Zager Michael G, Schlosser Paul M, Tran Hien T
North Carolina State University, Center for Research in Scientific Computation, Box 8205, Harrelson Hall, Raleigh, NC 27695-8205, USA.
Bull Math Biol. 2007 Jan;69(1):93-117. doi: 10.1007/s11538-006-9068-x.
Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data.
