A delayed nonlinear PBPK model for genistein dosimetry in rats

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.

Publication types

  • Comparative Study

MeSH terms

  • Animals
  • Bile / metabolism
  • Biliary Tract / drug effects
  • Biliary Tract / metabolism
  • Genistein / pharmacokinetics*
  • Genistein / pharmacology
  • Models, Biological*
  • Nonlinear Dynamics
  • Rats


  • Genistein