Steady-state equivalence of drug- and biomarker driven models in tumor growth experiments

Objectives: In this work we propose a tumor growth Pharmacokinetic-Pharmacodynamic (PK-PD) modelling approach in which a tumor-specific causal biomarker [1] is integrated as driver of tumor growth in xenograft. The main goal is to investigate the mathematical properties guaranteeing steady-state equivalence of the biomarker-driven tumor growth inhibition (TGI) model to a given PK-driven TGI model.A further objective is to derive steady-state relationships between drugs and biomarker that may help predicting the drug potency in experiments involving a new drug modulating the same biomarker. Methods: In order to characterize the steady-state behavior of a drug-driven TGI model, we evaluate the equilibrium value of the tumor weight, assuming that xenografted mice have been exposed to constant plasma concentrations of the drug, thus obtaining the so-called drug-to-tumor characteristic curve [2]. Moreover, we relate the drug potency properties of two drugs acting on the same causal biomarker. In particular, based on the steady-state equivalence between the (drug-driven) Simeoni [3] model and the proposed biomarker-driven B2-Simeoni model [2],[4], a mathematical relationship is found that allows predicting the antitumor potency of the second drug without the need of TGI data. Results: Since the equivalence of drug- and biomarker- driven models has been considered in steady-state conditions, we resort to a simulation approach to test also the equivalence in transient conditions, using realistic model parameters. Moreover, the relationship linking drug potency on tumor growth with its effect on biomarker dynamics, is tested on data taken from the literature concerning two antitumoral drugs acting on the same biomarker [5]. The models are identified using experimental PK data, and biomarker data for the two drugs while only tumor growth data for the first compound are employed. Then model properties are used to predict both the antitumor potency of the second drug and the associated tumor growth profile. Conclusions: In this work, starting from an established drug-driven TGI model, a biomarker-driven TGI model that is steady-state equivalent has been investigated. A relationship linking drug potency on tumor growth and drug effects on biomarker dynamics is obtained that can be used to predict the antitumoral drug potency of a new drug acting on the same path without the need of performing additional tumor growth experiments. This work was supported by the DDMoRe project (www.ddmore.eu). References: [1] M. Danhof, Mechanism-Based Pharmacokinetic-Pharmacodynamic Modeling-A New Classification of Biomarkers, Pharm Res, 22, 1432-1437 (2005) [2] M. L. Sardu, A. Russu, I. Poggesi, G. De Nicolao, “Tumor-growth inhibition in preclinical animal studies: steady-state analysis of biomarker-driven models”, PAGE 22 (2013) Abstr. 2880 [www.page-meeting.org/?abstract=2880] [3] P. Magni, M. Simeoni, I. Poggesi, M. Rocchetti, G. De Nicolao, “A mathematical model to study the effects of drugs administration on tumor growth dynamics”, Math. Biosci., 200, 127-151 (2006) [4] M. L. Sardu, A. Russu, G. De Nicolao, I. Poggesi, “Biomarker-driven models of tumor growth inhibition in preclinical animal studies” PAGE 21 (2012) Abstr. 2498 [www.page-meeting.org/?abstract=2498] [5] V. M. Rivera, R. Anjum, F. Wang, S. Zhang et al., “Efficacy and pharmacodynamics analysis of AP26113, a potent and selective orally active inhibitor of Anaplastic Linphoma Kinase (ALK)” Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 3623.