Applying mechanistic pharmacokinetic-pharmacodynamic models (PKPD) to describe the growth and inhibition of xenograft tumours in rats and mice by targeted anti-cancer agents.
James WT Yates (1), Neil Evans (2), Rhys DO Jones (1), Mike Walker (1), Patricia Schroeder (1), Joanne Wilson (1), Richard Dimelow (1), Frank Gibbons (1), Camila de Almeida(1)
(1) Oncology innovative medicines DMPK, AstraZeneca R&D Alderley Park, UK. (2) University of Warwick, School of Engineering, Coventry, UK, CV4 7AL
Objectives: Measurement of tumour volume over time could mask a range of changes due to underlying biology and treatment. Simeoni et al  published a mathematical model with drug-concentration induced cell damage, and transit-compartments to empirically describe populations of cells undergoing stages of cell damage and death. The model involves a number of assumptions: All healthy cells are equally susceptible to drug treatment at all times; drug action is linearly related to drug concentration; drug action causes cell damage and death. Ribba et al  recently demonstrated the utility of a mechanistic model that characterizes the tumor xenograft in terms of non-hypoxic, hypoxic, and necrotic cells and the drug action on these sub-populations of cells. We will illustrate several modeling examples of how a more mechanistic model can be developed.
Methods: We have adapted the models to be more mechanistic by incorporating features that describe: (1) the utility of biomarkers as a driver for growth inhibition; (2) multiple mechanisms of drug action on sub-populations of cells. We also extend the models to incorporate the spatial features of a tumor in an attempt to better describe the tumor micro-environment. Pharmacokinetic, biomarker and tumor growth data for example compounds have been used to demonstrate the utility of these mechanistic models. Structural identifiability analysis  was applied to check that parameters are estimable. Example data sets were then analysed to demonstrate the utility of the model.
Results: The model is identifiable and the parameters are practically identifiable. Incorporating non-linearity between drug exposure, biomarker response, and tumor growth inhibition allows observed differences between dosing schedules to be explained. Using a biomarker as the driver for tumor growth inhibition provides a more meaningful surrogate for pharmacological action, particularly in the situation where biomarker response to drug is significantly delayed compared to the pharmacokinetics. Modeling multiple mechanisms of action on sub-populations of cells can allow an accurate representation of the drug effect on the disease biology.
Conclusions: We demonstrate that adding mechanistic features to a descriptive model of drug-induced tumor growth inhibition makes it more representative of the disease biology and drug action. The model also could potentially be used for translation to the clinic from pre-clinical data.
 M. Simeoni et al. Cancer Res 64, 1094-1101 (2004)
 B. Ribba et al. Eur. J. Cancer, 47, 479-490 (2011)
 J. Yates et al. Exp. Op. Drug Metab and Tox. 5,295-302 (2009)