Development of a Biologically-Based Controlled Growth and Differentiation Model for Developmental Toxicology

The biologically-based dose-response model for developmental toxicology developed by Leroux et al. (1996) is extended. The original model had two basic states; precursor cells and differentiated cells with both states subject to a linear birth-death process. In this paper, a mathematical model, which is biologically and statistically based, is developed with a highly controlled birth and death process for precursor cells. This model limits the number of replications allowed in the development of a tissue or organ and more closely reflects the presence of a true stem cell population. The mathematical formulation of the Leroux et al. (1996) model was derived from a partial differential equation for the generating function that limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov p..