Technical Note: Break‐even dose level for hypofractionated treatment schedules

Abstract

To derive the isodose line R relative to the prescription dose below which irradiated normal tissue (NT) regions benefit from a hypofractionated schedule with an isoeffective dose to the tumor. To apply the formalism to clinical case examples. Methods: From the standard biologically effective dose (BED) equation based on the linear-quadratic (LQ) model, the BED of an NT that receives a relative proportion r of the prescribed dose per fraction for a given α/β-ratio of the tumor, (α/β) T , and NT, (α/β) NT , is derived for different treatment schedules while keeping the BED to the tumor constant. Based on this, the "break-even" isodose line R is then derived. The BED of NT regions that receive doses below R decreases for more hypofractionated treatment schedules, and hence a lower risk for NT injury is predicted in these regions. To assess the impact of a linear behavior of BED for high doses per fraction (>6 Gy), we evaluated BED also using the LQ-linear (LQ-L) model. Results:The formalism provides the equations to derive the BED of an NT as function of dose per fraction for an isoeffective dose to the tumor and the corresponding break-even isodose line R. For generic α/β-ratios of (α/β) T = 10 Gy and (α/β) NT = 3 Gy and homogeneous dose in the target, R is 30%. R is doubling for stereotactic treatments for which tumor control correlates with the maximum dose of 100% instead of the encompassing isodose line of 50%. When using the LQ-L model, the notion of a break-even dose level R remains valid up to about 20 Gy per fraction for generic α/β-ratios and D T = 2(𝛼∕𝛽). Conclusions: The formalism may be used to estimate below which relative isodose line R there will be a differential sparing of NT when increasing hypofractionation. More generally, it allows to assess changes of the therapeutic index for sets of isoeffective treatment schedules at different relative dose levels compared to a reference schedule in a compact manner.

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

“…For the high‐dose region ( r = 1.0), predictions of W BE obtained by the LQ‐L model show an inverse trend for large d for all combinations of α / β ‐ratios evaluated in this work: after reaching a minimum W BE , W BE starts to increase again monotonously, sometimes reaching W BE > 1 (see Figure 3). This behavior is due to the transition from a linear‐quadratic to a linear behavior at d T and is consistent with results from previous studies for CONV treatments 15,17 . It suggests that a therapeutically unfavorable intermediate hypofractionation regimen may exist for high‐dose regions (roughly for d between 3 and 15 Gy for the evaluated α / β ‐ratios) and that NT sparing may improve again for d beyond this regimen.…”

“…A more detailed discussion of these aspects can be found elsewhere. 3,4,15 Comparing the magnitude of W BE to experimental evidence about the magnitude of NT sparing by the FLASH effect for a given d and α/β-ratios makes it possible to assess if there is a net benefit predicted by the presented formalism.The comparison of W BE obtained with the LQ model for generic α/β-ratios of (α/β) NT = 3 Gy and (α/β) T = 10 Gy and r = 1.0 to FMF from single fraction experiments presented in Figure 4 shows that the magnitude of most FMF is larger than W BE for d < 30 Gy. This implies that currently most of the performed mammalian NT studies achieved an NT sparing by FLASH for large single doses that is not sufficient to outperform the NT sparing obtained by a normofractionated CONV treatment as predicted by the LQ model for the generic α/β-ratios and r = 1.0, but some experimental FMF demonstrate that in principle magnitudes similar to W BE can be reached, at least for specific tissues and endpoints.…”

“…We define the “break‐even NT sparing weighting factor” W BE for an NT region at the relative dose level r of the prescribed dose to be the NT sparing factor required to compensate the change in radiobiological damage of the NT for a hypofractionated treatment compared to a normofractionated treatment that is equieffective for the tumor (see Figure 1 and Table 1). W BE follows the same concept as the break‐even isodose level for hypofractionated CONV treatments 15,19 . Its principle is illustrated by the following example calculations.…”

“…W BE follows the same concept as the break-even isodose level for hypofractionated CONV treatments. 15,19 Its principle is illustrated by the following example calculations. Consider a normofractionated CONV treatment of 30 × 2 Gy (i.e., n NF = 30, d NF = 2 Gy) and assume α/βratios of (𝛼∕𝛽) T = 10 Gy and (𝛼∕𝛽) NT = 3 Gy for tumor and late-reacting NT, respectively (hereafter referred to as "generic α/β-ratios").…”

“…The FLASH effect has been observed for large single fraction doses and some hypofractionated schedules with $$d \gg 2\;{\rm{Gy}}$$, 7,13,14 and it is well known that hypofractionated schedules, which are isoeffective for the tumor, often increase toxicities in critical late‐reacting NT 3,15 . Therefore, as long as no substantial FLASH NT sparing for normofractionated schedules can be demonstrated for clinically relevant scenarios, a potential issue for a clinical transfer of the FLASH effect is that for many clinical scenarios, a normofractionated CONV treatment scheme may result in a better clinical outcome than a hypofractionated FLASH treatment, in case the FLASH effect is not compensating for any increase in radiobiological damage to critical late‐reacting NT for the hypofractionated treatment schedule.…”