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Implementation of dose superimposition to introduce multiple doses for a mathematical absorption model (transit compartment model)


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.

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We gratefully acknowledge Dr. Robert Bauer (ICON Development Solutions) for reviewing the manuscript and providing helpful comments.

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Correspondence to Jun Shen.


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)

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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).

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  • Dose superimposition
  • Mathematical absorption model
  • Transit compartment model
  • Multiple doses
  • WinNonlin