20 brain metastases out of 17 patients recently treated in our institution were chosen for the study. Lesions were selected to cover the full range of tumor sizes defined in protocol 90–05 of the Radiation Therapy Oncology Group (RTOG). No critical structures were in close proximity. Immobilized in a stereotactic mask (Brainlab AG, Feldkirchen, Germany) the patients had been scanned with a computerized tomography slice thickness of 1.25 mm. In the treatment planning system (Raystation9b, RaySearch Laboratories AB, Stockholm, Sweden), GTV and relevant organs at risk including whole brain were contoured based on a co-registered T1-weighted contrast-enhanced magnetic resonance image series. PTV was constructed from GTV by adding an isotropic margin of 3 mm. The margin is still within the recommendations of the national stereotactic radiotherapy working group [12]. It is necessary despite the use of a stereotactic mask and daily image guidance because of geometric inaccuracies of our imaging system (Elekta XVI cone beam computerized tomography) and the treatment device (Synergy, Elekta Solutions AB, Stockholm, Sweden) with 5 mm leaf width in isocenter distance. PTV sizes ranged from 1.4 to 29.5 cm3 (median 7.4 cm3) corresponding to equivalent effective diameters of isovolumetric spheres from 1.4 to 3.8 cm (median 2.4 cm).

Treatment planning was performed on anonymized patient data. Four experienced planners were asked to prepare a plan for 10 lesions each, following the guidelines in Table 1. To avoid bias, each planner only worked according to either the 80% concept or the SIB concept, so that in the end there were two plans from two different planners for each lesion. Care was taken to randomly assign the lesions such that each of the four possible combinations of planners occurred an equal number of times. In the planning system, per lesion two separate cases had been created for the two concepts. Additionally, the two planners assigned to the 80% concept were not familiar with the SIB concept. To reflect clinical practice, treatment technique was left to the planners’ own choice. With inverse planning, however, effort was to be made to mimic a dose distribution that is characteristic of 3D conformal radiotherapy. In no case, the dose maximum was to lie outside the GTV. Dose was calculated with collapsed cone algorithm in a 1 mm (isotropic) dose grid. A recalculation with a Monte Carlo dose engine was not necessary, because the Monte Carlo algorithm does not yield different results in the soft tissues of the brain. As this was a planning study, we did not perform dosimetric verification of inverse modulated plans as is normally done with Octavius 4D combined with Detector 1600 SRS (PTW Freiburg, Germany).

The following data were collected from each plan: Technical information (treatment technique, beam quality, number of arcs, number of monitor units and segments), dose-volume histogram parameters of PTV (D98%, D50%, D2%, Dmax, V35Gy), GTV (D98%, Dmean, D2%, Dmax), PTV without GTV (D2%), and whole brain (V24Gy as a predictor for RN). For the GTV, a heterogeneity index HI was calculated as

$$}}(GTV)=\frac}}_}-}}_}}}}_}}(GTV)$$

(1)

Furthermore, as recommended by Wilke et al. [10], a high dose conformity index according to Paddick, CIPaddick, was assessed for the PTV

$$}}}_}}}}}}}}=\frac}}_}}}\left(PTV\right)\right)}^}}}_}}}\cdot }}_}}}}}$$

(2)

V35Gy (PTV), V35Gy and VPTV denote the volume of the PTV inside the 35 Gy-isodose, the complete volume inside this isodose and the volume of the PTV, respectively. As a measure for the dose fall-off outside the PTV, we assessed the spatially averaged dose gradient SADG* proposed by Wösle in 2018 [13]. SADG* is the spatially averaged dose difference quotient in radial direction between isodose surfaces D1 and D2. Its unit is Gy/mm or %/mm.

$$}}}}}^}_}}_}^}}_}=\frac}}_-}}_}}}_-}}_\right)}_}}}}}= \frac}}_-}}_}_}<0$$

(3)

In [14], a simple method for its determination is provided: The PTV is modelled as an ellipsoid, and two concentric, equidistant ellipsoids are fitted to the isodose surfaces D1 and D2 by Newton’s iteration method to obtain ΔrΔD. This algorithm was implemented by one of us into the planning system by means of a script. For D1 the PTV-enclosing isodose value 35 Gy and for D2 half of it, 17.5 Gy, were chosen.

As a null hypothesis, we assumed that the two concepts, 80% and SiB, were equal. To judge the differences of the plan pairs, the Wilcoxon matched pairs signed rank test (two-sided) was employed [15] using Statistica (StatSoft, Tulsa OK, US). As V24Gy(brain) strongly depends on PTV size, a trend line was calculated first, and the differences of V24Gy(brain) between the two concepts were normalized to this trend line before applying the test.