Radiobiological and dosimetric impact of RayStation pencil beam and Monte Carlo algorithms on intensity‐modulated proton therapy breast cancer plans

Abstract Purpose RayStation treatment planning system employs pencil beam (PB) and Monte Carlo (MC) algorithms for proton dose calculations. The purpose of this study is to evaluate the radiobiological and dosimetric impact of RayStation PB and MC algorithms on the intensity‐modulated proton therapy (IMPT) breast plans. Methods The current study included ten breast cancer patients, and each patient was treated with 1–2 proton beams to the whole breast/chestwall (CW) and regional lymph nodes in 28 fractions for a total dose of 50.4 Gy relative biological effectiveness (RBE). A total clinical target volume (CTV_Total) was generated by combining individual CTVs: AxI, AxII, AxIII, CW, IMN, and SCVN. All beams in the study were treated with a range shifter (7.5 cm water equivalent thickness). For each patient, three sets of plans were generated: (a) PB optimization followed by PB dose calculation (PB‐PB), (b) PB optimization followed by MC dose calculation (PB‐MC), and (c) MC optimization followed by MC dose calculation (MC‐MC). For a given patient, each plan was robustly optimized on the CTVs with same parameters and objectives. Treatment plans were evaluated using dosimetric and radiobiological indices (equivalent uniform dose (EUD), tumor control probability (TCP), and normal tissue complication probability (NTCP)). Results The results are averaged over ten breast cancer patients. In comparison to PB‐PB plans, PB‐MC plans showed a reduction in CTV target dose by 5.3% for D99% and 4.1% for D95%, as well as a reduction in TCP by 1.5–2.1%. Similarly, PB overestimated the EUD of target volumes by 1.8─3.2 Gy(RBE). In contrast, MC‐MC plans achieved similar dosimetric and radiobiological (EUD and TCP) results as the ones in PB‐PB plans. A selection of one dose calculation algorithm over another did not produce any noticeable differences in the NTCP of the heart, lung, and skin. Conclusion If MC is more accurate than PB as reported in the literature, dosimetric and radiobiological results from the current study suggest that PB overestimates the target dose, EUD, and TCP for IMPT breast cancer treatment. The overestimation of dosimetric and radiobiological results of the target volume by PB needs to be further interpreted in terms of clinical outcome.


| INTRODUCTION
Intensity-modulated proton therapy (IMPT) is used for the treatment of breast cancer at many proton centers across the world. Literature 1,2 has shown that proton therapy for breast cancer could potentially reduce normal tissue complication probability (NTCP) by reducing side effects such as cardiac and pulmonary toxicities. It is paramount that the reduction of NTCP must be accompanied by an inhomogeneities. For instance, Saini et al. 3 found that MC is superior to PB when a range shifter is employed with oblique beams, large air gaps, and/or heterogeneous media. Taylor et al. 4 demonstrated that MC calculations are more accurate than PB calculations when compared to physical measurements. Shirey et al. 6 showed better accuracy of MC compared to PB when treatment involves the range shifter and superficial lesions.
Although superior dose prediction accuracy of MC over PB has been well established, [3][4][5][6][7][8] literature investigating the impact of RayStation PB and MC on IMPT breast cancer treatment is scarce. The investigation of proton dose calculation algorithms for breast treatment is particularly important due to the presence of a tumor at a shallower depth and range shifter in the proton beam path. The addition of range shifter at the end of the nozzle exit reduces the beam energy. This is necessary to achieve a full dose modulation of the tumor volume, but the range shifter creates an air gap between its downstream and patient surface, thus increasing in-air spot size. 9 Tommasino et al. 7 included five breast cancer patients and the treatment plans were optimized with PB and recalculated with PB and MC. Additionally, Tommasino et al. 7 performed the phantom measurements to demonstrate better accuracy using MC than using PB. Liang et al. 8 did a more comprehensive dosimetric study by including 20 breast cancer patients. In their study, 8 the authors used both PB and MC for plan optimization as well as dose calculations, whereas MC for plan optimization was not addressed by Tommasino et al. 7 It is worth noting that both studies evaluated PB and MC on IMPT breast plans using dosimetric indices. However, at the time of writing this paper, the radiobiological impact of RayStation PB and MC on IMPT breast plans is yet to be investigated. were not provided in detail in a previous publication. 8

2.A | Patients, CT simulation, and contouring
The current study consisted of ten female left breast cancer patients who have been treated using IMPT at our center between 11/2017 and 01/2019. All ten patients received treatment to the chest wall (CW) or whole breast. For all ten patients, the treatment also included regional lymph nodes. Patients were simulated on Siemens computed tomography (CT) Scanner (Siemens Healthcare, Forcheim, Germany) in head-first supine treatment position with arms above their heads based on our institutional protocol. This includes a vaclok and wing board for immobilization devices and a free breathing CT scan with a slice thickness of 2 mm.

2.B | Dose prescription and treatment planning
All ten patients were treated for a total dose of 50.4 Gy relative biological effectiveness (RBE) in 28 fractions on a ProteusPLUS PBS RANA ET AL. | 37 proton therapy system 10 (Ion Beam Applications, Louvain-la-Neuve, Belgium). Treatment plans were generated in RayStation (v6.1.1.2) using 1-2 beams, and each beam included the range shifter of 7.5 cm water equivalent thickness made up of lucite. A 5 mm setup uncertainty on CTV was used for the robust optimization for a total of seven scenarios. All treatment plans were robustly optimized with the goal of 95% of CTV receiving at least 95% of the prescription dose while minimizing dose to the OARs. All plans were computed with a dose calculation grid size of 3 mm. For each case, three plans were generated using identical beam angles, air gap, optimization structures, optimization constraints, and optimization settings. A sampling history of 10,000 ions/spot was used for MC optimization, and a statistical uncertainty of 0.5% was used for MC dose calculation.
1. PB-PB Plan: The plan was optimized using PB followed by dose calculation using PB.
2. PB-MC Plan: The plan was optimized using PB followed by dose calculation using MC.
3. MC-MC Plan: The plan was optimized using MC followed by dose calculation using MC.

2.C | Dosimetric analysis
The CTV_Total was evaluated for the mean dose (D mean ), the dose received by 99% of the volume (D 99% ), 95% of the volume (D 95% ), and 2% of the volume (D 2% ). The D mean was calculated for the left anterior descending artery (LAD), heart, and esophagus, whereas the dose received by 0.03 cc (D max ) was calculated for the skin. The ipsilateral lung (i.e., left lung) was evaluated for the relative volume that received 20 and 5 Gy(RBE) (V 20 and V 5 , respectively), whereas the contralateral lung (i.e., right lung) was evaluated for the V 5 .

2.D | EUD Analysis
Equivalent uniform dose evaluation was performed using the cumulative dose volume histograms (DVHs) of the proton treatment plans (PB-PB, PB-MC, and MC-MC). EUD is based on the Niemierko's phenomenological model. 11 The EUD 11,12 is defined as.
In eq. (1), a is a unit less model parameter that is specific to the normal structure or tumor of interest, and v i is unit less and represents the i th partial volume receiving dose D i in Gy. 11,12 Since the relative volume of the whole structure of interest corresponds to 1, the sum of all partial volumes v i will equal 1 11,12 The EQD is the biologically equivalent physical dose of 2 Gy. In eq (2), n f and d f = D/n f are the number of fractions and dose per fraction size of the treatment course, respectively. The α/β is the tissue-specific linear-quadratic (LQ) parameter of the organ being exposed. The EUD calculations in this study are based on the parameters listed in Table 1. 14-16

2.E | TCP Analysis
The Poisson linear quadratic (PoissonLQ) radiobiological model 13 employed within RayStation was used to estimate the TCP of CTV_Total, CTV_breast, CTV_AxI, CTV_AxII, CTV_AxIII, CTV_IMN, and CTV_SCVN. The TCP-PossionLQ model is defined as 13 : where, M, total number of voxels; D, total dose; D k,i , dose to the k th fraction to voxel i; n, total number of fractions; N 0 , initial number of

2.F | NTCP Analysis
The Lyman-Kutcher-Burman (LKB) model employed within RayStation 13 was used to calculate the NTCP of the heart, lung (ipsilateral), and skin. The LKB model is defined as 13 : where, D, total dose; D 50 , dose giving a 50% response probability; m, slope of the response curve; M, total number of voxels; n, parameter reflecting the biological properties of the organ specifying volume

2.G | Statistical analysis
In order to test the statistical significance of dosimetric and radiobiological results in the current study, the Mann-Whitney U-test was performed. A p value of less than 0.05 was considered to be statistically significant.

3.D | TCP analysis
3. Robust evaluation of the D 95% of the total clinical target volume (CTV_Total) in PB-PB (PB optimization followed by PB dose calculation), PB-MC (PB optimization followed by MC dose calculation), and MC-MC (MC optimization followed by MC dose calculation) plans for ten breast cancer patients. Each plan was evaluated for range uncertainty of ±3.5% and isocenter shifts of X = ±5 mm, Y = ±5 mm, and Z = ±5 mm. The acceptable robustness criteria for the intensity-modulated proton therapy breast was 95% of the CTV_Total is covered by at least 90% of the prescribed dose (i.e., D95% ≥ 45.36 Gy(RBE)).    92.9%; P = 0.345). Figure 6 shows the TCP of CTV_Total and in PB-PB, PB-MC, and MC-MC plans of an example patient. Table 7 shows the NTCP results for the heart, ipsilateral lung, and skin. There was no clear distinction among PB-PB, PB-MC, and MC-MC plans in terms of NTCP results. Based on the LKB model and published radiobiological parameters used in this study, the NTCPs were 0% for the heart, ≤0.2% for the skin, and 0.4% to 1.9% for the ipsilateral (left) lung. Figure 6 shows the NTCP of the heart, left lung, and skin in PB-PB, PB-MC, and MC-MC plans of an example patient.

3.E | NTCP analysis
3.F | Patient-specific quality assurance (QA) analysis Patient-specific QA measurement was done for PB-PB plans of all ten patients in a water tank using DigiPhant-PT (IBA Dosimetry, Schwarzenbruck, Germany) and MatriXX-PT (IBA Dosimetry, Schwarzenbruck, Germany). A 2D gamma analysis was performed between the calculated and measured 2D dose distributions using patient-specific QA module implemented within myQA software platform (IBA Dosimetry, Schwarzenbruck, Germany). For 2D gamma evaluation, we utilized 3% and 3 mm criteria and low-dose threshold of 10%. A gamma passing rate of ≥ 90% was considered to be an acceptable level. Table 8 shows the gamma evaluation results of all ten patients. The average 2D gamma was 94.0% ± 2.9% with a minimum of 90.1% and a maximum of 98.9%.
Tumor control probability of the total clinical target volumes for breast cancer patients (n = 10) in PB optimization followed by PB dose calculation, PB optimization followed by MC dose calculation, and MC optimization followed by MC dose calculation plans generated by intensity-modulated proton therapy technique.
F I G . 6. Tumor control probability clinical target volume (CTV_Total) and normal tissue complication probability (heart, skin, and left lung) in PB optimization followed by PB dose calculation, PB optimization followed by MC dose calculation, and MC optimization followed by MC dose calculation plans of an example patient.

| DISCUSSION
Previous studies on RayStation proton dose calculation algorithms were mostly focused on the dosimetric impact of algorithms involving either phantom 3-7 or disease sites. 5   F I G . 7. Computation time in minutes for intensity-modulated proton therapy breast plans (PB optimization followed by PB dose calculation and MC optimization followed by MC dose calculation) of ten breast cancer patients.
beam after traversing the range shifter and translation of angular distribution into a geometric spread of proton beam's cross-section at the detector/patient surfaces is critical. 9,21 It has been reported that recalculation of PB plans using MC will result in decrease in target dose and coverage. In a breast study by  20 It must be noted that radiobiological evaluation in our study was carried out based on radiobiological parameters that are derived from the conventional mega-voltage X-ray (photon) therapy. This is a limitation of our study. As more breast cancer patients are being treated using proton therapy and enrolled in clinical trials, there is a need for proton derived NTCP models correlating to the tissue toxicities of breast cancer patients. Due to lack of proton derived radiobiological parameters, researchers continue to use photon-derived NTCP models for proton therapy. 12,14,25 Recently, Blanchard et al. 24 validated photon-derived NTCP models that can be used to select head and neck patients for proton treatment.
The current study assumed constant RBE value of 1.1. Several publications 26,27 have demonstrated the existence of variable RBE for proton therapy and depend on the cell type, endpoint, LET, radiation dose, etc. The variability in RBE could lead to different α/β values, thus impacting EUD, TCP, and NTCP. 28 In this study, we did not explore the impact of variable RBE on IMPT breast plans. Our future work will investigate how the combination of variable RBE and proton dose calculation algorithm can affect the radiobiological results.
One of the challenges associated with MC plan optimization is the treatment planning efficiency. Figure 7 illustrates the computa-

| CONCLUSION
If RayStation MC is more accurate than PB as reported in the literature, dosimetric and radiobiological results from the current study suggest that PB overestimates the target dose, EUD, and TCP for IMPT breast cancer treatment. The overestimation of dosimetric and radiobiological results of the target volume by PB needs to be further interpreted in terms of clinical outcome. The use of RayStation MC for both plan optimization and dose calculation of IMPT breast cancer plans can provide optimal target coverage and radiobiological results (EUD and TCP for target volumes) with better accuracy.

ACKNOWLEDG MENTS
The authors thank our medical physics assistants (Michael Leyva and Victor Chirinos) for their assistance with patient-specific QA measurements.

CONFLI CT OF INTEREST
No conflicts of interest.