Compartmental modeling and analysis for carcinogenic experiments

Abstract

This dissertation proposes and analyzes a compartmental model for the process of formation of cancer tumors. The model is based explicitly on the biological theory concerning tumor formation. Models currently in the literature are discussed, and the current biological theory of the cancer process is presented. A compatible compartmental model is then formulated for the situation in which only low levels of carcinogen that do not adversely affect the body's repair system are encountered. The complete stochastic solution for the contents over time of the various compartments of the model is derived under very general assumptions. The special case of test animals that are protected from exposure to carcinogen from birth until the start of a long-term, low-dose carcinogenic experiment is then examined in some detail. Data is simulated for animals behaving according to the postulated model in a long-term, low-dose experiment. A nonlinear least squares procedure is developed for estimation of the parameters of the proposed model. The estimation procedure is illustrated by its application to simulated data from the proposed model. In conclusion, implications of the proposed model for other models in use are considered. The possibility of improving both the model and the estimation procedure are also considered.