Theoretical considerations on the validity of the Stewart-Hamilton principle in measuring cycle-averaged flows via histogram of indicator in the pulsating compartment.

It has been heuristically shown that the Stewart-Hamilton principle, adapted to external counting observables of system indicator histogram, A(t), its cycle-averaged equilibrium count rate, A(equ), and indicator volume of distribution in the body, V(body), is F/V(body) = A(equ)/integral of o infinity A(t)dt, where F is the cycle-averaged cardiac output. Since the method lacks the theoretical plausibility, it remained unclear whether it is an approximation and what conditions warrant its usability. This paper presents an exact derivation of the above equation. To fulfill it the generalizations of the stationary theory of indicator kinetics were set up that allowed for the conditions of pulsatile flows and volumes and the dependence of the distribution of transit times of indicator on the phase of the cardiac cycle. The assumptions utilized were that the tracer enters the compartment well mixed and convectively carried by the blood in concentrations that do not vary in the single cycle to a material extent. The method yields the cardiac output, even when the flow to a compartment is only a part of it, provided that the fraction of indicator that traversed the system equals the fraction of cardiac output that perfuses the compartment. It was shown that, when applied to a regurgitant ventricle, the method obtains the forward flow and that separate application of the method to each of the ventricles provides the theoretical basis for evaluation of the central-circulatory shunts.