Calculating dose from a 2.5 MV imaging beam using a commercial treatment planning system

Abstract Patient dose from 2.5 MV images on the TrueBeam linear accelerator is not easily quantified, primarily because this beam energy is not normally modeled by commercial treatment planning systems. In this work we present the feasibility of using the Eclipse® treatment planning system to model this beam. The Acuros XB and the AAA dose calculation algorithms were tested. Profiles, PDDs, and output factors were measured for the 2.5 MV unflattened imaging beam and used for beam modeling. The algorithms were subsequently verified using MPPG 5.a guidelines. Calculated doses with both algorithms agreed with the measurement data to within the following criteria recommended for conventional therapeutic MV beams: 2% local dose‐difference in the high‐dose region, 3% global difference in the low‐dose region, 3 mm distance to agreement in the penumbra, and a gamma pass rate of >95% for 3%/3 mm criteria. Acuros was able to accurately calculate dose through cork and bone‐equivalent heterogeneities. AAA was able to accurately calculate dose through the bone‐equivalent heterogeneity but did not pass within the recommended criteria for the cork heterogeneity. For the 2.5 MV imaging beam, both the AAA and Acuros algorithms provide calculated doses that agree with measured results well within the 20% criteria for imaging beams recommended by AAPM TG‐180.

geometry per disease site, which are likely not representative of other disease sites and nonstandard anatomies. Another method is to perform noncommercial dose calculations, such as Monte Carlo simulations, for patient-specific dose. These calculations are prohibitively time consuming and difficult to perform for normal clinical workflows.
To the authors' knowledge, the 2.5 MV beam has not been modeled by any commercial treatment planning system (TPS) before.
Eclipse® (Varian Medical Systems, Palo Alto, CA) is a commercial TPS that can be used to model therapeutic MV beams with nominal photon beam energies between 4 and 25 MV. 5 The purpose of this work was to validate the accuracy of the Eclipse TPS in modeling the 2.5 MV beam using an accepted model validation framework.
These algorithms are proposed as a tool for routine clinical dose calculations for this beam. Characteristics of the 2.5 MV beam models such as the photon spectrum, mean radial energy, and intensity profile are compared to a commissioned therapeutic beam model since 2.5 MV is lower than therapeutic energies that are typically modeled.

| MATERIALS AND METHODS
In this work we modeled the 2.5 MV imaging beam using both the Anisotropic Analytical Algorithm (AAA) and the Acuros XB algorithm (henceforth referred to as Acuros) in the Eclipse TPS. AAA is a convolution/superposition algorithm and Acuros is a linear Boltzmann transport equation (LBTE) solver. 5 The modeling workflow for this imaging beam was similar to the workflow for modeling therapeutic energy beams.

2.A | Beam model formation
All measured beam data were acquired on a Varian TrueBeam linac at the University of Wisconsin using a BluePhantom2 3D scanning tank (IBA Worldwide, Belgium). Both algorithms require the same input measurement data. Measured profiles were postprocessed by applying a median smoothing filter (5 mm width, 0.2 mm resolution), centering on the central axis for symmetric fields, interpolation to a 1 mm grid using a cubic spline, and mirroring by averaging both sides. Measured PDDs were postprocessed using a least-squares smoothing filter (5 mm width, 0.2 mm resolution) and interpolation to a 1 mm grid using a cubic spline. Measured beam characteristics such as d max and %dd(10 cm) were compared to those reported in the literature for a consistency check. 1,2 Table 1 shows a list of the measured beam data used for commissioning. A CC13 cylindrical ionization chamber (IBA Worldwide, Belgium; active volume = 0.13 cc, diameter = 6.0 mm) was used for all scanning measurements and an A12 ionization chamber (Standard Imaging, Middleton, WI; active volume = 0.64 cc, diameter = 6.1 mm) was used for point dose measurements. Effective point-of-measurement offsets recommended by AAPM TG-51 were applied as appropriate during beam data measurement. 6 In addition to the measured beam data in Table 1, both Eclipse   algorithms require nonmeasured commissioning data, which include: primary energy spectrum, mean radial energy (MRE), electron contamination, and spot size parameters. For typical therapeutic beams such as 6 MV, the Eclipse TPS contains a machine database that include these nonmeasured data for a model machine. For the 2.5 MV beam, these were generated specifically for this project since the database does not contain preconfigured data for this energy.
The primary energy spectrum data represent the energy distribution of the photons leaving the target. The 2.5 MV spectrum was generated by copying the 6 MV spectrum, scaling this down to have a maximum energy of 2.5 MV, and manually adjusting the bins until the calculated PDD curves were optimized.
The MRE curve represents the variation in the photon energy spectrum lateral from the central axis (CAX). For FFF beams, these data are primarily determined by the variation in the bremsstrahlung mean energy as a function of angle from the target. For the 2.5 MV beam, the MRE curve was initially estimated to be constant at 0.5 MV.
The electron contamination data model the relative fluence of electrons as a function of depth. 5 The electron fluence is calculated TG-51 protocol. 6 The beam quality conversion factor, k Q , was assumed to be equal to unity for this beam quality and ionization chamber. This assumption for this imaging beam has been found to be appropriate in previous publications. 1,9 Test 5.3 compares measured commissioning data to calculated data (in the treatment planning module) for a small and large field size.
In addition to the MU calibration condition check (Test 5. Profiles pass these tests if all of the following are true: <2% local dose-difference in the high dose region, <3% global dose-difference in the low-dose region and for PDDs, <3 mm distance to agreement in the penumbra region, and gamma pass rate of >95% using a criteria of 3%/3 mm. b Points A-F indicate locations of profiles or PDDs denoted in Fig. 1. The fields and setups for Tests 5.4-5.8 are shown in Fig. 1. The locations of acquired profiles for these tests are described in reproduced. The CT-electron density calibration of the scanner was verified using MPPG 5.a Test 6.1. 7 The voxels known to be waterequivalent material were overridden to the "Water" preset stored in the physical material table; this assigns the physical density, Hounsfield Units (HU), and electron density of those voxels, and helps minimize the effects of HU blurring at the boundaries. In addition, the bone-equivalent material (CIRS Inc., Norfolk, VA) was overridden to the "Bone" preset stored in the physical material table and a density of 1.90 g/cc was assigned corresponding to the measured physical density of the material. This minimized the effect of the artifacts from the high-Z bone-equivalent material in the CT simulation image.
The dose calculation resolution was 1 mm for all heterogeneity calculations.

| RESULTS
The optimal 2.5 MV spectrum used for commissioning both Acuros and AAA is shown in Fig. 3. The optimized MRE curves are shown in Fig. 4, and the intensity curves are shown in Fig. 5. The intensity curve was calculated by the optimizer; it is not an input in beam modeling. Figures 3-5 include data from 6 MV beam models for comparison. The electron contamination curves for AAA and Acuros are shown in Fig. 6.
The optimal effective spot size parameters are shown in Table 3.
A comparison of the profiles measured with a diode and the calculated profiles are shown in Fig. 7. The optimal spot size parameters in For SAD point doses for 4 × 4 cm 2 and 10 × 10 cm 2 fields, Acuros and AAA were able to reproduce the point dose within the same 0.5% tolerance for 10 of 10 and 9 of 10 of the measured doses, respectively.
Acuros and AAA were able to reproduce the measured commissioning profiles and PDDs (Test 5.3) to within the tolerance criteria specified in Table 2. In addition, both algorithms reproduced measured noncommissioning data (Tests 5.4-5.8) to within these criteria. The results of the heterogeneity Test 6.2 are shown in Table 5. was reproduced by Acuros to within 1% for the cork and 1.5% for the bone-equivalent heterogeneity. The AAA-calculated ratio differed from the measured ratio by 2.9% to 4.2% for the three cork setups.
For the two bone setups, AAA reproduced the measured ratio to within 1.8%.
A summary of the validation results for all tests is shown in Table 6. Typical calculation times for a 10 × 10 cm 2 field in a 50 × 50 × 50 cm 3 homogenous water tank with a 1 mm calculation grid were 36 s for AAA and 9 min, 33 s for Acuros. These calculation times will vary between processing units and should only be considered for relative comparison. Two of the nonmeasured Eclipse commissioning data inputs, the photon spectrum and spot sizes, are not optimized during beam model calculation. Therefore, the beam models were found to be sensitive to changes in the input photon spectrum and spot sizes,

| DISCUSSION
and not sensitive to the input electron contamination parameters and MRE curve. The same photon spectrum was found to be optimal for both Acuros and AAA.
For the MRE curve and electron contamination parameters, the inputs are starting points for the optimizer. Several variations of the MRE curve were input, but the optimizer converged on the same MRE curve independent of this MRE input. For the 2.5 MV beam, the input MRE curve was estimated as constant at approximately 0.5 MV, and the optimizer converged on the curves shown in Fig. 4 for our measured commissioning data.
The optimized electron contamination curve was different between Acuros and AAA, shown in Fig. 6. The Acuros-calculated electron contamination curve is monotonically decreasing with increasing depth. This was not observed for AAA. The electron contamination parameters input to AAA -Sigma0, Sigma1, and T A B L E 3 Optimal effective spot size parameters for Acuros and AAA.
F I G . 7. Comparison of profiles measured with a diode and calculated by Acuros and AAA. The calculation resolution is 1 mm. The setup is 100 cm SSD, 5 cm depth, and jaw-collimated 5 × 5 cm 2 field. These profiles were used to tune the spot size parameters.
RelativeFractionOfSigma0were modified to extremes, but the electron contamination curve was optimized to the same solution (shown in Fig. 6). These changes were used in combination with changes in the initial photon spectrum. For AAA, we were not able to change the optimized electron contamination curve different from what is shown in Fig. 6. The image quality from the 2.5 MV beam has been investigated in the literature. [1][2][3] Although image quality was not a primary motivator of this work, several properties of the beam commissioning parameters indicate the potential for higher image quality of the 2.5 MV beam compared to 6 MV. First, the energy spectrum of the 2.5 MV is much softer (Fig. 3), which increases the number of photons in the diagnostic/orthovoltage energy range where the photoelectric effect provides a mechanism for increased contrast. Second, the 2.5 MV beam is FFF, therefore the mean energy is lower than it would be with a flattening filter, and the mean energy is almost constant at all radial distances, at about 0.5 MV (Fig. 4).
The intensity profile of the 2.5 MV beam is not flat since it is an FFF beam, which must be managed with flood-field normalization for imaging. However, the bremsstrahlung photons are less forwardpeaked for a lower energy beam, which makes the intensity profile flatter as energy decreases. In The calculation of point doses using AAA was found to be sensitive to the resolution of the dose grid. For example, for Test 5.2 the deviation of AAA from model commissioning data ranged from 0.1% F I G . 8. Test 5.5 for AAA for a crossline profile at 5 cm depth along the central axis (passes through Point A in Fig. 1) that does not pass gamma (2%/2 mm) analysis by >95%. The gamma values are greater than unity only in the penumbra region. This profile was acquired with a CC13 ion chamber. to 1.2% for grid resolutions ranging from 1 to 2.5 mm. The 0.7% deviation reported in Table 6 was obtained with a grid resolution of  The loss of charged-particle equilibrium can be observed at the interfaces of heterogenous phantoms, as seen in Figs. 10 and 11. F I G . 9. Test 5.8 for Acuros for an inline profile at 15 cm depth (PDD = 34%) that does not pass gamma analysis (2%/2 mm) by >95%. The gamma values are greater than unity in the penumbra and low-dose region. This profile was acquired with a CC13 ion chamber.
T A B L E 5 Percent difference of ratio of dose above to below heterogeneity for each Setup in Test 6.2.

Setup
Measured ratio AAA over-estimates the dose beyond the heterogeneity for all three cork setups (see Table 5). For the setup in Fig. 10, the AAA-calculated ratio is less than the measured ratio by 3.2%, and would cause an over-estimation of the dose beyond a lung heterogeneity by 3.2%. For the bone heterogeneity measurements, both algorithms were able to reproduce the measured ratio to within 2%. Thus, Acuros should be used for the 2.5 MV beam energy if accuracy within 2% is desired when performing calculations in heterogeneous media.

| CONCLUSION
The 2.5 MV beam was able to be modeled with Eclipse using both the AAA and Acuros algorithms. The calculations from both algorithms were found to pass most MPPG 5.a validation tests using tolerances designed for therapeutic energy beams. The calculations from these algorithms are well within the tolerances recommended for imaging dose calculations, as specified by TG-180. 4 The validated models can be used during the treatment planning process to calculate patient-specific dose for 2.5 MV planar images and better inform clinicians and physicists on the risks and benefits of using this imaging beam.

ACKNOWLEDG MENTS
The authors thank the students and staff of the UWMRRC for their continued support, the UWRCL and UWADCL customers whose calibrations help support ongoing student research at the UWMRRC, and Charles Matrosic for his help in this work.

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