Modeling of the FLASH effect for ion beam radiation therapy

Normal tissue sparing has been shown in preclinical studies under the ultra-fast dose rate condition, so-called FLASH radiotherapy. The preclinical and clinical FLASH studies are being conducted with various radiation modalities such as photons, protons, and heavy ions. The aim of this study is to propose a model to predict the dependency of the FLASH effect on linear energy transfer (LET) by quantifying the oxygen depletion.

We develop an analytical model to examine the FLASH sparing effect by incorporating time-varying oxygen depletion equation and oxygen enhancement ratios according to LET. The variations in oxygen enhancement ratio (OER) are quantified over time with different dose rate (Gy/s) and LET (keV/μm). The FLASH sparing effect (FSE) is defined as the ratio of D_FLASH/D_conv where D_conv is the reference absorbed dose delivered at the conventional dose rate, and D_FLASH is the absorbed dose delivered at a high dose rate that causes the same amount of biological damage.

Our model suggests that the FLASH effect is significant only when the oxygen amount is at an intermediate level (10 ∼ 100 mmHg). The FSE is increased as LET decreases, suggesting that LET less than 100 keV/μm is required to induce FLASH sparing effects in normal tissue.

Oxygen depletion and recovery provide a quantitative model to understand the FLASH effect. These results highlight the FLASH sparing effects in normal tissue under the conditions with the intermediate oxygen level and low-LET region.