AJP - Regulatory, Integrative and Comparative Physiology, Vol 240, Issue 5 370-R383, Copyright © 1981 by American Physiological Society
Optimal control evaluation of left ventricular systolic dynamics
A. Livnat and S. M. Yamashiro
A model of the contracting left ventricle was developed, in which the left
ventricle was represented as a time-varying compliance. The vascular load
included the nonlinear (Bernoulli) resistance of the aortic valve, blood
inertance, and a Windkessel model of the arterial tree. Owing to the
obligatory aerobic nature of the heart, oxygen consumption can be used to
characterize the energy utilized by the myocardium. An adaptive control law
was developed for determining the systolic time course of ventricular
pressure and volume that minimizes cardiac oxygen consumption. Three main
determinants of myocardial oxygen consumption were included in the integral
criterion function: developed wall tension, inotropic state, and external
(mechanical) work. The optimal control problem was solved using the
Pontryagin maximum principle. The model could predict, in good agreement
with experimentally obtained data, systolic time course of ventricular
pressure and volume, as well as directional changes in the duration of
isovolumic contraction and ejection phase under various conditions of
end-diastolic volume, mean aortic pressure, and inotropic state.
