Extending the Tumor Static Concentration curve to average doses – a combination therapy example using radiation therapy
Tim Cardilin (1, 2), Astrid Zimmermann (3), Mats Jirstrand (2), Joachim Almquist (2,4), Samer El Bawab (5), and Johan Gabrielsson (6)
(1) Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, Gothenburg, Sweden, (2) Fraunhofer-Chalmers Centre, Gothenburg, Sweden, (3) Merck, Translational Innovation Platform Oncology, Darmstadt, Germany, (4) Systems and Synthetic Biology, Department of Biology and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden, (5) Merck, Global Early Development - Quantitative Pharmacology, Darmstadt, Germany, (6) Division of Pharmacology and Toxicology, Department of Biomedical Sciences and Veterinary Public Health, Swedish University of Agricultural Sciences, Uppsala, Sweden
Objectives: The recently developed concept of Tumor Static Concentration (TSC) is a valuable modeling tool for the quantitative analysis of combination therapies . 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  modified for radiation treatment. Model parameters were estimated using a mixed-effects approach implemented in Mathematica 10 . 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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