W. Krzyzanski (1), X. Yan (1), Y. Chen (1)
(1) Department of Pharmaceutical Sciences, University at Buffalo, NY, USA.
Objectives: The target mediated drug disposition (TMDD) model [1] has been adopted to describe pharmacokinetics for two drugs competing for the same receptor. A rapid binding assumption introduces total receptor and total drug concentrations while free drug concentrations CA and CB are calculated from the equilibrium (Gaddum) equations [2]. The Gaddum equations are polynomials in CA and CB of second degree that have explicit solutions involving complex numbers. The aim of this study was to develop numerical methods to solve the rapid binding TMDD model for two drugs competing for the same receptor that can be implemented in pharmacokinetic software.
Methods: Algebraic calculations and computer simulations were used to develop algorithms and investigate properties of solutions to the TMDD model with two drugs competitively binding to the same receptor. A general rapid binding TMDD model for two competing ligands incorporating new methods was coded in MATLAB 7.2. The applicability of these algorithms was demonstrated by simulating concentration-time profiles resulting from exogenous and endogenous IgG competing for the neonatal Fc receptor (FcRn), and darbepoetin competing with endogenous erythropoietin for the erythropoietin receptor. These models were implemented in Phoenix WinNonlin 6.0 and ADAPT 5, respectively.
Results: A rapid binding approximation of the TMDD model for two drugs competing for the same receptor has been proposed. The explicit solutions to the equilibrium equations employ complex numbers, which cannot be easily solved by pharmacokinetic software. Numerical bisection algorithm and differential representation were developed to solve the system instead of obtaining an explicit solution. The numerical solutions were validated by MATLAB 7.2 solver for polynomial roots. These methods were applied to solve the TMDD model for two case studies.
Conclusions: Numerical methods have been developed for solving of the rapid binding TMDD model describing two drugs competitively binding to the same receptor that can be easily implemented in any pharmacokinetic software. Two case studies involving monoclonal antibodies and growth factors have been presented.
References:
[1] Mager DE, Jusko WJ. General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokinet Pharmacodyn. 28:507-532 (2001).
[2] Kenakin TP. A pharmacology primer: theory, application and methods: Elsevier Academic; 2009.
Reference: PAGE 21 () Abstr 2483 [www.page-meeting.org/?abstract=2483]
Poster: Other Modelling Applications