A mechanistic investigation of the oxygen fixation hypothesis and oxygen enhancement ratio

Abstract

The presence of oxygen in tumours has substantial impact on treatment outcome; relative to anoxic regions, well-oxygenated cells respond better to radiotherapy by a factor 2.5-3. This increased radio-response is known as the oxygen enhancement ratio. The oxygen effect is most commonly explained by the oxygen fixation hypothesis, which postulates that radical-induced DNA damage can be permanently 'fixed' by molecular oxygen, rendering DNA damage irreparable. While this oxygen effect is important in both existing therapy and for future modalities such a radiation dose-painting, the majority of existing mathematical models for oxygen enhancement are empirical rather than based on the underlying physics and radiochemistry. Here we propose a model of oxygen-enhanced damage from physical first principles, investigating factors that might influence the cell kill. This is fitted to a range of experimental oxygen curves from literature and shown to describe them well, yielding a single robust term for oxygen interaction obtained. The model also reveals a small thermal dependency exists but that this is unlikely to be exploitable.

Keywords: oxygen; oxygen effect; radiation damage; radiotherapy.

Figure 1

Oxygen fixation hypothesis—a high energy electron created by an x-ray photon (e⁻) impinges upon a water molecule, liberating a proton (p⁺) and creating a hydroxyl radical (OH^•). This reactive molecule then impacts upon DNA, resulting in ionization damage, DNA^•. This can be readily repaired to its original state (DNA-H), but in the presence of molecular oxygen a peroxy radical is formed (DNA-OO^•), ‘fixing’ damage into a permanent irreparable state.

Figure 2

Model fit to historical OER data from (a) Koch et al (b) Whillians and Hunt (c) Ling et al (a) (d) Ling et al (b). 95% confidence intervals shown by dotted black lines.

Figure 3

Model fit from combined data sets shown with (a) standard x-axis (b) logarithmic X-axis for clarity. 95% confidence intervals shown by dotted black lines.

Figure 4

(a) Temperature dependence of φ over a 40 K range (b) projected OER curves at different temperatures.

Figure 5

Diffusion from a vessel of 5 μm radius at venous pressure (40 mmHg). At human body temperature, this example has oxygen consumption rate a = 5 × 10⁻⁷ m³ kg⁻¹ s⁻¹ with maximum diffusion distance 70.16 μm. Under low temperature (32 °C), Ω(T) = 2.7714 × 10⁷ mmHg kg m⁻³ and a ≈ 3.5 × 10⁻⁷ m³ kg⁻¹ s⁻¹, increasing diffusion distance to 84.22 μm, potentially increasing available oxygen for radiotherapy. Curves calculated from simple Krogh-type model as previously outlined [19].