Background: We present a pharmacodynamic model that describes the tumor volume evolution during and after treatment with radiation and in combination with a radio-sensitizing agent. A key contribution is the inclusion of a long-term radiation effect, which allows the model to describe distinct tumor behaviors including tumor eradication and tumor regrowth with different growth rates. Additionally, we introduce the concept of TSE (Tumor Static Exposure), the exposures of one or multiple compounds that result in tumor stasis and provide an example of its utility for optimizing drug combinations in oncology.
Methods: The model was challenged with data from four treatment groups (Vehicle, radiation, radiation + radiosensitizer 25 or 100 mg/kg) in xenograft study using a clinically relevant administration schedule (6 weeks treatment, 5 days on/2 days off) and a mixed-effects approach was used for model-fitting. The model incorporated a permanent inhibition of the natural growth rate. This step was required to capture the complete tumor eradication and the observed tumor regrowth with different rates with animals having slower regrowth compared to control animals. The presence of a radiosensitizer will lead to the same tumor evolution as if a higher dose of radiation had been administered. The model was applied to predict exposure combinations that result in tumor eradication using the TSE.
Results: The developed model captured experimental data from all treatment groups adequately, with the parameter estimates taking biologically reasonable values. Model simulation showed that tumor eradication is observed at total radiation dose of 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg/kg of a radiosensitizer.
Conclusions: The new model can describe different tumor dynamics including tumor eradication and tumor regrowth with different rates. The proposed model can be expanded for radiation in combination with chemical interventions or immunotherapy. The model and TSE can be applied to generate treatment predictions for different dosing schedules or determining drug synergies. The translational utility of the TSE concept is currently under investigation.
Funding: Tim Cardilin was supported by an education Grant from Merck Healthcare KGaA, Darmstadt, Germany. This work was also partially funded by the Swedish Foundation for Strategic Research (Grant no. AM13-0046).