Physiologically-based pharmacokinetic/pharmacodynamic modelling, mathematical model reduction and a mechanistic interpretation of simple empirical models
Hamilton Institute, National Univerisity of Ireland Maynooth
Objectives: During drug discovery, preclinical and clinical drug development, a variety of in vitro and in vivo data are generated to investigate the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug candidate. Based on these data, different modelling approaches are successfully used to understand, predict and optimize the PK/PD of drug candidates, most importantly classical compartment models, empirical PD models, physiologically-based PK (PBPK) models and systems biology models of targeted processes. So far, however, these modelling approaches are typically used mutual exclusive and with little cross-fertilization. The objective of this talk is to demonstrate the added value of cross-fertilization between the different modelling approaches--illustrated by establishing an explicit link between (i) classical compartment models and PBPK models for small molecule drugs, and (ii) empirical PD models and systems biology models of receptor systems targeted by monoclonal antibodies.
Methods: (i) Starting from an intriguing observation, we establish a new and very simple criterion for lumping (simplifying) detailed PBPK models. This allows us to explicitly establish a link between the parameters of the PBPK model and the lumped parameters of the simple compartment model. We introduce the notion of a minimal lumped model that can be directly linked to classical compartment PK models. (ii) Starting from a systems biology model of receptor trafficking and ligand-receptor interaction, we use mathematical model reduction techniques to link the detailed model to empirical models of drug-receptor interaction that have been used to analyse clinical data of monoclonal antibodies.
Results: (i) We establish the link between PBPK models and classical compartment model via minimal lumped models of low complexity (1-3 compartments) that retain a mechanistic interpretation. This allows us to reduce 13-18 compartment physiologically-based PK models to simple compartment models without compromising the predictions. Importantly, this enables a mechanistic interpretation of empirical compartment models. Applying the lumping approach to 25 diverse drugs, we identified characteristic features of lumped models for moderate-to-strong bases, weak bases and acids. We observed that for acids with high protein binding, the lumped model comprised only a single compartment. (ii) We establish a mechanistic PK/PD model for monoclonal antibodies targeting receptor systems by integrated systems biology models of drug-receptor inaction into empirical models of drug PK. We illustrate the approach for anti-EGFR antibodies in cancer therapy based on in vitro determined receptor system's parameters and pharmacokinetic data from cynomolgus monkeys. We contribute new insight and a simple criterion to the discussion, which model to use for receptor-mediated endocytosis of monoclonal antibodies.
Conclusions: Many drug-related data from different sources are generated during the drug discovery and development process. Physiologically and mechanism-based PK/PD modelling offers a way to integrate these data into a consistent framework , and mathematical techniques are available to link these detailed models to empirical PK/PD models, providing a mechanistic interpretation of the latter.
 S. Pilari and W. Huisinga, Lumping of Physiologically Based Pharmacokinetic Models and a Mechanistic Derivation of Classical Compartmental Models, Submitted (2010).
 B.-F. Krippendorff, K. KŁster, C. Kloft, W. Huisinga, Nonlinear Pharmacokinetics of Therapeutic Proteins Resulting from Receptor Mediated Endocytosis, J. Pharmacokinet. Pharmacodyn. Vol. 36 (2009), pp 239-260.
 B.-F. Krippendorfft, D. Oyarzun and W. Huisinga, Integrating cell-level kinetics into systemic pharmacokinetic models for optimizing biophysical properties of therapeutic proteins, Submitted (2010).