Numerical versus analytical integration of hormonal disappearance data

Abstract

After a single rapid injection of a hormone, evaluation of the metabolic clearance rate (MCR) and of its error is greatly facilitated when a numerical technique, such as the trapezoidal rule, is substituted for regression as a means of determining the area under the disappearance curve, which is the only parameter needed to characterize overall metabolism. Integration is achieved by summing trapezes defined through successive data points and the corresponding time intervals. The error in the resulting area, which is derived from the propagation of the independent errors of the trapezes, is proportionately related to the MCR. This method, which is applicable to any dynamic pattern of disappearance, provides the only available means of computing a realistic error for the MCR of a hormone which is distributed into several compartments. The statistical advantages of the numerical approach over regression analysis are illustrated in connection with experimental data pertaining to the disappearance from plasma, in the adult male rat, of thyrotropic hormone and of corticosterone which are respectively distributed into one and three compartments.