A radiobiological model of reoxygenation and fractionation effects

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Abstract

Purpose

The purpose of this study was to develop a radiobiological model of reoxygenation that fulfills the following goals: (a) Quantify the reoxygenation effect for different fractionations (b) Model the hypoxic fraction in tumors as a function of the number of radiation treatments. (c) Develop a simple analytical expression for a reoxygenation term in biological effect calculations.

Method

The model considers tumor cells in two compartments: an aerobic (or normoxic) population of cells and a hypoxic population including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters αA and βA as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells (Δ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we compare the effect of reoxygenation on biological response for a standard dose fractionation for nonsmall cell lung cancer (NSCLC) (d = 2 Gy, n = 33) to typical fractionations for stereotactic body radiotherapy (SBRT) and other nonstandard fractionations.

Results

The reoxygenation effect is parameterized for biological effect calculations and an analytic expression for the surviving fraction after n daily treatments is derived. The hypoxic fraction either increases or decreases with n depending on the reoxygenation parameter Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as −(n−1) · ln(1−Δ) providing a simple expression that can be introduced in biologically effective dose (BED) calculations. The model is used to compare fractionation schedules and quantitatively interpret results from molecular imaging studies of hypoxia. Based on the comparison of conventional fractionation and hypo- and hyper-fractionation for NSCLC, the value of Δ is estimated to be between 0.1 and 0.2 assuming plausible radiobiological parameters from the literature. This value is consistent with the preliminary analysis of the molecular imaging studies.

Conclusions

A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.

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