A mathematical absorption model (e.g. transit compartment model) is useful to describe complex absorption process. However, in such a model, an assumption has to be made to introduce multiple doses that a prior dose has been absorbed nearly completely when the next dose is administered. This is because the drug input cannot be determined from drug depot compartment through integration of the differential equation system and has to be analytically calculated. We propose a method of dose superimposition to introduce multiple doses; thereby eliminating the assumption. The code for implementing the dose superimposition in WinNonlin and NONMEM was provided. For implementation in NONMEM, we discussed a special case (SC) and a general case (GC). In a SC, dose superimposition was implemented solely using NM-TRAN abbreviated code and the maximum number of the doses that can be administered for any subject must be pre-defined. In a GC, a user-supplied function (FUNCA) in FORTRAN code was defined to perform dose superimposition to remove the restriction that the maximum number of doses must be pre-defined.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Savic RM, Jonker DM, Kerbusch T, Karlsson MO (2007) Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. J Pharmacokinet Pharmacodyn 34:711–726
Sun YN, Jusko WJ (1998) Transit compartments versus gamma distribution function to model signal transduction processes in pharmacodynamics. J Pharm Sci 87:732–737
Wilkins JJ, Savic RM, Karlsson MO, Langdon G, McIlleron H, Pillai G, Smith PJ, Simonsson US (2008) Population pharmacokinetics of rifampin in pulmonary tuberculosis patients, including a semimechanistic model to describe variable absorption. Antimicrob Agents Chemother 52:2138–2148
PharmPK Discussion Thread. http://www.boomer.org/pkin/PK05/PK2005336.html. Accessed 30 Nov 2010
Beal SL, Sheiner LB, Boeckmann AJ, Bauer RJ (2010) NONMEM 7.1.2 users guides. Icon Development Solutions, Ellicott City
Lindbom L, Pihlgren P, Jonsson EN (2005) PsN-Toolkit—a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput Methods Programs Biomed 79:241–257
R Development Core Team (2009) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0. http://www.R-project.org. Accessed 30 Nov 2010
Sarkar D (2009) Lattice: lattice graphics. R package version 0.17-26. http://CRAN.R-project.org/package=lattice. Accessed 30 Nov 2010
Debord J, Risco E, Harel M, Le MY, Buchler M, Lachatre G, Le GC, Marquet P (2001) Application of a gamma model of absorption to oral cyclosporin. Clin Pharmacokinet 40:375–382
Krzyzanski W (2011) Interpretation of transit compartments pharmacodynamic models as lifespan based indirect response models. J Pharmacokinet Pharmacodyn 38:179–204
Csajka C, Drover D, Verotta D (2005) The use of a sum of inverse Gaussian functions to describe the absorption profile of drugs exhibiting complex absorption. Pharm Res 22:1227–1235
Wang J, Weiss M, D’Argenio DZ (2008) A note on population analysis of dissolution–absorption models using the inverse Gaussian function. J Clin Pharmacol 48:719–725
Weiss M (1996) A novel extravascular input function for the assessment of drug absorption in bioavailability studies. Pharm Res 13:1547–1553
Zhou H (2003) Pharmacokinetic strategies in deciphering atypical drug absorption profiles. J Clin Pharmacol 43:211–227
We gratefully acknowledge Dr. Robert Bauer (ICON Development Solutions) for reviewing the manuscript and providing helpful comments.
Appendix 1: dose superimposition where all doses and dosing intervals are the same in WinNonlin
Appendix 2: dose superimposition (general solution) in WinNonlin
Appendix 3: dose superimposition in NONMEM (SC)
Appendix 4: dose superimposition in NONMEM (GC)
Appendix 5: user defined FORTRAN subroutine FUNCA (referred as sumdoset.f90 in Appendix 4)
About this article
Cite this article
Shen, J., Boeckmann, A. & Vick, A. Implementation of dose superimposition to introduce multiple doses for a mathematical absorption model (transit compartment model). J Pharmacokinet Pharmacodyn 39, 251–262 (2012). https://doi.org/10.1007/s10928-012-9247-3