A theoretical model of the red cell survival followed by means of random and cohort labeling

Abstract

The usual method of approximating the experimental curves of erythrocyte survival by combining the exponential and normal distribution is rather arbitrary. For the method of cohort labeling the authors introduce a function expressing the number of labeled erythrocytes in the blood: F( t) exp − at− b λ+1 t λ+1 the death probability function (Bergner,1962) belonging to it having the form μ( t) = a + bt λ The advantage of this function consists in its simplicity and generality, which enables it to include both the “random” and “determined” components of erythrocyte destruction as special cases, without tying oneself to this traditional interpretation of the mechanism of erythrocyte elimination however. The suitability of the function F(t) in the form given here is demonstrated by means of a comparison with the experimental data available for several species of mammals. Problems of mathematical correction of perturbing factors in the methods of cohort and random labeling are further discussed in the paper. It is, for example, an erroneous prolongation of the erythrocyte life span in the latter method, due to neglecting the exponential component of the elimination, and the perturbing influence of the gradual incorporation of the labeled material into erythrocytes, which is responsible for the increasing initial part of the curve in the former method. Only the method of cohort labeling of erythrocytes of the same age can yield the desired more detailed information on the course of elimination of the red cells from the population; the further methodical improvement should be directed to a more thorough analysis of the perturbing factors connected with this method.