Transitioning from measurement-based to combined patient-specific quality assurance for intensity-modulated proton therapy

Abstract

Objective:

This study is part of ongoing efforts aiming to transit from measurement-based to combined patient-specific quality assurance (PSQA) in intensity-modulated proton therapy (IMPT). A Monte Carlo (MC) dose-calculation algorithm is used to improve the independent dose calculation and to reveal the beam modeling deficiency of the analytical pencil beam (PB) algorithm.

Methods:

A set of representative clinical IMPT plans with suboptimal PSQA results were reviewed. Verification plans were recalculated using an MC algorithm developed in-house. Agreements of PB and MC calculations with measurements that quantified by the γ passing rate were compared.

Results:

The percentage of dose planes that met the clinical criteria for PSQA (>90% γ passing rate using 3%/3 mm criteria) increased from 71.40% in the original PB calculation to 95.14% in the MC recalculation. For fields without beam modifiers, nearly 100% of the dose planes exceeded the 95% γ passing rate threshold using the MC algorithm. The model deficiencies of the PB algorithm were found in the proximal and distal regions of the SOBP, where MC recalculation improved the γ passing rate by 11.27% (p < 0.001) and 16.80% (p < 0.001), respectively.

Conclusions:

The MC algorithm substantially improved the γ passing rate for IMPT PSQA. Improved modeling of beam modifiers would enable the use of the MC algorithm for independent dose calculation, completely replacing additional depth measurements in IMPT PSQA program. For current users of the PB algorithm, further improving the long-tail modeling or using MC simulation to generate the dose correction factor is necessary.

Advances in knowledge:

We justified a change in clinical practice to achieve efficient combined PSQA in IMPT by using the MC algorithm that was experimentally validated in almost all the clinical scenarios in our center. Deficiencies in beam modeling of the current PB algorithm were identified and solutions to improve its dose-calculation accuracy were provided.

Introduction

Pencil beam scanning (PBS) is becoming the predominant beam delivery technique in proton therapy because it provides more d to reduce the dose to normal tissues than does passive scattering method.^1–5 In PBS, intensity-modulated proton therapy (IMPT), beam properties, including energy, size, position and intensity are modulated on a spot-by-spot basis for tailoring the dose distribution to the tumor geometry, minimizing the radiation exposure in surrounding healthy tissues. The highly modulated treatment plan and highly conformable dose distribution in IMPT pose challenges to the beam delivery system and the dose-calculation engine. A slight deviation in beam delivery or approximation in dose calculation may lead to a significant discrepancy between the planned and delivered doses.

A key component in assuring the accuracy and safety of IMPT is a comprehensive patient-specific quality assurance (PSQA) program. PSQA is employed to verify the 1) the dose-calculation accuracy of the treatment planning system (TPS), 2) integrity of data transfer from the TPS to the accelerator control system and 3) delivery of the treatment.⁶ Most IMPT PSQA programs were initially developed based on experience with intensity-modulated radiation therapy (IMRT) QA, in which physical measurement of the dose distribution was widely used and considered to be the standard⁷ validation approach. In our institution, prior to treatment, patient treatment plans were verified on a field-by-field basis using conventional water phantom measurements. Due to the high modulation of intensity in IMPT and dramatic changes influence between energy layers, we measured planar dose distributions at multiple depths instead of single depth to sample the complex dose distribution in each field.⁶ The measurement at additional depths requires more beam time for the measurement itself and greater effort for data analysis, which are stressful under the 20 h clinical operations per weekday. This has led to our ongoing efforts of creating an effective and efficient QA program.⁸ The central piece of the infrastructure for our PSQA is a platform called HPlusQA,⁹ including analytical independent dose calculation,^10,11 automatic analysis of the comparisons of measured and calculated dose distribution and log file analysis.¹² One of the limitations of this implementation was that the independent dose calculation was based on an in-house developed analytical pencil beam (PB) algorithm, suffering from similar limitations of all analytical based algorithms. Therefore, we still perform the depth measurements in addition to the single dose plane verification for each field.

The current clinical TPS is Eclipse (Varian Medical Systems, Palo Alto, CA), which also uses an analytical PB convolution algorithm for dose calculation.^13,14 With the introduction of beam modifiers such as range shifters (RSs) and apertures into more treatment plans, the failure rate for PSQA increased to about 15% (June 2017–June 2018), which makes the tight work schedule for clinical operations even more stressful.

If the dose accuracy of TPS and the independent dose engines could achieve the confidence level, we would be able to reduce the additional depth measurements, moving toward an efficient combined (including independent dose calculation and log file analysis with or without dosimetric measurements) PSQA. However, general guidelines regarding the methodologies and tolerance levels for PSQA have yet to be established. As the counterpart to IMRT in radiotherapy, using the IMRT QA practice as a reference in IMPT is reasonable. In recently reported IMRT QA results, the average γ passing rate was nearly 100% for the 3%/3 mm criterion^15–18 and greater than 95% for the 3%/2 mm or 2%/2 mm criteria.^17,18 Based on the high passing rate and increased confidence about the TPS and delivery system in IMRT, physicists proposed to move from measurement-based to combined PSQA. Of note is that the failure rate in IMPT QA is higher than that in IMRT QA, with less strict γ index acceptance criteria (IMPT QA, “>90% γ passing rate using the 3%/3 mm criteria”¹⁴; IMRT QA, “>90% γ passing rate using the 3%/2 mm criteria”).¹⁹ We believe that if the passing rate of IMPT QA is comparable with that of IMRT QA, IMPT QA will also be more amenable to combined approach to improve the efficiency of clinical operations. Therefore, the first objective of the study is to determine whether use of better dose-calculation engine such as the Monte Carlo (MC) algorithm can increase the passing rate in PSQA to that in photon therapy, so that IMPT can be shifted toward combined approach.

Improving the dose-calculation algorithms used by the clinical TPS would also improve the PSQA passing rate, when compared with measurements and/or MC-based independent dose calculations. MC algorithms are becoming available for commercial proton TPS. On the other hand, MC results could also be used to improve the analytical dose models used by the TPS and independent dose engines. Improved analytical dose calculation can result in accuracy similar to that of MC-based dose calculation for some disease sites. The use of MC-based dose calculation is increasing in photon therapy practices, as well. However, due to the improvement of analytical dose-calculation algorithms, the passing rate in IMRT QA is so high than in clinical practice, the majority of centers currently use analytical dose-calculation algorithms, which are faster than and whose accuracy is as good as that of MC algorithms in terms of PSQA. Analytical dose-calculation algorithms in proton therapy are not as accurate as those in photon therapy. Replanning or dose correction was required frequently in complex treatment plans in order to meet the acceptance criteria of PSQA, which is time-consuming. Moreover, concerns about the dose-calculation accuracy confine proton therapy from being introduced to complex cases that get more dose sparing in critical organs over photon therapy. Improving the dose-calculation accuracy of the analytical algorithm not only facilitates the workflow of treatment planning and verification but also helps to expand the area treated with proton therapy. The second objective of this study was to use the MC algorithm to investigate the systematic beam modeling deficiencies of analytical dose-calculation algorithms and show the proton therapy community how to improve the beam modeling for IMPT.

Methods and materials

Proton beam delivery system

The IMPT was performed at a synchrotron-based proton beam delivery system (PROBEAT Proton Beam Therapy System, Hitachi America, Ltd, Tarrytown, New York). The 94 energies available range from 72.5 to 221.8 MeV, corresponding to proton beam ranges of 4–30.6 g/cm² in water. The system uses a 6.7 g/ cm² RS to bring back the shallowest Bragg peak to 0.3 g/cm². In the absence of RS, the in-air spot sizes at the isocenter in terms of full width at half maximum vary from 1.2 cm at the highest energy to 3.4 cm at the lowest energy. In the presence of RS, the spot sizes range from 1.3 to 3.2 cm.

Selection of treatment plans

To understand the inherent modeling limitations of analytical dose-calculation algorithms in clinical settings, 80 representative treatment plans that previously failed to meet the clinical PSQA criteria at some depth measurements were reviewed retrospectively. Our hypothesis that IMPT can be shifted toward combined PSQA using the MC algorithm could be confirmed if the MC algorithm could achieve confident PSQA results for these worse cases.

A total of 556 dose-plane measurements from 219 treatment fields were analyzed. They covered a wide range of real clinical plan settings concerning the beam range, spread-out Bragg peak (SOBP) width, field size, and use of RS and aperture. The treatment sites of the plans include the head and neck (45 cases), thorax (17 cases) and pelvis (18 cases). An RS only was used in 76 of these fields, and a combination of RS and aperture was used in 63 of them. Measured data for depths in the proximal, center and distal regions of the SOBP were included in the study. Detailed parameters of the treatment plans are listed in Table 1.

Table 1.

Planning characteristics for the 80 representative treatment plans

Characteristic	Head and neck	Thorax	Pelvis
Number of plans	45	17	18
Number of fields	131	47	41
Number of dose planes
Total	337	116	103
No beam modifier	30	96	78
RS	154	18	22
RS +aperture	153	2	3
Median nominal beam range, cm (range)	12.81 (4.99–23.49)	18.28 (7.02–25.98)	25.19 (4.33–28.67)
Median SOBP width, cm (range)	11.89 (4.98–21.81)	12.05 (4.3–20.54)	11.49 (4.33–22.47)

RS, range shifter; SOBP, spread-out Bragg peak.

Treatment planning using the Eclipse TPS

All patient treatment plans were optimized and calculated using the Eclipse TPS. The PB algorithm implemented in Eclipse calculates dose D (x,y,z) by convolving the three-dimensional dose distribution in water of a beamlet ${\displaystyle D_{E_i}^{beamlet}\left(x,y,d\left(z\right)\right)}$ with the undisturbed fluence in air, ${\displaystyle {\mathrm{\Phi }}_{E_i}\left(x,y,z\right)}$^20–23:

$${\displaystyle \begin{array}{ll}\mathrm{D}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=& \sum _{E_i}\sum _{beamle{t}_j}{\mathrm{\Phi }}_{E_i}\left(x_j,y_j,z\right)D_{E_i}^{beamle{t}_j}\\ & \left(x_j,y_j,d\left(z\right)\right)\left(x-x_j,y-y_j,d\left(z\right)\right)\end{array}}$$

in which z is the longitudinal distance from the origin and d(z) is the water-equivalent depth. The dose model for IMPT was commissioned using two Gaussian functions characterizing single-spot lateral profiles in air, the weight of which was adjusted to fit the field size effects measured in water.

Plans were optimized using either single-field optimization, in which each field was optimized individually, or multifield optimization, in which all fields were optimized simultaneously. An RS was used in each field covering a superficial tumor (water-equivalent depth lower than 4 cm), and an aperture was added to the RS if sparing of a critical organ adjacent to the tumor (e.g., spinal cord, lens) was difficult to achieve via optimization.

A verification plan was then generated by recalculating the patient treatment plans in a set of virtual images of the homogeneous water phantom. This verification plan, in which the measurement depths and planes of each field were defined, was exported to HPlusQA for subsequent dose comparisons. For each treatment field, at least three measurement depths ranging from the proximal to the distal regions of the SOBP were selected for verification.

Recalculation of verification plans using an MC-based fast dose calculator

Dose distributions in all of the verification plans were recalculated using an MC-based fast dose calculator (FDC).²⁴ The output files from FDC were converted to digital imaging and communications in medicine format and imported into the Eclipse TPS as a new verification plan. Dose comparison was performed using HPlusQA as in routine clinical practice. The FDC was described in detail previously.²⁴ In summary, this track-repeating algorithm retracks proton trajectories in a water phantom generated using Geant4 and calculates the dose deposition by scaling the step length and scattering angle between steps according to the relative mass density of material interacted with the proton. FDC has been validated against measurements of depth and lateral profiles in water for monoenergetic proton beams.²⁵ For patient dose calculation in IMPT, the FDC accuracy was demonstrated in a clinical case study of 23 patients using the full MC simulation Geant4 as the benchmark.²⁶

PSQA measurement

PSQA measurements were performed using a two-dimensional ion chamber array detector MatriXX (IBA Dosimetry, Schwarzenbruck, Germany) and a set of solid water blocks as buildup material. MatriXX was calibrated against the parallel ion chamber Markus (PTW Dosimetry, Freiburg, Germany). The ion chamber array and solid water blocks were positioned perpendicular to the beam direction. The measurement procedures consisted of the following three steps:

1. In the physics mode of the accelerator control system, 100 μ of a 10 × 10 cm spot-scanning field at a gantry angle of 270° was delivered to obtain the daily absolute dose-correction factor for MatriXX.

2. In the treatment mode of the accelerator control system, beams were delivered at the actual treatment gantry angle through MOSAIQ software program (Elekta Medical Systems, Sunnyvale, CA), and the dose was measured at 2, 5, or 10 cm water-equivalent depth according to the tumor depth. This step was termed MOSAIQ measurement.

3. In the physics mode of the accelerator control system, beams were delivered at a gantry angle of 270°, and the dose was measured at two or three additional depths. This step was termed depth measurement.

The measured planar dose distribution was compared with those calculated using the Eclipse TPS and FDC. The action level was set at a 90% γ passing rate using the 3%/3 mm criteria, where voxels with a dose lower than 10% of the normalization dose were excluded.

Data analysis

In clinical practice, for each dose plane, the γ passing rate using the 3%/3 mm criteria was evaluated. The results for the 2%/2 mm criteria were also evaluated to obtain more quantitative information on PSQA performance to assess the accuracy of the PB and MC algorithms. Agreement with measurements and percentage of dose planes passed the acceptance level were compared for PB and MC calculations. Comparisons of PSQA results between groups classified by the relative position of the SOBP, the use of beam modifiers, and the treatment sites were performed to identify the specific aspects of modeling deficiency for the PB algorithm. The MATLAB (release 2016b; Mathworks, Inc., Natick, MA) and SPSS (v. 24.0; IBM, Armonk, NY) were used for data processing and statistical analysis. The p-value threshold for significance was set at 0.05.

Results

Gamma passing rate distributions

Figure 1 presents the γ passing rate distributions when plans were calculated using the PB and MC algorithms. MC recalculation exhibited significantly improved agreement with measurements (Table 2). Only 71.4% of the dose planes passed the clinical acceptance criteria in the original PB calculation, whereas the percentage was 95.14% in the MC recalculation. For the 2%/2 mm criteria, MC recalculation improved the γ passing rate by an average of 11.65% when compared with the PB calculation. For the 3%/3 mm criteria, the mean (±standard deviation [SD]) γ passing rates were 91.61±11.62% and 98.00±3.77% for the PB and MC calculations, respectively.

Figure 1.

γ passing rates results using the 2%/2 mm (a) and 3%/3 mm (b) criteria for the PB and MC calculations. Abbreviations: PB, pencil beam; MC, Monte Carlo.

Table 2.

PSQA results for PB and MC algorithms

γ criteria	PB	MC
2%/2 mm
Mean (±SD) γ passing rate	82.15±16.84%	93.80±7.59%
Number of dose planes exceeded 90% γ passing rate (percentage)	249 (40.65%)	436 (78.42%)
3%/3 mm
Mean (±SD) γ passing rate	91.61±11.62%	98.00±3.77%
Number of dose planes exceeded 90% γ passing rate (percentage)	397 (71.40%)	529 (95.14%)
Number of dose planes exceeded 95% γ passing rate (percentage)	306 (55.04%)	488 (87.77%)

MC, Monte Carlo; PB, pencil beam; PSQA, patient-specific quality assurance.

Comparison of PSQA results at different region of SOBP

Comparisons of depth dose profiles and γ index score distributions at three depths in one field for a lung cancer patient are shown in Figure 2. Also, Figure 3a summarizes the γ passing rates using the 2%/2 mm and 3%3 mm criteria for dose planes at the proximal, center and distal regions of the SOBP. The MC algorithm performed much better than the PB algorithm in the proximal and distal regions, improving the γ passing rate by an average of 11.27% (p < 0.001) and 16.80% (p < 0.001), respectively, for the 3%/3 mm criteria. Use of the MC algorithm reduced the failure rate from 48.98 to 0% in the proximal regions, and reduced the failure rate in the distal regions from 65.57 to 10.66%, in which the failure rate is the percentage of dose planes that fail to meet the clinical acceptance criteria. The improvement was moderate in the center of the SOBP, where the mean (±SD) γ passing rates were 95.83±5.52% and 98.29±3.24% for the PB and MC algorithms, respectively.

Figure 2.

Depth dose profiles (a) and corresponding γ index score distributions (b) in the proximal, center and distal regions of the SOBP for the PB and MC algorithms in a lung cancer patient. Abbreviations: SOBP, spread-out Bragg peak; PB, pencil beam; MC, Monte Carlo.

Figure 3.

γ passing rates of the planar dose distribution calculated using the PB and MC algorithms for dose planes grouped by the relative depth of the SOBP (a), use of beam modifiers (b) and treatment site (c). In each colored box, the central red line indicates the median value, and the bottom and top edges represent the 25th and 75th percentiles, respectively. The whisker corresponds to the range within 1.5 times the interquartile from the edge of the box. Data outside this range are plotted as outliers (+). Abbreviations: SOBP, spread-out Bragg peak; PB, pencil beam; MC, Monte Carlo.

Comparison of PSQA results in the presence of beam modifiers

Figure 4 shows the depth dose profile and γ index score distributions at measured depths for a head and neck treatment field with RS. In Figure 3b, the γ passing rate results are compared for the PB and MC calculations in fields with and without beam modifiers. MC recalculation reduced the failure rate by 29.41%, 22.68%, and 17.72% in the subgroups with no beam modifier, RS, and both RS and aperture, respectively. In the subgroup with no beam modifier, the percentage of dose planes that exceeded 95% γ passing rate using 3%/3 mm criteria was 98.04% in the MC recalculation.

Figure 4.

Depth dose profiles (a) and the corresponding γ index score distributions (b) in the center, and distal SOBP regions for the PB and MC algorithms in a head and neck treatment plan using RS. Abbreviations: SOBP, spread-out Bragg peak; PB, pencil beam; MC, Monte Carlo; RS, range shifter.

For the 3%/3 mm criteria, MC recalculation showed greater improvement over PB calculation in the fields without beam modifiers (average increase in γ passing rate, 8.64%) than with beam modifiers (RS, 4.98%; RS +aperture, 5.20%). For the PB algorithm, better agreement with measurements was achieved in fields using beam modifiers (mean [±SD] γ passing rate, 92.20±10.14%) than in the subgroups without beam modifiers (mean [±SD] γ passing rate, 90.60±13.77%), but the difference was not significant (p = 0.164). However, the trend was different for the MC algorithm, with which the mean (±SD) γ passing rate in fields without beam modifiers (99.24±1.27%) was significantly higher than that in fields with RS (97.28±4.48%; p < 0.001). Also, the mean (±SD) γ passing rate of the fields with RS and aperture (96.56±4.52%) was slightly but significantly lower than that in fields using RS only (97.86±4.38%; p = 0.007) in MC recalculation. The outliers showed that the dose planes with the lowest γ passing rate for the PB and MC algorithms in fields without a beam modifier and fields with RS and aperture, respectively.

Comparison of PSQA results for different treatment sites

We also compared the γ passing rates for three treatment sites calculated using the PB and MC algorithms as shown in Figure 3c. For the MC algorithm, nearly 100% of the dose planes in the pelvis and thorax subgroups passed the clinical acceptance criteria, and the passing percentage in the head and neck subgroup was 92.28%. For the PB algorithm, despite the greater data variations resulting from the poor agreement in the distal region of the SOBP, the pelvis field had a higher median γ passing rate (97.9%) than did the thorax (94.15%) and head and neck (95.58%) fields. The percentages of dose planes met the acceptance criteria were 74.76, 64.66 and 72.70% in the pelvis, thorax and head and neck fields, respectively.

Discussion

As one of the core components of quality control in radiation oncology, PSQA is used to assess variations in treatment based on sufficient commissioning of the treatment system. The variations have three components: dose calculation, data transfer and machine delivery. Given the confidence in dose-calculation accuracy, the well-developed IMRT is geared toward combined PSQA, which would ease the measurement pressure and greatly enhance the operational efficiency in multiroom spot-scanning proton therapy centers. It could be adopted for IMPT only if confident QA results based on measurements can be justified. Based on the reasoning toward combined PSQA in IMRT, we established the following internal goal for IMPT combined PSQA: 98% of dose planes exceeding the 95% γ passing rate threshold for the TPS and secondary-check dose-calculation engine. First, for a change in clinical practice, this confidence level for dose-calculation accuracy was set in the perspective of executable implementation, for there are some uncertainties in dose measurements. Second, even in our depth measurements, we only used two additional depths which did not detect all potential dose-calculation errors in the depths not measured, the accurate independent dose calculation can check all depths. For this reason, we do not require independent dose calculation is in 100% agreement with measurement in two additional depths.

If this goal is met, we would focus PSQA measurement more on the delivery aspect. We believe that the end-to-end test performed using treatment plan data in the oncology information system with one set of dose measurement is complementary to routine machine QA and log-file-based treatment monitoring. The additional depth measurements, which were used for further verification of clinical TPS dose model, would be replaced by independent dose calculation with high degree of confidence. The results of our commissioned PB algorithm in IMPT were far from our internal goal. In the present retrospective study of suboptimal PSQA results, we found that for MC recalculation for verification plan, 93.89% of the dose planes met the γ passing rate threshold of at least 95% using the 3%/3 mm criteria, but this still did not meet our internal goal to adopt combined PSQA for IMPT. However, MC recalculation did significantly improve PB calculation. We found that if a field did not contain beam modifiers such as RS and aperture, almost 100% of the dose planes achieved a γ passing rate of 98%. We decided to use independent MC calculation to replace depth measurement with fields not containing beam modifiers after several months of further validation. We also observed a deficiency in our MC implementation in modeling RSs and apertures. We will continue to improve the MC algorithm so that dose calculation using it can completely replace additional depth measurements in our IMPT PSQA program.

For dose calculation of a verification plan in a water phantom, the typical FDC calculation time is 5–15 min, which is similar to the calculation time of the current independent dose calculation in HPlusQA. Therefore, replacing the independent dose-calculation engine in HPlusQA with MC algorithm would still fit within the clinical time frame in the aspect of independent dose verification. Furthermore, it would save a considerable amount of treatment room time by eliminating the additional depth measurements. Taking the oropharynx patients with bilateral target volumes receiving three-field IMPT as an example, the treatment room time for each patient would be reduced from 100 to 150 min to approximately 30–50 min depending on the number of patients measured per session.

Because the MC algorithm has limited availability for the most proton therapy centers (only an in-house MC algorithm is available at our center), improving PB algorithms has its merits. The major differences between the MC and PB algorithms were in the proximal and distal regions of the SOBP. In those regions, PB calculation poorly matched measurements, whereas the MC calculation agreed with the measured data very well. However, in the central SOBP region, the MC and PB calculations both agreed with the measurements very well.

Regarding modeling the RS, in the central SOBP region, both algorithms exhibited better agreement with measurements in the fields without beam modifiers than in those with beam modifiers. In a previous study,²⁷ we found that the air gap had a great impact on dose-calculation accuracy in the presence of RS and that the effect was neglected by the Eclipse TPS. By applying the MC-calculated dose correction factor for specific energy based on the actual air gap, the γ passing rate increased from 80.0 to 99.8%. The finding for the MC algorithm was in contrast with those reported by Winterhalter et al,²⁸ who did not observe a significant difference between the PSQA results for fields with and without RS. Such a difference may be attributed to different MC implementation, which remains to be figured out in future studies. In the distal region of the SOBP, the MC algorithm was less consistent with measurements in fields with RS than in those without RS, whereas the PB algorithm showed poorer agreement in the fields without RS than in those with RS. This suggested that the MC algorithm was less effective in modeling the effects of the RS and aperture in the distal falloff than in the central SOBP. Meanwhile, the PSQA data for MC calculation in fields with RS varied considerably. Additionally, we observed that implementation of an aperture substantially lowered the γ passing rate of the planer dose distribution for the MC algorithm. In summary, extensive experimental validations are required before the MC algorithm can be established as a gold standard for dose calculation.

We found that the PB algorithm was comparable with the MC algorithm in predicting the dose in the center of the SOBP. As shown in Figure 3a, the dose calculated by the Eclipse TPS matched well with the measurement in the central SOBP region, where the average γ passing rate was 95.83% and the data variation was relatively small. In this region, MC recalculation resulted in marginal improvement when compared with PB calculation, suggesting that the accuracy of the PB algorithm in predicting target coverage was comparable with that of the MC algorithm. The accuracy of the PB algorithm in the center of the SOBP was attributed to great effort devoted to tuning the beam parameters in a double Gaussian model to keep the calculated field size factor deviation from measurement within 2% during TPS commissioning.¹³ Our result is consistent with the findings of Yepes et al,²⁹ who reported that the median difference between the Eclipse TPS and FDC in D98 and D95 of the target volume was less than 2% in the entire cohort. Also, Winterhalter et al³⁰ compared dosimetric indices of treatment plans calculated using in-house developed PB and MC algorithms and found that all the indices of the planning target volume, differed by no more than 4%. Moreover, Shin et al³¹ experimentally observed that in PSQA, two algorithms did not differ significantly with regard to the γ passing rate at tumor depth, but their study was confined to simple prostate treatment plans. The present experimental validation, together with previous plan comparisons for a wide range of representative fields,²⁹ not only demonstrated better IMPT QA results for the MC algorithm than for the PB algorithm but also relieved concerns about the target coverage predicted by the PB algorithm.

Of note, for the PB algorithm, most of the PSQA failures occurred in the proximal and distal regions of the SOBP. Trnkova et al³² reported similar pronounced discrepancy between calculated and measured dose in the distal region in a detailed analysis of their PSQA outcomes. Our results are similar to those reported by Saini et al³³ for a heterogeneous lung phantom, in which the PB algorithm showed increasing mismatch with measurements in the distal region of the SOBP. Unlike the measurements in the central SOBP, measurements in the proximal and distal areas are sensitive to setup errors of measurement devices. A slight deviation in depth may cause a manifest dose discrepancy. As reported previously,⁸ in clinical practice, we extended the comparison between the measured and calculated doses to the dose planes that are 2 mm shallower and deeper than the nominal depth when the γ passing rate exceeded the clinical tolerance. Substantially improved agreement between measurement and MC recalculation (Figure 3a) over a wide range of dose planes demonstrated the inadequacy of beam modeling in PB algorithm could be another reason for the inconsistency with the doses measured at the nominal depth. Figure 5 compares the dose profiles computed using the PB and MC algorithms for the last energy layer extracted from the treatment field shown in Figure 2. The right side of Figure 5 depicts the longitudinal and transverse profiles of the pristine Bragg peak, in which spots with equal weight are evenly spaced. For the regular spot arrangement in the monoenergetic layer, doses calculated using the PB and MC algorithms were nearly identical, whereas for the clinically irregular spot arrangement, the dose calculated using the PB algorithm was lower than that calculated using the MC algorithm. Therefore, it is the limitation of low-dose envelope modeling in the PB algorithm that caused dose underestimation in the proximal and distal regions of the SOBP. The deviation to measurements in the proximal region of the SOBP was less pronounced than that in the distal region because the dose was deposited by a larger number of spots and energy layers, the radiation parameters of which is closer to the calibrated condition. To summarize, for the PB algorithm, a dose calibrated at limited depth under a broad beam of regular shape cannot adequately handle all of the possible clinical settings with a highly irregular spot arrangement and small fields. The MC algorithm, which tracks individual particle in each interaction with the medium, can predict the low-dose tail of single spot dose distribution more accurately. Thus, the MC algorithm consistently agreed with measurements at multiple depths. Jiang et al³⁴ revealed that it is possible to improve the predictive power of the PB algorithm by incorporating the power–law relationship into the long-tailed section of the dose distribution.

Figure 5.

Dose profiles calculated using the PB and MC algorithms at the highest energy in the clinical field (a) and regular geometric field (b). (c and e) The depth (c) and transverse dose profiles (e) of the field in a. (d and f) The depth (d) and transverse dose profiles (f) of the field in b. Orange lines, PB algorithm; blue lines, MC algorithm. Abbreviations: PB, pencil beam; MC, Monte Carlo.

Conclusion

We demonstrated that MC-based dose calculation can significantly improve the planar dose γ passing rate for IMPT PSQA. Given the results of this study, we believe that the second part of dose measurements can be eliminated, increasing clinical efficiency while maintaining treatment quality when MC algorithm was used as an independent dose calculation for the fields without RS. If beam modifiers are better modeled in the future MC algorithm, it is possible to use that MC algorithm for independent dose calculation in place of depth measurement of all treatment plans in our IMPT PSQA program. With additional Gaussian functions for single-spot fluence modeling, the PSQA results for the PB algorithm in the central SOBP were clinically acceptable, but an inherent deficiency in low-dose envelope modeling still hinders this algorithm from handling highly modulated spot arrangements at various depths. To achieve safe, high-quality, efficient IMPT, we recommend the vendor to implement an efficient MC-based dose-calculation engine into TPS. In addition, great effort should be devoted to validating field size effect, particularly in the presence of beam modifiers. For current users of the PB algorithm, further improving the dose-calculation accuracy by employing a power–law relationship for long-tail modeling or using MC simulations to generate the dose correction factor is necessary.