MLC‐based penumbra softener of EDW borders to reduce junction inhomogeneities

Abstract Junctions of fields are known to be susceptible to developing cold or hot spots in the presence of even small geometrical misalignments. Reduction of these dose inhomogeneities can be accomplished through decreasing the dose gradients in the penumbra, but currently it cannot be done for enhanced dynamic wedges (EDW). An MLC‐based penumbra softener was developed in the developer mode of TrueBeam linacs to reduce dose gradients across the side border of EDWs. The movement of each leaf was individually synchronized with the movement of the dynamic Y jaw to soften the penumbra in the same manner along the entire field border, in spite of the presence of the dose gradient of the EDW. Junction homogeneity upon field misalignment for side‐matched EDWs was examined with the MV imager. The fluence inhomogeneities were reduced from about 30% per mm of shift of the field borders for the conventional EDW to about 2% per mm for the softened‐penumbra plan. The junction in a four‐field monoisocentric breast plan delivered to the Rando phantom was assessed with film. The dose inhomogeneities across the junction in the superior‐inferior direction were reduced from about 20% to 25% per mm for the conventional fields to about 5% per mm. The dose near the softened junction of the breast plan with no shifts did not deviate from the conventional plan by more than about 4%. The newly‐developed softened‐penumbra junction of EDW (and/or open) fields was shown to reduce sensitivity to misalignments without increasing complexity of the planning or delivery. This methodology needs to be adopted by the manufacturers for clinical use.

and machine uncertainties on the dose distribution in the junction region were described, e.g., by Holupka et al. 1 and Rosenthal et al. 2 The impact on the dose volume histograms (DVH) of the uncertainties of the jaw positions in the junction in the four-fields monoisocentric breast radiotherapy was discussed recently by Hedin et al. 3 Fraas et al. utilized a match-line physical wedge to soften the gradients in the penumbra of diverging fields forming a junction, 4 while Sohn et al. used a similar concept (referred to as a physical penumbra modifier) to smooth out heterogeneities of the junction of abutting fields. 5 Shackford et al. softened the dose gradient of the penumbra by dynamically moving the jaws, and implemented this technique for the open fields in craniospinal treatment. 6 Hong et al. used overlapping IMRT-planned regions instead of a side-by-side matching of diverging fields. 7 Yom et al. employed field-in-field homogenization together with interfraction isocenter shifts to homogenize the dose distribution at the junction of diverging fields. 8 Application of the feathering concept to craniospinal irradiation by using three isocenters without beam edge matching was described by Cao et al. 9 Duan et al. described a technique of smoothing the junction between an open field and IMRT fields. 10  Zeng et al. 11 extended the technique of Duan et al. 10 to facilitate use of IMRT only, without a need for (nominally) static fields. The IMRT fields on one side of the (slightly overlapping fields) junction were optimized first using dose objectives with the doses stepped between 80% and 20%, followed by the entire-region optimization with the fields from the first optimization used as the base plan.
Garcia et al. applied the concept of stepped doses in sub-PTVs to longitudinally adjacent PTVs treated with helical TomoTherapy. 12 Wu et al. split the desired intensity (generated through optimization) in a large IMRT plan into two (or more) slightly overlapping intensity distributions such that the intensity in the junction area would be gradually reduced to zero in each region, and used the leaf sequence generator to obtain the leaf sequences. 13 The techniques described above add to the complexity of the plans. Moreover, most of them cannot be applied to junctions of fields employing enhanced dynamic wedges (EDW). 14 While inverse planning is often preferred, it is not always possible or practical. In some cases, 3D conformal radiation therapy (3DCRT) is practically as good as IMRT or VMAT, but allows reducing the monitor units (MU) and reducing the dose to healthy tissue. 15 In this paper we describe development of an MLC-based penumbra softener for 3DCRT that can be used concurrently with delivery of a combination of EDW and open fields. This design is an extension of the idea of a physical penumbra modifier, but we employ the MLC to dynamically modify the fluence instead of using a physical modifier. Use of the MLC instead of a physical modifier eliminates the need to mount the modifier at the gantry when softer penumbra is desired. The proposed solution was designed to restrict the magnitude of the dose dip or peak at a junction under 1 mm misalignment to no more than about 5%. This design goal was loosely based on the ICRU 50 recommendation to keep the dose in the PTV within 95% and 107% of the prescribed dose, 16 and the TG142 recommendation for the jaw position indicators, as well as the gantry or the collimator rotation isocenter being accurate within AE1 mm. 17

| MATERIALS AND METHODS
The softened penumbra fields and the conventional fields (except for the conventional fields used in the four-field breast plan) were deliv-

2.A. | The design
In a typical junction of static fields, reduction of sensitivity to misalignment from the nominal position (where the positions of 50% fluence coincide for both fields) can be accomplished through widening the penumbra of the individual fields. This is illustrated in Fig. 1 for the given amount of misalignment of one of the fields, doubling the width of the penumbra reduces the dip in the dose by a factor of two. For static fields for which jaws are used as the field borders facing the junction, increasing the penumbra width to the value of 2D can be achieved by moving (at constant velocity) the jaw forming the field border at the junction from x 0 À D to x 0 + D, where x 0 is the center of the junction. This strategy does not work for side matching of EDW fields. The problem is explained in Fig. 2 for the junction at x = 0. Initially, the X jaw is retracted from the field by D. The X jaw starts moving into the field as the dynamic Y jaw (from EDW) begins closing, and the X jaw completes the movement at x = ÀD when the dynamic Y jaw completes its movement at y = 'E'. The corresponding fluence profile across the x direction at y = 'E' is shown in Fig. 2(b) together with the fluence profile of the mirrored field that forms the junction, as well as the sum of the fluences. The summed-fluence profile is flat, i.e., a perfect junction is obtained. Unfortunately, the summed fluence profile is not flat at other y positions, and an example of a highly non-uniform summed profile is shown in 2D-wide penumbra centered at x = 0 for any value of y (let's call it y i ), the portion of the X collimator at y = y i needs to move from x = D to ÀD, but at a modified time sequence. Movement of this portion of the X collimator needs to be completed precisely at the instant t i when the dynamic Y jaw begins to over-shadow it. Considering t i depends on position y i , to provide independence of the penumbra width on y i , velocity, v i , of movement of each portion of the X collimator must be: This necessitates dynamic bending of the X collimator, see Fig. 3.
We obtained the dynamic bending effect by employing the MLC.
As in the conventional EDW, 14 where the open phase ends at MU 0 , and velocity c 0 of the leaf is While all leaves will finish their movement at the junction center minus D (the start position of the entire sequence), they will not complete the movement simultaneously. As explained earlier, each section of the bendable collimator, i.e., each leaf, needs to move from x = D at the start of the dynamic phase to x = ÀD at the instant when the dynamic Y jaw over-shadows the leaf. To accomplish this, the velocity c i of leaf i should be: where the dynamic phase begins at MU 0 and the dynamic Y jaw overshadows the leaf i at MU i . This is illustrated in Fig. 4(c): the leaves at y = À9.75 cm, À9.25 cm and À8.75 cm have completed their movement (after being over-shadowed by the Y1 jaw) and the leaves at y > À8.75 cm continue traveling to their final destination.
In both phases the X2 jaw trails 0.25 cm behind the slowest-moving leaf in order to reduce the inter-leaf leakage.
While the main concept is explained above, below are additional details:Because the width of each leaf is non-zero, the MU when the dynamic Y jaw is over-shadowing a given leaf is not uniquely defined. We defined such MU when the dynamic Y jaw meets the center of the leaf.    Table 1, and drawn in Fig. 6  In contrast, the discrepancy for the conventional junction is much larger, see Figs. 8(b) and 8(d), and is about 30% for 1 mm of The fields used in the conventional four-field monoisocentric (right) breast plan delivered to Rando phantom covered anteriorly with layers of superflab to the total thickness of 3 cm. The nominal values in the softened penumbra plan are the same, but the junction-side X border of every field is softened AE2 cm sup-inf from the monoisocenter.   The process reserves an option to switch to the conventional approach.
While the dose distribution across the junction of the softenedpenumbra junction is close to the distribution from a conventional plan, it is not identical. This should not be a problem clinically, as it is the plan with the softened penumbra that is to be evaluated for meeting the plan objectives, including dose heterogeneity inside the PTV within À5% and 7% of the prescribed dose, and absence of hot spots. In some cases, the softened-penumbra plan may be actually   Softened penumbra field borders might also be considered when disease progresses, and a larger PTV might be needed in the future.
This would happen when treating a breast as tangents, with a possibility of treating the axillary nodes in the future: the superior borders of the tangents would be softened out initially, and the nodal fields with softened inferior borders would be added in the future when required.
Half-body irradiation could also benefit from this approach through reduction of junction artifacts upon matching the opposite body half in the future. Ideally, the fields would be delivered under extended source-to-skin distance (SSD) with rotated couch to keep the (future) junction in the axial plane, and subfields would be employed to even Softened-penumbra fields might also improve junction quality for junctions that are not geometrically matched, e.g., when large fields are delivered without couch rotation, and the fields are only matched at a single depth, e.g., at the skin.

ACKNOWLEDGMENTS
The authors thank Mr Dave Moreau for assistance with technical writing.

CONFLI CT OF INTEREST
A provisional patent for the design was filed with USPTO.