In the following section, we analyze all target volumes nonregarding the number of metastases per patient to determine differences in the various scenarios for a flattened 6 MV beam without further dependence on the number of treated lesions per plan.

Whenever additional arcs were allowed, the TPS indeed made use of these additional degrees of freedom. Thus, for scenario 1 and 3, i.e., when no extra arcs were allowed, the overall minimum number of used arcs was 7. For scenario 2 and 4, i.e., with extra arcs, at least 11 and 12 arcs were used, respectively. The maximum was 14 arcs for all scenarios, which is also the largest possible number of arcs.

Despite this fact, the number of monitor units (MU) is not significantly different between the scenarios. Mean values range between 11,434.0 ± 6067.6 MU and 12,183.9 ± 6250.7 MU, the minimum is between 5339.0 MU and 5757.0 MU and maximum values fall between 24,770.0 MU and 32,472.0 MU. Maximum values were all attained for the same patient (patient #17, 28 metastases) for all four scenarios. The left-hand side of Fig. 2 shows the number of monitor units per scenario for all metastases.

Boxplots showing the number of monitor units needed for the different scenarios for all plans and the subgroups separately. There was a significant difference between scenario 1 and 2 in subgroup B. (*p = 0.036)

Increasing the margin as a function of the GTV-to-isocenter distance (scenario 4) significantly increases the mean cumulative volume of PTVs from 3.35 cm3 to 4.89 cm3 (p < 0.001).

Volume coverage was evaluated using the dose covering 99% of the PTV, i.e., D99%. The minimum D99% within all scenarios was 20 Gy, which was input as an obligatory objective and was always satisfied in the optimization due to the planning technique.

No significant differences in global V12Gy were found in the comparison of scenario 1 vs. 2, and 1 vs. 3, respectively. Cumulative V12Gy for scenario 4 with a mean value of 23.57 cm3, however, was significantly higher (p < 0.00013) when compared with scenario 2 with a mean V12Gy of 17.78 cm3, which is plausible, considering that the target volumes are significantly larger. A visualization of this data is shown in Fig. 3.

Boxplots showing the cumulative V12Gy of the healthy brain minus planning target volume (PTV) for the different scenarios for all plans and the subgroups separately. (* significant at p < 0.05)

For sparing of the hippocampus, there was no significant difference for the mean or maximum dose when comparing the scenarios 1 vs. 2 or 1 vs. 3. However, for scenarios 2 vs. 4 we saw a significantly different mean dose, where scenario 2 yielded lower doses to the hippocampus (2.13 ± 1.84 Gy) than scenario 4 (2.35 ± 1.64 Gy, p = 0.013). The different subgroups show a tendency to higher mean doses the larger the number of lesions is per plan. This is plausible as the overall dose in the brain, i.e., the low-dose bath, rises the more metastases are irradiated.

In scenario 4, the maximum dose was 4.57 ± 3.82 Gy which compared to 4.04 ± 3.98 Gy in scenario 2 was significantly higher (p = 0.004). This effect is once again caused by the larger target volumes in scenario 4.

Adding arcs or changing the DCA complexity did not result in better local Paddick CI. In contrast, margin increase showed a slight but statistically significant improvement from an average local CI of 0.61 for scenario 2 to 0.67 for scenario 4 (p < 0.0001) as shown in Fig. 4. Figure 4 also shows gradient indices which were similar for scenario 1 vs. scenario 2, whereas for comparison of scenario 1 and 3 a significant increase from an average local GI of 5.98 in scenario 1 to 6.15 in scenario 3 was found (p < 0.0005). Increasing the margin in scenario 4 improves the average local GI to 5.31 compared to 5.97 in scenario 2 (p < 0.0001). Global CI and GI values were slightly different for the scenarios as shown in Table 3. While the mean global GI was better in scenario 1 compared to scenario 3, a better CI was achieved in scenario 3. Again, coming from the larger target volumes, the best CI and GI values were reached for scenario 4.

Boxplots showing the Paddick conformity index (CI), gradient index (GI), the number of missing GIs and the normalized number of missing GIs for the different scenarios for all plans and the subgroups separately. (* significant at p < 0.05)

Due to the leaf width, sufficient coverage is more easily achievable for larger target volumes, resulting in a steeper gradient (i.e., GI closer to 1) in scenario 4 compared to the smaller margin approaches.

The system is unable to generate a GI whenever the 50% isodoses (in this case 10 Gy) of two or more metastases overlap. We used this information to obtain a parameter for “dose bridges”, regions of isodose confluence between two metastases by counting the number of missing GIs.

Figure 4 shows that while this parameter is similar when looking at all metastases, there was a tendency for the subgroups to have more dose bridges the more metastases were planned with a single isocenter, which is plausible given the larger number of lesions and resulting closer spatial proximity (and also, possible statistical permutations). Therefore, we additionally considered a scaled value by dividing the number of dose bridges by the number of metastases within a single plan.

In order to get a better idea of the low dose distribution, we then evaluated the volume that had received 10% of the prescribed dose (V10%). Addition of arcs did not significantly change the V10%, but increasing the DCA complexity to a maximum in scenario 3 (427.72 ± 437.95 cm3) resulted in a 4% higher V10% compared to scenario 1 (453.39 ± 430.2 cm3, p = 0.0024). Scenario 4 reached a V10% of 514.4 ± 466.82 cm3 which was more than 10% higher compared to scenario 2 (464.28 ± 440.88 cm3, p < 0.0001). An example of how much the different scenarios (2–4) affect the low dose distribution is presented in Fig. 5.

Dose distribution of a patient with 17 lesions for plans according to the scenarios 2, 3 and 4 with an energy of 6 MV (upper row) and scenarios 2 and 3 for 6 MV flattening filter free beams (FFF; lower row). The effects of a larger margin in scenario 4 for more distant metastases can be seen for the lesion in the left hemisphere

In the following section, the target volumes within each subgroup were examined to evaluate differences according to the number of lesions within a single plan. Since the changes for scenario 4 are consistent for all groups, arising from the larger PTV sizes and not from a change in planning settings, we just consider scenarios 1–3 in this comparison.

For 3–5 metastases, a median of 8 arcs was used in scenarios 1 and 3, and significantly more (p = 0.008) in scenario 2, where in median 12 arcs were used. This addition did not significantly improve the quality of the plans in terms of monitor units, dose coverage and overdose. We found a significant difference in D99% for scenario 1 vs. 3 (p < 0.017), but this difference would not be clinically relevant as it only amounts to an absolute difference of less than ±0.1 Gy for the mean values.

Local Paddick CI and GI were not improved by additional arcs only (scenario 1 vs. 2). Comparison of scenarios 1 and 3 showed slight improvement in CI (from 0.73 ± 0.08 to 0.74 ± 0.09 in scenario 3, p = 0.05); on the other hand GI increased (from 4.67 ± 1.23 to 4.88 ± 1.18 in scenario 3, p = 0.019).

Of all subgroups, we saw the least isodose overlaps in this group. This is associated with the lower number of lesions, since the number of missing GIs rises with the number of metastases (Fig. 4).

This subgroup did not differ in V10% for scenarios 1, 2 and 3. Mean values were 142.15 ± 119.78 cm3, 141.22 ± 134.34 cm3 and 147.15 ± 132.35 cm3, respectively. Likewise, for global V12Gy there were no significant differences between scenarios 1 vs. 2 and 1 vs. 3.

Only subgroup with 6–10 metastases showed a significant difference in MU for the comparison of scenario 1 with 2. Here, a significant increase from an average of 9597.83 MU to 12,546.83 could be observed, which however did not influence the dosimetric plan quality.

Neither of the modifications in the different scenarios improved global V12Gy.

The cumulated volume of the normal tissue exposed to low dose irradiation (global V10%) increased from 352.10 ± 83.73 cm3 in scenario 1 to 383.57 ± 72.51 cm3 in scenario 3 when the DCA complexity was limited (p = 0.036), while addition of arcs did not change the V10%. Increased PTV margins again lead to a greater volume of 431.14 ± 132.15 cm3 compared to scenario 2 (369.24 ± 88.78 cm3, p = 0.036).

For plans with 6–10 metastases, on average half of the lesions shared the 50% isodose with one or more other lesions, regardless of which scenario was chosen. As shown in Fig. 4, there was no difference in the number of missing GIs.

Looking at the different scenarios for this subgroup with 11 or more metastases, a minimum of 10 and a maximum of 14 arcs was necessary for optimization of each plan.

We found no significant difference in D99% between scenarios 1 and 2. Allowing additional arcs did not improve coverage or increase the number of arcs, as the maximum number of arcs was already exhausted. Also, no significant differences regarding monitor units were observed. As the number of lesions is very high, restriction of DCA complexity does not seem to have an impact on the number of monitor units in these cases. A statistically significant difference in D99% was found between scenarios 1 and 3 (20.43 ± 0.37 Gy for scenario 1 vs. 20.34 ± 0.40 Gy for scenario 3, p = 0.032); however, this again would not be deemed clinically relevant.

Considering quality indices, the local GI was found to be significantly higher for scenario 3 (7.66 ± 1.71) compared with scenario 1 (7.36 ± 1.17, p < 0.005).

The V10% was similar for all scenarios, with an average value between 1135.15 ± 165.15 cm3 for scenario 1 and 1165.73 ± 136.75 cm3 for scenario 3. On average more than half of the lesions shared the 50% isodose with one or more other metastases, regardless of the scenario and without statistically significant differences.

After replanning, we compared scenario 2 and 3 regarding the difference arising from applying a flattening filter free beam of the same photon energy.

With 6X FFF, global V12Gy decreased significantly compared with the according 6X plans. On average scenario 2 yielded an 8.1% lower V10Gy (25.39 cm3 for 6X and 23.33 cm3 for 6X FFF, p < 0.001) and a 7.5% lower V12Gy (28.74 cm3 for 6X and 26.58 cm3 for 6X FFF, p = 0.0014) for FFF vs. flat beams. Yet no difference was apparent in the V10% data.

There was no significant difference in local GIs between the 6X and 6X FFF plans, regardless of which scenario was used. Scenario 3 did not produce significantly different local Paddick CIs for the two energies, but for scenario 2 the difference was significant (p < 0.001) with a mean CI of 0.61 for 6X and a slightly lower mean Paddick CI of 0.60 for 6X FFF (statistically significant, but not clinically relevant).

For both scenarios, the number of monitor units increased for the FFF beam. While for a flattened beam on average 12,159.85 ± 6261.43 MU for scenario 2 and 12,265.40 ± 7328.33 MU were necessary, for an FFF beam the number rises by 14.7% for scenario 2 (13,951.15 ± 7573.42 MU, p < 0.001) and 13.1% for scenario 3 (13,866.45 ± 8612.68 MU, p < 0.001). The maximum number of monitor units was reached for scenario 3 and 6X FFF with 38,263 MU (patient #17, 28 metastases).

The number of monitor units needed for 6X FFF compared with 6X increases in dependence of the maximum distance from the center of the lesion to the isocenter, i.e., the field size. This is shown in Fig. 6.

Number of monitor units needed for 6X FFF compared with 6X and number of monitor units needed for 6X FFF divided by the number of monitor units for 6X in dependence of the distance from the center of the lesion to the isocenter

To determine to what extent the increased amount of monitor units for the FFF plans is counteracted by the higher dose rate, we measured the actual treatment time on our linac for a representative subset of plans. The flattening filter free plans required approximately half of the total delivery time for treatment compared to the regular 6X plans, for example 13.95 min instead of 26.55 min and 16.85 min instead of 31.85 min (patient #16 with 6 metastases and patient #7 with 17 metastases, respectively).