3D‐printable lung phantom for distal falloff verification of proton Bragg peak

Abstract In proton therapy, the Bragg peak of a proton beam reportedly deteriorates when passing though heterogeneous structures such as human lungs. Previous studies have used heterogeneous random voxel phantoms, in which soft tissues and air are randomly allotted to render the phantoms the same density as human lungs, for conducting Monte Carlo (MC) simulations. However, measurements of these phantoms are complicated owing to their difficult‐to‐manufacture shape. In the present study, we used Voronoi tessellation to design a phantom that can be manufactured, and prepared a Voronoi lung phantom for which both measurement and MC calculations are possible. Our aim was to evaluate the effectiveness of this phantom as a new lung phantom for investigating proton beam Bragg peak deterioration. For this purpose, we measured and calculated the percentage depth dose and the distal falloff widths (DFW) passing through the phantom. For the 155 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were 0.40 and 0.39 cm, respectively. For the 200 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were both 0.48 cm. Our results indicate that both the measurements and MC calculations exhibited high reproducibility with plastinated lung sample from human body in previous studies. We found that better results were obtained using the Voronoi lung phantom than using other previous phantoms. The designed phantom may contribute significantly to the improvement of measurement precision. This study suggests that the Voronoi lung phantom is useful for simulating the effects of the heterogeneous structure of lungs on proton beam deterioration.

distal falloff. [4][5][6] This amplification may inadvertently cause an increase in the radiation dose to normal tissues or a decrease in the radiation dose to cancer cells.
In previous research, a heterogeneous random voxel calculation model, in which soft tissue and air are randomly allotted to equal the average density of lungs, we call this porous walled structure phantom or random voxel phantom, was used to investigate beam deterioration using Monte Carlo (MC) simulation. 7 The researchers fabricated a three-dimensional (3D) printed porous walled structure phantom to verify the calculation results and the measurement. To print the 3D phantom from the data, a different support material from the main unit must be used to compile the 3D structure, and it must be removed at the end. However, because the model is randomly composed, in case of porous walled structure phantom, some spaces may be created where the support material cannot be removed. As a result, the randomness of the physical phantom that can be fabricated with a 3D printer, is limited. Therefore, we devised a 3D printable lung phantom that is not limited in randomness and can be employed to perform not only calculations but also advanced measurements, by using a mathematical technique called Voronoi tessellation.
The purpose of this research was to verify the effectiveness of the new lung phantom developed using Voronoi tessellation, by comparing the Bragg peak deterioration of the proton beam with that observed in previous research, using both measurements and MC calculations.

2.A.1 | Voronoi tessellation
We focused on using Voronoi tessellation to print a lung structure.
Voronoi tessellation is a mathematical technique, in which a perpendicular straight line is made at the midpoint of the line between neighboring points, dividing an area into the regions that are closest to each point [ Fig. 1(a)]. In this study, we used centroidal Voronoi tessellation (CVT), 8,9 where the generating point in each region is also the center of mass. Because the gaps between the generating points are uniform, we used this tessellation with the aim of decreasing directional dependence related to the structure.

2.A.2 | Lung phantom using Voronoi tessellation
In this study, MeshLab (JS16.03), 10 an open-source modeling program for 3D model design was used. The generating points were placed in a 4 cm × 4 cm × 4 cm cube using the Poisson disk distribution 11 and Lloyd's algorithms, 8,9 installed as functions of MeshLab [ Fig. 1(b)]. A Voronoi tessellation was created using these points, and the basic shape of the phantom was developed by structuralizing the Voronoi tessellation lines [ Fig. 1(c)]. It was possible to make a porous branch structure using the structuralized dividing lines [ Fig. 1(d)]. A porous branch structure has the advantage of easy removal of the support material. This means that it is possible to create a phantom with less design error than conventional porous walled structures. Afterward, based on studies of human lungs, 12,13 we developed a Voronoi lung phantom with a density of 0.237 g/ cm 3 and branch diameters of 0.4-0.8 mm to approximate an average adult lung. The joint part of the branches was thicker and about 1.6 mm in diameter at maximum. The Voronoi lung phantom was fabricated with an inkjet 3D printer AGILISTA-3100 (KEYENCE) in the Medical Workshop and the Open Facility Network Office at the Research Facility Center for Science and Technology of the University of Tsukuba. Transparent acrylic urethane resin (density: 1.11 g/ cm 3 ) was used to form the model. In order to verify that the support material was removed, the design density was compared with the density of the actual phantom.

2.B | Comparison parameters
We compared the Voronoi lung phantom's distal falloff widths (DFW) and peak values obtained from the measurements and MC calculations with those of a previously studied plastinated human lung sample. 7 The DFW is defined as the distance required for the radiation dose distribution to fall from 80% to 20% after a peak. The peak value is the value of the peak, taking a pristine peak to be standard, i.e., normalized with the maximum dose of the pristine peak.
We measured and simulated the percentage depth dose (PDD), from which the DFW and peak values were calculated. The method to measure the PDD with an IP is described in the literature. 15 A polymethyl methacrylate (PMMA) (1.17 g/cm 3 ) container was used for this purpose. The IP was inserted at an angle of 10°. The oblique incidence changes the distance the protons pass through the sensitive layer of the IP, which also changes the signal intensity. Therefore, in the previous study, 15 the change in signal intensity was used to determine the optimum angle for compensating the LET dependency of IP. By measuring with IP at 10°, the measurement result in the distal falloff part was in agreement with that using parallel plate ionization chamber in water. For details on this technique, please refer to the literature. 15 The IP that was used was a BAS-MS (FUJI FILM), the scanning device was an FLA-7000 (FUJI FILM), and the analysis software was KOKETSU ET AL.

2.D | Monte Carlo simulation
The MC simulations reproduced the PMRC's double scattered beamline using the Particle and Heavy Ion Transport Code System (PHITS) ver3.02. 16 In a previous study, 17 for the PMRC beamline, the PDD of a 155 MeV proton beam was evaluated using Monte Carlo simulation, and the measured values were reproduced. In this study, Monte Carlo simulations were carried out by adapting that calculation system. The calculation system used the same geometry as used for the measurements [ Fig. 2  F I G . 3. The created three-dimensional data (a) were converted to voxel data (b) for Monte Carlo calculation by particle and heavy ion transport code system. Each voxel represented a volume of 0.4 mm × 0.4 mm × 0.4 mm. The structural parts that appear white are defined by acrylic urethane resin with a density of 1.11 g/cm 3 ; the other parts are defined by air.
The cutoff energies for protons and electrons were set to 1 and 0.1 MeV, respectively. The calculations for the simulation were performed with sufficient number of particles so that the statistical error for radiation doses was 1% or less up to a point 20% past the peak. The voxel size for calculating the depth dose was 0.2 mm because of trade-off between statistical error and realistic computation time.

2.E | Comparison with tough lung phantom
We compared the effects of the heterogeneous random structure in the conventional and the Voronoi lung phantom. We used tough lung phantom (Kyotokagaku) as a conventional phantom. The tough lung phantom has a density of 0.33 g/cm 3 (phenol formaldehyde resin) and is a uniform plate-like phantom, with no heterogeneous structure. The experimental system was the same as in Fig. 2(b). In order to correct the difference in density with Voronoi lung phantom

2.F | Comparison with treatment planning system (TPS)
We compared our setup with the general treatment planning system (TPS) with pencil beam algorithm 18 to investigate the effects of heterogeneous structure in near-clinical conditions. VQA ver. 2.01 (Hitachi) was used as TPS. To perform the calculation for TPS, we took the CT of the Voronoi lung phantom we created. We obtained 0.977 mm × 0.977 mm × 0.625 mm (0.625 mm as slice thickness) with the best resolution in the range used in the clinic. CT was performed with an Optima 580w (GE). The experimental system was the same as in Fig. 2(b). We calculated the PDD for the energy levels of 155 and 200 MeV. We chose 30 mm as the spread-out Bragg peak (SOBP) width, often used in the treatment of lungs, to compare with MC calculations. The TPS's voxel size for calculating the depth dose was 0.1 mm of the minimum reading size, while that of MC was 0.2 mm.

3.A | Voronoi lung phantom
A view and enlarged view of the constructed lung phantom are shown in Fig. 4. The measured density of this lung phantom was 0.237 g/cm 3 , which was consistent with the design. At more than three decimal places, the design density was 0.2371 g/cm 3 , and the actual phantom density was 0.2369 g/cm 3 . The error was < 0.1%.
Hence, it can be said that the design was reproduced with high accuracy.
All measurements and calculations reported in this study were performed using this phantom.

3.B | Results of comparison between measurements and MC calculations
The results for the pristine peak normalized by the maximum dose The results for the DFW and peak value are shown in Table 1. Based on these results, the Voronoi lung phantom was judged to be suitable to simulate a plastinated lung sample made from the human body.   Table 2.  Table 2.

4.A | Comparison between measurements and MC calculations
The measurements and MC calculations were both sufficiently consistent in comparison to the results from the previous study. 7 We compared the results obtained in this study to those obtained using an independent theoretical formula to investigate the validity of this experiment.
Assuming that the Bragg peak widening in the 80-20% portion, which defines DFW, follows a Gaussian distribution (σ), it becomes DFW≒1:13σ (1) where, using the formula above, σ pristine ＝ 2.12 mm for the pristine peak and σ Voronoi = 3.53 mm for the Voronoi lung phantom at 155 MeV, and σ pristine ＝ 3.13 mm for the pristine peak and σ Voronoi = 4.24 mm for the Voronoi lung phantom at 200 MeV.
In addition, σ hetero , the effect of introducing a heterogeneous material, can be determined from the following equation: Ultimately, the effect of heterogeneity σ hetero was σ hetero = 2.82 mm for 155 MeV and σ hetero = 2.86 mm for 200 MeV.
Additionally, from the theoretical formula in the literature, 7 σ 2 (z) is given by where p is determined as the average density of the Voronoi lung phantom (i.e., p = 0.237 g/cm 3 for our phantom), z is the diameter of the phantom (i.e., z = 4 cm for our phantom), and Δ is the size of the structure that makes up the phantom.
T A B L E 2 Distal falloff widths (DFW) results for tough lung phantom and treatment planning system (TPS

4.B | Results of tough lung phantom and TPS
The conventional tough lung phantom, whose density is only con- It should be noted that this study did not address lung movement. However, by using a stretchable material and the shape of the Voronoi lung phantom, it is possible to measure the influence of lung motion. 19 In future work, we plan to simulate lung motion by changing the stretchable material. Such investigations may be able to contribute toward improvement of the precision of measurements and calculations in radiation therapy.

CONFLI CT OF INTEREST
The authors declare no conflict of interest.