| Homeostatic control of organ size during early development of cancer is not preserved in current models of carcinogenesis. This issue is becoming increasingly important in animal toxicology studies where growth of pre-cancerous focal lesions can be quantified. The most widely accepted model of carcinogenesis is the two-stage model introduced by Armitage and Doll and later modified to include stochastic growth in each stage. These models fall into the general class of interconnected birth-death processes with immigration and emigration. Recent research has focused on methods for the analysis of tumor incidence and focal lesion data. This research extends such work by controlling the expected size of the affected organ through the use of a system of ordinary differential equations (ODE's), derived from Kolmogorov forward equations, to calculate the expected size of the organ during the animal's lifespan. These are then used to modify the rates of the stochastic process to provide homeostatic control for tissue growth. As the foci grow, model birth rates decrease and death rates increase to prevent uncontrolled growth. Numerical methods for sequential solution to the ODE's for expectation and incidence are developed. Methods for the estimation of model parameters are shown and illustrated with an example. |
