Fall 2017 – Algebraic Formula Predicting Preload Recruitable Stroke Work from Cardiac End-Diastolic and End-Systolic Pressure-Volume Relationships

Preload recruitable stroke work (PRSW) is a fundamental characterization of cardiac function that is purportedly independent of preload and afterload. It is typically expressed as an empirical relationship between stroke work (SW) and end-diastolic volume (Ved). This relationship has been reported to be strikingly linear over large ranges of end-diastolic volumes in multiple mammalian species. Although the slope and intercept of the PRSW relationship shift significantly with different heart failure phenotypes, there is currently no means to predict a priori how changes in contractility, diastolic stiffness, or unstressed volume will affect the PRSW. Therefore, the purpose of the present work was to develop an algebraic formula for the PRSW relationship in terms of standard parameters characterizing systolic and diastolic function. Four simple assumptions were made. First, the end-systolic pressure-volume relationship was assumed to be linear, characterized by end-systolic elastance (Ees) and end-systolic unstressed volume. Second, the end-diastolic pressure was assumed to be an exponential function of end-diastolic volume, characterized by parameters describing diastolic stiffness. Third, either mean arterial pressure (MAP) or systemic resistance were assumed to be constant. Fourth, MAP was assumed to approximate end-systolic pressure. Solving for SW as a function of Ved resulted in a nearly linear relationship. The PRSW relationship was linearized using a Taylor series approximation, which yielded simple formulas for the slope and intercept of the PRSW relationship in terms of Ees and diastolic stiffness. The slope was found to be predominantly determined by MAP, elucidating the difficulties encountered using PRSW as an index of cardiac contractility.