Structural Design, Analysis and Testing of 3D Water Phantom for Proton Therapy

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It includes a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. The lifting platform and high-precision three-dimensional servo are the key factors which can affect the accuracy of proton beam measurement. The 3D water phantom structure design is carried out to realize proton beam dose detection. Finite element analysis model is established to carry out mechanical mechanics analysis of the 3D water phantom structure. During scanning detection, the vibration generated by the servo motor operation may cause the 3D water phantom structure resonance, carry out modal analysis and harmonic response analysis, calculate the 3D water phantom intrinsic frequency and motor operation vibration frequency within the possible resonance intervals. In addition, the 3D water phantom model was utilized to carry out Bragg peak detection experiments at different energies for proton therapy. proton therapy Bragg peak 3D water phantom stress analysis intrinsic frequency Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Cancer is one of the major health challenge in the word, causing serious impacts on human health and life, and the incidence and mortality of cancer are on the rise globally [ 1 ]. According to the latest estimates from the International Agency for Research on Cancer (IARC), by 2022, nearly 20 million new cancer cases will be diagnosed globally each year, resulting in an estimated 9.7 million deaths [ 2 ]. Traditional treatments for cancer mainly include surgical resection, chemotherapy and radiotherapy. However, the treatment of advanced and metastatic tumors is ineffective, and radiotherapy usually lacks selectivity, it prone to cause serious damage to normal tissues and organs and body functions [ 3 ]. Proton therapy as an advanced radiotherapy technique, can be applied to many types of cancer with significant advantages, such as lower side effects, more precise treatment, and shorter treatment time [ 4 – 6 ]. It kills cancer cells by proton beams (positively charged particles), which characterized by a gradual deceleration and release of energy as it penetrates the body's tissues until a high-dose energy peak (Bragg's peak) is formed at the tumor site and precise treatment of the tumor site is achieved. [ 7 – 11 ]. This precise treatment reduces the damage to the surrounding normal tissues to a maximum extent [ 12 , 13 ] In proton therapy, the accuracy of the dose calculation method of the proton therapy planning system directly affects the dose distribution between the tumor target area and normal tissues, it play a critical role in the success or failure of radiation therapy [ 14 ]. 3D water phantom is an important tool for detecting the dose technical index of proton therapy [ 15 – 17 ], which consists of a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. The water tank is equipped with stepper motors and moving sliders to realize 3D movement and positioning in the water. The ionization chambers are mounted on the X-axis of the 3D water phantom's three-dimensional servo by support for detecting the proton beam dose. The water in the 3D water phantom is used to simulate the human body (uniform body phantom), which can more accurately simulate the effect of proton beams passing through human tissues [ 18 , 19 ], ensuring the treatment plan and the actual treatment dose are consistent, and ensuring patient receives the intended treatment dose, thereby improving the accuracy and safety of the treatment. The main support structure of the 3D water phantom is designed using high-strength 316L stainless steel. However, under loading conditions such as gravity, the water tank structure still produces small deformations, which need to be analyzed to predict the magnitude and location of the deformations of the tank structure and calibrated during the measurement of the proton beam dose. Therefore, it is necessary to establish a finite element analysis model of 3D water phantom system based on the finite element calculation method to proceed the displacement deformation and stress analysis of the 3D water phantom structure. Simultaneously, in the process of proton beam dose detection before surgery, it is necessary to drive the silk rod slider mechanism through the servomotor, and the three-dimensional servo moves with the depth of beam irradiation. It is possible that the vibration of the servomotor itself may cause resonance of the three-dimensional servo [ 20 ], which leads to the error in the measurement of the beam dose and affects the final therapeutic effect. Analyze the modal analysis of the 3D water phantom, investigate the intrinsic frequency and vibration pattern of the 3D water phantom structure under different modal orders, and study the resonance range of the structure of the 3D water phantom that may be induced by the operation of the servo motor. Finally, based on the 3D water phantom structure, the model is manufactured and the proton beam dose test is completed. 2. Structural design 3D water phantom includes a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. A human body is composed of 90% water, so water is used in the 3D water phantom to simulate human tissue [ 19 , 21 ]. The water tank is made of transparent Perspex, which has better beam performance (stable equivalent water thickness, and less scattering effect on the beam). The lifting platform is used to simulate patient position and to adjust the height of the water phantom prior to proton beam dose detection. Three-dimensional servos are used to support the position of the ionization chamber in the X, Y and Z axes in order to measure the proton beam dose at different positions during proton beam dose detection. Lifting platform consists of a removable platform base and a three-dimensional servo, as well as a leveling knob for horizontal height adjustment. The three-dimensional servo structure composed of X, Y, Z-axis guide rails, servo motor drive system, screw mechanism, etc. The travel of the X, Y, Z-axis guide rails is determined according to the needs of the measurement, as shown in Table 1 , for the proton beam mass measurement of the guide rail travel requirements. The main material of the three-dimensional mobile structure is 316L stainless steel, which can realize long time submerged in water and proton irradiation conditions to ensure the material strength and high precision operation [ 22 ]. Figure 1 shows the main structure of the main part of the 3D water phantom. Table 1 Parameter requirements for guideway travel X-axis Y-axis Z-axis Precision Direction 480mm 480mm 410mm 0.1mm As shown in Fig. 2 , it is the Y-axis guide structure of the three-dimensional servo, the servo motor drives the slider to move through the high-precision screw mechanism, the guide rail adopts the I-beam structure, the slider is fixed on the guide rail through the pulleys, and the screw is a ball screw structure, which is connected with the servo motor through the coupling. The stepping accuracy of the rail is controlled by the servo motor and the screw, the motor model is SF0192, the rated speed is 600rpm and the control accuracy is 0.022°. The diameter of the screw is 10mm, the lead is 2mm, and the stroke control accuracy is 0.05mm. 3. 3D water phantom structure analysis optimization 3.1 structural analysis According to the 3D water phantom designed in Section 2 , a 3D finite element analysis model is established to carry out static and modal analysis under the working condition of the water phantom. For the water tank structure, there is a linear relationship \(\:\sigma\:=E\epsilon\:\) between the stress \(\:\sigma\:\) and strain \(\:\epsilon\:\) of the water phantom [ 23 ]. Under certain conditions, the elastic modulus E , shear modulus G and Poisson's ratio ν are all constant values, where \(\:G=E/\left(2\right(1+v\left)\right)\) . Therefore, the strain-stress relationship that can be obtained by solving the 3D water phantom model in three directions: $$\:\left\{\begin{array}{c}{\epsilon\:}_{x}=\frac{1}{E}\left[{\sigma\:}_{x}-\upsilon\:\left({\sigma\:}_{y}+{\sigma\:}_{z}\right)\right]\\\:{\epsilon\:}_{y}=\frac{1}{E}\left[{\sigma\:}_{y}-\upsilon\:\left({\sigma\:}_{x}+{\sigma\:}_{z}\right)\right]\\\:{\epsilon\:}_{z}=\frac{1}{E}\left[{\sigma\:}_{z}-\upsilon\:\left({\sigma\:}_{y}+{\sigma\:}_{x}\right)\right]\end{array}\right.$$ 1 The structural material of the water phantom is considered to be isotropic, and its elastic relationship between strain and stress can be expressed as: $$\:\left\{\begin{array}{c}{\sigma\:}_{x}=2G{\epsilon\:}_{x}+\lambda\:\theta\:\\\:{\sigma\:}_{y}=2G{\epsilon\:}_{y}+\lambda\:\theta\:\\\:{\sigma\:}_{z}=2G{\epsilon\:}_{z}+\lambda\:\theta\:\end{array}\right.$$ 2 Where is the Lame's constant [ 24 , 25 ], \(\:\lambda\:=\frac{E\nu\:}{\left(1+\nu\:\right)\left(1-2\nu\:\right)}\) In constructing the finite element analysis of the 3D water phantom, component models including the lift mechanism and the three-dimensional servo are established to simulate the load transfer process of the water phantom system as accurately as possible. As shown in Fig. 3 , it is the established water phantom finite element mesh model. The three-dimensional servo is installed inside the water tank, and the water tank is mounted on the lifting platform, finally, the pedestal of the lifting platform is constrained to be fixed on the ground. During the working process of the water phantom, the inside of the water tank is filled with water, and in the analysis, the equivalent load is loaded on the inside wall of the tank to simulate the weight of water. According to section 2 , the three-dimensional servo is a motion system composed of servo motor, screw and slider. The slider is stuck on the guide rail through the roller in three directions, the slider as a whole has the degree of freedom along the direction of the guide rail, and the slider and the guide rail are rolling friction. In the whole mechanism, the screw provides axial positioning. The material properties used in the finite element calculations are shown in Table 2 . Table 2 Properties of material Material Modulus of elasticity (Pa) Density (kg/m 3 ) Poisson's ratio 316L 2×10 11 7850 0.3 Perspex 3.2×10 9 1190 0.35 6061 Aluminum 7.1×10 10 2770 0.33 Under the condition of its own and equivalent water weight, the cloud diagram of deformation and stress distribution of the three-dimensional servo as shown in Fig. 4 . In particular, for the three-dimensional servo, the maximum stress is concentrated in the part of the X-axis ionization chamber mounting platform in contact with the guide rail, with a stress value of 9.5 MPa, and the maximum deformation is also in this position, where \(\:{D}_{def1}=\) 0.405mm. Meanwhile, the deformation of the ionization chamber support platform which is installed at the 3D servo X-rail in its motion region has been solved, and the result is shown in Fig. 5 . The X, Y coordinate axes in the figure represent the displacement coordinates of the ionization chamber support platform in the X, Y direction, and the Z coordinate axis represents the amount of deformation that occurs in the vertical direction (in the direction of the Z-axis rail of the three-dimensional servo). In the proton beam mass test experiment, this dimension needs to be compensated to meet the accuracy requirements of the measurement. 3.2 Modal Analysis and Harmonic Response Analysis Meanwhile, during the proton beam mass testing process, the three-dimensional servo relying on motor drive needs to be started frequently, which may cause resonance. Therefore, based on the structural analysis, modal analysis is required to analyze the vibration pattern and frequency of each order, and predict whether the main structure of the 3D water phantom will resonate. The intrinsic frequency and vibration pattern of the 3D water phantom structure can be solved by modal analysis [ 26 ], and the vibration differential equation of the water phantom system is: $$\:M\ddot{x}+C\dot{x}+Kx=f$$ 3 where M is the mass matrix of the 3D water phantom, C is the damping matrix, and K is the structural stiffness matrix of the water phantom. Using the coordinate transformation matrix, the physical coordinate x is substituted into Eq. ( 3 ) through coordinate transformation, which is converted into the system vibration differential equation (expressed in modal coordinates) under the modal coordinates q to realize the decoupling of the original vibration differential equation of the system. At the same time, both sides of the equation are multiplied simultaneously to obtain: $$\:{\varPhi\:}^{T}M\varPhi\:\ddot{q}+{\varPhi\:}^{T}C\varPhi\:\dot{q}+{\varPhi\:}^{T}K\varPhi\:q={\varPhi\:}^{T}f$$ 4 Decoupling Eq. ( 4 ) yields: $$\:\left\{\begin{array}{c}{\varPhi\:}^{T}M\varPhi\:={M}_{p}\\\:{\varPhi\:}^{T}C\varPhi\:={C}_{p}\\\:{\varPhi\:}^{T}K\varPhi\:={K}_{p}\end{array}\right.$$ 5 This can be obtained by combining Eq. ( 4 ) and Eq. ( 5 ): $$\:{M}_{p}\ddot{q}+{C}_{p}\dot{q}+{K}_{p}q={f}_{p}$$ 6 Equation ( 6 ) is a system of n-order differential equations, and the individual coordinates (i = 1, 2, ..., n) are independent of each other and can be solved individually, realizing the decoupled calculation of the 3D water phantom modal analysis equations. The intrinsic frequency and vibration mode of the 3D water phantom structure are the main factors affecting the vibration of the structure, and the modal harmonic response analysis is carried out on the basis of the structural analysis. As shown in Fig. 6, the cloud diagram of the vibration mode distribution of the first 6 orders of the water tank system. The first-order modal analysis contributes the most to the structural response, which is the main vibration mode. In the first order modal calculation, the 3D water phantom has an intrinsic frequency of 7.6787 Hz, which produces X-direction vibration shapes at the end of Z-axis and Y-axis. See Table 3 for specific intrinsic frequency and vibration mode parameters for each order. Table 3 Results of the first 6 orders of modal analysis Ordinal number Natural frequency (Hz) Vibration pattern 1 7.6787 X and Y-rail ends 2 7.9123 Y-rail ends 3 21.428 X-rail ends 4 26.357 X-rail ends 5 26.594 Y-rail ends and Lifting platform 6 28.129 Lifting platform The three-dimensional water phantom system, whose motion occurs in the proton beam energy measurement, is driven by a servo motor, and the relationship between the rotational speed of the motor and the vibration frequency is usually estimated by using n = 60f/p [ 27 ]. The operating speed of the motor is within the rated speed of 600 rpm, and the vibration frequency is about 10 Hz. According to the modal analysis, the first-order and second-order intrinsic frequencies of the 3D water phantom structure are in the range of 7.6787 Hz and 7.9123 Hz, respectively. Once the motor's operating frequency and the intrinsic frequency of the 3D water phantom structure are close to each other, it is possible to generate resonance. On the basis of the modal analysis results, the 3D water phantom structure is analyzed for harmonic response. The relationship between the amplitude and phase angle of the 3D water phantom structure at frequencies between 7.0 Hz and 8.75 Hz is shown in Fig. 7 . At the frequency of 7.9 Hz, the amplitude reaches a maximum of 0.26 mm, at which time the phase angle is about − 90°. In order to avoid resonance, the motor running speed should be avoided between 450rpm and 497rpm. 4. 3D water phantom testing During the test, protons are accelerated by a cyclotron and reach the treatment head through a transport system [ 28 ], where the proton beam stream is directed into the 3D water phantom at an angle of 90° or 270°. The proton beam energy is measured by means of an ionization chamber. The measurement ionization chamber in the 3D water phantom is Stingray. it consists of a parallel plate ionization chamber with a diameter of 120 mm and a bracket specially designed for mounting the chamber on the X-rail. The reference ionization chamber is IBA Stealth and is mounted outside the 3D water phantom by means of a support fixed to the water tank and a plastic frame for the ionization chamber with dimensions of \(\:22.8\text{c}\text{m}\times\:22.8\text{c}\text{m}.\) The block diagram of the overall process of carrying out Bragg peak testing using a 3D water phantom can be simplified as in Fig. 8 , where the Perspex water tank is placed in the measurement area and then adjusted in height and horizontal position using a lifting mechanism. The scanning size of the ionization chamber is set on the control computer program, and with the three-dimensional servo control program and controller, the automatic scanning function during measurement can be realized. Figure 9 shows the main part of the 3D water phantom. When the 3D water phantom system is utilized for dose testing, the proton beam incidence angle can be from 0° to 360°, as shown in Fig. 10 for Bragg peak testing using a fixed treatment head with an incidence angle of 0°. In the experiment, tests are conducted at 80 MeV, 90 MeV, 110 MeV, 140 MeV, 150 MeV, and 193 MeV proton beam energies. The proton beam passes through the treatment head, passes through the reference ionization chamber, enters the water through the Perspex tank wall, and finally reaches the measurement ionization chamber. Since the physical thickness ( \(\:{t}_{m}\) ) and material properties of the components in the proton beam path are different, they need to be transformed into water equivalent thicknesses (WET) \(\:{t}_{w}\) [ 28 – 31 ], calculations are performed by the following formula: $$\:{t}_{w}={t}_{m}\frac{{\rho\:}_{m}}{{\rho\:}_{w}}\frac{{\stackrel{-}{S}}_{m}}{{\stackrel{-}{S}}_{w}}$$ In which, \(\:{\rho\:}_{m}\) is the density of the proton beam passing through the component structural material on the 3D water phantom, \(\:{\rho\:}_{w}\) is the density of the water, \(\:{\stackrel{-}{S}}_{m}\) and \(\:{\stackrel{-}{S}}_{w}\) are the mean proton mass stopping power values for the material and water. Based on the developed 3D water phantom structure, the total depth formula is as follows: $$\:{\text{T}}_{\text{w}}=\sum\:{t}_{{m}_{i}}+{R}_{d}$$ In which, \(\:{\text{R}}_{\text{d}}\) is Correction parameters for structural deformation. Figure 11 shows the test results of the 3D water phantom at 80 MeV, 90 MeV, 110 MeV, 140 MeV, 150 MeV, and 193 MeV proton beam energies. The peak energy depths are 51.1 mm, 63.1 mm, 90.1 mm, 138.1 mm, 156.1 mm, and 241.1 mm. For the proton beam, 80% of the furthest range in the water, according to the data reference of the national institute of standards and technology [ 32 ]. We compare the experimental measurements, with the theoretical values, to be obtained in Table 4 . Through the table, the measured depths differ from the theoretical values by less than 0.5%. Table 4 Comparison of the same type of 3D water phantom testing Energy (MeV) Gas pedal Flow Intensity (nA) Treatment head Converted flow intensity (nA) Tests Peak (mm) Nominal Peak (mm) Peak Difference (mm) misalignment (%) 80 320 0.16(0.05%) 51.74 51.76 0.02 0.0386 90 250 0.15(0.06%) 63.61 63.89 0.28 0.4383 110 160 0.17(0.11%) 90.97 91.28 0.31 0.3434 140 80 0.16(0.21%) 139.47 139.6 0.13 0.0931 150 60 0.15(0.26%) 156.97 157.6 0.63 0.3997 193 30 0.27(0.9%) 242.77 243.9 1.13 0.4633 5. Conclusions 3D water phantom is an important tool to detect the dose technical index of proton system, according to the requirements of proton therapy system on 3D water phantom, carry out the development of high-precision 3D water phantom prototype, the scanning size of the prototype is 480mm×480mm×410mm, precision 0.1mm, using the silk rod guide mechanism for motion control. At meanwhile, according to the finite element analysis method, the finite element analysis model of the main structure of the 3D water phantom has been established, and the structural strength of the 3D water phantom has been calibrated, and the maximum stress load of the 3D water phantom is 25.388 MPa and the maximum displacement deformation is 0.315 mm under the equivalent gravity condition. On the basis of the strength analysis, modal analysis is carried out, and the intrinsic frequency and vibration mode of the 3D water phantom structure has calculated. The intrinsic frequencies of the first six orders are respectively 7.6787Hz, 7.9123Hz, 21.428Hz, 26.357Hz, 26.594Hz, 28.129Hz. While the 3D water phantom is in operation, the speed of the drive motor is about 50rpm and the vibration frequency of the motor is about 0.833Hz, therefore there is no resonance. In addition, based on the 3D water phantom prototype, the testing of proton beam Bragg peak which under the beam energies of 80MeV, 90MeV, 110MeV, 140MeV, 150MeV and 193MeV, the peak energy depths were 51.1mm, 63.1mm, 90.1mm, 138.1mm, 156.1mm and 241.1mm respectively. Comparing with the theoretical nominal depths, and the error ranges are all controlled at 0.5%. Satisfy the demand for precision in use. In the next step, more comprehensive testing work will be carried out on the developed 3D water phantom prototype, such as depth dose distribution, range stability test. Declarations Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Data will be made available on request. Acknowledgements The authors are grateful to those who have given helpful advice. The research is supported by Hefei CAS Ion Medical and Technical Devices Co., Ltd. Funding Declaration This work is supported by the 3D water phantom research program of Hefei CAS Ion Medical and Technical Devices Co., Ltd, grants No.JSCP2204. References Y. Liu, Z. Zheng, Understanding the global cancer statistics 2022: growing cancer burden, Sci China Life Sci (2024). https://doi.org/10.1007/s11427-024-2657-y. F. Bray, M. Laversanne, H. Sung, J. Ferlay, R.L. Siegel, I. Soerjomataram, A. Jemal, Global cancer statistics 2022: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA Cancer J Clin 74 (2024) 229–263. https://doi.org/10.3322/caac.21834. A. Urruticoechea, R. Alemany, J. Balart, A. Villanueva, F. Viñals, G. Capellá, Recent advances in cancer therapy: an overview, Curr Pharm Des 16 (2010) 3–10. https://doi.org/10.2174/138161210789941847. S. Baliga, T.I. Yock, Proton beam therapy in pediatric oncology, Curr Opin Pediatr 31 (2019) 28–34. https://doi.org/10.1097/MOP.0000000000000724. W.D. Newhauser, R. Zhang, The physics of proton therapy, Phys. Med. Biol. 60 (2015) R155. https://doi.org/10.1088/0031-9155/60/8/R155. J.B. Farr, J.B. Flanz, A. Gerbershagen, M.F. Moyers, New horizons in particle therapy systems, Med Phys 45 (2018) e953–e983. https://doi.org/10.1002/mp.13193. F. Verhaegen, R.-G. Wanders, C. Wolfs, D. Eekers, Considerations for shoot-through FLASH proton therapy, Phys. Med. Biol. 66 (2021) 06NT01. https://doi.org/10.1088/1361-6560/abe55a. M. Kang, S. Wei, J.I. Choi, C.B. Simone, H. Lin, Quantitative Assessment of 3D Dose Rate for Proton Pencil Beam Scanning FLASH Radiotherapy and Its Application for Lung Hypofractionation Treatment Planning, Cancers (Basel) 13 (2021) 3549. https://doi.org/10.3390/cancers13143549. S. Wei, H. Lin, J.I. Choi, R.H. Press, S. Lazarev, R. Kabarriti, C. Hajj, S. Hasan, A.M. Chhabra, C.B. Simone, M. Kang, FLASH Radiotherapy Using Single-Energy Proton PBS Transmission Beams for Hypofractionation Liver Cancer: Dose and Dose Rate Quantification, Front Oncol 11 (2021) 813063. https://doi.org/10.3389/fonc.2021.813063. P. van Marlen, S. van de Water, M. Dahele, B.J. Slotman, W.F.A.R. Verbakel, Single Ultra-High Dose Rate Proton Transmission Beam for Whole Breast FLASH-Irradiation: Quantification of FLASH-Dose and Relation with Beam Parameters, Cancers (Basel) 15 (2023) 2579. https://doi.org/10.3390/cancers15092579. P. van Marlen, W.F.A.R. Verbakel, B.J. Slotman, M. Dahele, Single-fraction 34 Gy Lung Stereotactic Body Radiation Therapy Using Proton Transmission Beams: FLASH-dose Calculations and the Influence of Different Dose-rate Methods and Dose/Dose-rate Thresholds, Adv Radiat Oncol 7 (2022) 100954. https://doi.org/10.1016/j.adro.2022.100954. S. Wei, H. Lin, J.I. Choi, C.B. Simone, M. Kang, A Novel Proton Pencil Beam Scanning FLASH RT Delivery Method Enables Optimal OAR Sparing and Ultra-High Dose Rate Delivery: A Comprehensive Dosimetry Study for Lung Tumors, Cancers (Basel) 13 (2021) 5790. https://doi.org/10.3390/cancers13225790. M. Pennock, S. Wei, C. Cheng, H. Lin, S. Hasan, A.M. Chhabra, J.I. Choi, R.L. Bakst, R. Kabarriti, C.B. Simone Ii, N.Y. Lee, M. Kang, R.H. Press, Proton Bragg Peak FLASH Enables Organ Sparing and Ultra-High Dose-Rate Delivery: Proof of Principle in Recurrent Head and Neck Cancer, Cancers (Basel) 15 (2023) 3828. https://doi.org/10.3390/cancers15153828. S.M. Schellhammer, S. Gantz, A. Lühr, B.M. Oborn, M. Bussmann, A.L. Hoffmann, Technical Note: Experimental verification of magnetic field-induced beam deflection and Bragg peak displacement for MR-integrated proton therapy, Med Phys 45 (2018) 3429–3434. https://doi.org/10.1002/mp.12961. A. Anand, N. Sahoo, X.R. Zhu, G.O. Sawakuchi, F. Poenisch, R.A. Amos, G. Ciangaru, U. Titt, K. Suzuki, R. Mohan, M.T. Gillin, A procedure to determine the planar integral spot dose values of proton pencil beam spots, Med Phys 39 (2012) 891–900. https://doi.org/10.1118/1.3671891. J. Schieferecke, S. Gantz, A. Hoffmann, J. Pawelke, Investigation of contrast mechanisms for MRI phase signal-based proton beam visualization in water phantoms, Magn Reson Med 90 (2023) 1776–1788. https://doi.org/10.1002/mrm.29752. H. Fuchs, F. Padilla-Cabal, A. Hummel, D. Georg, Technical Note: Design and commissioning of a water phantom for proton dosimetry in magnetic fields, Med Phys 48 (2021) 505–512. https://doi.org/10.1002/mp.14605. G. Cui, J. Duan, Y. Yang, F.-F. Yin, Technical Note: Investigation of the dosimetric impact of stray radiation on the Common Control Unit of the IBA Blue Phantom2, J Appl Clin Med Phys 21 (2020) 191–196. https://doi.org/10.1002/acm2.12769. M.J. LaRiviere, P.M.G. Santos, C.E. Hill-Kayser, J.M. Metz, Proton Therapy, Hematol Oncol Clin North Am 33 (2019) 989–1009. https://doi.org/10.1016/j.hoc.2019.08.006. G. He, Z. Huang, R. Qin, D. Chen, Numerical Prediction of Electromagnetic Vibration and Noise of Permanent-Magnet Direct Current Commutator Motors With Rotor Eccentricities and Glue Effects, IEEE Trans. Magn. 48 (2012) 1924–1931. https://doi.org/10.1109/TMAG.2011.2178100. M.E. Howard, J.M. Denbeigh, E.K. Debrot, N.B. Remmes, M.G. Herman, C.J. Beltran, A High-Precision Method for In Vitro Proton Irradiation, International Journal of Particle Therapy 7 (2020) 62–69. https://doi.org/10.14338/IJPT-20-00007.1. S. Li, Z. Gao, J. Xiong, L. Fan, J. Chen, K. Ma, L. Yang, B. Lu, Study on Single-Layer and Single-Channel Microstructure of 304 Stainless Steel Using Joule Heat Additive Manufacturing, Crystals 13 (2023) 1573. https://doi.org/10.3390/cryst13111573. A.C. Ugural, S.K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, Pearson Education, 2011. G. Nakamura, Identification of Lame parameters from boundary measurements, (1993). E.W. Weisstein, Lamé Constants. Eric Weisstein’s World of Physics, (n.d.). https://scienceworld.wolfram.com/physics/LameConstants.html M. Geradin, D.J. Rixen, Mechanical Vibrations: Theory and Application to Structural Dynamics, John Wiley & Sons, 2015. J.F. Gieras, Permanent Magnet Motor Technology: Design and Applications, Third Edition, 3rd ed., CRC Press, Boca Raton, 2009. M.F. Moyers, A.S. Vatnitsky, S.M. Vatnitsky, Factors for converting dose measured in polystyrene phantoms to dose reported in water phantoms for incident proton beams, Med Phys 38 (2011) 5799–5806. https://doi.org/10.1118/1.3639119. A. Smith, M. Gillin, M. Bues, X.R. Zhu, K. Suzuki, R. Mohan, S. Woo, A. Lee, R. Komaki, J. Cox, K. Hiramoto, H. Akiyama, T. Ishida, T. Sasaki, K. Matsuda, The M. D. Anderson proton therapy system, Med Phys 36 (2009) 4068–4083. https://doi.org/10.1118/1.3187229. R. Zhang, W.D. Newhauser, Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation, Phys Med Biol 54 (2009) 1383–1395. https://doi.org/10.1088/0031-9155/54/6/001. S. Stuchebrov, A. Bulavskaya, A. Grigorieva, M. Banshchikova, E. Bushmina, O. Chernova, V. Saburov, I. Miloichikova, Determination of the water equivalent thickness of 3D printed samples for the therapeutic proton beams, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1061 (2024) 169119. https://doi.org/10.1016/j.nima.2024.169119. Stopping Power and Range Tables for Protons, (n.d.). https://physics.nist.gov/cgi-bin/Star/ap_table.pl Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 15 Nov, 2024 Reviews received at journal 28 Oct, 2024 Reviewers agreed at journal 12 Oct, 2024 Reviewers agreed at journal 05 Oct, 2024 Reviewers invited by journal 05 Oct, 2024 Editor assigned by journal 23 Sep, 2024 Submission checks completed at journal 23 Sep, 2024 First submitted to journal 19 Sep, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5117428","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":378770483,"identity":"1bd4e7d0-e39c-4f5d-b93a-738ea8a5f12f","order_by":0,"name":"Xinzhi Liu","email":"","orcid":"","institution":"School of Mechatronic Engineering, Anhui University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xinzhi","middleName":"","lastName":"Liu","suffix":""},{"id":378770484,"identity":"6db6d901-9106-40fb-8267-076110f20e8c","order_by":1,"name":"Kaisong Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIie3RMQrCMBSA4YgQl2jXFCUOXqAQyHkahEwRdOvgUKjYQd3rLTp2rAjBITp3VLyAbgqCFh0VUzeHfHN+kvcCgGX9IdiI8vX1BonTiFZ7PxibkxZS/FgLW9Sdq76318qcECx7tBYSnhaSuYdJvcLDkIbtUcaomwgR8BACJ575hlkWqr3UgjjoqAqedQDW29Rwy05gBBV1YyEKriHw8MCQYMnK5M7TXLIhn9YrJZQ2p5CnG8lAtaRc8iHR8Llk7GuFjLN04yjPT8HrK8+XYEycePE9eYN+O25ZlmV99ADfFk5QlFjopgAAAABJRU5ErkJggg==","orcid":"","institution":"School of Mechatronic Engineering, Anhui University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Kaisong","middleName":"","lastName":"Wang","suffix":""},{"id":378770485,"identity":"b0cfbdce-b828-43b3-b451-e273bf04071d","order_by":2,"name":"Jianghua Wei","email":"","orcid":"","institution":"Hefei CAS Ion Medical and Technical Devices Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Jianghua","middleName":"","lastName":"Wei","suffix":""},{"id":378770486,"identity":"d668870e-4016-4b43-8663-ac7c7424260f","order_by":3,"name":"Liang Hong","email":"","orcid":"","institution":"Hefei CAS Ion Medical and Technical Devices Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Liang","middleName":"","lastName":"Hong","suffix":""},{"id":378770487,"identity":"067513d1-29bc-4b85-ba84-fe85feedf0e0","order_by":4,"name":"Bin Lan","email":"","orcid":"","institution":"Hefei CAS Ion Medical and Technical Devices Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Bin","middleName":"","lastName":"Lan","suffix":""},{"id":378770488,"identity":"f38f0963-8233-471f-bb39-ee2c2e7e9387","order_by":5,"name":"Zhoushun Guo","email":"","orcid":"","institution":"Hefei CAS Ion Medical and Technical Devices Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Zhoushun","middleName":"","lastName":"Guo","suffix":""}],"badges":[],"createdAt":"2024-09-19 13:41:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5117428/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5117428/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":70491348,"identity":"c1fb77cb-0bf3-444f-934a-32b5abe610e4","added_by":"auto","created_at":"2024-12-03 17:09:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":377331,"visible":true,"origin":"","legend":"\u003cp\u003e3D water phantom structure\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/7f886f3cec5744cb08775513.png"},{"id":70491688,"identity":"7bf5e099-1e4d-4bb3-8f6f-92e20d69ddfc","added_by":"auto","created_at":"2024-12-03 17:17:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":342122,"visible":true,"origin":"","legend":"\u003cp\u003eY-axis guide slide structure\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/efbec7e983cbc4b4393416ce.png"},{"id":70491349,"identity":"b5a332e6-c515-41ca-813c-686434dd45c4","added_by":"auto","created_at":"2024-12-03 17:09:05","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":915946,"visible":true,"origin":"","legend":"\u003cp\u003efinite element model\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/6874145ae57545855d2af662.png"},{"id":70491691,"identity":"1abc4a9a-8239-47eb-bd2b-84aa444a944c","added_by":"auto","created_at":"2024-12-03 17:17:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":206277,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement distribution and stress distribution cloud diagram of three-axis moving mechanism\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/c88cd71fc28997297a2a02cb.png"},{"id":70491689,"identity":"75d937ae-e03f-4421-a808-b920faefe7c7","added_by":"auto","created_at":"2024-12-03 17:17:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":511619,"visible":true,"origin":"","legend":"\u003cp\u003eDeformation cloud of the ionization chambers support platform at the range of motion\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/ad20e7ba6736c5543e2160e2.png"},{"id":70491352,"identity":"3553dbbf-1292-43fb-a7d2-cb21905de0f0","added_by":"auto","created_at":"2024-12-03 17:09:05","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2007111,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution and displacement maps\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/97f334e3ae7cba5946516eb7.png"},{"id":70491358,"identity":"9d6c27ac-e7f4-4bdc-ba95-279398369b57","added_by":"auto","created_at":"2024-12-03 17:09:06","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":198425,"visible":true,"origin":"","legend":"\u003cp\u003eAmplitude and phase angle versus frequency for 3D water phantom structures\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/0e9bd986517d818da3c4c2ad.png"},{"id":70491354,"identity":"6485ec3a-8fea-414d-949a-2a1453294d2e","added_by":"auto","created_at":"2024-12-03 17:09:05","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":140067,"visible":true,"origin":"","legend":"\u003cp\u003e3D water phantom control block diagram\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/d4b973ab67cfb8ee1b7cb3d2.png"},{"id":70491690,"identity":"5fa1a48c-49e6-4700-86f5-3ced3c28907d","added_by":"auto","created_at":"2024-12-03 17:17:05","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":739721,"visible":true,"origin":"","legend":"\u003cp\u003eSystem of 3D water phantom\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/73a773c27c459486c1b8fe3e.png"},{"id":70491356,"identity":"8e06c080-9a29-4550-a209-697d0758ad9e","added_by":"auto","created_at":"2024-12-03 17:09:05","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":597286,"visible":true,"origin":"","legend":"\u003cp\u003e3D water phantom proton beam energy test site\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/f4cdd4ddad3bcf0bfcb6a341.png"},{"id":70491357,"identity":"1fd670bc-670f-4370-aa0b-01c8b161bd38","added_by":"auto","created_at":"2024-12-03 17:09:06","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":150756,"visible":true,"origin":"","legend":"\u003cp\u003eProton Beam Energy Testing of 3D water phantom\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/e040920bec11b98a355a5195.png"},{"id":70492247,"identity":"feb78ce2-3890-4b68-9acd-a775b6cd3841","added_by":"auto","created_at":"2024-12-03 17:25:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8713800,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5117428/v1/436699bf-5045-4d68-88f2-ad5e26b30048.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Structural Design, Analysis and Testing of 3D Water Phantom for Proton Therapy","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eCancer is one of the major health challenge in the word, causing serious impacts on human health and life, and the incidence and mortality of cancer are on the rise globally [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. According to the latest estimates from the International Agency for Research on Cancer (IARC), by 2022, nearly 20\u0026nbsp;million new cancer cases will be diagnosed globally each year, resulting in an estimated 9.7\u0026nbsp;million deaths [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTraditional treatments for cancer mainly include surgical resection, chemotherapy and radiotherapy. However, the treatment of advanced and metastatic tumors is ineffective, and radiotherapy usually lacks selectivity, it prone to cause serious damage to normal tissues and organs and body functions [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eProton therapy as an advanced radiotherapy technique, can be applied to many types of cancer with significant advantages, such as lower side effects, more precise treatment, and shorter treatment time [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. It kills cancer cells by proton beams (positively charged particles), which characterized by a gradual deceleration and release of energy as it penetrates the body's tissues until a high-dose energy peak (Bragg's peak) is formed at the tumor site and precise treatment of the tumor site is achieved. [\u003cspan additionalcitationids=\"CR8 CR9 CR10\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This precise treatment reduces the damage to the surrounding normal tissues to a maximum extent [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eIn proton therapy, the accuracy of the dose calculation method of the proton therapy planning system directly affects the dose distribution between the tumor target area and normal tissues, it play a critical role in the success or failure of radiation therapy [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. 3D water phantom is an important tool for detecting the dose technical index of proton therapy [\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], which consists of a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. The water tank is equipped with stepper motors and moving sliders to realize 3D movement and positioning in the water. The ionization chambers are mounted on the X-axis of the 3D water phantom's three-dimensional servo by support for detecting the proton beam dose. The water in the 3D water phantom is used to simulate the human body (uniform body phantom), which can more accurately simulate the effect of proton beams passing through human tissues [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], ensuring the treatment plan and the actual treatment dose are consistent, and ensuring patient receives the intended treatment dose, thereby improving the accuracy and safety of the treatment.\u003c/p\u003e \u003cp\u003eThe main support structure of the 3D water phantom is designed using high-strength 316L stainless steel. However, under loading conditions such as gravity, the water tank structure still produces small deformations, which need to be analyzed to predict the magnitude and location of the deformations of the tank structure and calibrated during the measurement of the proton beam dose. Therefore, it is necessary to establish a finite element analysis model of 3D water phantom system based on the finite element calculation method to proceed the displacement deformation and stress analysis of the 3D water phantom structure. Simultaneously, in the process of proton beam dose detection before surgery, it is necessary to drive the silk rod slider mechanism through the servomotor, and the three-dimensional servo moves with the depth of beam irradiation. It is possible that the vibration of the servomotor itself may cause resonance of the three-dimensional servo [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], which leads to the error in the measurement of the beam dose and affects the final therapeutic effect. Analyze the modal analysis of the 3D water phantom, investigate the intrinsic frequency and vibration pattern of the 3D water phantom structure under different modal orders, and study the resonance range of the structure of the 3D water phantom that may be induced by the operation of the servo motor. Finally, based on the 3D water phantom structure, the model is manufactured and the proton beam dose test is completed.\u003c/p\u003e"},{"header":"2. Structural design","content":"\u003cp\u003e3D water phantom includes a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. A human body is composed of 90% water, so water is used in the 3D water phantom to simulate human tissue [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The water tank is made of transparent Perspex, which has better beam performance (stable equivalent water thickness, and less scattering effect on the beam). The lifting platform is used to simulate patient position and to adjust the height of the water phantom prior to proton beam dose detection. Three-dimensional servos are used to support the position of the ionization chamber in the X, Y and Z axes in order to measure the proton beam dose at different positions during proton beam dose detection.\u003c/p\u003e \u003cp\u003eLifting platform consists of a removable platform base and a three-dimensional servo, as well as a leveling knob for horizontal height adjustment. The three-dimensional servo structure composed of X, Y, Z-axis guide rails, servo motor drive system, screw mechanism, etc. The travel of the X, Y, Z-axis guide rails is determined according to the needs of the measurement, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, for the proton beam mass measurement of the guide rail travel requirements. The main material of the three-dimensional mobile structure is 316L stainless steel, which can realize long time submerged in water and proton irradiation conditions to ensure the material strength and high precision operation [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the main structure of the main part of the 3D water phantom.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameter requirements for guideway travel\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eX-axis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eY-axis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZ-axis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePrecision\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDirection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e480mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e480mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e410mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it is the Y-axis guide structure of the three-dimensional servo, the servo motor drives the slider to move through the high-precision screw mechanism, the guide rail adopts the I-beam structure, the slider is fixed on the guide rail through the pulleys, and the screw is a ball screw structure, which is connected with the servo motor through the coupling.\u003c/p\u003e \u003cp\u003eThe stepping accuracy of the rail is controlled by the servo motor and the screw, the motor model is SF0192, the rated speed is 600rpm and the control accuracy is 0.022\u0026deg;. The diameter of the screw is 10mm, the lead is 2mm, and the stroke control accuracy is 0.05mm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. 3D water phantom structure analysis optimization","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 structural analysis\u003c/h2\u003e \u003cp\u003eAccording to the 3D water phantom designed in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, a 3D finite element analysis model is established to carry out static and modal analysis under the working condition of the water phantom. For the water tank structure, there is a linear relationship \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:=E\\epsilon\\:\\)\u003c/span\u003e\u003c/span\u003e between the stress \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e and strain \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\epsilon\\:\\)\u003c/span\u003e\u003c/span\u003e of the water phantom [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Under certain conditions, the elastic modulus \u003cem\u003eE\u003c/em\u003e, shear modulus \u003cem\u003eG\u003c/em\u003e and Poisson's ratio \u003cem\u003eν\u003c/em\u003e are all constant values, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G=E/\\left(2\\right(1+v\\left)\\right)\\)\u003c/span\u003e\u003c/span\u003e. Therefore, the strain-stress relationship that can be obtained by solving the 3D water phantom model in three directions:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}{\\epsilon\\:}_{x}=\\frac{1}{E}\\left[{\\sigma\\:}_{x}-\\upsilon\\:\\left({\\sigma\\:}_{y}+{\\sigma\\:}_{z}\\right)\\right]\\\\\\:{\\epsilon\\:}_{y}=\\frac{1}{E}\\left[{\\sigma\\:}_{y}-\\upsilon\\:\\left({\\sigma\\:}_{x}+{\\sigma\\:}_{z}\\right)\\right]\\\\\\:{\\epsilon\\:}_{z}=\\frac{1}{E}\\left[{\\sigma\\:}_{z}-\\upsilon\\:\\left({\\sigma\\:}_{y}+{\\sigma\\:}_{x}\\right)\\right]\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe structural material of the water phantom is considered to be isotropic, and its elastic relationship between strain and stress can be expressed as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}{\\sigma\\:}_{x}=2G{\\epsilon\\:}_{x}+\\lambda\\:\\theta\\:\\\\\\:{\\sigma\\:}_{y}=2G{\\epsilon\\:}_{y}+\\lambda\\:\\theta\\:\\\\\\:{\\sigma\\:}_{z}=2G{\\epsilon\\:}_{z}+\\lambda\\:\\theta\\:\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere is the Lame's constant [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:=\\frac{E\\nu\\:}{\\left(1+\\nu\\:\\right)\\left(1-2\\nu\\:\\right)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eIn constructing the finite element analysis of the 3D water phantom, component models including the lift mechanism and the three-dimensional servo are established to simulate the load transfer process of the water phantom system as accurately as possible. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, it is the established water phantom finite element mesh model. The three-dimensional servo is installed inside the water tank, and the water tank is mounted on the lifting platform, finally, the pedestal of the lifting platform is constrained to be fixed on the ground. During the working process of the water phantom, the inside of the water tank is filled with water, and in the analysis, the equivalent load is loaded on the inside wall of the tank to simulate the weight of water.\u003c/p\u003e \u003cp\u003eAccording to section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the three-dimensional servo is a motion system composed of servo motor, screw and slider. The slider is stuck on the guide rail through the roller in three directions, the slider as a whole has the degree of freedom along the direction of the guide rail, and the slider and the guide rail are rolling friction. In the whole mechanism, the screw provides axial positioning. The material properties used in the finite element calculations are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eProperties of material\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModulus of elasticity\u003c/p\u003e \u003cp\u003e(Pa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePoisson's ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e316L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c2\"\u003e \u003cp\u003e2\u0026times;10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7850\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerspex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c2\"\u003e \u003cp\u003e3.2\u0026times;10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6061 Aluminum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c2\"\u003e \u003cp\u003e7.1\u0026times;10\u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2770\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUnder the condition of its own and equivalent water weight, the cloud diagram of deformation and stress distribution of the three-dimensional servo as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. In particular, for the three-dimensional servo, the maximum stress is concentrated in the part of the X-axis ionization chamber mounting platform in contact with the guide rail, with a stress value of 9.5 MPa, and the maximum deformation is also in this position, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{def1}=\\)\u003c/span\u003e\u003c/span\u003e0.405mm. Meanwhile, the deformation of the ionization chamber support platform which is installed at the 3D servo X-rail in its motion region has been solved, and the result is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The X, Y coordinate axes in the figure represent the displacement coordinates of the ionization chamber support platform in the X, Y direction, and the Z coordinate axis represents the amount of deformation that occurs in the vertical direction (in the direction of the Z-axis rail of the three-dimensional servo). In the proton beam mass test experiment, this dimension needs to be compensated to meet the accuracy requirements of the measurement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Modal Analysis and Harmonic Response Analysis\u003c/h2\u003e \u003cp\u003eMeanwhile, during the proton beam mass testing process, the three-dimensional servo relying on motor drive needs to be started frequently, which may cause resonance.\u003c/p\u003e \u003cp\u003eTherefore, based on the structural analysis, modal analysis is required to analyze the vibration pattern and frequency of each order, and predict whether the main structure of the 3D water phantom will resonate. The intrinsic frequency and vibration pattern of the 3D water phantom structure can be solved by modal analysis [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], and the vibration differential equation of the water phantom system is:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:M\\ddot{x}+C\\dot{x}+Kx=f$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere M is the mass matrix of the 3D water phantom, C is the damping matrix, and K is the structural stiffness matrix of the water phantom. Using the coordinate transformation matrix, the physical coordinate x is substituted into Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) through coordinate transformation, which is converted into the system vibration differential equation (expressed in modal coordinates) under the modal coordinates q to realize the decoupling of the original vibration differential equation of the system. At the same time, both sides of the equation are multiplied simultaneously to obtain:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\varPhi\\:}^{T}M\\varPhi\\:\\ddot{q}+{\\varPhi\\:}^{T}C\\varPhi\\:\\dot{q}+{\\varPhi\\:}^{T}K\\varPhi\\:q={\\varPhi\\:}^{T}f$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eDecoupling Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) yields:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}{\\varPhi\\:}^{T}M\\varPhi\\:={M}_{p}\\\\\\:{\\varPhi\\:}^{T}C\\varPhi\\:={C}_{p}\\\\\\:{\\varPhi\\:}^{T}K\\varPhi\\:={K}_{p}\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis can be obtained by combining Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e):\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{M}_{p}\\ddot{q}+{C}_{p}\\dot{q}+{K}_{p}q={f}_{p}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEquation (\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) is a system of n-order differential equations, and the individual coordinates (i\u0026thinsp;=\u0026thinsp;1, 2, ..., n) are independent of each other and can be solved individually, realizing the decoupled calculation of the 3D water phantom modal analysis equations.\u003c/p\u003e \u003cp\u003eThe intrinsic frequency and vibration mode of the 3D water phantom structure are the main factors affecting the vibration of the structure, and the modal harmonic response analysis is carried out on the basis of the structural analysis. As shown in Fig.\u0026nbsp;6, the cloud diagram of the vibration mode distribution of the first 6 orders of the water tank system. The first-order modal analysis contributes the most to the structural response, which is the main vibration mode. In the first order modal calculation, the 3D water phantom has an intrinsic frequency of 7.6787 Hz, which produces X-direction vibration shapes at the end of Z-axis and Y-axis. See Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for specific intrinsic frequency and vibration mode parameters for each order.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eResults of the first 6 orders of modal analysis\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOrdinal number\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNatural frequency\u003c/p\u003e\n \u003cp\u003e(Hz)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVibration pattern\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.6787\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX and Y-rail ends\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.9123\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eY-rail ends\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21.428\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX-rail ends\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e26.357\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eX-rail ends\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e26.594\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eY-rail ends and Lifting platform\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28.129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLifting platform\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eThe three-dimensional water phantom system, whose motion occurs in the proton beam energy measurement, is driven by a servo motor, and the relationship between the rotational speed of the motor and the vibration frequency is usually estimated by using \u003cem\u003en\u0026thinsp;=\u0026thinsp;60f/p\u003c/em\u003e [\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e]. The operating speed of the motor is within the rated speed of 600 rpm, and the vibration frequency is about 10 Hz. According to the modal analysis, the first-order and second-order intrinsic frequencies of the 3D water phantom structure are in the range of 7.6787 Hz and 7.9123 Hz, respectively. Once the motor\u0026apos;s operating frequency and the intrinsic frequency of the 3D water phantom structure are close to each other, it is possible to generate resonance. On the basis of the modal analysis results, the 3D water phantom structure is analyzed for harmonic response. The relationship between the amplitude and phase angle of the 3D water phantom structure at frequencies between 7.0 Hz and 8.75 Hz is shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. At the frequency of 7.9 Hz, the amplitude reaches a maximum of 0.26 mm, at which time the phase angle is about \u0026minus;\u0026thinsp;90\u0026deg;. In order to avoid resonance, the motor running speed should be avoided between 450rpm and 497rpm.\u003c/p\u003e\n"},{"header":"4. 3D water phantom testing","content":"\u003cp\u003eDuring the test, protons are accelerated by a cyclotron and reach the treatment head through a transport system [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], where the proton beam stream is directed into the 3D water phantom at an angle of 90\u0026deg; or 270\u0026deg;. The proton beam energy is measured by means of an ionization chamber. The measurement ionization chamber in the 3D water phantom is Stingray. it consists of a parallel plate ionization chamber with a diameter of 120 mm and a bracket specially designed for mounting the chamber on the X-rail. The reference ionization chamber is IBA Stealth and is mounted outside the 3D water phantom by means of a support fixed to the water tank and a plastic frame for the ionization chamber with dimensions of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:22.8\\text{c}\\text{m}\\times\\:22.8\\text{c}\\text{m}.\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eThe block diagram of the overall process of carrying out Bragg peak testing using a 3D water phantom can be simplified as in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e, where the Perspex water tank is placed in the measurement area and then adjusted in height and horizontal position using a lifting mechanism. The scanning size of the ionization chamber is set on the control computer program, and with the three-dimensional servo control program and controller, the automatic scanning function during measurement can be realized. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the main part of the 3D water phantom. When the 3D water phantom system is utilized for dose testing, the proton beam incidence angle can be from 0\u0026deg; to 360\u0026deg;, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e for Bragg peak testing using a fixed treatment head with an incidence angle of 0\u0026deg;.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the experiment, tests are conducted at 80 MeV, 90 MeV, 110 MeV, 140 MeV, 150 MeV, and 193 MeV proton beam energies. The proton beam passes through the treatment head, passes through the reference ionization chamber, enters the water through the Perspex tank wall, and finally reaches the measurement ionization chamber.\u003c/p\u003e \u003cp\u003eSince the physical thickness (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{m}\\)\u003c/span\u003e\u003c/span\u003e) and material properties of the components in the proton beam path are different, they need to be transformed into water equivalent thicknesses (WET) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{w}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan additionalcitationids=\"CR29 CR30\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], calculations are performed by the following formula:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{t}_{w}={t}_{m}\\frac{{\\rho\\:}_{m}}{{\\rho\\:}_{w}}\\frac{{\\stackrel{-}{S}}_{m}}{{\\stackrel{-}{S}}_{w}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn which, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the density of the proton beam passing through the component structural material on the 3D water phantom, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{w}\\)\u003c/span\u003e\u003c/span\u003e is the density of the water, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{S}}_{m}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{S}}_{w}\\)\u003c/span\u003e\u003c/span\u003e are the mean proton mass stopping power values for the material and water. Based on the developed 3D water phantom structure, the total depth formula is as follows:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\text{T}}_{\\text{w}}=\\sum\\:{t}_{{m}_{i}}+{R}_{d}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn which, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{R}}_{\\text{d}}\\)\u003c/span\u003e\u003c/span\u003e is Correction parameters for structural deformation.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the test results of the 3D water phantom at 80 MeV, 90 MeV, 110 MeV, 140 MeV, 150 MeV, and 193 MeV proton beam energies.\u003c/p\u003e \u003cp\u003eThe peak energy depths are 51.1 mm, 63.1 mm, 90.1 mm, 138.1 mm, 156.1 mm, and 241.1 mm. For the proton beam, 80% of the furthest range in the water, according to the data reference of the national institute of standards and technology [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. We compare the experimental measurements, with the theoretical values, to be obtained in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Through the table, the measured depths differ from the theoretical values by less than 0.5%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of the same type of 3D water phantom testing\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy\u003c/p\u003e \u003cp\u003e(MeV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGas pedal Flow Intensity\u003c/p\u003e \u003cp\u003e(nA)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTreatment head Converted flow intensity\u003c/p\u003e \u003cp\u003e(nA)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTests Peak\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNominal Peak\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePeak Difference\u003c/p\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003emisalignment\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16(0.05%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e51.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0386\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15(0.06%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e63.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e63.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.4383\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.17(0.11%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e90.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e91.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.3434\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16(0.21%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e139.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e139.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.0931\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15(0.26%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e156.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e157.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.3997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.27(0.9%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e242.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e243.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.4633\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003e3D water phantom is an important tool to detect the dose technical index of proton system, according to the requirements of proton therapy system on 3D water phantom, carry out the development of high-precision 3D water phantom prototype, the scanning size of the prototype is 480mm\u0026times;480mm\u0026times;410mm, precision 0.1mm, using the silk rod guide mechanism for motion control. At meanwhile, according to the finite element analysis method, the finite element analysis model of the main structure of the 3D water phantom has been established, and the structural strength of the 3D water phantom has been calibrated, and the maximum stress load of the 3D water phantom is 25.388 MPa and the maximum displacement deformation is 0.315 mm under the equivalent gravity condition. On the basis of the strength analysis, modal analysis is carried out, and the intrinsic frequency and vibration mode of the 3D water phantom structure has calculated. The intrinsic frequencies of the first six orders are respectively 7.6787Hz, 7.9123Hz, 21.428Hz, 26.357Hz, 26.594Hz, 28.129Hz. While the 3D water phantom is in operation, the speed of the drive motor is about 50rpm and the vibration frequency of the motor is about 0.833Hz, therefore there is no resonance.\u003c/p\u003e \u003cp\u003eIn addition, based on the 3D water phantom prototype, the testing of proton beam Bragg peak which under the beam energies of 80MeV, 90MeV, 110MeV, 140MeV, 150MeV and 193MeV, the peak energy depths were 51.1mm, 63.1mm, 90.1mm, 138.1mm, 156.1mm and 241.1mm respectively. Comparing with the theoretical nominal depths, and the error ranges are all controlled at 0.5%. Satisfy the demand for precision in use.\u003c/p\u003e \u003cp\u003eIn the next step, more comprehensive testing work will be carried out on the developed 3D water phantom prototype, such as depth dose distribution, range stability test.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eDeclaration of Competing Interest\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003eData availability\u003c/p\u003e\n\u003cp\u003eData will be made available on request.\u003c/p\u003e\n\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eThe authors are grateful to those who have given helpful advice. The research is supported by Hefei CAS Ion Medical and Technical Devices Co., Ltd.\u003c/p\u003e\n\u003cp\u003eFunding Declaration\u003c/p\u003e\n\u003cp\u003eThis work is supported by the 3D water phantom research program of Hefei CAS Ion Medical and Technical Devices Co., Ltd, grants No.JSCP2204.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eY. Liu, Z. Zheng, Understanding the global cancer statistics 2022: growing cancer burden, Sci China Life Sci (2024). https://doi.org/10.1007/s11427-024-2657-y.\u003c/li\u003e\n\u003cli\u003eF. Bray, M. Laversanne, H. Sung, J. Ferlay, R.L. Siegel, I. Soerjomataram, A. Jemal, Global cancer statistics 2022: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA Cancer J Clin 74 (2024) 229\u0026ndash;263. https://doi.org/10.3322/caac.21834.\u003c/li\u003e\n\u003cli\u003eA. Urruticoechea, R. Alemany, J. Balart, A. Villanueva, F. Vi\u0026ntilde;als, G. Capell\u0026aacute;, Recent advances in cancer therapy: an overview, Curr Pharm Des 16 (2010) 3\u0026ndash;10. https://doi.org/10.2174/138161210789941847.\u003c/li\u003e\n\u003cli\u003eS. Baliga, T.I. Yock, Proton beam therapy in pediatric oncology, Curr Opin Pediatr 31 (2019) 28\u0026ndash;34. https://doi.org/10.1097/MOP.0000000000000724.\u003c/li\u003e\n\u003cli\u003eW.D. Newhauser, R. Zhang, The physics of proton therapy, Phys. Med. Biol. 60 (2015) R155. https://doi.org/10.1088/0031-9155/60/8/R155.\u003c/li\u003e\n\u003cli\u003eJ.B. Farr, J.B. Flanz, A. Gerbershagen, M.F. Moyers, New horizons in particle therapy systems, Med Phys 45 (2018) e953\u0026ndash;e983. https://doi.org/10.1002/mp.13193.\u003c/li\u003e\n\u003cli\u003eF. Verhaegen, R.-G. Wanders, C. Wolfs, D. Eekers, Considerations for shoot-through FLASH proton therapy, Phys. Med. Biol. 66 (2021) 06NT01. https://doi.org/10.1088/1361-6560/abe55a.\u003c/li\u003e\n\u003cli\u003eM. Kang, S. Wei, J.I. Choi, C.B. Simone, H. Lin, Quantitative Assessment of 3D Dose Rate for Proton Pencil Beam Scanning FLASH Radiotherapy and Its Application for Lung Hypofractionation Treatment Planning, Cancers (Basel) 13 (2021) 3549. https://doi.org/10.3390/cancers13143549.\u003c/li\u003e\n\u003cli\u003eS. Wei, H. Lin, J.I. Choi, R.H. Press, S. Lazarev, R. Kabarriti, C. Hajj, S. Hasan, A.M. Chhabra, C.B. Simone, M. Kang, FLASH Radiotherapy Using Single-Energy Proton PBS Transmission Beams for Hypofractionation Liver Cancer: Dose and Dose Rate Quantification, Front Oncol 11 (2021) 813063. https://doi.org/10.3389/fonc.2021.813063.\u003c/li\u003e\n\u003cli\u003eP. van Marlen, S. van de Water, M. Dahele, B.J. Slotman, W.F.A.R. Verbakel, Single Ultra-High Dose Rate Proton Transmission Beam for Whole Breast FLASH-Irradiation: Quantification of FLASH-Dose and Relation with Beam Parameters, Cancers (Basel) 15 (2023) 2579. https://doi.org/10.3390/cancers15092579.\u003c/li\u003e\n\u003cli\u003eP. van Marlen, W.F.A.R. Verbakel, B.J. Slotman, M. Dahele, Single-fraction 34 Gy Lung Stereotactic Body Radiation Therapy Using Proton Transmission Beams: FLASH-dose Calculations and the Influence of Different Dose-rate Methods and Dose/Dose-rate Thresholds, Adv Radiat Oncol 7 (2022) 100954. https://doi.org/10.1016/j.adro.2022.100954.\u003c/li\u003e\n\u003cli\u003eS. Wei, H. Lin, J.I. Choi, C.B. Simone, M. Kang, A Novel Proton Pencil Beam Scanning FLASH RT Delivery Method Enables Optimal OAR Sparing and Ultra-High Dose Rate Delivery: A Comprehensive Dosimetry Study for Lung Tumors, Cancers (Basel) 13 (2021) 5790. https://doi.org/10.3390/cancers13225790.\u003c/li\u003e\n\u003cli\u003eM. Pennock, S. Wei, C. Cheng, H. Lin, S. Hasan, A.M. Chhabra, J.I. Choi, R.L. Bakst, R. Kabarriti, C.B. Simone Ii, N.Y. Lee, M. Kang, R.H. Press, Proton Bragg Peak FLASH Enables Organ Sparing and Ultra-High Dose-Rate Delivery: Proof of Principle in Recurrent Head and Neck Cancer, Cancers (Basel) 15 (2023) 3828. https://doi.org/10.3390/cancers15153828.\u003c/li\u003e\n\u003cli\u003eS.M. Schellhammer, S. Gantz, A. L\u0026uuml;hr, B.M. Oborn, M. Bussmann, A.L. Hoffmann, Technical Note: Experimental verification of magnetic field-induced beam deflection and Bragg peak displacement for MR-integrated proton therapy, Med Phys 45 (2018) 3429\u0026ndash;3434. https://doi.org/10.1002/mp.12961.\u003c/li\u003e\n\u003cli\u003eA. Anand, N. Sahoo, X.R. Zhu, G.O. Sawakuchi, F. Poenisch, R.A. Amos, G. Ciangaru, U. Titt, K. Suzuki, R. Mohan, M.T. Gillin, A procedure to determine the planar integral spot dose values of proton pencil beam spots, Med Phys 39 (2012) 891\u0026ndash;900. https://doi.org/10.1118/1.3671891.\u003c/li\u003e\n\u003cli\u003eJ. Schieferecke, S. Gantz, A. Hoffmann, J. Pawelke, Investigation of contrast mechanisms for MRI phase signal-based proton beam visualization in water phantoms, Magn Reson Med 90 (2023) 1776\u0026ndash;1788. https://doi.org/10.1002/mrm.29752.\u003c/li\u003e\n\u003cli\u003eH. Fuchs, F. Padilla-Cabal, A. Hummel, D. Georg, Technical Note: Design and commissioning of a water phantom for proton dosimetry in magnetic fields, Med Phys 48 (2021) 505\u0026ndash;512. https://doi.org/10.1002/mp.14605.\u003c/li\u003e\n\u003cli\u003eG. Cui, J. Duan, Y. Yang, F.-F. Yin, Technical Note: Investigation of the dosimetric impact of stray radiation on the Common Control Unit of the IBA Blue Phantom2, J Appl Clin Med Phys 21 (2020) 191\u0026ndash;196. https://doi.org/10.1002/acm2.12769.\u003c/li\u003e\n\u003cli\u003eM.J. LaRiviere, P.M.G. Santos, C.E. Hill-Kayser, J.M. Metz, Proton Therapy, Hematol Oncol Clin North Am 33 (2019) 989\u0026ndash;1009. https://doi.org/10.1016/j.hoc.2019.08.006.\u003c/li\u003e\n\u003cli\u003eG. He, Z. Huang, R. Qin, D. Chen, Numerical Prediction of Electromagnetic Vibration and Noise of Permanent-Magnet Direct Current Commutator Motors With Rotor Eccentricities and Glue Effects, IEEE Trans. Magn. 48 (2012) 1924\u0026ndash;1931. https://doi.org/10.1109/TMAG.2011.2178100.\u003c/li\u003e\n\u003cli\u003eM.E. Howard, J.M. Denbeigh, E.K. Debrot, N.B. Remmes, M.G. Herman, C.J. Beltran, A High-Precision Method for In Vitro Proton Irradiation, International Journal of Particle Therapy 7 (2020) 62\u0026ndash;69. https://doi.org/10.14338/IJPT-20-00007.1.\u003c/li\u003e\n\u003cli\u003eS. Li, Z. Gao, J. Xiong, L. Fan, J. Chen, K. Ma, L. Yang, B. Lu, Study on Single-Layer and Single-Channel Microstructure of 304 Stainless Steel Using Joule Heat Additive Manufacturing, Crystals 13 (2023) 1573. https://doi.org/10.3390/cryst13111573.\u003c/li\u003e\n\u003cli\u003eA.C. Ugural, S.K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, Pearson Education, 2011.\u003c/li\u003e\n\u003cli\u003eG. Nakamura, Identification of Lame parameters from boundary measurements, (1993).\u003c/li\u003e\n\u003cli\u003eE.W. Weisstein, Lam\u0026eacute; Constants. Eric Weisstein\u0026rsquo;s World of Physics, (n.d.). https://scienceworld.wolfram.com/physics/LameConstants.html\u003c/li\u003e\n\u003cli\u003eM. Geradin, D.J. Rixen, Mechanical Vibrations: Theory and Application to Structural Dynamics, John Wiley \u0026amp; Sons, 2015.\u003c/li\u003e\n\u003cli\u003eJ.F. Gieras, Permanent Magnet Motor Technology: Design and Applications, Third Edition, 3rd ed., CRC Press, Boca Raton, 2009.\u003c/li\u003e\n\u003cli\u003eM.F. Moyers, A.S. Vatnitsky, S.M. Vatnitsky, Factors for converting dose measured in polystyrene phantoms to dose reported in water phantoms for incident proton beams, Med Phys 38 (2011) 5799\u0026ndash;5806. https://doi.org/10.1118/1.3639119.\u003c/li\u003e\n\u003cli\u003eA. Smith, M. Gillin, M. Bues, X.R. Zhu, K. Suzuki, R. Mohan, S. Woo, A. Lee, R. Komaki, J. Cox, K. Hiramoto, H. Akiyama, T. Ishida, T. Sasaki, K. Matsuda, The M. D. Anderson proton therapy system, Med Phys 36 (2009) 4068\u0026ndash;4083. https://doi.org/10.1118/1.3187229.\u003c/li\u003e\n\u003cli\u003eR. Zhang, W.D. Newhauser, Calculation of water equivalent thickness of materials of arbitrary density, elemental composition and thickness in proton beam irradiation, Phys Med Biol 54 (2009) 1383\u0026ndash;1395. https://doi.org/10.1088/0031-9155/54/6/001.\u003c/li\u003e\n\u003cli\u003eS. Stuchebrov, A. Bulavskaya, A. Grigorieva, M. Banshchikova, E. Bushmina, O. Chernova, V. Saburov, I. Miloichikova, Determination of the water equivalent thickness of 3D printed samples for the therapeutic proton beams, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1061 (2024) 169119. https://doi.org/10.1016/j.nima.2024.169119.\u003c/li\u003e\n\u003cli\u003eStopping Power and Range Tables for Protons, (n.d.). https://physics.nist.gov/cgi-bin/Star/ap_table.pl\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-korean-physical-society","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of the Korean Physical Society](https://link.springer.com/journal/40042)","snPcode":"40042","submissionUrl":"https://submission.springernature.com/new-submission/40042/3","title":"Journal of the Korean Physical Society","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"proton therapy, Bragg peak, 3D water phantom, stress analysis, intrinsic frequency","lastPublishedDoi":"10.21203/rs.3.rs-5117428/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5117428/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eProton therapy is an advanced radiation therapy technique that allows for precise treatment of the tumor site. 3D water phantom system is the important testing equipment for proton therapy,which can guarantee the dose before treatment, realize dose distribution scanning detection. It includes a lifting platform, a high-precision three-dimensional servo, ionization chambers, a control system and a water tank. The lifting platform and high-precision three-dimensional servo are the key factors which can affect the accuracy of proton beam measurement. The 3D water phantom structure design is carried out to realize proton beam dose detection. Finite element analysis model is established to carry out mechanical mechanics analysis of the 3D water phantom structure. During scanning detection, the vibration generated by the servo motor operation may cause the 3D water phantom structure resonance, carry out modal analysis and harmonic response analysis, calculate the 3D water phantom intrinsic frequency and motor operation vibration frequency within the possible resonance intervals. In addition, the 3D water phantom model was utilized to carry out Bragg peak detection experiments at different energies for proton therapy.\u003c/p\u003e","manuscriptTitle":"Structural Design, Analysis and Testing of 3D Water Phantom for Proton Therapy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-03 17:09:00","doi":"10.21203/rs.3.rs-5117428/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-11-16T02:35:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-28T11:49:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"40770279860542382977488366514430655482","date":"2024-10-12T11:19:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"316692230577932500563323786657850925","date":"2024-10-05T10:23:18+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-10-05T09:03:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-24T02:14:19+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-09-23T07:45:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of the Korean Physical Society","date":"2024-09-19T13:38:44+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-korean-physical-society","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of the Korean Physical Society](https://link.springer.com/journal/40042)","snPcode":"40042","submissionUrl":"https://submission.springernature.com/new-submission/40042/3","title":"Journal of the Korean Physical Society","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0bfd7dcc-7aa4-444c-90ff-e1de0effe0e2","owner":[],"postedDate":"December 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-12-20T00:08:07+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-03 17:09:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5117428","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5117428","identity":"rs-5117428","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}