To examine the fractionation problem in more detail, researchers from Massachusetts General Hospital and Harvard Medical School (Boston, MA) analysed the interdependence between the optimal fractionation scheme and spatial dose distribution. They went on to derive a criterion under which hypofractionation is indicated, using the biologically effective dose (BED) model (*Phys. Med. Biol.* **58** 159).

The BED is dependent on a tissue's α/β-ratio, where a small α/β-ratio implies high sensitivity to fractionation. For a homogeneously irradiated organ-at-risk (OAR), the BED model suggests that hypofractionation is optimal if the α/β-ratio of the OAR is larger than the α/β-ratio of the tumour multiplied by a sparing factor (the fraction of the delivered dose that's received by the OAR).

In this study, the authors extended this approach to consider inhomogeneous OAR dose distributions. "Hypofractionation has become a hot topic in radiation therapy and the BED model is the main concept for determining fractionation schemes," explained lead author Jan Unkelbach. "Almost all of the literature on optimizing fractionation schemes is based on a single dose level in the OAR. But in reality, OAR dose is inhomogeneous."

### Decision criterion

The researchers defined an effective sparing factor for use with inhomogeneous OAR dose. For a parallel OAR, this factor was derived by minimizing the integral BED in the OAR for a fixed tumour BED, and can be directly computed from the dose-volume histogram (DVH). For a serial structure, the researchers aimed to minimize the maximum BED in the OAR. Here, the effective sparing factor is equivalent to the maximum sparing factor over all OAR voxels.

The decision on whether to hypofractionate depends on both the effective sparing factor and the parameter *R*, which is the α/β-ratio of the OAR divided by the α/β-ratio of the tumour. According to the model, if the effective sparing factor is less than *R*, the optimal regimen is hypofractionation; if it is greater than *R*, then hyperfractionation is optimal.

The researchers applied this model to a lung cancer treatment, using lung tissue DVHs taken from three literature studies. The value of *R* was 0.4, taken from an α/β-ratio of 4 in normal lung (which represents a parallel OAR) and 10 in the tumour. One case compared DVHs for a 3D-conformal photon plan and a conformal proton plan for a lung tumour. Here, the effective sparing factor was 0.64 for photons and 0.7 for protons, suggesting that standard fractionation would be superior to hypofractionation in both cases.

In a comparison between a 3D-conformal radiotherapy and tomotherapy, the effective sparing factors were 0.66 and 0.41, respectively. This suggests that standard fractionation is best for the conformal plan, but that hypofractionation would be almost equally good for tomotherapy.

Finally, the team considered a planning study on stereotactic body radiotherapy (SBRT), examining the DVH for a volumetric-modulated arc therapy (VMAT) plan for a small tumour close to the chest wall. The effective sparing factor was 0.37, confirming the institution's decision that this patient was eligible for SBRT, i.e. hypofractionation.

The researchers concluded that, while it is often assumed that more conformal dose distributions justify hypofractionation, within the validity of the BED model, it is only optimal in specific situations. For example, the model supports hypofractionation for small tumours treated with rotational therapy. In this case, a large volume of lung tissue is exposed to low dose and benefits from hypofractionation, compensating for adverse effects in the high-dose region.

Conversely, hypofractionation is not necessarily optimal for proton therapy. This is because current proton techniques reduce the low-dose bath, thus reducing the volume of lung that benefits from hypofractionation, but don't lower the volume of lung exposed to high doses.

Unkelbach notes that it should be easy to introduce this decision process into the clinic. "It only requires that the effective sparing factor is evaluated for the given dose distribution," he explained.

The team is now working towards a more complete understanding of optimal fractionation, as well as examining simultaneous optimization of dose distributions and fractionation. "This gives rise to non-uniform fractionation schemes in which it can be beneficial to deliver treatment plans that vary from fraction to fraction," Unkelbach told *medicalphysicsweb*. "In the long term, we aim to extend this to a framework for spatio-temporal radiotherapy planning in which dose delivery is optimized not only spatially but also over time."