Models for the Interpretation of Experiments Using Tracer Compounds

Abstract

The formulation of explicit quantitative models of isotope exchange is necessary before certain quantities of biological interest can be estimated from experimental results. This point can be illustrated by reference to the estimation of total body albumin from measurements on the distribution of I131 labelled albumin. Denote by V the volume of the vascular compartment, by f the asymptotic value of the fraction of total labelled body albumin which is in the vascular compartment, and by x the blood concentration of unlabelled albumin. A common estimate of total body albumin is then Vx/f. An alternative estimate in common use is total body albumin = Vx/[A1/[SIGMA]Ai], where the time course of blood concentration is [SIGMA]Aie -[lambda]it , the [lambda]i >o and A1 corresponds to the exponential with the smallest k. The two estimates may differ by a considerable amount. A multi-compartment model, in which the amount leaving a compartment in unit time is proportional to the amount in it, the proportionality constants being time independent, provides the basis for a third estimate. The values of these constants, referred to as rate constants, can often be estimated from labelling experiments. Knowledge of these constants permits the computation of limits within which "total body albumin" must fall. The estimate Vx/f will always fall within these limits, whereas the estimate Vx/[A1/[SIGMA]Ai] need not. When metabolism is slow relative to transfer, however, all estimates are in close agreement. The least square estimation of the values of the rate constants from the observations, involves several statistical problems. Thus, the usual Newton-Raphson iterative computation procedures need not converge, or if they do, may not converge to the correct answer, because the sum of squares surface may contain a saddle point.