ON THE CORRECTION FOR RADIOACTIVE DECAY IN PHARMACOKINETIC MODELING

The question of how to include radioactive decay during biological mod eling with first-order differential equations was considered. Modeling may involve either experimental data y(t) or decay-corrected data z(t ) [=exp(lambda t)y(t) where lambda is the decay constant] for each com partment. It is sometimes assumed that the latter are solutions to cor responding purely pharmacokinetic models (no decay). We primarily comp ared the two analyses in the case where the model did not require simu ltaneous consideration of both labeled and unlabeled material. A gener al theorem was found which limits the use of decay-corrected data to p harmacokinetic models containing Linear, homogeneous differential equa tions. By way of verification, an example of this model type was analy zed for a chimeric monoclonal antibody biodistribution in man. Even in this case, statistically significant differences between the two solu tions showed that one may find different model parameters depending up on which data set (y or z) was analyzed. For other mathematical forms, the analyst must include the physical decay in all relevant compartme nts. By analyzing an open, quadratic model, effects of not including d ecay were seen to be maximized if the biological rate constant was gre ater than or equal to lambda, the physical decay constant. Finally, us ing monoclonal antibody-antigen reactions, similar discrepancies betwe en the z functions and the pharmacokinetic variables were demonstrated . This result was found to persist even if competitive molecules were included. We conclude that decay-corrected data may be shown, but shou ld not be entered into-the modeling equations unless the latter are of the linear, homogeneous form.