The minimal FLASH sparing effect needed to compensate the increase of radiobiological damage due to hypofractionation for late-reacting tissues

Abstract

Purpose: 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.

Methods: 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.

Results: 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.

Conclusions: 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.

Keywords: BED; FLASH effect; LQ model; LQ-L model; hypofractionation.

FIGURE 1

Diagram illustrating the principal research question addressed in this work. For hypofractionated (HF) ultra‐high dose rate (UHDR) radiotherapy (RT) to be favorable compared to normofractionated (NF) conventional dose rate (CONV) RT with the same relative dose distribution (i.e., the same geometric sparing r), the FLASH effect needs to reduce radiobiological damage (RD) to critical normal tissue (NT) regions more than a NF CONV treatment would do. This minimum RD reduction is quantified in this work by the “break‐even NT sparing weighting factor” W _BE and is obtained by requiring that RD to the tumor (T) and the NT are the same for the NF CONV treatment and the HF UHDR treatment. Symbols are defined in Table 1.

FIGURE 2

Break‐even normal tissue (NT) sparing factor W _BE as predicted by the linear‐quadratic (LQ) and LQ‐linear (LQ‐L) models for different relative doses levels r as a function of ultra‐high dose rate (UHDR) dose per fraction d (a) and as a function of UHDR fraction number n (b) for a set of hypofractionated treatment schedules with a BED₁₀ of 72 Gy to the tumor. A FLASH modifying factor smaller than W _BE needs to be reached for a hypofractionated UHDR treatment with dose per fraction d, to be advantageous for a tissue region at dose level r, compared to a normofractionated conventional dose rate treatment. The generic α/β‐ratios of (α/β)_NT = 3 Gy and (α/β)_T = 10 Gy for late‐reacting NT and tumors, respectively, were used for the calculations. Markers indicate integer fraction numbers n for a BED₁₀ of 72 Gy to the tumor. A normofractionated treatment with $d=2\mathrm{Gy}$ is indicated by a gray dashed vertical line.

FIGURE 3

Break‐even normal tissue (NT) sparing factor W _BE as predicted by the linear‐quadratic (LQ) and LQ‐linear (LQ‐L) models as a function of dose per fraction d for relative dose levels r of 1.0 (a) and 0.5 (b). Curves for different combinations of (α/β)_NT‐ratios (2, 3, 5, and 10 Gy) and (α/β)_T‐ratios (5, 10, and 20 Gy) are displayed. A normofractionated treatment with $d=2\mathrm{Gy}$ is indicated by a gray dashed vertical line.

FIGURE 4

Points display FLASH modifying factors (FMF) for different mammalian organs/body parts derived from single fraction experiments as a function of single fraction ultra‐high dose rate (UHDR) dose (data reproduced from Ref. [14]). Break‐even normal tissue (NT) sparing factors W _BE as a function of dose per fraction to the NT are displayed as predicted by the linear‐quadratic (LQ) (solid lines) and LQ‐linear (LQ‐L) (dashed lines) models for a generic scenario using α/β‐ratios of (α/β)_NT = 3 Gy and (α/β)_T = 10 Gy for late‐reacting NT and the tumor, respectively, and r = 1.0. W _BE values are displayed for a dose per fraction range from 2 to 40 Gy. An FMF smaller than W _BE (i.e., dark‐shaded area for the LQ model and light‐shaded area for the LQ‐L model) needs to be reached by a hypofractionated UHDR treatment with dose per fraction d, to be advantageous for a tissue region at dose level r, compared to a normofractionated conventional dose rate treatment. A normofractionated treatment with $d=2\mathrm{Gy}$ is indicated by a gray dashed vertical line.