Monolix benefits from external modules to manage complex ODE: Illustration with a population analysis of Irinotecan and its metabolites.
B. Ribba, K. Chatel, M. Tod, P. Girard, G. Freyer, B. Tranchand
Université de Lyon, Lyon, F-69003, France; Université Lyon 1, Ciblage Thérapeutique en Oncologie (EA3738), Faculté de Médecine Lyon-Sud, Oullins, F-69921, France.
Objectives: The wish to develop integrative mathematical models to better monitor anti-cancer drugs pharmacokinetic (PK), efficacy and toxicity requires the extension of population approaches to deal with complex ordinary differential equation (ODE) models that become difficult to identify with classical population PK softwares.
Methods: To illustrate this methodological issue, PK data of Irinotecan (CPT-11) and three of its metabolites, 7-ethyl-10-Hydroxycamptothecin (SN38), 7-ethyl-10-Hydroxycamptothecin glucuronide (SN38G), and 7-ethyl-10-[4-N-(acid5-aminopentanoïque)-1-piperidino]-carbonyloxycamptothécine (APC), coming from 162 patients enrolled in pediatric phase I and phase II clinical trials representing 5345 observations (33 observations on average per patients; 45 per patient enrolled in the phase I and 21 per patient enrolled in the phase II; 9.3 observations in average for CP11, 7.1 for SN38, 7.7 for SN38G and 8.9 for APC) were analyzed. The full model was characterized by starting from Irinotecan concentration data only (step 0) and plugging successively SN38 (step 1), SN38G (step 2), and finally APC (step 3). Monolix 2.3.1 with the use of CVODE Software Package  was compared to NONMEM ADVAN7, ADVAN6 (Runge-Kutta Verner order 5 and 6), ADVAN8 (ADAMS), and ADVAN9 (Livermore solver /ODEPACK).
Results: Monolix 2.3.1 using external C++ modules allowed us to characterize efficiently the different structural models. CPT-11 and SN-38 data (step 1) have been fitted by a linear model with four compartments; successive step (CPT-11, SN-38 and SN-38G) resulted in a five compartment model while the full model (step 3) was constituted by seven compartments. Model was validated based on goodness of fit. Computational times were ranging from 13 (step 1) to 33 minutes (step 3). Using the same “sequential” procedure, data analysis was much more difficult to handle with NONMEM VI. As an example, step 1 lasted for 19 minutes with ADVAN7/FO. More detailed comparison is ongoing.
Conclusions: Monolix coupled with the external C++ modules constitutes a relevant tool to develop physiologically-based PK/PD models. Hopefully, the full PK model of Irinotecan will provide a rational identification of covariates and will be informative on the role of its metabolites.
 Cohen, S.D., and A.C. Hindmarsh. CVODE, a Stiff/Nonstiff ODE Solver in C. Computers in Physics, 10, 2, pp. 138-143, March/April 1996.