The interest in the dose reduction to the contralateral structures has been widely explored in the last years, aiming to minimize the increased risk of secondary cancer induction due to the low dose bath. The classical VMAT (as PartArc) cannot reduce the low dose at the level of the tangential beam setting. Over the last decade, many authors described the VMAT solution with two short arcs mimicking the tangential treatment fields [8,9,10,11,12]. Fogliata et al. [10] and Rossi et al. [9] implemented this technique using avoidance sectors, as described in the present work. The VMAT approach of reducing the en-face entrance of the primary radiation has been proven to be the most beneficial solution, especially concerning the contralateral structure irradiation. Different authors compared this solution to the classical solution of the dual partial arc of about 200–250° each. The ratio of the mean doses to the contralateral breast and lung between the "butterfly" and the classical VMAT with continuous arc can be determined from different published works. From Pasler et al. [13], the ratios were 0.60 and 0.37 for the contralateral breast and lung, respectively.

Similarly, the results from Maier et al. [14] presented ratios of 0.72 and 0.59, 0.56 and 0.39 in the case of FFF beams; Xi et al. [15] reported data leading to ratios of 0.67 and 0.54; Viren et al. [16] of 0.46 and 0.56, Fogliata et al. [10] had ratios of 0.27 and 0.19, for breast and lung, respectively. This approach, reducing the mean dose to the contralateral structures, can also reduce the risk of secondary cancer induction, as proven by Fogliata et al. [7]. Other studies evaluating the same risk using VMAT for breast treatments showed an increased risk with the classical VMAT technique [5, 6], but in those studies, there was no specific attempt in the contralateral dose reduction, as in Paganetti et al. [6], where among the planning goal there was the mean dose to the contralateral breast to be less than 7 Gy.

Other solutions aiming to mimic the dose distribution of the tangential beam setting did focus on hybrid solutions with various combinations of tangential 3D conformal or IMRT beams with VMAT [20, 21]. These approaches outlined the difficulty of breast planning, which might be enhanced for particular anatomies, where the full VMAT solution improves the quality of the resulting doses [29].

The application of KBP planning with RapidPlan to breast treatments has been explored by different groups, particularly in the last few years [30,31,32,33,34,35], showing interest in such an approach.

It is clear that, since the best selection of the portion of the arc en-face the breast depends on the patient's anatomy, there is interest in benefitting from the predictive power of the knowledge-based planning models. The ideal scenario is to define a workflow where, starting from simple geometry (e.g. the classical continuous partial VMAT arcs), the model predicts DVH estimations, especially for the contralateral structures, and then can guide the optimization engine to find the best solution (e.g. zeroing the dose rate where needed) to achieve the clinical aims.

This study presented some criticalities related to this approach. On the one hand, we analyzed the ability of the RapidPlan models to estimate the DVH of structures receiving dose purely from scattered radiation with the avoidance sectors application. On the other hand, the study evaluated the ability of PO to optimize the plan toward the estimation in the case where the information of the zero dose rate sector is missing.

In the present study, as shown in the regression plots of the RapidPlan models, the contralateral structures did not present a clear correlation between the geometric and the dosimetric features, with an angular coefficient close to zero (Figs. 2 and 3). This might be related to the fact that the most significant component of the dose to those organs is the scattering. In such conditions, the dose estimation accuracy can be inferior in the structures far from the target. Spruijt et al. [36], discussing the out-of-field doses in breast irradiation with flattened and FFF beams, pointed out that there is an underestimation of the out-of-field dose calculated with the AAA algorithm (a type “b” algorithm). Considering the dose to the contralateral structures, the type of calculation algorithm should be taken into account because it could affect both the DVH estimation and the final dose calculation.

Moreover, for the DVH estimation, a non-negligible part of the contralateral organs is partitioned as an “out-of-field” region, where the means-and-std concept is used instead of the PCA-regression model, and the final DVH estimation is obtained as the relative sum of each region of the partition, weighted by the corresponding relative volume. In addition, the direct reconstruction from the principal component scores obtained from the regression model in these "extreme" conditions of the OAR far from the target could produce a curve that is not monotonically decreasing. This might also contribute to the unexpected estimated DVH shape of the contralateral structures, as shown in the second row of Fig. 4.

The mean doses of the contralateral structures (and in part of the heart), estimated by the AvoidArcModel, were higher than the corresponding mean doses of the input plans (AvoidArc). This is not the case for the homolateral lung and all the PartArc structures estimated by the PartArcModel, where the mean estimated dose is generally lower than the original plans. The inability of the AvoidArcModel to estimate mean doses to the contralateral OARs as low as those of the input plans derives from the missing information on the avoidance sector. The control points in that sector are used, during the model generation, to determine the OAR in-field region (where the PCA-regression model is used), while a large portion of the OAR volume should instead be managed as an out-of-field region, with the simplified mean-and-std model. The presence of the avoidance sectors in the original plans seems to determine an inconsistency in the data extraction phase. The RP_Butterfly cases instead show consistency between the geometric and the dosimetric information leading to a DVH estimation that is compatible with the actual beam arrangement (the sectors with zero dose rate in the AvoidArc plans are sectors with no beam in Butterfly and RP_Butterfly plans).

The case of RP_VMAT, where the avoidance sector was not included in the optimization while the optimization objectives did, is particularly interesting. Here the contralateral structures were better spared than the RP_AvoidArc plans, although not as much as in RP_AvoidArc + Avoid. The reasons for these differences could be a too low priority generated by the model, combined with the fact that PO does not reduce the dose rate below 0.2 MU/°, limiting the possibility of decreasing the contralateral doses.

The beam geometry influences the DVH estimation. A proof also comes from the mean doses estimated for the contralateral structures (where this fact is more pronounced) by the same AvoidArcModel in the two conditions of the avoidance sector defined or not in the optimization phase for the same initial beam geometry. In the first case, with the avoidance sector, the mean estimated doses to contralateral breast and lung were 0.4 and 0.3 Gy, respectively. Values to compare with 0.6 and 1.6 Gy, respectively, of the estimations in the case of no avoidance sector defined.

In summary, the model is able to produce good and consistent DVH estimations relative to the input data only in the case where the beam geometry information is correctly extracted and used in the model training or if the planner manually adjusts the beam geometry (avoidance sector), but this confirms the need of such information to the DVH estimator.

Regarding the homolateral structures, once the proper geometrical information is assigned, as in the PartArc or Butterfly cases, the plans generated with RapidPlan outperform the original plans only for the structure with soft tissue density (heart), while this is not the case for the low-density organ (lung), as shown for example in Table 4. This reduced performance in low-density structures is not generated by the RapidPlan process (the DVH estimation is, in fact, lower than the input plans), while it should be sought inside the optimization. A possible reason might be related to the fact that the irradiation of the lung presents an important scatter component. This is mainly in DIBH patients, as in this work, where the lung density is lower, as shown in [37], where the mean mass density is reported to reduce from 0.27 g/cm3 in free-breathing condition to 0.16 g/cm3 in DIBH. In such a case, the dose calculation algorithm used during the optimization iterations is not sufficiently accurate to account for scattering.

The Photon Optimizer in Eclipse has a tool, other than the avoidance sector, called avoidance structure. Those structures where the tool is activated will be shielded by closed MLC when the structure is before the target in the beam's-eye-view or whenever its projection is in the beam's-eye-view (as different options). However, due to MLC limitations, there could be some unexpected apertures or small beams irradiating the selected contralateral structures, and the transmitted dose increases the structure dose. For that reason, in the presented study, the used avoidance tool was in terms of the sector (with no radiation in a defined gantry rotation interval) instead of structure (with MLC closing toward the specified structures). However, it could also be of interest to evaluate a model generated by plans using that avoidance tool.

In this work, no skin flash was applied, although breast VMAT plans in the clinical practice have to include it by adding a virtual bolus (or body expansion) and optimizing on a target expanded inside the bolus to take into account the missing CTV to PTV margin in the skin direction. The rationale for not applying this important step was to evaluate the optimizer's ability to reduce the dose rate without confounding factors arising from the skin flash adoption. The clinical need for the skin flash in VMAT planning remains clear. The RapidPlan models used in clinical practice should be generated starting from plans with virtual bolus and target expansion.

The limited number of patients used in this study was sufficient for the scope of the work, which was not a clinical use of the presented models. It is important to mention that a model configured for clinical purposes should better include a larger number of patients adequately selected.