Lumping of Physiologically Based Pharmacokinetic Models and a Mechanistic Derivation of Classical Compartmental Models
Sabine Pilari and Wilhelm Huisinga
Department of Mathematics and Computer Science, Freie Universitšt Berlin, Germany; and Hamilton Institute, National University of Ireland Maynooth (NUIM), Ireland
Objectives: In drug discovery and development, classical compartment models and physiologically based pharmacokinetic (PBPK) models are successfully used to analyze and predict the pharmacokinetics of drugs. So far, however, both approaches are used exclusively or in parallel, with little to no cross-fertilization. An approach that directly links classical compartment and PBPK models is highly desirable.
Methods: We reduce the dimensionality of a PBPK model to derive mechanistically lumped compartment models and establish a direct link to classical compartment models by interpreting the mechanistically lumped parameters in terms of the classical pharmacokinetic parameters. We exploit the fact that drug concentrations in different compartments of the PBPK model are often strongly kinetically dependent of each other. This dependence is quantified and exploited in order to establish the lumped model and relate the lumped compartment concentrations back to the original ones.
Results: We derived a new mechanistic lumping approach for reducing the complexity of PBPK models that has several advantages over existing methods: Perfusion and permeability rate limited models can be lumped---in any order and into any number of lumped compartments. The lumped model allows for predicting the original organ concentrations. The volume of distribution at steady state is preserved by the lumping method. To inform classical compartmental model development, we introduce the concept of a minimal lumped model that allows for predicting the venous plasma concentration with as few compartments as possible. The minimal lumped parameter values may serve as initial values for any subsequent parameter estimation process.
Conclusions: The proposed lumping approach established for the ﬁrst time a direct derivation of simple compartment models from PBPK models and enables a mechanistic interpretation of classical compartment models. The reduction of PBPK models allows for translating prior knowledge on the pharmacokinetics of a compound given in form of a PBPK model into the development of classical compartmental models in all stages of the drug development process.