A flexible nonlinear feedback system that captures diverse patterns of adaptation and rebound

AAPS J. 2008;10(1):70-83. doi: 10.1208/s12248-008-9007-x. Epub 2008 Feb 22.


An important approach to modeling tolerance and adaptation employs feedback mechanisms in which the response to the drug generates a counter-regulating action which affects the response. In this paper we analyze a family of nonlinear feedback models which has recently proved effective in modeling tolerance phenomena such as have been observed with SSRI's. We use dynamical systems methods to exhibit typical properties of the response-time course of these nonlinear models, such as overshoot and rebound, establish quantitive bounds and explore how these properties depend on the system and drug parameters. Our analysis is anchored in three specific in vivo data sets which involve different levels of pharmacokinetic complexity. Initial estimates for system (k(in), k(out), k(tol)) and drug (EC(50)/IC(50), E(max)/I(max), n) parameters are obtained on the basis of specific properties of the response-time course, identified in the context of exploratory (graphical) data analysis. Our analysis and the application of its results to the three concrete examples demonstrates the flexibility and potential of this family of feedback models.

Publication types

  • Review

MeSH terms

  • Adaptation, Physiological* / physiology
  • Feedback* / physiology
  • Nonlinear Dynamics*
  • Pharmaceutical Preparations / metabolism


  • Pharmaceutical Preparations