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, a dapted to external counting observables of system indicator histogram, A(t), its cycle-averaged equilibrium count rate, A(equ), and indicato r volume of distribution in the body, V-body, is F/V-body = A(equ)/int egral(0)(infinity)A(t)dt, where F is the cycle-averaged cardiac output . Since the method lacks the theoretical plausibility, it remained unc lear whether it is an approximation and what conditions warrant its us ability. This paper presents an exact derivation of the above equation . To fulfill it the generalizations of the stationary theory of indica tor kinetics were set up that allowed for the conditions of pulsatile flows and volumes and the dependence of the distribution of transit ti mes of indicator on the phase of the cardiac cycle. The assumptions ut ilized were that the tracer enters the compartment well mixed and conv ectively carried by the blood in concentrations that do not vary in th e single cycle to a material extent. The method yields the cardiac out put, even when the flow to a compartment is only a part of it, provide d 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 t he ventricles provides the theoretical basis for evaluation of the cen tral-circulatory shunts.