Density scaling of phantom materials for a 3D dose verification system

Abstract In this study, the optimum density scaling factors of phantom materials for a commercially available three‐dimensional (3D) dose verification system (Delta4) were investigated in order to improve the accuracy of the calculated dose distributions in the phantom materials. At field sizes of 10 × 10 and 5 × 5 cm2 with the same geometry, tissue‐phantom ratios (TPRs) in water, polymethyl methacrylate (PMMA), and Plastic Water Diagnostic Therapy (PWDT) were measured, and TPRs in various density scaling factors of water were calculated by Monte Carlo simulation, Adaptive Convolve (AdC, Pinnacle3), Collapsed Cone Convolution (CCC, RayStation), and AcurosXB (AXB, Eclipse). Effective linear attenuation coefficients (μ eff) were obtained from the TPRs. The ratios of μ eff in phantom and water ((μ eff)pl,water) were compared between the measurements and calculations. For each phantom material, the density scaling factor proposed in this study (DSF) was set to be the value providing a match between the calculated and measured (μ eff)pl,water. The optimum density scaling factor was verified through the comparison of the dose distributions measured by Delta4 and calculated with three different density scaling factors: the nominal physical density (PD), nominal relative electron density (ED), and DSF. Three plans were used for the verifications: a static field of 10 × 10 cm2 and two intensity modulated radiation therapy (IMRT) treatment plans. DSF were determined to be 1.13 for PMMA and 0.98 for PWDT. DSF for PMMA showed good agreement for AdC and CCC with 6 MV x ray, and AdC for 10 MV x ray. DSF for PWDT showed good agreement regardless of the dose calculation algorithms and x‐ray energy. DSF can be considered one of the references for the density scaling factor of Delta4 phantom materials and may help improve the accuracy of the IMRT dose verification using Delta4.


| INTRODUCTION
It is necessary to verify the agreement between dose distributions calculated by a radiation treatment planning system (RTPS) and delivered by a linear accelerator (linac) for intensity modulated radiation therapy (IMRT). 1,2 A number of approaches and systems have been developed for this verification. [2][3][4][5][6][7][8][9][10][11][12][13] Recently, three-dimensional (3D) dose verification systems consisting of a solid phantom and detector arrays have become commercially available. These 3D dose verification systems can measure the absorbed dose at thousands of measurement points, and they are efficient in verifying the 3D dose distribution.
IMRT dose verifications should be evaluated more accurately. Kly et al. 14 showed that institutional patient-specific IMRT quality assurance (QA) does not necessarily detect unacceptable plans. In their study, 14% of plans accepted by institutional IMRT QA were described as fail by an audit. In other words, even if an IMRT plan is accepted by one verification system, this does not ensure that the plan will be accepted by another verification system. Although various causes can be considered for this discrepancy, commissioning of verification systems is important to ensure the evaluation certainty.
Because the verification is basically comparing the dose distributions in a solid phantom measured by the detectors and that calculated by the RTPS, the appropriate density scaling factor of the solid phantom used in the verification system should be adopted in the RTPS, where the density scaling factor is defined as a density to be assigned for the phantom material in RTPS (e.g., physical density, relative electron density, or other value).
A number of studies for IMRT 3D dose verification systems have been reported. One of these 3D dose verification systems (Delta4 (ScandiDos, Inc., Ashland, VA, USA)) consists of 1069 silicon diodes arranged on two orthogonal boards in polymethyl methacrylate (PMMA) or Plastic Water Diagnostic Therapy (PWDT) as shown in Fig. 1. It has been used for IMRT patient-specific QA, 13,[15][16][17][18][19][20] commissioning of volumetric modulated arc therapy (VMAT), 21 and comparisons of dose calculation algorithms. 22,23 However, these studies had an approximately 2% dose difference resulting from the difference in density scaling factors of the phantom materials. Pham et al. 15 and Feygelman et al. 18 evaluated Delta4 with the same photon energy, phantom material, and RTPS; the former adopted a density scaling factor of 1.19, while the latter adopted 1.14 for the PMMA phantom. Other studies 13,17,19,[21][22][23] have not reported the adopted density scaling factor, and their appropriateness has not been discussed so far.
The purpose of this study was to clarify the optimum density scaling factor for PMMA and PWDT in order to improve the accuracy of the calculated dose distributions in the phantom materials of Delta4. The density scaling factors proposed in this study (DSF) for PMMA and PWDT were determined from measurements and calculations with several algorithms. The appropriateness of the DSF was validated by dose verifications with several plans using commercially available algorithms.

2.A.1 | Measurements of l eff
Tissue-phantom ratios (TPRs) in water, PMMA, and PWDT were measured at field sizes of 10 9 10 and 5 9 5 cm 2 with 6 and 10 MV x rays from linacs (Clinac iX and 21EX (Varian Medical Systems, Palo Alto, CA, USA)). Calibration slab phantoms of Delta4 were stacked, and an ionization chamber (30013, PTW, Freiburg, Germany) was set at a source-to-chamber distance (SCD) of 100 cm, as shown in Fig. 2 The geometries of the phantoms in the calculations were modeled to be the same as the measurement. The phantoms were assigned as water but the physical densities were varied from 0.96 to 1.19 g/cm 3 .
The reasons for assigning the material of the phantoms as water were: Appearance of a 3D dose verification system (Delta4, ScandiDos). The silicon diodes are placed at 5 mm intervals in a central 6 cm 9 6 cm area and at 10 mm intervals elsewhere in a 20 cm 9 20 cm area on two orthogonal boards in the cylindrical phantom materials with a diameter of 22 cm. The standard detector geometry is depicted ("X"). If the attachment for sagittal-coronal option was used, the detector geometry could be rotated to the "+" orientation.
(a) the phantoms could not be assigned as PMMA for AdC and PWDT for AdC, CCC, and AXB, and (b) the physical density of the materials other than water could not be changed from the default physical density for CCC and AXB. For the Monte Carlo simulation, the phantom materials were generated in PEGS (Preprocessor for EGS). 27 The phase space data of the particles were scored and validated by comparing between calculated and measured depth dose and off-axis ratio in water, and they were used in all simulations. The simulations were repeated until a statistical uncertainty of less than 0.1% was obtained.
For the RTPS dose calculations, the grid size was 2 mm for AXB and 1 mm for the other dose calculation algorithms because dose using AXB with a grid size of 1 mm could not be calculated under several conditions due to a shortage of computer memory resources. The reference depth of the TPRs was set to the shallowest depth. The l eff at each condition were determined from the slope of the exponential regression curve approximating the TPR curve.

2.B | Determining DSF
DSFs were determined through comparisons of the measured and calculated TPRs. To compare the TPRs between the measurements and calculations, the ratios of l eff in phantom and water ((l eff ) pl,water ) were used. The measured (l eff ) pl,water were obtained by dividing the l eff measured in phantoms by the l eff measured in water. The calculated (l eff ) pl,water were obtained by dividing the l eff calculated with various density scaling factors by the l eff calculated with the density scaling factor of 1.0. Although the beam qualities of the linacs used in this study were consistent, the l eff calculated with the density scaling factor of 1.0 had a small variation among the dose calculation algorithms due to the modeling accuracy. This normalization is to make the changes of the slope of the TPRs for density scaling factors independent of the modeling accuracy of the each dose calculation algorithm.
The measured (l eff ) pl,water were used as the reference value in the comparisons. The calculated (l eff ) pl,water were obtained as a function of the density scaling factors. The regression line approximating the median values of the (l eff ) pl,water calculated by the dose calculation algorithms for several density scaling factors was drawn. When the regression line matched the measured (l eff ) pl,water , the density scaling factor was set to DSF regression for the x-ray energy, field size, and phantom material. Finally, for each phantom material, the mean value of DSF regression was used to define DSF.
Additionally, specific DSFs for dose calculation algorithms (sDSF) were determined. Individually, the regression line approximating the (l eff ) pl,water calculated by each dose calculation algorithm for several density scaling factor was drawn. When each regression line matched the measured (l eff ) pl,water , the density scaling factor was set to sDSF of the dose calculation algorithm for a given condition. EDs of PMMA and PWDT are 1.159 and 1.003, respectively. 28,29 The following dose calculation algorithms were used for the verification: AdC (Pinnacle 3 ver. 9.0 for PMMA and 9.10 for PWDT), CCC, and AXB. Three plans were used for the verifications: one was 10 9 10, which denotes a static field of 10 9 10 cm 2 with static gantry angles of 45°and 315°for the "+" (sagittal-coronal option) detector geometry and 0°for the "X" (standard) detector geometry.

2.C | Dose verifications with different density scaling factors
The others were IMRT plans using "mock head&neck" and "mock prostate" in AAPM TG-119. 30 The IMRT plans were created following the dose constraints shown in AAPM TG-119. 30 The delivery techniques for the IMRT plans were step-and-shoot in Pinnacle 3 and VMAT in the others. Before all measurements, the dose per monitor unit (DMU) of each x-ray energy was obtained in accordance with the standard dosimetry protocol, and the daily machine output was corrected by the daily correction factor from the built-in Delta4 software. These dose verifications were evaluated according to the pass rate of the global gamma index (gGI) for different criteria (2%/2 mm and 1%/1 mm) and the median of the global dose deviation (gDD) with the lower dose threshold of 20%. The normalization doses for the gGI and gDD were set to the measured dose at the isocenter for 10 9 10 and 2.0 Gy for the IMRT plans.
Example of the phantom geometry used to measure TPRs. Normally, the manufacturer provides one slab for buildup, one slab for chamber insert, and one slab for backscatter in order to measure the absorbed dose at a depth of 4.25 cm in PMMA and 4.95 cm in PWDT for the cross-calibration of Delta4. This figure shows four PWDT buildup slabs, one PWDT chamber insert slab (SCD = 100 cm, depth = 15.45 cm), and one PMMA slab for backscatter. The manufacture provides only PMMA for the backscatter slab. In this study, several sets of the calibration slab phantoms were stacked to measure TPRs at several depths. To calculate TPRs in the Monte Carlo simulation and RTPS, the geometry and phantoms were modeled the same as the geometry of the measurements.  respectively. At a field size of 5 9 5 cm 2 , DSF regression of 6 and 10 MV x ray were 1.13 and 1.14 for PMMA, and 0.98 and 0.99 for PWDT, respectively. Therefore, DSF in this study was determined as 1.13 for PMMA and 0.98 for PWDT, as given in Table 1.

3.A | l eff of TPRs
At a field size of 10      | 109 dose should become gradually higher when the adopted density scaling factor becomes gradually lower. However, the median of gDD using ED (1.159) was not between that using PD (1.19) and DSF (1.13). This may be due to the coarse resolution of the mass attenuation coefficient in an older version of Pinnacle 3 , as pointed out by Dickof. 31 Except for AXB within PMMA, the pass rates of gGI increased and median of gDD moved close to 0% from the PD to DSF. The tendency was consistent regardless of the dose calculation algorithms, verification plans, and x-ray energy within PWDT, as shown in Table 3. DSF for PWDT showed good agreement between the measured and calculated dose distributions under multiple conditions. On the other hand, as shown in Table 2, DSF for PMMA showed good agreement between those in AdC and CCC with 6 MV x ray, and AdC for 10 MV x ray for 10 9 10. The PD or ED showed good agreement between those in AXB with 6 MV x ray, and CCC and AXB with 10 MV x ray for 10 9 10. The results within PMMA varied depending on the dose calculation algorithms and x-ray energy.
Although the dose verifications of 10 9 10 for AXB within PMMA were conducted in three institutions after the absolute dose calibration for the Delta4 detectors, these results were unchanged. This removes the dependence of these results on site-specific errors such as linac output, cross-calibration of Delta4, or beam data in RTPS.
In Tables 2 and 3

| DISCUSSION
The choice of density scaling factor has a large effect on the ability to accurately calculate dose distributions in the Delta4 phantoms.
T A B L E 2 Summary of the pass rates (%) of gGI with the criteria of 2%/2 mm and 1%/1 mm, and median (%) of gDD of several dose calculation algorithms with physical density (PD), relative electron density (ED), and DSF for PMMA.  38 was the reference for the relative electron T A B L E 3 Summary of the pass rates (%) of gGI with the criteria of 2%/2 mm and 1%/1 mm, and median (%) of gDD of several dose calculation algorithms with physical density (PD), relative electron density (ED), and DSF for PWDT.  28,29,39 The DSF are the lowest density scaling factor acquired theoretically.
DSF was shown to be the optimum density scaling factor for PWDT regardless of the dose calculation algorithm and x-ray energy.
Furthermore, the changes of the (l eff ) pl,water calculated by the dose calculation algorithms were consistent at each density scaling factor for PWDT. On the other hand, these changes were not consistent for PMMA. Specifically, these changes of AdC were lower than those of other dose calculation algorithms and those of AXB were higher in several conditions, as shown in Figs. 3 and 4. The reason these differences occurred in treating different densities of water for PMMA was difficult to specify because the details of the dose calculation algorithms related to treat different densities of water in the calculations opened to the public were limited. At least, the results showed the possibility that optimum density scaling factor for AdC may become higher than DSF such as ED and the one for AXB may become lower than DSF through the dose verifications.
However, in the dose verifications for PMMA, DSF was the optimum density scaling factor in AdC and CCC with 6 MV x ray, and AdC with 10 MV x ray. The PD or ED may be the optimum density scaling factor in AXB with 6 MV x ray, and CCC and AXB with 10 MV x ray, nevertheless none of the (l eff ) pl,water calculated by the dose calculation algorithms matched the measured (l eff ) pl,water at PD and ED, as shown in Fig. 2. A reason for the considerable deviation may be the accuracy of the absorbed dose calculation in a higher density of water. Because DSF were obtained from the slopes of the TPRs, the DSF were not found to be an appropriate density scaling factor for the absorbed dose calculation in different densities of water. If there was some mismatch or uncertainty between the slope of the depth dose and absorbed dose calculated in a different density of water, it should be corrected by something other than the density scaling factor.

| CONCLUSIONS
The difference in density scaling factors caused a bigger dosimetric difference than the pass/fail criterion. We clarified DSF of PMMA and PWDT from measurements and calculations, and validated the appropriateness of DSF. The DSF were lower than not only the PD but also the ED. DSF can be used as a reference for the density scaling factor of the Delta4 phantom material in multiple clinical institutions and may help improve the accuracy of the IMRT dose verification using Delta4.