Investigating spatial fractionation and radiation induced bystander effects: a mathematical modelling approach

Radiation induced bystander effects (RIBEs) have been shown to cause death in cells receiving little or no physical dose. In standard radiotherapy, where uniform fields are delivered and all cells are directly exposed to radiation, this phenomenon can be neglected. However, the role of RIBEs may become more influential when heterogeneous fields are considered. Mathematical modelling can be used to determine how these heterogeneous fields might influence cell survival, but most established techniques account only for the direct effects of radiation. To gain a full appreciation of how non-uniform fields impact cell survival, it is also necessary to consider the indirect effects of radiation. In this work, we utilise a mathematical model that accounts for both the direct effects of radiation on cells and RIBEs. This model is used to investigate how spatially fractionated radiotherapy plans impact cell survival in vitro. These predictions were compared to survival in normal and cancerous cells following exposure to spatially fractionated plans using a clinical linac. The model is also used to explore how spatially fractionated radiotherapy will impact tumour control in vivo. Results suggest that spatially fractionated plans are associated with higher equivalent uniform doses (EUDs) than conventional uniform plans at clinically relevant doses. The model predicted only small changes changes in Normal Tissue Complication Probability (NTCP), compared to the larger protection seen clinically.. This contradicts a central paradigm of radiotherapy where uniform fields are assumed to maximise cell kill and may be important for future radiotherapy optimisation.