Mathematical Analysis of Coronary Autoregulation and Vascular Reserve in Closed-Loop Circulation

Abstract

The autoregulatory capacity of the coronary circulation has traditionally been studied in open-loop animal models where the coronary circulation was decoupled from the systemic circulation. In the closed-loop circulation, changes in arterial pressure alter coronary flow. Pressure variations can be caused by changes in cardiac contractility, preload, afterload, and heart rate. These changes also affect myocardial oxygen consumption. To maintain equilibrium between oxygen supply and consumption, coronary flow is altered by the autoregulation mechanism. Coronary resistance must change to produce the required change in coronary flow. The direction of change in coronary resistance is not directly predictable. Increased arterial pressure may result in either increased or decreased coronary resistance. To study the changes in coronary resistance in response to changes in arterial pressure that are produced by circulatory parameters, we used mathematical models. Coronary resistance was calculated to obtain equilibrium between ventricular oxygen consumption and supply for different values of contractility, preload, afterload, and heart rate. Maximum coronary resistance, indicating largest coronary vascular reserve and highest efficiency of arterial pressure generation, was defined as an optimal condition. The model predicted that the optimal value of cardiac contractility is its resting value. Minimizing end-diastolic volume and heart rate and maximizing peripheral resistance were shown to improve ventricular coronary vascular reserve. These observations suggest that afterload reduction therapy may not be beneficial for improving myocardial oxygen balance while venous vasodilatation and heart rate reduction result in greater coronary reserve.