Johannes Schropp (1), William J. Jusko (2) and Gilbert Koch (3)
(1) Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany (2) Department of Pharmaceutical Sciences, State University of New York at Buffalo, Buffalo NY, USA (3) Pediatric Pharmacology and Pharmacometrics Research Center, University Children’s Hospital of Basel (UKBB), Basel, Switzerland
Objectives: We extend competitive, uncompetitive and non-competitive drug-drug interaction (DDI) mechanisms with target-mediated drug disposition (TMDD). We investigate quasi-equilibrium (QE) [1] and quasi-steady state (QSS) approximations [2] for DDI TMDD models and present the implementation in standard PKPD software.
Methods: The QE- or QSS approximation of DDI TMDD systems contains a coupled non-linear equation system for the complexes. Such a model form is a so-called differential-algebraic equation (DAE). In contrast to the single drug case, explicit solving of these equation systems with respect to the free drug concentrations is challenging or even impossible [3]. Hence, two solutions are possible for implementation: (i) implementation of the DAE form, or (ii) development of an equivalent reformulation as ordinary differential equation without any equation system.
Results: Implementation of the DAE and the equivalent ODE form is presented in NONMEM (ADVAN9) and R. Fundamental differences of the QE or QSS approximation of the DDI TMDD system compared to the single drug case exist. For example, special considerations are necessary for intravenous bolus administrations. For complex DDI TMDD systems, the QSS approximation is no longer appropriate to reduce all binding rates by their dissociation constant.
Conclusions: Implementation of QE or QSS approximations of DDI TMDD systems is no longer straightforward compared to the single drug case. We developed an ODE formulation which can be simply implemented in any PKPD software. Further fundamental differences compared to the single drug case are revealed and discussed.
References:
[1] Mager DE, Krzyzanski W (2005) Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition. Pharm Res 22(10):1589-96
[2] Gibiansky L, Gibiansky E, Kakkar T, Ma P (2009) Approximations of the target-mediated drug disposition model and identifiability of model parameters. J Pharmacokinet Pharmacodyn 35(5):573-91
[3] Yan X, Chen Y, Krzyzanski W (2012) Methods to solving rapid binding target-mediated drug disposition model for two drugs competing for the same receptor. J Pharmacokinet Pharmacodyn 39(5):543-60
Reference: PAGE 25 () Abstr 5714 [www.page-meeting.org/?abstract=5714]
Poster: Methodology - New Modelling Approaches