Uniqueness of Solutions to Compartmental Models of Population Pharmacokinetics for Drugs Undergoing Complex Metabolism
Purpose: To investigate parameter identifiability and uniqueness of solutions to compartmental population pharmacokinetic (PPK) models for drugs with complex metabolism.
Methods: As a solution to parameter identifiability, fixing volume of distribution (VOD) of a parent drug (P) or its metabolites has been extensively reported during PPK model development when neither excretion data for each species were available nor metabolite doses were separately administered. A hypothetical P and its metabolites (M1 and M2) with a metabolic pathway P ® M1 « M2 was used to simulate the development of a 5-compartment PPK model (2 for P, 1 for M1 and 2 for M2) in NONMEM® and 1200 PK samples from 240 patients for P, M1, and M2 were collected at 0, 1, 2, 4, and 24 hrs after an IV infusion (90 min) of 200 mg P. Elimination characteristics of the drug were assumedly known from prior metabolism/mass balance studies.
Results: The solution to the mass balance differential equations in this PPK model was not unique. The PPK model fit all concentration profiles equally well when the VOD of P, M1, and/or M2 was fixed at different values, and the PK parameter estimates (PE) were either unreasonable or misleading depending on the value at which VOD was fixed. When elimination characteristics were used as boundary conditions through clearances to the model, the obtained PK parameter estimates were unique and interpretable.
Conclusion: Elimination characteristics, rather than VOD, assumed or available from prior studies, should be utilized to guarantee the uniqueness and interpretability of PPK parameter estimates.
American Society for Clinical Pharmacology and Therapeutics (ASCPT), Atlanta, Georgia, March 2002
By A J Xiao and J Fiedler-Kelly