Modelling the interplay between hypoxia and proliferation in radiotherapy tumour response

Abstract

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.

Treatment planning evaluation and optimization should be biologically and not dose/volume based

“…[9][10][11][12][13][14] We are in an exciting age of predictive model development. This is an opportunity that we should not ignore: given the mathematical nature of these models, only medical physicists are equipped to lead the effort of clinical adoption (e.g., see the Biosuite software system developed by Nahum and colleagues).…”

Beyond the margin recipe: the probability of correct target dosage and tumor control in the presence of a dose limiting structure

“…The TCP function we applied (equation (1)) was not necessarily intended to be mechanistically or clinically realistic (Webb and Nahum 1993, Zaider and Minerbo 2000, Jeong et al 2013), but merely served as the simplified parameterization of a smooth non-linear relation between dose and effect. Non-linear dose accumulation over fractions could have been considered explicitly during evaluation, but would effectively only have resulted in variations of the shape and steepness of the TCP curve.…”

Cell inactivation by combined low dose-rate irradiation and intermittent hypoxia

“…In clinical treatment, as fi rst indicated by early animal studies (Th omlinson 1968, Van Putten and Kallman 1968) daily fractionation is believed to reoxygenate the hypoxic cells between dose fractions and thereby improve cell kill. Today this is seen as one of the rationales for dose fractionation (Kallman 1972, Brown 2007 and is worked into mathematical models for optimalization of radiotherapy (Jeong et al 2013). Th e ultimate effi ciency of this reoxygenation is, however, still obscure and dependent 1983).…”