A predictive model studying the impact of timing and order for the combination-regime of spatially fractionated radiation therapy and stereotactic body radiation therapy

Abstract Background. The radiobiological effects induced by spatially fractionated radiation therapy (SFRT), a specialized cancer treatment technique in which radiation is delivered in a non-uniform pattern, play a crucial role in cancer therapy. Purpose. To develop a comprehensive mathematical framework for simulating and predicting tumor volume changes following RT, encompassing both stereotactic body RT (SBRT) and SFRT. This framework will facilitate the exploration of various SFRT-SBRT combination regimens to deepen understanding of SFRT’s role in tumor treatment. Methods. The tumor cell compartments are classified into active and inactive tumor cells, the latter resulting from radiation, and modeled using ordinary differential equations. We propose a novel mathematical forecasting framework that integrates both the dynamic carrying capacity and proliferative potential of tumor cells following radiation therapy, accounting for the biological interactions between the tumor, immune system, and irradiation. Data from five patients, collected during and after RT, are used for parameter estimation, and the model is subsequently applied to predict tumor response to various SFRT-SBRT treatment regimens. Results. For the SFRT + SBRT treatment protocol, the model indicates that the time intervals between SFRT and SBRT significantly influence the treatment outcomes. A 1 month interval may represent the optimal scenario for achieving early and efficient tumor shrinkage, while an interval of less than 2 weeks could disrupt the bystander effect and the early immune response triggered by SFRT, leading to a less favorable treatment outcome. Additionally, the SFRT + SBRT protocol is generally more effective than the SBRT + SFRT protocol in controlling tumor growth. Conclusions. These results demonstrate that our comprehensive mathematical model effectively captures a range of tumor volume dynamics across different RT protocols. It enables accurate prediction of patient outcomes, which can be applied to design optimized RT plans for SBRT and SFRT, ensuring efficient tumor shrinkage.