**Tumor Static Exposure for anticancer combinations in early drug discovery**

Tim Cardilin (1,2), Mats Jirstrand (1), Floriane Lignet (3), Samer El Bawab (3), and Johan Gabrielsson (4)

(1) Fraunhofer-Chalmers Centre, Gothenburg, Sweden, (2) Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden, (3) Merck Healthcare KGaA, Translational Medicine - Quantitative Pharmacology, Darmstadt, Germany, (4) Division of Pharmacology and Toxicology, Department of Biomedical Sciences and Veterinary Public Health, Swedish University of Agricultural Sciences, Uppsala, Sweden

**Objectives:** Examine how the Tumor Static Exposure (TSE) concept can help guide early drug discovery, particularly for combination treatments with two or more drugs.

**Methods: **TSE is a model-based prediction of the necessary exposure to a drug or combination of drugs that results in tumor shrinkage. TSE has been derived as an important quantity for single-agent treatments as well as combinations of drugs, and combinations involving radiation treatment [1-3]. When a population approach such as mixed-effects modeling is used, TSE predictions can be made to ensure tumor shrinkage not only for the median, but for a larger percentage of the population. Several published examples are given in order to highlight how TSE is:

1) Defined and can be derived for a given model

2) Used to assess synergy and optimize combination treatments

3) Used to understand between-subject variability

4) Useful when translating results from animals to humans

**Results:** TSE can be derived from a quantitative tumor model based on a steady-state condition where the growth rate of tumor cells is equal to the kill rate induced by one or multiple anti-cancer agents. TSE is then computed using the estimated parameter values from the model, which results in a point, curve, or surface consisting of all exposure combinations that result in tumor stasis. Exposure combination above TSE will lead to tumor shrinkage, whereas exposure combinations below TSE lead to tumor growth. The first example shows a TSE curve for combinations of cetuximab, an EGFR-inhibitor, and cisplatin [1]. TSE and mixed-effects modeling are used together to predict the necessary exposure to achieve tumor regression for 90% of the population. The second example involves combinations of radiation and a radiosensitizing agent [2]. The associated TSE curves consists of all combinations of daily radiation doses and radiosensitizer concentrations that will lead to tumor shrinkage. A strong synergistic effect is seen via a pronounced curvature of the associated TSE curve. TSE is also used to show that an optimal combination of radiation and radiosensitizer could significantly reduce the total exposure and consequently reduce toxicity. Such techniques could be useful when selecting candidates to move forward within an early discovery setting. The third example involves radiation and a different radiosensitizing agent [3]. A heat map is generated that shows the net tumor growth/shrinkage rates associated with different combinations of radiation and radiosensitizer. In particular, the TSE curve is given as a special case when the net growth rate is zero. Such a heat map allows combinations to be evaluated at greater exposure levels when the tumor is required to shrink at a certain rate. The translational potential of TSE is also explored by allometric scaling of the system parameters.

**Conclusions: **The three examples illustrate that TSE is a useful concept that can be derived and used for a variety of tumor models. TSE has a clear biological interpretation as the combinations of drug exposures that are sufficient to achieve tumor shrinkage. TSE can be used to assess the synergy of a combination, to optimize combination treatments, and can also help with translational efforts. TSE could be particularly useful when selecting drug candidates in early drug discovery.

**References:**

[1] Cardilin T, Almquist J, Jirstrand M, Sostelly A, Amendt C, El Bawab S, Gabrielsson J. Tumor Static Concentration Curves in Combination Therapy, AAPS J. (2017)

[2] Cardilin T, Almquist J, Jirstrand M, Zimmermann A, El Bawab S, Gabrielsson J. Model-based evaluation of radiation and radiosensitizing agents in oncology. CPT: Pharmacometrics & Syst. Pharmacol*.* (2018).

[3] Cardilin T, Almquist J, Jirstrand M, Zimmermann A, Lignet F, El Bawab S, Gabrielsson J. Modeling of radiation therapy and radiosensitizing agents in tumor xenografts. PAGE 27 (2018) Abstr 8654 [www.page-meeting.org/?abstract=8654]