and then by an analog computer with e(t) approximated to the physiological data. Quantitative relationships among various hemodynamic parameters are obtained, and these appear to be in good agreement with the physiological characteristics of the left ventricle.</sup>