Radiological tissue equivalence of deformable silicone‐based chemical radiation dosimeters (FlexyDos3D)

Abstract FlexyDos3D, a silicone‐based chemical radiation dosimeter, has great potential to serve as a three‐dimensional (3D) deformable dosimetric tool to verify complex dose distributions delivered by modern radiotherapy techniques. To facilitate its clinical application, its radiological tissue needs to be clarified. In this study we investigated its tissue‐equivalence in comparison with water and Solid Water (RMI457). We found that its effective and mean atomic numbers were 40% and 20% higher and the total interaction probabilities for kV x‐ray photons were larger than those of water respectively. To assess the influence of its over‐response to kV photons, its HU value was measured by kV computed tomography (CT) and was found higher than all the soft‐tissue substitutes. When applied for dose calculation without correction, this effect led to an 8% overestimation in electron density via HU‐value mapping and 0.65% underestimation in target dose. Furthermore, depth dose curves (PDDs) and off‐axis ratios (profiles) at various beam conditions as well as the dose distribution of a full‐arc VMAT plan in FlexyDos3D and reference materials were simulated by Monte Carlo, where the results showed great agreement. As indicated, FlexyDos3D exhibits excellent radiological water‐equivalence for clinical MV x‐ray dosimetry, while its nonwater‐equivalent effect for low energy x‐ray dosimetry requires necessary correction. The key findings of this study provide pertinent reference for further FlexyDos3D characterization research.

Over the past decade, two novel gel-type dosimeters have been proposed, both of which work in similar physical principles as radiochromic gel dosimeters but are not of hydrogel matrix: the polyurethane dosimeter known as Presage and the silicone dosimeter as FlexyDos3D. Proposed in 2003 10 and driven by sustained scientific efforts 11 on modification, characterization, and application, Presage has become a commercial product available for radiotherapy community (Heuris Inc, Lawrence, NJ, USA). FlexyDos3D, first proposed in 2015, [12][13][14] is relatively young and still at the early stage of research and development.
FlexyDos3D is made of silicone elastomer with radiochromic leuco dyes and halogens as radiosensitive agents. When exposed to ionizing radiation, the color forming leuco dyes react with free radical initiators in the halogens. The reactions subsequently induce changes in optical absorption, which are quantitatively related to the localized absorbed dose and therefore the dose distribution can be remapped via calibration. Since silicone elastomer, the matrix material, is optically transparent and mechanically flexible, FlexyDos3D is not only an ideal dosimeter to fabricate deformable anthropomorphic dosimeter phantoms 12,13 but also suitable for optical-CT readout without artifacts caused by sample flasks or Schlieren bands. 15 In the meantime, the chemical recipe of FlexyDos3D has been optimized by Høye et al. 16 to exhibit desired dose-rate independent and linear dose response.
From the perspective of clinical radiotherapy quality assurance (QA), an ideal dosimeter should be radiologically tissue-equivalent over the energy range of radiation beams. The water-equivalence of hydrogel and Presage has been evaluated with valuable references for research and clinical practice. [17][18][19] While De Deene et al. 12 has reported that FlexyDos3D dosimeters of the original chemical formula have larger mass attenuation coefficients for low energy, its tissue equivalence has not been fully studied yet. In this paper, we investigate the tissue equivalence of the optimized dose-rate independent FlexyDos3D in a wellrounded hybrid approach by theoretical calculation, x-ray CT measurement and Monte Carlo simulation.
The results are compared with water as benchmark and Solid Water (RMI457) as reference, a commercial water substitute for radiotherapy dosimetry. 20 The rest of the paper is organized as follows: Section 2 details the elemental composition of FlexyDos3D and the methods to assess its tissue-equivalence; Sections 33 and 44 presents and discusses the radiological properties and dosimetric quantities of interest; Section 5 summarizes the major conclusions.

| MATERIALS AND METHODS
The fabrication method of the finely tuned dose rate independent FlexyDos3D was first presented. Then its elemental composition was derived and used as material information for the following theoretical calculation and Monte Carlo simulation. In this work, tissue-equivalence were assessed from four aspects: (a) key physical parameters of radiological interest were first calculated, including equivalent electron density, effective atomic number, and interaction probabilities; (b) Housefield unit (HU) value was measured by kilovoltage (kV) computed tomography (CT) and the impact of its deviation from water to treatment planning system (TPS) dose calculation were evaluated; (c) magavoltage (MV) relative dosimetry indices, that is, percentage depth doses (PDD) and profiles were modeled by Monte Carlo simulation; (4) a toy volumetric modulated arc therapy (VMAT) treatment was computationally delivered to FlexyDos3D and reference materials by Monte Carlo and their dose distributions were compared.

2.A | FlexyDos3D fabrication and elemental composition
To fabricate dose-rate independent FlexyDos3D dosimeters, 16  Based on the chemical formula and weight fraction of each component, the equivalent elemental composition of FlexyDos3D was determined as listed in Table 1 with water and Solid Water as reference.

2.B | Electron density, effective and mean atomic number calculation
Electron density, effective atomic number and mean atomic number are key theoretical quantities to radiological evaluate tissue-equivalence.
For each material, the electron number per cubic cm (ρ e ), electron number per gram (n e ) and relative electron density (r e ) (named as real density in Eclipse (Varian Medical Systems Inc.)) were calculated by: where N A is the Avogadro's number, ρ is the mass density, and Z i , A i , and w i are respectively the atomic number, atomic mass number and weight fraction of element i.
According to ICRU Report No. 35, 21 the mean atomic number Z mean was calculated by eq. (4). In the meantime, the effective atomic number Z eff was determined using the classic Mayneord formula 22,23 as in eq. (5): where f i is the mass fraction, a i is the electron fraction, and M Ai is the molar mass of element i.

2.C | Photon interaction probabilities and electron stopping powers
For kV imaging and MV treatment photon beams, photoelectric absorption, Compton scattering, and pair production effect are governing interactions between x-ray photons and the materials that photons traverse, and the interaction probabilities can be defined by mass attenuation coefficients as: where (τ/ρ), (σ/ρ), (κ/ρ) are the mass attenuation coefficient of photoelectric absorption, Compton scattering, and pair production, respectively, and (μ/ρ) is the total mass attenuation coefficient. The mass attenuation coefficients of different materials were calculated using the NIST XCOM database with mixure rule option over the energy span from 1 to 20 MeV. 24 For electron radiotherapy beams, projectile electrons from a linac deposit energy along traverse paths in travelling media by exciting and ionizing atoms. In the process of interaction with electrons, stopping powers are recommended quantities to evaluate tissue equivalence in ICRU Report 44. 25 Herein, we used NIST ESTAR database 26 with the mixture rule option to calculate the mass collisional stopping powers (S c /ρ), mass radiative stopping powers (S r /ρ), and total mass stopping powers (S t /ρ) of different materials over the energy range from 10 keV to 20 MeV: 2.D | KV x-ray CT based HU value and the derived electron density In radiotherapy treatment planning, dose calculation is based on the equivalent patient/phantom electron density distribution derived from kV CT images via HU value to electron density calibration.
Herein, we first measured the HU value of FlexyDos3D and compared with that tissue substitutes. Following the fabrication procedure in Section 2.2.1A, a cylindrical FlexyDos3D insert phantom (diameter = 30 cm, height = 8 cm) was made as shown in Figs Linux cluster. 27 Manufacturer-distributed phase space files scored above the upper jaw were used to sample initial particle state, whereas the jaws and collimators are modeled according to geometry description provided by the manufacturer. 28 Particle histories were set according to the field size, ranging from 4 × 10 9 to 5 × 10 10 , in order to achieve a mean statistical uncertainty of 0.5% (k = 1) over all the voxels with doses greater than 50% of the maximum dose. The cross-section data were generated by the PEGS4 Alongside the simulation results, detector-measured PDD and profile curves were also given. The reference-field and large-field measurements were from TrueBeam Representative Beam Data (RBD). 30 We contoured part of the rod as a structure (denoted as DOS) to mimic a volumetric dosimeter inserted into the phantom. Inside DOS, we contoured a tumor-like small volume as toy gross tumor volume (GTV), which was targeted by a one-course full-arc VMAT plan as shown in Fig. 3. After treatment planning in Eclipse, the treatment plan and structure information (stored in DICOM-RP and DICOM-RT files) were imported into our Monte Carlo platform as in Section 2.E2.6 for further processing.
With consideration of computing resource limits, the resolution of the phantom was down-sampled to 3 mm to achieve converged dose scores within reasonable time. An in-house python script was used to assign water as the material of the phantom except DOS. Similarly, the material inside DOS was assigned to water, solid water, and FlexyDos3D interchangeably to obtain different dose distribution within corresponding material. In DOSXYZnrc, Source 21 was used to simulate the VMAT beam delivery, where a BEAMnrc program was compiled as a particle source (dynamic library) for the DOSXYZnrc simulation. 33 The movement of jaws and MLCs, the rotation of the collimator, and the rotation of the gantry within the frame of reference of the irradiated phantom were all synchronized with MU indices. Primary particle histories were set at 1 × 10 10 such that a mean statistical uncertainty of 0.5% (k = 1) over the voxels with at least 50% global maximum dose.
T A B L E 2 Electron density, effective atomic number, and mean atomic number for materials of interest.

3.B | Photon interaction probabilities
The total mass attenuation coefficients (μ/ρ) of FlexyDos3D, Solid Water, and water are plotted in Fig. 4(a), and the relative ratios normalized by water are shown in Fig. 4(b). According to the general trend, the curves can be separated into three parts: in the energy range below 100 keV, the characteristic K-edge of FlexyDos3D can be easily identi- | 93 difference less than 2%; for the energy beyond 1 MeV, the curves become slightly divergent, where (μ/ρ) of FlexyDos3D is 5% higher than water and Solid Water exhibits 2% under-response to water.

Figs. 5(a)-5(c). It is obvious that photoelectric effect plays a dominant
role for all the three materials when photon energies are below 100 keV. Since the cross-section of photoelectric effect is approximately proportional to cube of atomic number, 23 that is Z 3 , the difference of fractional probabilities around 50 keV between FlexyDos3D and water is as large as 20%. When photon energies increase all the way to 20 MeV, Compton scattering becomes dominant, the crosssection of which is closely related to electron density. As calculated in Section 3.3.1A, r e between FlexyDos3D and water is as small as 0.19%. This can well explain the negligible probability difference. For photons with energies beyond the threshold value of 1.02 MeV, pair production starts to occur and the interaction probability increases slightly as photon energy goes up. Since the cross-section of pair production is dependent on Z 2 /A, the differences between FlexyDos3D Solid Water and water indicate that FlexyDos3D has a slightly larger Z 2 /A value than both Solid Water and water.

3.C | Electron stopping powers
The stopping powers of FlexyDos3D, Solid Water, and water are plotted in Figs. 6(a)6(d). We can see in Fig. 6  exhibits about 10% lower stopping power over the energy from 1 keV to 10 MeV, but the discrepancy gets narrower gradually to less than 1% from 10 to 20 MeV.

3.D | HU value measured by kV x-ray CT
The HU values of tissue substitute rods were calculated within circular ROIs as shown in Fig. 7(a), and the results are listed in Fig. 7(b).
The uncertainties drawn as error bars are expressed as the standard deviation (k = 1) of HU values in each contoured structure. It is evident that for kV x-ray beam FlexyDos3D has a high HU value (123.9 ± 9.5), which is much larger than water (−2.79 ± 8.7) and other soft tissue substitutes (for example, HU Liver = 43.6 ± 7.3 and HU Muscle = 43.2 ± 9.2) and 53.9% of the trabecular bone substitute (228.255 ± 8.5). Although silicone has a similar density to water, HU values from CT scans reveal FlexyDos3D performs more like highdensity tissues rather than soft tissues. This can be attributed to the fact in Section 3.B that FlexyDos3D has larger photon interaction probabilities than water for photons with energies less than 100 keV, which are the major x-ray photons produced by x-ray tubes and utilized in clinic for medical imaging purpose.

3.E | Electron density overestimation effect on dose calculation
The HU-value to relative-electron-density (r e ) conversion curve in our Eclipse is shown in Fig. 8(a), where the measured HU-value and theoretically calculated r e pair, that is, (123.9, 1.0019) is highlighted as red dot. We can see that the real r e value of FlexyDos3D is below the conversion curve and its corresponding HU is about 20, which means that the r e derived by HU-value conversion is larger than its real value. If uncorrected, this would lead to about 8% overestimation of r e .
To quantitatively analyze this r e over-estimation effect on dose calculation, we calculated the 3D gamma of the dose distribution with and without HU correction. The criteria we used is 1%/1mm, and the reference was the dose distribution calculated with water replacement (HU = 0). The 3D gamma is 100% for both cases.
In the meantime, we defined relative dose difference (denoted as DIFF) as below in (7) to further evaluate the impact of electron density effect and the effectiveness of HU correction.
where x = 20 represents the dose distribution where the ROI's HU value related to the correct FlexyDos3D electron density value, and x = 124 represents the dose distribution where the ROI's HU value was directly measured from the x-ray CT images.
The results in the dose-maximum plane are illustrated in Figs. 8(c) and 8(d). We can see that without HU correction the DIFF values of the ROI are generally about 0.65% under-estimated, ranging from −1.002% to 0.743%; those with HU correction are much smaller between −0.128% and 0.082%.

3.F | PDD curves
The simulated PDD curves in FlexyDos3D, Solid Water, and water at various field sizes are plotted in Fig. 9(a) for 6-MV and Fig. 9(b) for 10-MV. The uncertainties represented as error bars are generally less than 0.6% for 2 cm × 2 cm and 10 cm × 10 cm, and smaller than 1% for 40 cm × 40 cm.
As  In Fig. 9 we can see that the simulated PDDs in FlexyDos3D, Solid Water, and water change highly in phase with each: the depth dose first increases from the surface and then decreases gradually with maximum at 1.5 cm for the small and reference fields and 1.4 cm for the large field. What's more, the curves are so close to each other that the discrepancies of each point data at the same depth are blended within error bars.

Carlo simulation
The dose distribution in the dose-maximum plane inside the waterfilled DOS structure is illustrated in Fig. 11(a), where we can see fast dose fall-off around the hotspot GTV region. The relative dose difference between FlexyDos3D and water, calculated in a similar way as in eq. (7), ranges from −1.027% to 0.821%, and as shown in Fig. 11(b) the differences are generally random and we did not observe any biased effect. In the meantime, the 3D gamma with the water-filled dose distribution as reference was calculated. The criteria we used were 3%/3 mm, 2%/2 mm, and 1%/1 mm, and the pass rates with dose interpolation were 100%, 100%, and 99.2% respectively. The high pass rates can be partly attributed to the small and unbiased dose differences as shown in Fig. 11(b), and partly to dose interpolation used in gamma calculation.  The simulated PDD and profiles for 6 and 10 MV validated by measurements exhibit great water-equivalence of FlexyDos3D not only in reference fields, but also in fields as small as 2 cm × 2 cm and as large as 40 cm × 40 cm. It is noted that silicon-based semiconductor detectors have been reported to overresponse in small and large fields, 34,35 but this phenomenon is not observed in Flexy-Dos3D, which is well worth of further investigation. As for the dose distribution comparison of the full-arc VMAT plan computationally delivered to water and FlexyDos3D, the differences are within 1%

| DISCUSSION
and we do not perceive any biased error pattern.
According to previous research 36,37 and our experience, the mechanical deformability of FlexyDos3D can be tuned by modifying the elastomer base to CA ratio. This is one of its outstanding properties, which can be utilized to mimic organs of various stiffness. In this study, we only used the vendor-recommended radio of 10:1 for tissue-equivalence evaluation. Although changing the ratio may modify some properties of FlexyDos3D, considering the equal mass density and highly similar elemental composition between elastomer base and CA, we believe that impact to the tissue equivalence is as small as negligible and consistent conclusions still can be drawn. water and Solid Water as reference, FlexyDos3D is found to exhibit excellent water-equivalence for MV photon, but poor soft tissue equivalent performance for kV photon. The higher HU value of Flex-yDos3D measured by kV CT is found to induce underdose to target, which can be eliminated by HU correction. As indicated, from the perspective of radiological tissue equivalence, FlexyDos3D can serve as an acceptable water-equivalent dosimeter for clinical use for MV radiotherapy x-ray beams, while the nonwater-equivalence effect for kV photons requires HU correction for kV CT based dose calculation. If FlexyDos3D is to be used in low energy x-ray dosimetry, we believe that further corrections on its-water-equivalence are needed.

| CONCLUSION
The findings of this study provide pertinent reference for further FlexyDos3D characterization.