Theoretical analysis of the dose dependence of the oxygen enhancement ratio and its relevance for clinical applications

Abstract

BackgroundThe increased resistance of hypoxic cells to ionizing radiation is usually believed to be the primary reason for treatment failure in tumors with oxygen-deficient areas. This oxygen effect can be expressed quantitatively by the oxygen enhancement ratio (OER). Here we investigate theoretically the dependence of the OER on the applied local dose for different types of ionizing irradiation and discuss its importance for clinical applications in radiotherapy for two scenarios: small dose variations during hypoxia-based dose painting and larger dose changes introduced by altered fractionation schemes.MethodsUsing the widespread Alper-Howard-Flanders and standard linear-quadratic (LQ) models, OER calculations are performed for T1 human kidney and V79 Chinese hamster cells for various dose levels and various hypoxic oxygen partial pressures (pO2) between 0.01 and 20 mmHg as present in clinical situations in vivo. Our work comprises the analysis for both low linear energy transfer (LET) treatment with photons or protons and high-LET treatment with heavy ions. A detailed analysis of experimental data from the literature with respect to the dose dependence of the oxygen effect is performed, revealing controversial opinions whether the OER increases, decreases or stays constant with dose.ResultsThe behavior of the OER with dose per fraction depends primarily on the ratios of the LQ parameters alpha and beta under hypoxic and aerobic conditions, which themselves depend on LET, pO2 and the cell or tissue type. According to our calculations, the OER variations with dose in vivo for low-LET treatments are moderate, with changes in the OER up to 11% for dose painting (1 or 3 Gy per fraction compared to 2 Gy) and up to 22% in hyper-/hypofractionation (0.5 or 20 Gy per fraction compared to 2 Gy) for oxygen tensions between 0.2 and 20 mmHg typically measured clinically in hypoxic tumors. For extremely hypoxic cells (0.01 mmHg), the dose dependence of the OER becomes more pronounced (up to 36%). For high LET, OER variations up to 4% for the whole range of oxygen tensions between 0.01 and 20 mmHg were found, which were much smaller than for low LET.ConclusionsThe formalism presented in this paper can be used for various tissue and radiation types to estimate OER variations with dose and help to decide in clinical practice whether some dose changes in dose painting or in fractionation can bring more benefit in terms of the OER in the treatment of a specific hypoxic tumor.

On the importance of prompt oxygen changes for hypofractionated radiation treatments

“…1 can be written as the following in a similar way to Wenzl and Wilkens (2011) and Carlson et al (2006): $$lnS\approx -{\alpha }_a/false(\mathrm{italicOER}false)D-{\beta }_a/{false(\mathrm{italicOER}false)}^2{GD}^2.$$…”

“…The linear-quadratic equation can be written as follows as a function of the partial pressure, p: $$lnSfalse(pfalse)=-false({\alpha }_a/false[\mathrm{italicOER}false(pfalse)false]false)D-false({\beta }_a/{false[\mathrm{italicOER}false(pfalse)false]}^{2}false){GD}^2,$$ where the second term traditionally contains timing information for repair in G, the Lea-Catcheside factor. The local partial pressure of oxygen in the interstitium will provide an oxygen enhancement factor (OER) according to the treatment in Wenzl and Wilkens (2011). A similar tactic is taken by Carlson et al (2006).…”

Mitochondrial stress controls the radiosensitivity of the oxygen effect: Implications for radiotherapy

“…No analysis of the differing effects of low-dose or high-dose on OER curves has been pursued, although the review of Wenzl and Wilkens [49] noted variable OER behavior. Indeed, OER values can increase, decrease or remain nearly constant with increasing radiation doses, depending on the cell line and radiation exposure used.…”

The reoxygenation of hypoxia and the reduction of glucose metabolism in head and neck cancer by fractionated radiotherapy with intensity-modulated radiation therapy

“…Although the oxygen enhancement ratio of X-ray radiation is > 2.0, it is impossible to irradiate more than 200 % of the standard dose for a hypoxic tumor, due to the radiation damage to the surrounding normal tissue [11]. In addition, reoxygenation of hypoxic areas may occur in an early phase of a fractionated radiation treatment course, which increases the radiosensitivity of a malignant tumor.…”