Improved electron collimation system design for Elekta linear accelerators

Abstract Prototype 10 × 10 and 20 × 20‐cm2 electron collimators were designed for the Elekta Infinity accelerator (MLCi2 treatment head), with the goal of reducing the trimmer weight of excessively heavy current applicators while maintaining acceptable beam flatness (±3% major axes, ±4% diagonals) and IEC leakage dose. Prototype applicators were designed initially using tungsten trimmers of constant thickness (1% electron transmission) and cross‐sections with inner and outer edges positioned at 95% and 2% off‐axis ratios (OARs), respectively, cast by the upstream collimating component. Despite redefining applicator size at isocenter (not 5 cm upstream) and reducing the energy range from 4–22 to 6–20 MeV, the designed 10 × 10 and 20 × 20‐cm2 applicator trimmers weighed 6.87 and 10.49 kg, respectively, exceeding that of the current applicators (5.52 and 8.36 kg, respectively). Subsequently, five design modifications using analytical and/or Monte Carlo (MC) calculations were applied, reducing trimmer weight while maintaining acceptable in‐field flatness and mean leakage dose. Design Modification 1 beveled the outer trimmer edges, taking advantage of only low‐energy beams scattering primary electrons sufficiently to reach the outer trimmer edge. Design Modification 2 optimized the upper and middle trimmer distances from isocenter for minimal trimmer weights. Design Modification 3 moved inner trimmer edges inward, reducing trimmer weight. Design Modification 4 determined optimal X‐ray jaw positions for each energy. Design Modification 5 adjusted middle and lower trimmer shapes and reduced upper trimmer thickness by 50%. Design Modifications 1→5 reduced trimmer weights from 6.87→5.86→5.52→5.87→5.43→3.73 kg for the 10 × 10‐cm2 applicator and 10.49→9.04→8.62→7.73→7.35→5.09 kg for the 20 × 20‐cm2 applicator. MC simulations confirmed these final designs produced acceptable in‐field flatness and met IEC‐specified leakage dose at 7, 13, and 20 MeV. These results allowed collimation system design for 6 × 6–25 × 25‐cm2 applicators. Reducing trimmer weights by as much as 4 kg (25 × 25‐cm2 applicator) should result in easier applicator handling by the radiotherapy team.


| INTRODUCTION
Our cancer center has seven Elekta Infinity radiotherapy accelerators (MLCi2 treatment head) with custom electron beams spanning 7-20 MeV (R 90 values of 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, and 6.0 AE 0.1 cm) and having slightly modified scattering foils. 1,2 Their in-field (depth dose and beam flatness) and out-of-field (leakage) dose distributions are well suited for radiotherapy; however, our clinic feels there is opportunity for improved delivery technology by reducing electron applicator weights. Table 1 shows Elekta applicators are considerably heavier than comparable Varian applicators, primarily due to their trimmer weights.
Therefore, this study's purpose was to develop a methodology for designing electron collimation that produces Elekta applicators weighing no more than comparable Varian applicators. We have produced X-ray jaw settings and trimmer designs for a set of five applicators (6 9 6, 10 9 10, 14 9 14, 20 9 20, and 25 9 25 cm 2 at isocenter), based on the design process of 10 9 10 and 20 9 20-cm 2 applicators for 6-20 MeV beams. Our design for the Elekta MLCi2 treatment head should also apply to the newer Agility treatment head with only slight modifications, although that evaluation was not part of this study.
The criteria for suitability of collimator designs were that (a) applicator trimmer weights meet our design goals, (b) in-field beam flatness criteria 3 are met, and (c) out-of-field leakage dose meet IEC specifications. 4 The criteria used to evaluate in-field beam uniformity was that described by Hogstrom 1,3 for which off-axis dose should not vary from central-axis dose by more than AE3% along major axes (AE4% along diagonals) in a region contained within 2 cm of the field edge (2√2 cm along diagonals). IEC states that mean dose in the leakage region, measured at 1-cm depth along the major and diagonal axes from 4 cm outside field edge to M 10 (geometric projection of primary collimator ∪ 10 cm outside field edge), should not exceed an energy-dependent value (1.0%-1.8% of maximum central-axis dose, D max ). In addition, maximum dose in this region, measured along major and diagonal axes from 2 cm outside the field edge to the geometric projection of M 10 , should not exceed 10.0% of D max . 4 The present work utilizes both in air, pencil-beam dose calculations (Huizenga and Storchi 5 ) and MC dose calculations 1 for the Elekta Infinity. The in-field pencil-beam dose calculations have been validated by Pitcher, 2 and the MC calculations for the Elekta beam

2.A | Collimation system design specifications
This study designed a new Elekta electron collimation system, which like the current one, has five applicators (6 9 6, 10 9 10, 14 9 14, 20 9 20, and 25 9 25 cm 2 ). The new collimation system specified field sizes at isocenter unlike the current system, which specifies them at the final trimmer position (5 cm above isocenter). This adjustment decreased trimmer weights by approximately 3%.
Also, the new collimation system was designed for 6-20 MeV electron beams, a reduction from 4 to 22 MeV currently allowed by Elekta. Any treatment requiring an energy less than 6 MeV can be treated with a 6-MeV beam and bolus. 6 Decreasing 22-20 MeV was justified by the increase in R 90 with increasing E p,0 being small at energies greater than 20 MeV. 7 This reduction allowed narrower and thinner trimmers, reducing applicator trimmer weights by approximately 30%.
Based on initial MC studies, 2 three design parameters were established and maintained throughout the collimation system initial design process. First, tungsten was used for all applicator trimmers, based on their producing less leakage dose than copper or lead trimmers. Second, trimmers were designed 0.53-cm (9.6-g cm À2 ) thick, which reduced electron dose in water immediately distal to the trimmer to 1% of D max with no shielding present for a 20-MeV beam. Third, the upper and middle trimmer inner edges were aligned with beam divergence, which reduced leakage dose outside the field. Also, the lower trimmer inner edge divergence angle had little impact on leakage dose, allowing them to be parallel to central axis, consistent with inner edges typical of patientspecific Cerrobend inserts.

2.B | Initial design
The initial design used a method based on shielding primary electron dose, 8,9 for which inner and outer trimmer edges intercepted the penumbra from the upstream collimating component (95% and 2% of central-axis dose, respectively) for the lowest beam energy (6 MeV). Thus, X-ray and collimator-scattered electron doses were ignored. The collimating components consisted of X-ray jaws and upper, middle, and lower applicator trimmers, whose downstream trimmer surfaces were located at z-positions of 70, 80, and 95 cm, respectively (73.3, 86.2, and 95 cm, respectively, for current Elekta 10 9 10 and 20 9 20-cm 2 applicators). The resulting applicator designs had trimmers weighing 6.87 and 10.49 kg, respectively, exceeding those of current Elekta applicators (5.52 and 8.36 kg, respectively) and our objective (5.00 and 7.10 kg, respectively). Varian trimmer weights were estimated as the measured full applicator weight minus 1.5 kg.
Hence, five modifications were made to the initial designs to reduce trimmer weights to acceptable levels, while maintaining acceptable in-field flatness and out-of-field leakage dose. These modifications, which focused on 10 9 10 and 20 9 20-cm 2 applicators, included (a) beveling outer trimmer edges, (b) optimizing upper and middle trimmer z-positions, (c) determining inner trimmer edge positions, (d) determining X-ray jaw positions for each energy, and (e) determining thicknesses and bevel shapes of each trimmer.

2.C | Design modification 1-Beveling outer trimmer edges
The trimmer's outer cross-section, referred to as the "outer trimmer edge", was beveled, matching the thickness required to stop electrons (1% transmission) to off-axis position of the 2% fluence offaxis ratio (OAR) of each beam energy (E). These off-axis positions, located 2.05r x outside the projection of the upstream collimator's inner edge, were determined for energies 6-20 MeV (1-MeV spacings). The OAR is given by where z' and z represent central-axis distances from the virtual source position to the position of the upstream and downstream collimating components, respectively, and T air (E) is the electron scattering power in air.
A virtual source position 94 cm from isocenter, used for all beam energies, was determined at 7 MeV using Schr€ oder-Babo methodology. 10 r SW (E), sigma of the Gaussian virtual source width, was determined from eq. (2), using r x (E) of measured profiles and calculation of the air-scatter term using, T air (E) = 0.00554ÁE À1.78 , based on the 10-MeV ICRU 35 11 value and Werner's approximation. 12 The resulting value of 2.0 cm for r SW was used for all energies.

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Optimization was performed in three iterations. Each iteration's optimal design started the next iteration, and parameter step sizes decreased with each iteration. Table 2 shows approximate upper and lower boundaries and step sizes for each of the five parameters. All other design parameters, including bevel shape calculation parameters, were maintained.
In-field flatness was evaluated for each applicator design from OARs calculated using Huizenga and Storchi's 5 analytical model of the primary electron beam, which uses scattering moment profiles to transport primary electron fluence profiles in air through multiple collimation levels (X-ray jaws and three trimmers) to isocenter. 2 Calculations were performed at 6 MeV, the lowest energy and that most likely to fail flatness due to having the greatest scattering power. Major axes OARs (in-plane and cross-plane) were considered acceptably flat if the OAR varied (decreased) from central-axis dose by ≤2% at the edge of the uniformity region (2 cm inside field edge). The 2% threshold should ensure that the OAR did not vary from central-axis value by >4%, the maximum variation allowed for acceptable diagonal profiles. 3

2.E.2 | Step 2-Adjustments using MC calculations
When MC calculations revealed that the collimation system designed in Step 1 narrowly failed our flatness criteria, 3 four modified designs for the 10 9 10 and 20 9 20-cm 2 applicators were created by incrementally increasing inner edge OARs produced from Step 1 optimizations, while maintaining trimmer z-positions. This stepped trimmers and jaws outward from central axis, improving in-field flatness while slightly increasing applicator weights. Table 3  and 20 9 20-cm 2 applicators, those producing the least applicator trimmer weight, while maintaining acceptable in-field flatness, were selected for continuing the collimation system design process.  applicator and 89%, 72%, and 55% for the 20 9 20-cm 2 applicators.

2.G.1 | Trimmer thickness reduction analysis
The 20 9 20-cm 2 applicator from Design Modification 4 was modified one trimmer at a time (the other two maintaining full thickness); thickness was reduced by scaling the variable trimmer thicknesses by various percentages (c.f. Fig. 3). For the lower and middle trimmers, trimmer thicknesses were reduced by 7%, 14%, 21%, and 35%; for the upper trimmer, thicknesses were reduced by 7%, 14%, 21%, 35%, and 49%, producing 13 new applicator designs. BEAMnrc MC simulations were performed for each of the 13 20 9 20-cm 2 applicator designs at 20 MeV. Dose at 1-cm depth in water was calculated using methodology detailed in Design Modification 3. T A B L E 4 Off-axis X-ray jaw positions (cm), expressed as "In-Plane x Cross-Plane" position projected to isocenter, for the three collimation system designs analyzed in Design Modification 4 for 7, 13, and 20 MeV beams. The three designs, "Unadjusted Jaw Positions" (results of Design Modification 3), "Jaw Adjustment A", and "Jaw Adjustment B", correspond to 95%, 75%, and 55% OAR values at the upper trimmer inner edge, respectively for the 10 9 10-cm 2 applicator, and to 89%, 72%, and 55%, respectively, for the 20 9 20-cm 2 applicator.  These results were used to assess in-field flatness and out-of-field, patient-plane leakage dose of the final collimation system designs.

3.
A | Design modification 1-Beveling outer trimmer edges Figure 5, an in-plane cross-sectional scaled drawing of 20 9 20-cm 2 applicator trimmers, compares the initial design with the modified design whose beveled outer edges remove material, reducing trimmer weights. Table 5 lists trimmer weights and percent weight reductions following each design modification, showing 14.7% and 13.8% weight reductions for the 10 9 10 and 20 9 20-cm 2 applicators, respectively.

3.B | Design modification 2-Optimizing upper and middle trimmer z-positions
Results in Fig. 6 show isomass plots versus upper and middle trim-      Fig. 9 for the 20 9 20-cm 2 applicator at 7, 13, and 20 MeV. The three designs, labelled "Unadjusted Jaw Positions", "Jaw Adjustment A", and "Jaw Adjustment B", correspond to T A B L E 5 Summary of weight reduction results for each step in collimation design process. For 10 9 10 and 20 9 20-cm 2 applicators, trimmer weights and corresponding percent weight reductions, both step-to-step (Mod.) and cumulative (Cum.), following each design modification are shown.   Table 5 shows these designs reduced trimmer weights by 7.5% and 4.9% for the 10 9 10 and 20 9 20-cm 2 applicators, respectively.
In addition, Fig. 9 results show that adjusting the jaws inward decreased out-of-field leakage dose. This effect increased with energy due to greater jaw adjustment, having negligible effect at 7 MeV. Compared to the "Unadjusted Jaw Positions" design, the "Jaw Adjustment B" design decreased the 20-MeV beam mean percent leakage dose from 1.26% to 0.82% for the 10 9 10-cm 2 applicator and from 1.21% to 0.89% for the 20 9 20-cm 2 applicator.
3.E | Design modification 5-Determining trimmer thickness and bevel shape  Table 3. The Uniformity Limit Marker "⊕" indicates minimum dose at edge of uniformity region (2√2 cm inside field corner) required for in-field flatness.
trimmer thickness than bevel shape adjustment. Therefore, a 50% (49% rounded) thickness reduction was selected for the upper trimmer. Although only investigated for the 20 9 20-cm 2 applicator, these same modifications were implemented for the 10 9 10-cm 2 applicator, both resulting in applicator trimmer weight reductions of approximately 31% (c.f. Table 5).  Table 6. In addition, Table 6 data shows that mean percent leakage doses for 10 9 10 and 20 9 20-cm 2 applicators were less than IEC limits at 7, 13, and 20 MeV. tively; however, all were well below IEC limits (c.f. Table 6).

4.C | Utilizing results for new electron collimation system design
Our 10 9 10 and 20 9 20-cm 2 applicator designs (trimmers and X-ray jaw settings) provide the basis for a new Elekta electron collimation system with lighter applicators, including 6 9 6, 14 9 14, and 25 9 25-cm 2 applicators for 6-20 MeV beams. New applicator sizes retain design parameters from the 10 9 10 and 20 9 20-cm 2 applicators (i.e., z-positions, materials, inner edge divergence angles, outer edge bevel forming fluence matching OARs, and trimmer thicknesses) except for OARs at each trimmers inner edge; the 6 9 6 and 25 9 25-cm 2 applicators used the same OARs as the 10 9 10 and 20 9 20-cm 2 applicators, respectively, for a 6-MeV beam. The 14 9 14-cm 2 applicator OARs were linearly interpolated between the 10 9 10 and 20 9 20-cm 2 OARs for a 6-MeV beam. X-ray jaw positions for each energy were determined by linearly interpolating the OARs at the upper trimmer inner edge between the 6-MeV value and 55% at 20 MeV for all applicators (c.f. Table 8).
Calculated weights of these newly designed trimmers for the five Elekta applicators are compared with weights of current applicators and trimmers in Table 9. These results illustrate that our new collima- To allow the occasional benefit of small adjustments (e.g., AE1 cm at isocenter) from factory-specified jaw settings, such "robustness" can be achieved by increasing the width of the constant-thickness portion of the upper trimmer, which slightly increases the weight.
For the 20 9 20-cm 2 applicator, the estimated cost is 0.4 kg cm À1 , which should allow applicator trimmer weights to remain well below both targeted and existing Elekta applicator weights.

4.E | Further investigation of new collimation system
The prototype collimation system was designed for the MLCi2 treatment head. However, Elekta's Agility treatment head has replaced (a) cross-plane jaws having curved inner edges with MLC, increasing inner edge area, and (b) in-plane jaws having diverging inner edges with curved ones. Both alterations could generate increased leakage dose. 1 Hence, MC calculations should be performed for our prototype 10 9 10 and 20 9 20-cm 2 applicators using the Agility treatment head to evaluate in-field flatness and out-of-field leakage dose, allowing for any necessary design adjustments.

| CONCLUSIONS
This study demonstrated a process for designing an Elekta electron collimation system having significantly lighter applicators. 10 9 10 and 20 9 20-cm 2 applicators were designed with trimmer weights of 3.73 and 5.09 kg, respectively, well below current weights (5.52 and 8.36 kg, respectively) and our design goals (5.00 and 7.10 kg, respectively). Based on MC calculations at 7, 13, and 20 MeV, both applicator designs produce acceptable in-field flatness and out-of-field leakage. These results have been used to design a new collimations system for 6-20 MeV electron beams with 6 9 6 to 25 9 25-cm 2 applicators.
The design of the new electron collimation system (X-ray jaw settings and applicators) for the Elekta Infinity (MLCi2 treatment head) has been validated by fabricating 10 9 10 and 20 9 20-cm 2 prototype applicators and measuring dose. Results of that study confirmed acceptable in-field flatness and out-of-field leakage dose 2 and will be reported subsequently.

ACKNOWLEDG EMENTS
Portions of this research were conducted with high-performance computational resources provided by Louisiana State University (http://www.hpc.lsu.edu).

CONFLI CTS OF INTEREST
This research was funded in part through a research agreement with Elekta Limited.