Normal tissue (NT) sparing by ultra-high dose rate (UHDR) irradiations compared to conventional dose rate (CONV) irradiations while being isotoxic to the tumor has been termed "FLASH effect" and has been observed when large doses per fraction (d ≳ 5 Gy) have been delivered. Since hypofractionated treatment schedules are known to increase toxicities of late-reacting tissues compared to normofractionated schedules for many clinical scenarios at CONV dose rates, we developed a formalism based on the biologically effective dose (BED) to assess the minimum magnitude of the FLASH effect needed to compensate the loss of late-reacting NT sparing when reducing the number of fractions compared to a normofractionated CONV treatment schedule while remaining isoeffective to the tumor.
By requiring the same BED for the tumor, we derived the "break-even NT sparing weighting factor" W _BE for the linear-quadratic (LQ) and LQ-linear (LQ-L) models for an NT region irradiated at a relative dose r (relative to the prescribed dose per fraction d to the tumor). W _BE was evaluated numerically for multiple values of d and r, and for different tumor and NT α/β-ratios. W _BE was compared against currently available experimental data on the magnitude of the NT sparing provided by the FLASH effect for single fraction doses.
For many clinically relevant scenarios, W _BE decreases steeply initially for d > 2 Gy for late-reacting tissues with (α/β) _NT ≈ 3 Gy, implying that a significant NT sparing by the FLASH effect (between 15% and 30%) is required to counteract the increased radiobiological damage experienced by late-reacting NT for hypofractionated treatments with d < 10 Gy compared to normofractionated treatments that are equieffective to the tumor. When using the LQ model with generic α/β-ratios for tumor and late-reacting NT of (α/β) _T = 10 Gy and (α/β) _NT = 3 Gy, respectively, most currently available experimental evidence about the magnitude of NT sparing by the FLASH effect suggests no net NT sparing benefit for hypofractionated FLASH radiotherapy (RT) in the high-dose region when compared with W _BE . Instead, clinical indications with more similar α/β-ratios of the tumor and dose-limiting NT toxicities [i.e., (α/β) _T ≈ (α/β) _NT ], such as prostate treatments, are generally less penalized by hypofractionated treatments and need consequently smaller magnitudes of NT sparing by the FLASH effect to achieve a net benefit. For strongly hypofractionated treatments (>10-15 Gy/fraction), the LQ-L model predicts, unlike the LQ model, a larger W _BE suggesting a possible benefit of strongly hypofractionated FLASH RT, even for generic α/β-ratios of (α/β) _T = 10 Gy and (α/β) _NT = 3 Gy. However, knowledge on the isoeffect scaling for high doses per fraction (≳10 Gy/fraction) and its modeling is currently limited and impedes accurate and reliable predictions for such strongly hypofractionated treatments.
We developed a formalism that quantifies the minimal NT sparing by the FLASH effect needed to compensate for hypofractionation, based on the LQ and LQ-L models. For a given hypofractionated UHDR treatment scenario and magnitude of the FLASH effect, the formalism predicts if a net NT sparing benefit is expected compared to a respective normofractionated CONV treatment.