A mathematical model of dilution curves for flow study.

THE PURPOSE of this paper is to present a mathematical model of dilution curves obtained by precordial detection of concentration of an intravenously injected radioactive tracer. The analysis makes possible formulation of equations relating parameters of the curve to cofunctions of the curve, such as cardiac output, central circulating blood volume, and volume of heart chambers. The presentation is facilitated by a review of the graphical method of interpretation of these curves. Stewart suggested determination of cardiac output by a dye-dilution method. Hamilton and his co-workers' developed circulation studies based on observatioii of the varying concentration of an injected dye as it passed from the heart. If a small volume of concentrated dye is injected into a vessel emptying into the heart, the average concentration of the dye as it leaves the heart will be a function of the diluting volume which passed through the heart during the time of measurement. Thus, the parameters of the dilution curve permit, among other things, calculation of the cardiac output expressed as volume of flow per unit time. Since the total amount of material injected must eventually leave the heart, this amount may be equated to the product of the cardiac output, time of flow, and the average concentration of the material leaving the heart. The latter is equal to the product of the cardiac output and the instantaneous concentration of ma-