# TDF Plan: Hypofractionation

### Constant total dose:

Consider a standard fractionation regimen consisting of 30 fractions of 200 cGy. The total dose = 60 Gy. Ignoring tumor repopulation and assuming generic α/β ratios of 10 for acute and 3 for late reactions, the BED(acute) = 72.0 Gy(10.0) and BED(late) = 100.0 Gy(3.0). If the absolute dose is held constant at 60 Gy, using fewer fractions to deliver the 60 Gy causes the dose/fraction to increase, while increasing the number of fractions causes the dose/fraction to decrease. The consequences of these changes are illustrated in the figure below. For constant total dose, biological effect is inversely proportional to the number of fractions. For instance, increasing the number of fractions to 40 x 150 cGy (blue highlight) decreases the BED(acute) by 4% to 69.0 Gy(10.0) and decreases the BED(late) by 10% to 90.0 Gy(3.0). For hypofractionations, 60 Gy delivered as 20 fractions of 300 cGy (green highlight) increases the BED(acute) by 8% to 78.0 Gy(10.0) and increases BED(late) by 20% to 120.0 Gy(3.0) compared to the standard 30 x 200 cGy regimen. Therefore, using fewer fractions to deliver the same total dose results in increased BED which presumably means more severe biological effect. The magnitude of the relative increase in biological effect is also inversely proportional to α/β, ie the severity of late sequellae to normal tissues with low α/β increases more rapidly than the severity of acute reactions in the tumor.

The inverse relationship between biological effect to normal tissue and number of fractions is the basic rational for fractionated therapy. Of course, as the number of fractions increases the economic and logistical costs of therapy become greater, and if the number of fractions becomes too great, then tumor repopulation becomes an issue. Hypofractionation is therefore of perpetual interest to the practice of radiation therapy because of its potential to reduce costs, but has historically been discouraged due to the increasing severity of late sequellae. The advent of technologies such as IMRT and SBRT which surround the tumor with a steep dose gradient and thereby allow large doses to be delivered to the tumor while simultaneously sparing the surrounding tissue now make hypofractionation plausible. In the plot on the right, BED for constant total dose of 60 Gy is plotted for α/β of 3 (blue) and 10 (red). The heavy solid lines are the linear-quadratic-linear (LQα/β-LDT) model with DT = 2α/β (for an explanation of the LQ-L model and hypofractionation follow this link: linear-quadratic models). The dashed lines are the conventional linear-quadratic (LQ) model. The conventional LQ model is thought to overestimate the severity of reactions at high dose per fraction because it does not accurately model the experimentally observered linear-quadratic-linear dose-response at high dose. The LQ-L curves may be a better estimate of biological effect with fractions of high dose. In TDF Plan, the conventional LQ model is used when the course modality is EBRT. The LQ-L model is used whenever the course modality is SBRT or SRS. Course modality is set from the modality popup menu in the IMR group. | This figure plots BED for constant total dose of 60 Gy for α/β of 3 (blue) and 10 (red). The heavy solid lines are the linear-quadratic-linear (LQα/β-LDT) model with DT = 2α/β (for an explanation of the LQ-L model and hypofractionation follow this link: linear-quadratic models). The dashed lines are the conventional linear-quadratic (LQ) model.

### Constant acute and late effects:

When changing the number of fractions compared to some reference regimen (e.g. 30 x 200 cGy), one might opt to deliver either equivalent acute biological effect to the tumor (ie maintain the same probability of tumor control) or to constrain late sequellae by delivering the same biological effect to the late responding tissues. This is illustrated in the tables above and the figure to the right. Reopopulation effects have been ignored in these examples. In these figures it is assumed that we have an acutely responding tumor with α/β = 10 and late responding normal tissues with α/β = 3. Above we see that courses of (20 x 281 cGy), (30 x 200 cGy) and (40 x 156 cGy) all deliver equivalent acute biologically effective doses of 72 Gy(10.0). Presumably this results in equivalent tumor control. However, reducing the number of fractions from (30 x 200 cGy) to (20 x 281 cGy) increased the late biological effectiveness from 100.0 Gy(3.0) to 108.8 Gy(3.0). Conversely, using 40 fractions instead of 30 reduces late effects. This is also illustrated in the figure on the right. Plotted in blue, we see that for constant acute reactions equivalent to 72 Gy(10.0), the LQ model predicts that increasing the number of fractions decreases late reactions and reducing the number of fractions increases late reactions. The following discussion is a hypothetical implication of LQ-L dose-response under specific circumstances and must not be applied to any clinical situation: Please read Some implications of linear-quadratic-linear radiation dose-response with regard to hypofractionation for a more comprehensive explanation. If, however, and only if, the low α/β reactions exhibit LQ-L behavior, the LQ-L model with DT = 2α/β predicts that the relative severity of LQ-L late reactions could hypothetically peak at 5 fractions because below this number of fractions the dose per fraction which results in constant tumor control exceeds DT of the lower α/β tissues (6 Gy) for which response has become linear (on the log-linear plot). Below 5 fractions, as the number of fractions decreases, the dose per fraction required to maintain constant tumor control certainly continues to increase, but the dose-response curve for the higher α/β tumor continues bending downward being driven by the βD2 quadratic term. It may not become linear until about 20 Gy. The result is that the response of the high α/β tumor could become relatively more severe compared to the response of low α/β tissues for which dose-response is now linear. Courses of (20 x 265 cGy), (30 x 200 cGy) and (40 x 162 cGy) all deliver equivalent late biologically effective doses of 100 Gy(3.0). Using 20 fractions instead of 30, however, decreases acute biological effect from 72.0 Gy(10.0) to 67.1 Gy(10.0). Using 40 fractions instead of 30 increases the acute effects to 75.6 Gy(10.0). This is also illustrated in the figure on the right. Plotted in red, we see that for constant late reactions equivalent to 100 Gy(3.0), the LQ model predicts that increasing the number of fractions increases the acute biological effects or conversely using fewer fractions reduces acute reactions. The LQ-L model in this case predicts behavior converse to that observed for the constant acute effects. |

### Benefits of steep dose gradients:

The examples above assume that both the acute and late responding tissues receive the same relative dose/fraction as the reference regimen. If, however, the dose/fraction delivered to the late responding (e.g. normal) tissues surrounding the tumor can be reduced compared to the reference regimen by collimation and sophisticated intensity modulation (e.g. IMRT, CyberKnife, etc...) without reducing the dose delivered to the tumor, one can use fewer fractions of higher dose per fraction without exceeding normal tissue tolerances. For example, lets assume that the steeper dose gradient outside the target volume made possible by IMRT and/or radiosurgery treatment modalities reduces the dose to normal tissue surrounding the target volume by only 6% compared to what it would have been for the historic reference regimen when normal tissue tolerance was established. Nearby normal tissue that in the past might have received the full 30 x 200 cGy regimen would now be receiving 30 x 188 cGy/fraction instead. Plotted in the figure on the right we see that a 6% dose reduction causes the BED(3.0) for late effects for a 20 fraction regimen to match the BED(3.0) of the 30 fraction reference regimen (darker blue). So in this case we might be able to reduce both the number of fractions and the severity of late reactions compared to the historic reference regimen. |

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