A comprehensive dosimetric study of Monte Carlo and pencil‐beam algorithms on intensity‐modulated proton therapy for breast cancer

Abstract PB algorithms are commonly used for proton therapy. Previously reported limitations of the PB algorithm for proton therapy are mainly focused on high‐density gradients and small‐field dosimetry, the effect of PB algorithms on intensity‐modulated proton therapy (IMPT) for breast cancer has yet to be illuminated. In this study, we examined 20 patients with breast cancer and systematically investigated the dosimetric impact of MC and PB algorithms on IMPT. Four plans were generated for each patient: (a) a PB plan that optimized and computed the final dose using a PB algorithm; (b) a MC‐recomputed plan that recomputed the final dose of the PB plan using a MC algorithm; (c) a MC‐renormalized plan that renormalized the MC‐recomputed plan to restore the target coverage; and (d) a MC‐optimized plan that optimized and computed the final dose using a MC algorithm. The DVH on CTVs and on organ‐at‐risks (OARs) from each plan were studied. The Mann–Whitney U‐test was used for testing the differences between any two types of plans. We found that PB algorithms significantly overestimated the target dose in breast IMPT plans. The median value of the CTV D99%, D95%, and Dmean dropped by 3.7%, 3.4%, and 2.1%, respectively, of the prescription dose in the MC‐recomputed plans compared with the PB plans. The magnitude of the target dose overestimation by the PB algorithm was higher for the breast CTV than for the chest wall CTV. In the MC‐renormalized plans, the target dose coverage was comparable with the original PB plans, but renormalization led to a significant increase in target hot spots as well as skin dose. The MC‐optimized plans led to sufficient target dose coverage, acceptable target hot spots, and good sparing of skin and other OARs. Utilizing the MC algorithm for both plan optimization and final dose computation in breast IMPT treatment planning is therefore desirable.


| INTRODUCTION
Due to its unique energy absorption profile, proton therapy has several critical advantages over photon therapy. It provides excellent target coverage and minimized cardiac and pulmonary exposure for post-lumpectomy and post-mastectomy irradiation. [1][2][3] Indeed, the interest in proton therapy for breast cancer has substantially increased over the past decades, as evidenced by the recently opened, 1700-patient, randomized trial of proton vs photon therapy for breast cancer patients (RADCOMP, NCT: 02603341) 4 and the many publications on this subject. 5 Clinical dose calculations for proton therapy are primarily obtained using the pencil-beam (PB) algorithm, which assumes that the material on the central axis is laterally infinite and the modeling of nuclear reaction and multiple Coulomb scattering can only be approximate. This leads to inaccurate dose distributions in the presence of complex geometries and heterogeneous environments. 6 In comparison, the Monte Carlo (MC) algorithm simulates particle propagation through materials by randomly sampling the cross section of interactions. 7 Thus, MC dose calculation is considered the most accurate method to compute doses in radiation therapy. Several phantom studies comparing proton dose distributions calculated with PB and MC algorithms have demonstrated that the MC algorithm provides more accurate treatment planning than the PB algorithm. [8][9][10][11][12] For example, the recently published Imaging and Radiation Oncology Core (IROC) lung phantom study 12  Most of the existing studies evaluating algorithms were conducted on phantoms and focused on high-density gradients and small-field dosimetry. Although a limited number of studies [13][14][15] have evaluated the dose calculation errors in patients, the primary focus was still high-gradient tissue inhomogeneity. Due to the high-gradient tissue inhomogeneity involved in treatment sites such as the thorax, large PB accuracy deficiencies are expected and have been confirmed by previous studies. 14,15 However, sites such as the breast and chest wall (CW), have not been thoroughly investigated. The accuracy of the PB algorithm may not initially be questioned for the more homogenous site of breast. However, due to the use of a range shifter and the presence of a relatively large air gap in intensity-modulated proton therapy (IMPT) for breast cancer, PB algorithms may lead to meaningful dose distribution calculation errors.
Indeed, in the benchmark study of RayStation (RaySearch Laboratories, Stockholm, Sweden) PB and MC dose calculation algorithms, Saini et al. 10 found that dose discrepancies of up to 8% occurred at shallow depths between the phantom measurement and the PB computation for a large air gap situation when a range shifter was used. Proton therapy for breast cancer falls into this same category, namely the combination of the use of a range shifter and a relatively large air gap between the range shifter and the patient. Clearly, studies of the dose errors inherent in the PB algorithm for IMPT breast cancer cases are necessary.
In the current study, we systematically investigated the dosimet-

| MATERIALS AND METHODS
The study was approved by the Institutional Review Board.

2.A | Patients
This single institution study consisted of 20 female patients (8 postmastectomy and 12 post-lumpectomy) who received IMPT to the whole breast or CW and regional lymph nodes (with the exception of one patient who received IMPT to the breast only) between 06/ 2017 and 06/2018. Patients received IMPT to the breast/CW and internal mammary nodes (IMN), axillary level I-III nodes (AxI-III), and supraclavicular nodes (SCV) (n = 17); breast and IMN and AxI-III (n = 1); CW and IMN (n = 1); and breast only (n = 1).

2.B | Simulation, target volumes, and OARs
All patients were simulated in the supine position with arms above their heads using a standard wing board and a Vac-Lok immobilization bag. Four-dimensional computed tomography (4DCT) scans with a slice thickness of 2 mm were acquired using a Philips Brilliance Big Bore CT (Philips Healthcare, Eindhoven, The Netherlands). The average CT images were transferred to MIM (MIM Software Inc., Beachwood, OH) for contouring. The CTV structures, including breast tissue or CW, IMN, AxI, AxII, AxIII, and SCV, were contoured on the average CT images. All CTV structures were combined to generate the total CTV, which was expanded by 5 mm (excluding the skin, heart, esophagus, thyroid, and lung +3 mm), and then smoothed to create the planning PTV. Organ-at-risk (OAR) structures, including the heart, ventricles (combined right and left), left anterior LIANG ET AL. | 129 descending artery (LAD), left lung, right lung, esophagus, and thyroid, were also contoured on the average CT. A layer skin structure of 5 mm (for intact breasts) or 3 mm (for CW) inward from the body was also contoured.

2.C | Treatment planning
The average CT images and the contours were transferred to RayStation (V6.1) for treatment planning. The dose prescription was 50 Gy(RBE) in 25 fractions. For each plan, two en-face angles between 0°and 30°were used. A water equivalent 7.4-cm Lucite ranger shifter was used for each beam. The selective robust optimization strategy 16 with both robust objectives and normal objectives was used to achieve a robust plan against uncertainties with desirable dose distribution. To be more detailed, the plan was robust optimized on all CTV structures with 5-mm setup uncertainty and 3.5% range uncertainty, and normal optimization on the planning PTV was also included in the objective function. The OARs were optimized on the nominal scenario as they receive minimum dose and no risk of exceeding the tolerance under setup and range error scenarios. All optimizations were carried out on a 2-mm calculation grid for 200 iterations. The target dose was evaluated on CTVs, as detailed below. For each patient, four plans were generated using RayStation TPS: 1. PB plan: The PB algorithm was used for optimization and final dose computation. The plan was normalized to 95% of the PTV covered by 95% of the prescription dose.
2. MC-recomputed plan: The PB plan was recomputed using the MC algorithm with 0.5% statistical uncertainty. The statistical error is the mean one standard deviation error over all voxels having a dose above 50% of the maximum dose. Identical pencil-beam scanning (PBS) energy layers, spot geometry and weighting, and monitor units were used for the recomputation.
3. MC-renormalized plan: The MC-recomputed plan was renormalized to 95% of the PTV covered by 95% of the prescription dose.
4. MC-optimized plan: While maintaining the identical objective function, including the robust optimization settings used in the PB plan, but resetting the PBS energy layers, spot geometry and weighting and monitor units, the plan was then reoptimized using the MC algorithm with a sampling history of 50,000 ions/spot, and a final dose computed using the MC algorithm with 0.5% statistical uncertainty. Thereafter, the plan was normalized to 95% of the PTV covered by 95% of the prescription dose.

2.D | Dosimetric evaluation and comparison
For all of the above plans, the hot spot dose received by 2% of the volume (D 2% ), the minimum dose received by 99% of the volume (D 99% ), the mean dose (D mean ), the relative volume that received 95% of the prescription dose (V 95% ), and the dose received by 95% of the total CTV and each CTV (CTV breast/CW, CTV IMN, CTV AxI, CTV AxII, CTV AxIII, CTV SCV) (D 95% ) were recorded. The treatment goal was for 95% of each CTV to receive at least 95% of the prescription dose. The dose volume information for OARs was studied for the heart, ventricles, LAD, ipsilateral lung, contralateral lung, esophagus, thyroid, and skin. In addition, the Radiation Therapy Oncology Group (RTOG) conformity index (CI) and homogeneity index (HI) were calculated. The CI was defined as V Target 95% =V Body 95% , where V Target 95% is the target volume receiving 95% of the prescription dose and V Body 95% is the total irritated volume receiving 95% of the prescription dose. Here, we used 95% of the prescription dose in the calculation instead of 100% because all plans were normalized to D 95% to 95% of the prescription dose. The HI was defined as the ratio of D 95% over D 5% . For any plan, the CI and HI fell in the range of 0 to 1.0, with CI = 1.0 for an ideally conformal plan and HI = 1.0 for an ideally homogeneous plan. The Mann-Whitney U-test was used for testing the differences between any two types of plans. A P < 0.05 was considered to be statistically significant. While the MC-renormalized plan restored the CTV D 95% coverage, it had a much larger tail in the high-dose region on the DVH plot compared with the PB plan. The MC-optimized plan provided optimal CTV coverage and homogeneous dose distribution. Table 1 lists the dose statistics for the total CTV in the PB plans, the MC-recomputed plans, the MC-renormalized plans, and the MCoptimized plans. When the PB plans were recomputed using MC for the final dose, the median value of CTV D 99% , D 95% , and D mean dropped by 3.7%, 3.4%, and 2.1%, respectively, of the prescription dose, which rendered the plans not meeting our treatment goal of CTV D 95% ≥ 95% of the prescription dose. The median value of CTV volume that receives 95% of the prescription dose (CTV V 95% ) dropped by 21.8%. The CTV dose coverage reductions were all statistically significant, with P < 10 −5 . The mean and standard deviation (SD) of the dose difference between the MC-recomputed plans and PB plans on CTV D 99% , D 95% , and D mean were 3.3% (2.1%), 3.5%

| RESULTS
(1.0%), and 2.0% (0.4%) of the prescription dose, respectively. The mean and SD of the CTV V 95% difference was 19.8% (10.2%). After renormalization (the MC-renormalized plans), the CTV D 95% , and D 99% were restored (Table 1) In the studied patient cohort, there are three patients with fewer targets of lymph nodes. We have reviewed the data on these three patients and found that there is no systematical trend in these three | 131 patient's data falling close to the either extreme of the range on any studied dose indices. Therefore, including these three cases does not introduce bias in the results.

3.
A | Impact of final dose computation algorithm on each CTV structure: As shown above, the PB algorithm overestimated the target coverage. We further analyzed the target coverage in terms of D 95% and V 95% for each CTV structure separately (

3.B | Comparison between MC-renormalized plans and MC-optimized plans
As shown above, the PB plans significantly overestimated the dose to target, and the MC-renormalized plans were able to T A B L E 1 Median (range) of CTV doses and relative volumes that receive 95% of the prescription dose in four types of plans.  The doses are displayed as percentage of the prescription dose. a The CI on the MC-recomputed plans is not a good plan quality evaluation metric as the CTV coverage is compromised. restore the target coverage. Nonetheless, the target dose heterogeneity increased upon MC-renormalization and exceeded acceptable levels in some cases. We, therefore, investigated the effect of MC optimization. Both the MC-renormalized plans and MCoptimized plans met our CTV coverage goal of D 95% ≥ 95% of the prescription dose. However, the MC-renormalized plans had a significantly higher target hot-spot dose (D 2% ) than the MC-optimized plans.
Since the MC-renormalized plans and MC-optimized plans were able to meet the treatment goal on the CTVs, we compared the dose volume information on OARs to see which plan provided better sparing. Table 3 summarizes the median (range) of the dose volume information on OARs. The doses to the heart, ventricles, and LAD are very small for the right breast/CW patients. Therefore, only the data from the left breast/CW patients were included in the study of these OARs. Similarly, only the data from patients who received the T A B L E 2 Median (range) of D 95% and V 95% overestimation on each CTV structure by the PB plans compared with the MC-recomputed plans. The Dose differences (PB plans -MC-recomputed plans) on OARs also shown here.

CTVs
Breast  | 133 SCV irradiation were included for the study of esophagus and thyroid. As Table 3 shows, the MC-renormalized plans and MC-optimized plans led to similar dose to the heart, ventricles, lungs, and thyroid, but the MC-optimized plans reduced the maximum dose to the esophagus. The MC-optimized plans were also able to provide significantly better skin sparing than the MC-renormalized plans. The MC-optimized plans showed better CI and HI compared with the MC-renormalized plans (Table 3), although the improvement in CI was not statistically significant. Consistent with significantly higher hot spots (D 2% ) in the MC-renormalized plans, the HI was significantly improved (closer to 1) in the MC-optimized plans than in the MC-renormalized plans.
There were no appreciable differences between the MC-renorma- rithm. 13 However, this dose error may not directly translate to PBS treatment for breast cancer, due to the different components that the proton beam passes through before reaching the patient between these two delivery techniques.
We conducted a comprehensive study in 20 clinical breast cancer cases treated with IMPT to investigate the impact of dose algorithms on treatment plans. Our main concern when analyzing the dose difference in the target volume was whether the PB algorithm would substantially overestimate the target dose as compared with the MC algorithm. Thus, if the PB algorithm was used for planning, the target would be irradiated at a lower dose than prescribed, thereby potentially increasing the risk of recurrence. We found that the PB plans significantly overestimated the dose to the target.
These dose overestimations by the PB algorithm warrant further investigation to assess clinical significance.
Although the MC algorithm models the beam more accurately than the PB algorithm, the extended optimization time, especially when robust optimization is applied, is a major concern for planning efficiency.
We have found that an IMPT plan robust optimized on 147 scenarios with a MC algorithm for a breast and regional lymph nodes case on  photon therapy) but also on nuclear reactions that are best calculated with MC. For breast cancer IMPT, beams with a range shifter and a relatively large air gap are used to treat the large target volume extended to the patient surface. Accurate modeling of the nuclear halo resulting from the large-angle scattered particles from nuclear reactions is essential. Proton therapy offers more conformal dose distributions and better OAR sparing for breast cancer, as compared with photon therapy. To ensure these advantages translate into real clinical benefits, accurate dose calculation for breast proton therapy is essential.
In the current study, we have performed a robustness evaluation on the MC-optimized plans. In the worst case scenario of a 5-mm setup error and a 3.5% range uncertainty, all MC-optimized plans reached 95% of CTV covered by at least 90% of the prescription dose, which is our institutional acceptance criteria. In addition, we also chose two extreme cases with the largest and smallest CTV volumes, to perform robustness evaluation on the MC-renormalized plans. The CTVs' D 95% coverage in the worst case scenario from the MC-renormalized plans and the MC-optimized plans were found comparable.

| CONCLUSION
The PB algorithm significantly overestimates the target dose in breast IMPT plans when compared with MC recalculation. The magnitude of the target dose overestimation warrants further investigation to assess clinical significance. The target dose overestimation is higher for CTV CW than for CTV breast. Although MC-renormalized plans restore the target dose coverage, they lead to significantly increased hot spots in the target and significantly higher skin dose.
The MC-optimized plans are able to provide sufficient target dose coverage, acceptable target hot spots, and good sparing for skin and other OARs. Therefore, utilizing the MC algorithm for both plan optimization and final dose computation in breast IMPT treatment planning is desirable.

ACKNOWLEDGMENTS
We would like to thank Katherine Casey-Sawicki, MA, in the Office of Research for editing and preparing this manuscript for submission.

CONF LICTS OF INTEREST
No conflicts of interest.