A Two-Compartment Model of System Response of Tumour to Ionizing Radiation

Radiation therapy is one of the major treatments in oncology, used in at least 40% of cancer patients. Despite significant progress in patient outcomes, radioresistance remains a key clinical challenge. As established, radioresistance is driven mainly by protective and evasive mechanisms activated in cancer cells under irradiation. Along with the clinical development of therapeutic methods to suppress radioresistance, mathematical modeling offers distinct advantages in investigating the molecular mechanisms of radioresistance and facilitates development of therapeutic strategies to overcome it. In this work, we developed a two-compartment model of tumour dynamics under irradiation with various fractionated regimens. The model integrates a description of microscopic molecular processes in cancer cells with the simulation of macroscopic processes observed in experiments and clinic. At the macroscopic level, the model accounts for the compartments of proliferating cells and non-proliferating cells, the latter of which undergo apoptosis as a result of irradiation. At the microscopic level, the model simulates activation of the protective mechanisms of cancer cell against radiation, specifically the antioxidant system defending cancer cell against radiation-induced oxidative stress and the repair of DNA damages caused by radiation. These two molecular mechanisms activated by radiation serve as the primary drivers of radioresistance in various cancers and mitigate radiotherapy outcomes. Validation of the model against experimental data showed that it accurately describes the macroscopic characteristics of the treatment, specifically the time dependence of tumour volume of the rhabdomyosarcoma under single-dose irradiation ranging from 10 to 30 Gy. This enabled us to evaluate the microscopic characteristics of the tumour protective response to irradiation, namely the activation of the antioxidant and DSB repair systems. The parametrized model then was applied to simulate conventional, hypofractionated, and hyperfractionated radiotherapy regimens for rat rhabdomyosarcoma tumour, allowing for a comparison of major fractionated regimes used in clinic.