Suruchi Bakshi (1), Elizabeth C. de Lange (1), Piet H. van der Graaf (1), Meindert Danhof (1), and Lambertus A. Peletier (2)
(1)Systems Pharmacology, Division of Pharmacology, LACDR, Leiden University, (2) Mathematical Institute, Leiden University
Objectives: To explain the unexpected multi-stationarity observed in a nonlinear precursor-pool model of prolactin (PRL) response to dopamine D2 receptor antagonists, to extract meaningful parameter regions and to gain insight into the model behaviour using the techniques of dynamical systems analysis.
Methods: The nonlinear PRL pool model was converted into a dimensionless version using suitable concentration and time scaling. Steady states (SSs) of the dimensionless model were determined and their stability was studied using phase-plane analysis. Bifurcation analysis was performed to study the change of stability properties with changes in a critical parameter. Phase-plane analysis, combined with simulations, was used to explain the dynamics of the model in response to a drug challenge and the observed multi-stationarity.
Results: The pharmacodynamics of PRL in plasma has been modelled by means of a precursor-pool model which includes a positive feedback loop of plasma PRL on its own synthesis in the lactotroph pool, making it a nonlinear system [1]. Using mathematical analysis we have shown that positive feedback has resulted in occurrence of multiple SSs with different stability properties. One of the SSs is the baseline PRL in absence of drug administration. This is the physiologically desired SS, whereas the other SS is physiologically undesired. Stability of each SS, coupled with the drug PK, plays a role in determining which SS is predicted by the model. We have been able to deduce a parametric restriction under which the desired SS is stable. The work highlights the importance of mathematical analysis in pharmacological models [2].
Conclusions: Techniques of dynamical systems analysis of differential equation have been successfully applied to the nonlinear model of PRL response to explain the observed multi-stationarity and the parametric dependence of stability properties.
References:
[1] Stevens J, Ploeger B, Hammarlund-Udenaes M, Osswald G, van der Graaf PH, Danhof M and de Lange ECM, Mechanism-based PKPD model for the prolactin biological system response following an acute dopamine inhibition challenge: quantitative extrapolation to humans. Journal of Pharmacokinetics and Pharmacodynamics. 2012;39(5):463-477.
[2] Bakshi S, de Lange ECM, vd Graaf Piet H, Danhof M and Peletier LA, Understanding the behaviour of systems pharmacology models: mathematical analysis of differential equations. CPT: Pharmacometrics and Systems Pharmacology, Submitted.
Reference: PAGE 25 () Abstr 5706 [www.page-meeting.org/?abstract=5706]
Poster: Methodology - Model Evaluation