Verification of Acuros XB dose algorithm using 3D printed low‐density phantoms for clinical photon beams

Abstract The transport‐based dose calculation algorithm Acuros XB (AXB) has been shown to accurately account for heterogeneities primarily through comparisons with Monte Carlo simulations. This study aims to provide additional experimental verification of AXB for clinically relevant flattened and unflattened beam energies in low density phantoms of the same material. Polystyrene slabs were created using a bench‐top 3D printer. Six slabs were printed at varying densities from 0.23 to 0.68 g/cm3, corresponding to different density humanoid tissues. The slabs were used to form different single and multilayer geometries. Dose was calculated with Eclipse™ AXB 11.0.31 for 6MV, 15MV flattened and 6FFF (flattening filter free) energies for field sizes of 2 × 2 and 5 × 5 cm2. EBT3 film was inserted into the phantoms, which were irradiated. Absolute dose profiles and 2D Gamma analyses were performed for 96 dose planes. For all single slab configurations and energies, absolute dose differences between the AXB calculation and film measurements remained <3% for both fields in the high‐dose region, however, larger disagreement was seen within the penumbra. For the multilayered phantom, percentage depth dose with AXB was within 5% of discrete film measurements. The Gamma index at 2%/2 mm averaged 98% in all combinations of fields, phantoms and photon energies. The transport‐based dose algorithm AXB is in good agreement with the experimental measurements for small field sizes using 6MV, 6FFF and 15MV beams adjacent to various low‐density heterogeneous media. This work provides preliminary experimental grounds to support the use of AXB for heterogeneous dose calculation purposes.

Acuros XB has previously been investigated and validated with Monte Carlo simulations (VMC++, EGS4 etc) in heterogeneous geometries 2,7,8 and compared with other dose calculation algorithms. 9 Inhomogeneities have been simulated in varying complexity in terms of geometry, density, and material compositions for different field sizes and energies. 3 In most of these cases Monte Carlo simulations, which is generally considered the gold standard in dose calculation, were used as the main reference for the algorithm validation. In general, AXB provides a fast and accurate alternative to Monte Carlo calculations for patient dose calculation. This has been demonstrated by good Gamma agreement (>86% pass rates for 3%/ 3 mm) for heterogeneous settings (normal lung, very low density lung, and bone) when compared with MC calculations, and as an improvement over AAA in terms of improved accuracy and reduced computation time for lung VMAT plans.  17 and thorax phantom 18 to evaluate AXB for IMRT and volume modulated arc therapy (VMAT), using TLDs and Gaf-Chromic EBT2 film to obtain absolute point dose and planar dose measurements, respectively. Furthermore, the majority of studies were limited to only using 6MV beam energy. The present investigation looks to provide much needed data on experimental validation of AXB for a variety of clinically relevant beam energies, particularly in the case of lung VMAT and SBRT treatments, in a variety of 3D-printed, low-density geometries.
Published dosimetric comparisons have shown that the main advantage of AXB is accurate dose calculation in low-density tissues. 2,[18][19][20] Since AXB uses a density-to-material mapping table, it would be prudent to verify the algorithm experimentally in the range of both high-and low-density tissues. To experimentally validate the algorithm in both density ranges, phantoms need to be fabricated with the same tissue equivalent materials. In this work, we have investigated only the low-density range for clinical energies of interest in the small field sizes, due to inherent limitations of the 3`D printing fabrication process employed. That said, the investigation of small field size and low-density tissue range for AXB validation is of clinical relevance as these conditions are akin to those of lung SBRT treatments, which has been a topic of interest with respect to the application of AXB. [21][22][23][24][25] To this end, we have designed and developed phantoms of consistent material composition but with variable densities using a desktop 3D printer. In the context of inhomogeneities in treatment planning algorithms, dosimetric scalability (via methods such as equivalent path length) and their validation is of particular interest.
To our knowledge, there is no economical and commercial equivalent of variable density plastics available in the market. This work looks to supplement the Monte Carlo validation of the AXB algorithm performed thus far, with experimental evidence for a variety of clinically relevant photon energies, in small fields and low-density phantoms. This work is also unique in the dosimetric applicability of cost-effective 3D desktop printing in a cancer centre.  Each polystyrene slab was surrounded by 4 cm of Solid Water TM (Gammex-RMI, Middleton, WI, USA) above and 5 cm below. Customcut Perspex sheets were used to surround the slab laterally to minimize air gaps between layers. Figure 1 shows a schematic representation of the phantom setup for two geometries tested: single-slab and multiple-slabs. For the single-slab, GafChromic EBT3 (Ashland Advanced Materials, Bridgewater, NJ, USA) films were placed above (depth P in Fig. 1) and below (depth Q in Fig. 1) the polystyrene slab.

2.A | Experimental setup and geometry
Variable density slabs were swapped to create 6 single-slab phantom configurations. For the multi-slab phantom, slabs 3, 6, and 4 ( Table 1) were stacked with the films placed above, below and between each of the layers of polystyrene (depths A through D in Fig. 1). All seven phantoms were CT-scanned with a 3 mm slice thickness.

2.B. | Dose calculation and measurements
The CT datasets were imported into Eclipse TM (Varian Medical System) treatment planning system, and dose calculations were performed for 6MV, 6FFF (6MV Flattening Filter Free) and 15MV beams from a Varian TrueBeam TM linear accelerator. The irradiations were planned for field sizes of 2 9 2 cm 2 and 5 9 5 cm 2 with source-to-surface distance (SSD) set to 100 cm. These smaller, clinically-relevant field sized are typical of lung SBRT treatments, where we would expect more challenges for the dose calculation accuracy in low-density media. A dose of 200 cGy was planned to a 4 cm depth ( Fig. 1

depth P).
From the previous AXB studies, 1,3,10-14 most of the institutions used a default dose grid of 2.5 mm for dose computation, therefore a calculation grid size of 2.5 mm was chosen for the AXB dose calculations with dose reported as dose-to-medium. AXB can also report dose-to-water; however, it was not pursued in our study. 27 The decision of reporting dose-to-water or dose-to-medium has been a point of discussion in the past and justification of our choice in this study is provided in Discussion. No volume of the radiation field was allowed to travel through the lateral Perspex.  For a single slab phantom of low-density 0.23 g/cm 3 (Slab 4), dose was also computed with the commonly available AAA. Dose planes were extracted both at depths P and Q for the three energies and both field sizes.
All films and fabricated plastic slabs were aligned using external fiducial markings (BBs), placed on the phantom before CT simulation.
The irradiations were done for all six single slab phantom setups and the multi-slab setup, for two radiation fields and three beam energies with radiochromic films placed as shown in Fig. 1. Prior to each irradiation, the output of the linear accelerator was verified with an ionization chamber in a SolidWater TM phantom. The ionization chamber calibration is traceable to a primary standard at NRCC (National Research Council of Canada).

2.C | Film dosimetry
GafChromic EBT3 film, which was designed for clinical dosimetry, was used in all of the studies. Small (4 9 4 cm 2 ) EBT3 film calibration strips from the same batch were cut and marked for orientation.
The films were reproducibly placed in a plastic template and scanned The dose-to-water at 5 cm depth was determined from ionization measurements and using cross-calibration factors related to absolute dosimetry using AAPM TG51 protocol guidelines.
All calibration film strips were scanned as previously described at the same location on the scanner, 24 AE 4 h after irradiation to ensure the optical density of the polymerized film has stabilized. Pre-irradiation images were used to account for zero dose background intensity. for the multi-slab setup, calculated by Eclipse using AXB were exported and compared with the film measurements obtained from the GafChromic EBT3 films. We repeated irradiations for one configuration to verify the reproducibility. DoseLab Pro version 6.50 was used to perform film calibration and comparisons with calculated dose planes. Two-dimensional local Gamma evaluation was performed for each film using 2% absolute dose and 2 mm distance-toagreement criteria with a 10% dose cutoff threshold. 29 3. | RE SULTS

3.A | Single slab phantom measurements
Absolute dose profiles were extracted in the cross-plane direction from the films and compared with AXB calculated dose profiles for all configurations of slabs, energies and field sizes. Figures 2 and 3 show the profiles for the single slab phantom (density 0.68 g/cm 3 [slab 6]) for field sizes of 2 9 2 and 5 9 5 cm 2 , respectively. The ratio of measured-to-calculated dose is also superimposed onto each profile. Dotted horizontal lines (AE3% relative error) are drawn for guidance. All measurements and computations were found to be within 3% of each other, excluding the 90-10% penumbra regions.
Absolute dose profiles were extracted from the films at depth P and Q for Slab 4 (slab with lowest available density of 0.23 g/cm 3 ) and compared with corresponding computed profiles from AAA and AXB for the three energies and the 5 9 5 cm 2 field size. Figure 4 shows the absolute profiles and relative difference between computation and measurements. The results show that both algorithms were within 3% of the film measurements for all three energies in the high-dose region.
For all planar doses, 2D Gamma analyses were performed. Table 2 shows failure rates for each absolute 2D Gamma analysis for 6MV, 6FFF and 15 MV beams and the stated 2%/2 mm criteria.
All measured Gamma data showed pass rates ranging from 96.7% to 100% for all three beam energies and both field sizes at depths Q and P in the single slab phantoms.

3.B | Multi-slab phantom measurements
Reasonable profile agreement was observed at all depths in the multi-slab phantom to within 3% of computation. Table 2 also summarizes the 2D Gamma analysis for the multi-slab phantom geometry for all energies, field sizes, and depths (A through D). As a whole, all Gamma indices were able to achieve >95% pass rate with the majority of indices exceeding a high pass rate of~98% for 2%/2 mm evaluation criterion for all energies and both field sizes in the multi-slab ZAVAN ET AL. of radiotherapy such as the development of 3D printed electron bolus. 32 We have shown that a simple, inexpensive, and desktopbased printer can fabricate uniform and homogeneous phantom materials with minimal effort. 26  For the single slab phantom geometry ( Fig. 2 and For a small field of 2 9 2 cm 2 , the agreement also remained within 3% of dose measurements close to the center axis of the beam, deteriorating only in the penumbra region of the beam. Kan et al. 16 investigated the differences in dose at distal interfaces using 6MV beams and AXB for 2 9 2 cm 2 fields and obtained differences in up to 6% across media interfaces. 15   Although strict alignment of printed slabs was observed between the simulation and measurements, slight variations from setup to setup could also result in disagreements, especially close to field edges. We used two tools for analysis: (1) The absolute dose profiles along the cardinal axes and (2) planar dose comparison using 2D Gamma analysis. The profiles require absolute alignment between the measurement and computations. This method is affected by T A B L E 2 Absolute 2D Gamma failure rates, 2%/2 mm criteria at depths P and Q for the single-layer configuration, and depths A, B, C, and D for the multi-layer configuration. step-size resolution, especially in the penumbra, and suffers when using the same evaluation criteria for the high-dose regions and penumbra. Gamma analysis is somewhat forgiving in terms of alignment using distance to agreement along with the absolute doses.
The AAPM TG 53 report recommends a 3%/3 mm acceptance criterion between calculated and measured dose distributions for commissioning a treatment planning system. 33  In the multi-slab phantom configuration, dose profile agreement is achievable within 3% of measurements at all depths. Table 2 lists 2D planar Gamma analysis for all energies and the two field sizes; in all cases 97.1-100% of points pass the Gamma criteria. This is a strong indication of accurate modeling of radiation transport through multi-density layers for the tested 6MV, 6FFF and 15 MV beams.
Central axis discrete depth dose (Fig. 6) show that the achievable agreement is within 5%. This may be due to mixture voxels created at each interface in the phantom and the coarse spacing of the dose grid. 35 The mixture voxels consisting of both air and plastic are F I G . 5. Planar gamma index for the 2 9 2 cm 2 15MV beam (top) and 5 9 5 cm 2 6FFF beam (bottom) at depths Q (left) and P (right) with a slab of density 0.68 g/cm 3 .
created along all interfaces between these materials. The voxel material is an average of air to plastic contents available in a voxel.
The measured dose is systematically lower due to the formation of an air gap for the shallow layer, resulting in a slight offset in the rest of the interfaces.
Several sources of uncertainty need to be considered when interpreting the film measurements. In this study, all measurements were performed using GafChromic ETB3 films commissioned with an inherent inaccuracy of 2%, which remains the main contributor to uncertainties in the measurements.
TrueBeam TM output was recorded prior to measurements and the variation was found to be <1% of the beam output. Uncertainties in setup were thoroughly analyzed for potential variations between CT simulation and actual radiation delivery. Dose planar measurements were done above and below 3D printed slabs, which resulted in various interfaces causing an uncertainty of about 2 mm due to the reproducibility of setup. This can cause a dose variation of about 2% at depths P and Q. Uncertainty due to SSD setup was determined to be <1 mm. The 3D printed blocks can vary by as much as AE0.5 mm in thickness between each block, and has the potential for creating a F I G . 6. Central axis depth dose plots for the multi-slab geometry. Energies shown are 6MV (top), 6FFF (middle), and 15MV (bottom) for field sizes 5 9 5 cm 2 (left) and 2 9 2 cm 2 (right). Media used from left to right: Solid Water, slab 3 (0.51 g/cm 2 ), slab 6 (0.68 g/cm 2 ), slab 4 (0.23 g/cm 2 ), and Solid Water. Discrete film measurements are plotted. The error bars represent one standard deviation of the mean of an ROI of 3 9 3-pixel width around the center. Color overlay of rectangular blocks approximately shows the various density slabs.
small air gap adjacent to the upper interface at depth P. Each layer of EBT3 film is approximately 0.25 mm thick which can add up to 1 mm for a multi-slab phantom geometry. Table 3 provides a concise summary and description of various sources of uncertainty.
Another source of uncertainty arises from overlapping dosimetric quantities-dose-to-water, dose-to-medium and dose-to-plastic in our experiments. The quantity measured with film is dose-to-water, which is obtained by converting optical density to dose. EBT3 film is known to be tissue equivalent in the Compton interaction range of energies and low Z eff for the low-energy component of MV photons. 18,26,28 The treatment machine is calibrated in terms of dose-to-water according to the national and international dosimetry protocols. The differences between dose-to-water and dose to most soft tissues are clinically insignificant (within 2%). 31,36,37 The overall uncertainty of all the setup and delivery, taken in quadrature (as in Table 3), is estimated to be below 3%.
Through this work, we have provided an experimental framework for validation of transport-based dose calculation in single-slab and multi-slab low-density geometries for common clinical beam energies. By developing custom phantoms using materials tailored to specific clinical needs, one can characterize the specific modeling capabilities of new dose calculation engines.

| CONCLUSIONS
The advanced dose algorithm AXB was found to provide satisfactory agreement with experimental measurements using 6MV and 15MV flattened photon beams, as well as for unflattened 6FFF beams in low-density heterogeneous media. This work provides an experimental evaluation of AXB algorithm for dose calculations in the challenging scenario of small fields irradiating low-density regions, such as lung and adipose tissue. This provides added confidence in using this dose calculation algorithm in clinically relevant scenarios, such as the treatment of small lesions with relatively small field sizes in regions located at or in close proximity to soft tissue, low-density interfaces, such as SBRT treatments for non-small cell lung cancer.
T A B L E 3 Uncertainty analysis for experimental validation of AXB using 3D printed polystyrene slabs.