Development of a biologically-based controlled growth and differentiation model for developmental toxicology.
Amathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential equation for the generating function. This formulation 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.
Whitaker
Shree Y
SY
Laboratory of Computational Biology and Risk Analysis, National Institute of Environmental Health Sciences, 111 T. W. Alexander Drive, Bldg. 101, MD A3-06, Research Triangle Park, North Carolina 27709, USA. whitake2@niehs.nih.gov
Tran
Hien T
HT
Portier
Christopher J
CJ
D000818:Animals; D002454:Cell Differentiation / Q000502:physiology*; D002455:Cell Division / Q000502:physiology*; D008390:Markov Chains; D008954:Models, Biological; D013234:Stem Cells / Q000166:cytology / Q000502:physiology; D013269:Stochastic Processes; D014116:Toxicology / Q000379:methods