Michael R. Dunlavey, Robert H. Leary
Certara/Pharsight Corp.
Objectives: Savic et al [1] give a closed-form computation to model absorptive delay through multiple transit compartments, where the number of compartments is a parameter to be estimated. It works for single delta-function inputs sufficiently separated in time. It is desirable to be able to model such absorption in a way that easily handles arbitrary dosing sequences and steady-state determination.
Methods: A statement is included in the Pharsight Modeling Language (PML) that models a delay of time MTT (Mean Transit Time, estimated) as a discrete sequence of N+1 compartments, where N (non-negative) is estimated and is the number of transitions, all of equal rate. N need not be integer, as log-domain interpolation between integer numbers of compartments can be used. The underlying model implemented by the statement consists of a system of ordinary differential equations. When the interpolation is performed in the log-domain, the error fraction between the interpolated and closed-form solution depends only on the number of transitions, not on time, and it can be exactly corrected.
Results: Absorption models are compared between a PML statement implementation, an implementation using explicit ODEs written in PML, and ,where applicable, the Savic model using a closed form absorption delay function.
Conclusions: The discrete method with interpolation compares well with the closed form method, and is not limited to delta-function inputs well separated in time.
References:
[1] R. M. Savic, D. M. Jonker, T. Kerbusch, M. O. Karlsson, "Implementation of a transit compartmental model for describing drug absorption in pharmacokenetic studies", J. of Pharmacokinetics Pharmacodynamics (2007)) 34:711-726
Reference: PAGE 22 () Abstr 2796 [www.page-meeting.org/?abstract=2796]
Poster: Absorption and Physiology-Based PK