Mathematical modelling of time-dependent radiobiological effects in radiotherapy using In vivo tumour dynamics.

In the present study the impact of a prolonged dose-delivery time on tumour control was evaluated by using a mathematical tumour model calibrated with in vivo tumour volume data. While in vitro studies have reported reduced radiobiological effects with extended dose-delivery time, the in vivo relevance remains uncertain. Here, such effects were explored across various fractionation protocols and temporal delivery conditions. A biologically based mathematical model was developed using tumour volume data from CT26 murine models subjected to different radiation protocols (5 × 2 Gy, 1 × 7 Gy, and 3 × 4 Gy). The model integrated microdosimetric kinetic modelling (MKM) and ordinary differential equations to simulate tumour dynamics. Simulations were conducted for dose-delivery times of 0, 10, 30, 60, and 120 min, and the changes in tumour volume relative to instantaneous delivery (0 min) were evaluated. All protocols exhibited increased tumour volumes with longer delivery times. The 1 × 7 Gy protocol showed the highest effect, with a 5% increase in tumour volume at approximately 42.5 min. The 5 × 2 Gy protocol maintained tumour volumes within 5% even at delivery times exceeding 100 min. These dose-delivery time thresholds for a 5% volume increase differed between early (1 day post-irradiation) and late (30 days) evaluations. Prolonged dose-delivery time could compromise tumour control, with its impact varying by fractionation protocol. The results obtained provide a framework to quantify time sensitivity in radiotherapy, and they support the use of mathematical tumour models to assess the impact of potential dose uncertainties arising from prolonged dose-delivery times on tumour control.