Analysis of left ventricular function by optimization models

Abstract

The development of a new hierarchical optimization model for explaining left ventricular function is summarized. In the model, arterial load is described by three linear time-invariant differential equations. End-diastolic volume, linear end-systolic pressure-volume relation, heart rate, and nominal ejection time are given. Under these constraints, ventricular function is described by optimality criteria that are based on minimizing an index of myocardial oxygen consumption per beat. Also forces developed during ejection and ventricular efficiency are taken into account in the cost functions of the model. The model predicts ventricular stroke volume, time courses of root aortic flow and pressure, and ejection time. These predictions are in accordance with experimental data from an isolated canine heart preparation. In the measurements analyzed, arterial load has been changed while end-diastolic volume, contractility, and heart rate have been kept constant. Thus the analysis shows that the left ventricular response to a change in arterial load can be predicted by an optimization model. The results also suggest that energy economy and efficiency are essential features of left ventricular function.