Constrained optimization of ventricular efficiency in normal and failing hearts

Optimal ventriculoarterial coupling, in terms of maximal energetic efficiency, was recently analyzed by analytic and experimental studies. Whereas for normal hearts the analytic predictions agreed well with measured data, failing hearts were found to operate remote from the predicted optimal conditions. An analysis of optimal coupling is developed in the present study, based on constrained optimization. The constraints are based on the concept that the system must comply with physiological requirements (restrictions) under all conditions. Optimization using the mean pressure as a constraint yielded results similar to the unconstrained case in the normal heart but different with the failing heart: in the failing heart the optimal arterial elastance was found to be larger than the ventricular elastance, whereas the opposite was predicted by the unconstrained optimization. If an additional constraint on the end-systolic pressure is used, a unique solution of the coupling state is obtained. The predicted coupling ratio was found to match published data from normal subjects and heart failure patients, where in the latter group it was found to be remote from the optimal efficiency state. An increase in ventricular contractility and reduction in afterload were shown to shift the nonoptimal coupling state toward the optimal one. This prediction complies with the use of inotropic agents and vasodilators as the mainstay of heart failure treatment. This study may provide a convenient framework of analysis for the assessment of the ventriculoarterial coupling and for the evaluation of the cardiovascular effects of specific drug treatments.