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Extending the Tumor Static Concentration curve to average doses - a combination therapy example using radiation therapy

Authors Tim Cardilin
Astrid Zimmermann
Mats Jirstrand
Joachim Almquist
Samer El Bawab
Johan Gabrielsson
Published in Proceedings of the 25th Annual meeting of the Population Approach Group in Europe, PAGE2016. Lisboa, Portugal, 7-10 Juni 2016
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Language en
Subject categories Pharmacology and Toxicology, Informatics and systems science, Applied mathematics


Objectives: The recently developed concept of Tumor Static Concentration (TSC) is a valuable modeling tool for the quantitative analysis of combination therapies [2]. Here, we set out to extend TSC to situations where (average) doses are known but drug exposure data is not available. Methods: Data consisted of Patient-Derived xenografts from combination therapy studies using ionizing radiation and a probe compound. Modelling was based on a Tumor Growth Inhibition (TGI) model [3] modified for radiation treatment. Model parameters were estimated using a mixed-effects approach implemented in Mathematica 10 [1]. A TSC-like curve was derived from tumor stasis assumptions where one of the plasma concentrations was replaced with average radiation dose over time. Results: Drug exposure of the probe compound was successfully modeled using a one compartment exposure model. Initial attempts to model the combination efficacy data were not able to explain the effect from the combination arm. The TGI model was subsequently modified to account for potential interaction effects between the probe compound and radiation treatments. The radiation treatment-modified TGI model was then used to derive a TSC-like curve that determines all pairs of radiation doses and drug concentrations for which the tumor is kept in stasis. This curve exhibits significant curvature, reflecting the synergistic effects of administering the radiation therapy and drug together. The TSC-like curve can be used to improve the administration schedule of the treatment. Conclusions: A model-based method for evaluation of anticancer combination therapy was extended from the use of tumor static plasma concentrations to also include average drug doses. Although used for radiation therapy in this example, the method can also be applied for regular compounds when drug exposure data is not available.

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