Modelling the interplay between hypoxia and proliferation in radiotherapy tumour response.

A tumour control probability computational model for fractionated radiotherapy was developed, with the goal of incorporating the fundamental interplay between hypoxia and proliferation, including reoxygenation over a course of radiotherapy. The fundamental idea is that the local delivery of oxygen and glucose limits the amount of proliferation and metabolically-supported cell survival a tumour sub-volume can support. The model has three compartments: a proliferating compartment of cells receiving oxygen and glucose; an intermediate, metabolically-active compartment receiving glucose; and a highly hypoxic compartment of starving cells. Following the post-mitotic cell death of proliferating cells, intermediate cells move into the proliferative compartment and hypoxic cells move into the intermediate compartment. A key advantage of the proposed model is that the initial compartmental cell distribution is uniquely determined from the assumed local growth fraction (GF) and volume doubling time (TD) values. Varying initial cell state distributions, based on the local (voxel) GF and TD, were simulated. Tumour response was simulated for head and neck squamous cell carcinoma using relevant parameter values based on published sources. The tumour dose required to achieve a 50% local control rate (TCD50) was found for various GFs and TD's, and the effect of fraction size on TCD50 was also evaluated. Due to the advantage of reoxygenation over a course of radiotherapy, conventional fraction sizes (2-2.4 Gy fx(-1)) were predicted to result in smaller TCD50's than larger fraction sizes (4-5 Gy fx(-1)) for a 10 cc tumour with GFs of around 0.15. The time to eliminate hypoxic cells (the reoxygenation time) was estimated for a given GF and decreased as GF increased. The extra dose required to overcome accelerated stem cell accumulation in longer treatment schedules was estimated to be 0.68 Gy/day (in EQD26.6), similar to published values derived from clinical data. The model predicts, for a 2 Gy/weekday fractionation, that increased initial proliferation (high GF) should, surprisingly, lead to moderately higher local control values. Tumour hypoxia is predicted to increase the required dose for local control by approximately 30%. Predicted tumour regression patterns are consistent with clinical observations. This simple yet flexible model shows how the local competition for chemical resources might impact local control rates under varying fractionation conditions.