Quantifying the effect of air gap, depth, and range shifter thickness on TPS dosimetric accuracy in superficial PBS proton therapy

Abstract This study quantifies the dosimetric accuracy of a commercial treatment planning system as functions of treatment depth, air gap, and range shifter thickness for superficial pencil beam scanning proton therapy treatments. The RayStation 6 pencil beam and Monte Carlo dose engines were each used to calculate the dose distributions for a single treatment plan with varying range shifter air gaps. Central axis dose values extracted from each of the calculated plans were compared to dose values measured with a calibrated PTW Markus chamber at various depths in RW3 solid water. Dose was measured at 12 depths, ranging from the surface to 5 cm, for each of the 18 different air gaps, which ranged from 0.5 to 28 cm. TPS dosimetric accuracy, defined as the ratio of calculated dose relative to the measured dose, was plotted as functions of depth and air gap for the pencil beam and Monte Carlo dose algorithms. The accuracy of the TPS pencil beam dose algorithm was found to be clinically unacceptable at depths shallower than 3 cm with air gaps wider than 10 cm, and increased range shifter thickness only added to the dosimetric inaccuracy of the pencil beam algorithm. Each configuration calculated with Monte Carlo was determined to be clinically acceptable. Further comparisons of the Monte Carlo dose algorithm to the measured spread‐out Bragg Peaks of multiple fields used during machine commissioning verified the dosimetric accuracy of Monte Carlo in a variety of beam energies and field sizes. Discrepancies between measured and TPS calculated dose values can mainly be attributed to the ability (or lack thereof) of the TPS pencil beam dose algorithm to properly model secondary proton scatter generated in the range shifter.

tions for a single treatment plan with varying range shifter air gaps. Central axis dose values extracted from each of the calculated plans were compared to dose values measured with a calibrated PTW Markus chamber at various depths in RW3 solid water. Dose was measured at 12 depths, ranging from the surface to 5 cm, for each of the 18 different air gaps, which ranged from 0.5 to 28 cm. TPS dosimetric accuracy, defined as the ratio of calculated dose relative to the measured dose, was plotted as functions of depth and air gap for the pencil beam and Monte Carlo dose algorithms. The accuracy of the TPS pencil beam dose algorithm was found to be clinically unacceptable at depths shallower than 3 cm with air gaps wider than in water when a range shifter was used. Do not use the device in these situations." 4 RayStation updated the language in the RayStation 6 User Manual to explain the reasoning for the inaccurate dose calculation and suggests the use of the Monte Carlo dose engine to more accurately calculate dose in such situations. 5 One of the main benefits of proton therapy is the ability to control the distal range of the treatment field by taking advantage of the Bragg Peak. This allows for the treatment of target volumes located proximal to normal tissue or organs at risk with little dosimetric detriment to the non-target volumes. 6 When target volumes are located relatively deep in the patient, the accuracy of the TPS is sufficient. 1,3 Targets such as chest wall, however, can have a significant portion of the target volume located a depths shallower than 3 cm. At such shallow depths, the minimum beam energy has a range greater than the target depth. A range shifter placed in the beamline sufficiently reduces beam energy such that full dose modulation is achievable at the patient surface. The ProteusONE is capable of producing a minimum beam energy of 70 MeV, which has a range in water of approximately 4.1 cm. 7 WKCC commissioned a 3.5 cm physical thickness (4.1 cm water-equivalent thickness) Lexan range shifter to treat shallow target volumes with the ProteusONE.
Other proton therapy systems with minimum beam energies of 100 MeV would require a range shifter with approximately 7.5 cm water-equivalent thickness. 7 As noted above, the use of range shifters for shallow treatments can be problematic for a TPS using a pencil beam dose algorithm.
Though most commercially available proton TPSincluding Pinnacle, 8 XiO, 9 Eclipse, 10 and RayStation 4use pencil beam dose algorithms, no published studies could be found which quantify the functional dependence of TPS dosimetric accuracy on depth or air gap. A selection of publications have quantified TPS accuracy for multiple depths with a fixed air gap, 11 and other works have generally noted that a pencil beam algorithm breaks down with large air gaps and shallow depths. 2,4,5,12 This study, for the first time, systematically quantifies the dosimetric accuracy of a proton pencil beam dose algorithm as a function of range shifter air gap and treatment depth for superficial proton PBS treatments. Moreover, this study performed an identical analysis using the RayStation 6 Monte Carlo proton dose engine to determine the improvement in dosimetric accuracy one may expect when using Monte Carlo. Finally, a smaller subset of this study performed similar measurements with a thicker range shifter to identify the relationship between pencil beam TPS accuracy and range shifter thickness. This data was then tested against patient treatment plans to confirm its applicability to the clinical treatment environment. To further confirm the dosimetric accuracy of the RayStation 6 Monte Carlo dose algorithm at beam energies and field sizes other than those described above, MC-calcu-

2.B | Experimental setup
The optimized treatment plan was exported to MOSAIQ (Elekta, Sunnyvale, CA, USA) and delivered by the IBA ProteusONE compact-gantry proton therapy system with a 3.5 cm Lexan range shifter inserted in the retractable snout. Dose was measured with the PTW T23343 Markus chamber (PTW, Freiburg, Germany) embedded in SP34 RW3 solid plate phantom material (IBA-Dosimetry, Schwarzenbruck, Germany). Dose measurements at a given depth were taken for each air gap by simply moving the range shifter snout to the appropriate position. When all data for one depth were acquired, the chamber was repositioned to the appropriate depth in the phantom, the vertical couch position was adjusted to keep the isocenter position constant, and the measurement process was repeated for all depth/air gap combinations. MatriXX PT with the Markus chamber showed the MatriXX PT CAX dose to be accurate within 0.4%. This daily output correction factor (P DO ) is the ratio of the baseline central-axis dose determined during machine commissioning to the measured daily CAX dose, and was included in the TRS-398 absorbed dose calculation. 13 D w;Q ¼ M raw N D;w;Q0 k Q;Q0 P T;P P ion P pol P elec P DO (1)      All further analysis of dosimetric accuracy excludes these surface doses, as they are clearly significant outliers in otherwise consistent data.

3.B | Pencil beam algorithm dosimetric accuracy
The dosimetric accuracy of the TPS pencil beam algorithm has a dependence on both depth and air gap, as shown in Figs. 1(a) and   1(b). PB-calculated TPS doses become more accurate at increasing depths and at decreasing air gaps. When the air gap is relatively small, the TPS accuracy is clinically acceptable (within 3%) at all depths 2 mm and deeper. As the air gap widens, dosimetric accuracy degrades, especially at the shallowest depths. The depth dependence of pencil beam dose algorithm accuracy is strongest in the shallowest 1 cm, eventually stabilizing beyond 3 cm. Table 1 bins the information from Figs. 1(a) and 1(b), while Table 3 shows the complete set of data acquired.    Table 4 shows all Monte Carlo data. Figures 1(a), 1(b), 2(a), and 2(b) show a representative subset of the data which allows the observer to understand the trends while minimizing clutter.

3.D | Range shifter thickness
Previous works by the authors have reported findings from similar tests, which directly compared the air gap and depth dependences of a 3.5 cm (4.1 cm WET) range shifter to a 6.5 cm (7.4 cm WET) range shifter. On average, the dosimetric error of the thicker range shifter was found to be approximately 50% greater than the thinner range shifter. 15 T A B L E 7 Depth, extended air gap, estimated errors, and total expected dose difference for paraspinal fields using PB and MC dose engines.

3.E | Clinical validation of data using patient plans
As a clinical test of this data, shallow QA dose planes of a chest wall patient and a patient with paraspinal mets were calculated with both PB and MC dose engines and compared via c-analysis. The paraspinal plan was also tested with extended air gaps to illustrate the difference between a well-planned treatment with air gaps less than 10 cm and a sub-optimal plan with air gaps greater than 15 cm.
Given the depth and air gap for each field, the expected dose error of the PB and MC calculations were determined by interpolating data in Tables 3 and 4, respectively. The difference of PB and MC dosimetric errors represents the total expected dose difference between datasets. If the data in Tables 3 and 4 Table 7 shows the corresponding data for the paraspinal patient when the air gap has been extended an additional 10 cm for each fieldthese fields have been identified as Field 03a RPO and Field 04a RPO.
A series of c-analyses were performed for each field, with the %D criteria incrementally increased until nearly all points (>99%) passed, as shown in Table 8 This confirms the applicability of the data collected in this work with respect to other clinical patient treatment plans.

3.F | Validation with commissioning data
Because the majority of data collected for this work were based on a single treatment field, three additional fields of varying energy and field size were modeled in the TPS and compared against measured data. Figure 3 shows three separate plotsone for each treatment fieldwhich depict the depth dose curves as calculated by RaySta-

| CONCLUSION
For the first time, this study comprehensively quantifies TPS dosimetric accuracy of range-shifted proton fields as a function of depth, air gap, and range shifter thickness. When pencil beam dose algorithms are used to create superficial PBS treatments, the air gap should be reduced as much as patient setup allows, and range shifter thickness should be minimized to correspond with the range of the machine's minimum energy. Poor modeling of secondary proton scatter generated in the range shifter, also known as the nuclear halo effect, is the main contributor to TPS dose overestimation. 5 As mentioned by RayStation and as confirmed by this study, implementation of a Monte Carlo dose engine has helped mitigate this error.

ACKNOWLEDGMENTS
We wish to thank Dr. Kuanling (Gwen) Chen and Dr. Matthew Maynard for their assistance, expertise, and impromptu sanity checks.
Without their guidance, we could not have completed this project.

CONFLI CT OF INTEREST
The authors have no conflicts of interest to disclose.