1 Development of a Biologically-Based Controlled Growth and Differentiation Model for Developmental Toxicology Shree Y. Whitaker 1 , Hien T. Tran 1 and Christopher J. Portier 2 Abstract 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 process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed. KEY WORDS: teratology; multistate process; cellular kinetics 1. Introduction There has been considerable research into the mechanistic basis through which environmental exposures can initiate and promote disease processes. Much of this research has focused on the molecular and biochemical basis describing the interaction of chemical and physical agents with healthy tissue. Most environmental health risk assessments are focused on the rates of morbidity and mortality in human populations following an environmental exposure. The linkage between basic biology and disease incidence in environmental health is best described using a tool which is focused on the incidence of disease and which can fully utilize the emerging science [1,2] . Disease incidence is generally described by counting events (e.g. disease prevalence in a population) or by early, functional failure of an entire organ system (e.g. disease incidence per year). Data endpoints such as these require a different mathematical treatment than the mathematical treatment applied to absorption, distribution and metabolism data endpoints [3] . While the mechanistic basis for 1 Center for Research in Scientific Computation, Department of Mathematics, Box 8205, North Carolina State University, Raleigh, North Carolina 27695-8205. 2 Laboratory of Computational Biology for Risk Analysis, National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709.