對質子射束特性的了解與其對應射源模型的建立是所有質子治療蒙地卡羅相關應用不可或缺的起始點。本研究旨在探討用於筆型射束掃描質子治療機的蒙地卡羅射源模型。藉由一系列的模擬與量測數據的比較，本研究發展出一套公開文獻上最好的射源模型。射源參數的建立、測試與驗證的結果將在本文詳細說明。
在質子治療的射束傳遞技術中，筆型射束掃描不同於擾動式與被動式散射技術，其射束不需要經過散射的過程以得到腫瘤範圍內的均勻劑量分佈，因此，射束機頭中的零組件對射源項的模擬影響並不是太大。然而，由於以筆型射束掃描技術所得到的均勻劑量，是以多個具有獨特特性的射束累加在一起而得到的，故每個射束的特性就需要精準描述。本研究首先比較四個常見蒙地卡羅程式(FLUKA、GEANT4、MCNP與PHITS)在質子治療劑量計算的性能。確認所有蒙地卡羅程式皆能於標準10×10 cm2照野下得到95%以上的加馬通過率(3mm/3%)。本研究選擇使用GEANT4進行後續射源模型的探討。本研究使用質子治療中心每月品保量測的結果做為射源模型發展的基礎，比較不同射源模型所建立參數以及其所呈現的優缺點。
本研究提出了一套能接近完美還原品保結果的射源模型，並將該射源模型與文獻中的另外兩種射源模型進行深入的比較。三種模型在單一質子束的比較中差異極為明顯；但本研究所提出的射源模型與品保結果最為相近。雖然在簡單治療計劃的案例中，三種模型皆能得到92%以上的(3mm/3%)加馬通過率；最後在考慮有射束準直儀的案例中，本研究的射源模型與目前商用蒙地卡羅治療計劃系統和實驗量測值最相符。針對未來先進質子治療技術的發展，例如要求極小射束尺寸或加裝複雜的射束準直器，我們可預期此一射源模型的有效性將更加凸顯。

The understanding of proton beams’ properties and the development of corresponding source models are the critical initial point of Monte Carlo (MC) application for proton therapy. The purpose of this study is to discuss the Monte Carlo (MC) source models developed for pencil beam scanning (PBS) proton machine. By series of comparison between simulation and measurement, this study has developed the best source model among the published literature. The construction of the source parameters, testing and verified results will be described in detail in this article.
Among the beam delivery techniques in proton therapy. Unlike wobbling and passive scattering techniques, proton beams in PBS do not require scattering process to obtain an uniform dose distribution in tumor; therefore, the simulation of the source term is not severely susceptible to components inside the beam nozzle. Yet since the uniform dose distribution delivered by PBS consists of numerous proton beams each with unique property, accurate description of each beam’s property is a necessity. This study first compares the dose distribution calculated for proton therapy using various MC codes including FLUKA、GEANT4、MCNP and PHITS. Ensuring that, in the case of a standard 10×10 cm^2 field, the gamma passing rates (3%/3mm) of all four codes are all above 95%. Eventually, GEANT4 is used in the following study. The development of the source models in this study is based on the monthly QA results from proton therapy center.
This study has proposed a souce model that could almost perfectly reproduce the QA results. We then compared this source model with other two models in the literature in-depth. The three source models show extremely obvious discrepancies in the case of single beam simulation; yet in the reproduction QA results, the proposed model is able to present the best agreement with the experimental data. Although in simple treatment cases, all three models have over 92% gamma passing rate (3%/3mm); finally in the case considering collimators, the proposed model shows the best agreement with the commercial MC-based Treatment Planning System (TPS) and experimental data. For the development of proton therapy technology in the future, for instance, extremely small-size proton beam or cases with complex collimators, we could expected that the effectiveness of this souce model would be emphasized.

[1] A. Mairani, T. T. Böhlen, A. Schiavi, T. Tessonnier, S. Molinelli, S. Brons, G. Battistoni, K. Parodi, and V. Patera, "A Monte Carlo-based treatment planning tool for proton therapy," Phys. Med. Biol . vol. 53, no. 8, pp. 2471-2490, 2013.
[2] 楊子毅, "簡化型蒙地卡羅射源模型 應用於筆型射束掃描質子治療之劑量計算研究," 碩士, 核子工程與科學研究所, 國立清華大學, 新竹, 2014.
[3] H. Paganetti, "Range uncertainties in proton therapy and the role of Monte Carlo simulations," Phys. Med. Biol., vol. 57, no. 11, pp. R99-R117, 2012.
[4] W. G. Shin, M. Testa, H. S. Kim, J. H. Jeong, S. B. Lee, Y. J. Kim, and C. H. Min, "Independent dose verification system with Monte Carlo simulations using TOPAS for passive scattering proton therapy at the National Cancer Center in Korea," Phys. Med. Biol., vol. 62, no. 19, pp. 7598-7616, 2017.
[5] S. J. Dowdell, B. Clasie, N. Depauw, P. Metcalfe, A. B. Rosenfeld, H. M. Kooy, J. Flanz, and H. Paganetti, "Monte Carlo study of the potential reduction in out-of-field dose using a patient-specific aperture in pencil beam scanning proton therapy," Phys. Med. Biol., vol. 57, no. 10, pp. 2829-2842, 2012.
[6] RaySearch MC TPS, http://people.na.infn.it/~mettivie/MCMA%20presentation/17%20Aula%20Magna/17_30_Traneus.pdf. (2/2).
[7] H. Jiang and H. Paganetti, "Adaptation of GEANT4 to Monte Carlo dose calculations based on CT data," Med. Phys., vol. 31, no. 10, pp. 2811-2818, 2004.
[8] H. Paganetti, H. Jiang, K. Parodi, R. Slopsema, and M. Engelsman, "Clinical implementation of full Monte Carlo dose calculation in proton beam therapy," Phys. Med. Biol. , vol. 53, no. 17, pp. 4825-4853, 2008.
[9] L. Grevillot, D. Bertrand, F. Dessy, N. Freud, and D. Sarrut, "A Monte Carlo pencil beam scanning model for proton treatment plan simulation using GATE/GEANT4," Phys. Med. Biol., vol. 56, no. 16, pp. 5203–5219 2011.
[10] F. Fiorini, N. Schreuder, and F. V. d. Heuvel, "Technical Note: Defining cyclotron-based clinical scanning proton machines in a FLUKA Monte Carlo system," Med. Phys., vol. 45, no. 2, pp. 963-970, 2018.
[11] J. Soltani-Nabipour, D. Sardari, and G. Cata-Danil, "Sensitivity of the Bragg Peak curve to the average ionization potential of the stopping medium," Rom. Journ. Phys., vol. 54, no. 3-4, pp. 321-330, 2009.
[12] NIST, https://www.nist.gov/. (10/22).
[13] H. Paganetii, Proton Therapy Physics: Boca Ration. FL : CRC Press/Taylor & Francis, 2012.
[14] R. R. Wilson, "Radiological Use of Fast Protons," Radiology, vol. 47, no. 5, pp. 487-491, 1946.
[15] M. Durante and H. Paganetti, "Nuclear physics in particle therapy: a review," Rep. Prog. Phys., vol. 79, no. 9, 2016, Art. no. 096702.
[16] T. Bortfeld and W. Schlegel, "An analytical approximation of depth - dose distributions for therapeutic proton beams," Phys. Med. Biol., vol. 41, no. 8, pp. 1331-1339, 1996.
[17] D. Jette and W. Chen, "Creating a spread-out Bragg peak in proton beams," Phys. Med. Biol., vol. 56, no. 11, pp. N131-N138, 2011.
[18] I. Park, "A new approach to produce spread-out Bragg peak using the MINUIT fit," Curr. Appl. Phys., vol. 9, no. 4, pp. 852-855, 2009.
[19] L. Lin, C. G. Ainsley, T. Mertens, O. D. Wilde, P. T. Talla, and J. E. McDonough, "A novel technique for measuring the low-dose envelope of pencil-beam scanning spot profiles," Phys. Med. Biol., vol. 58, no. 12, pp. N171-N180, 2013.
[20] H. Paganetti, "Relative biological effectiveness (RBE) values for proton beam therapy. Variations as a function of biological endpoint, dose, and linear energy transfer," Phys. Med. Biol. , vol. 59, no. 22, pp. R419-R472, 2014.
[21] J. S. Loeffler and M. Durante, "Charged particle therapy: Optimization, challenges and future directions," M. Nat. Rev. Clin. Oncol., vol. 10, no. 7, pp. 411-424, 2013.
[22] H. A. Bethe, "Moliere's Theory of Multiple Scattering," Phys. Rev., vol. 89, no. 6, pp. 1256-1266, 1953.
[23] V. E. Bellinzona, M. Ciocca, A. Embriaco, A. Fontana, A. Mairani, M. Mori, and K. Parodi, "On the parametrization of lateral dose profiles in proton radiation therapy," Phys. Med., vol. 31, no. 5, pp. 484-492, 2015.
[24] H. W. Lewis, "Multiple Scattering in an infinite Medium," Phys. Rev., vol. 78, no. 5, pp. 526-529, 1950.
[25] R. Mohan and D. Grosshans, "Proton therapy – Present and future," Adv. Drug. Deliv. Rev., vol. 109, pp. 26-44, 2017.
[26] "Prescribing, Recording, and Reporting Proton-Beam Therapy," in "ICRU 78," INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, ICRU2007 vol. 7.
[27] PTCOG https://www.ptcog.ch/. (10/02).
[28] K. Yasui, T. Toshito, C. Omachi, K. Hayashi, K. Tanaka, K. Asai, A. Shimomura, R. Muramatsu, and N. Hayashi, "Evaluation of dosimetric advantages of using patient-specific aperture system with intensity-modulated proton therapy for the shallow depth tumor," J. Appl. Clin. Med. Phys., vol. 19, no. 1, pp. 132-137, 2018.
[29] F. C. Charlwood, A. H. Aitkenhead, and R. I. Mackay, "A Monte Carlo study on the collimation of pencil beam scanning proton therapy beams," Med. Phys., vol. 43, no. 3, pp. 1462-1472, 2016.
[30] D. E. Hyer, P. M. Hill, D. Wang, B. R. Smith, and R. T. Flynn, "A dynamic collimation system for penumbra reduction in spot-scanning proton therapy: Proof of concept," Med. Phys., vol. 41, no. 9, 2014, Art. no. 091701.
[31] D. E. Hyer, P. M. Hill, D. Wang, B. R. Smith, and R. T. Flynn, "Effects of spot size and spot spacing on lateral penumbra reduction when using a dynamic collimation system for spot scanning proton therapy," Phys. Med. Biol . vol. 59, no. 22, pp. N187-N196, 2014.
[32] A. Moignier, E. Gelover, D. Wang, B. Smith, R. Flynn, M. Kirk, L. Lin, T. Solberg, A. Lin, and D. Hyer, "Theoretical Benefits of Dynamic Collimation in Pencil Beam Scanning Proton Therapy for Brain Tumors: Dosimetric and Radiobiological Metrics," Int. J. Radiat. Oncol. Biol. Phys., vol. 95, no. 1, pp. 171-180, 2016.
[33] E. Gelover, D. Wang, P. M. Hill, R. T. Flynn, M. C. Gao, S. Laub, M. Pankuch, and D. E. Hyer, "A method for modeling laterally asymmetric proton beamlets resulting from collimation," Med. Phys., vol. 42, no. 3, pp. 1321-1334, 2015.
[34] PTW https://ptw.de/. (10/02).
[35] CNMC http://www.cnmcco.com/. (10/02).
[36] Geant4 User Documentation https://geant4.web.cern.ch/support/user_documentation. (10/21).
[37] FLUKA HADROTHErapy, http://www.fluka.org/fluka.php?id=man_onl&sub=20. Available: http://www.fluka.org/fluka.php?id=man_onl&sub=20 (11/19).
[38] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce, M. Asai, D. Axen, S. Banerjee, G. Barrand, F. Behner, L. Bellagamba, J. Boudreau, L. Broglia, A. Brunengo, H. Burkhardt, S. Chauvie, J. Chuma, R. Chytracek, G. Cooperman, G. Cosmo, P. Degtyarenko, A. Dell’Acqua, G. Depaola, D. Dietrich, R. Enami, A. Feliciello, C. Ferguson, H. Fesefeldt, G. Folger, F. Foppiano, A. Forti, S. Garelli, S. Giani, R. Giannitrapani, D. Gibin, J. J. Gómez, Cadenas, I. Gonz!, G. G. Abril, G. Greeniaus, W. Greiner, V. Grichine, A. Grossheim, S. Guatelli, P. Gumplinger, R. Hamatsu, K. Hashimoto, H. Hasui, A. Heikkinen, A. Howard, V. Ivanchenko, A. Johnson, F. W. Jones, J. Kallenbach, N. Kanaya, M. Kawabata, Y. Kawabata, M. Kawaguti, S. Kelner, P. Kent, A. Kimura, T. Kodama, R. Kokoulin, M. Kossov, H. Kurashige, E. Lamanna, T. Lampén, V. Lara, V. Lefebure, F. Lei, M. Liendl, W. Lockman, F. Longo, S. Magni, M. Maire, E. Medernach, K. Minamimoto, P. M. d. Freitas, Y. Morita, K. Murakami, M. Nagamatu, R. Nartallo, P. Nieminen, T. Nishimura, K. Ohtsubo, M. Okamura, S. O’Neale, Y. Oohata, K. Paech, J. Perl, A. Pfeiffer, M. G. Pia, F. Ranjard, A. Rybin, S. Sadilov, E. D. Salvo, G. Santin, T. Sasaki, N. Savvas, Y. Sawada, S. Scherer, S. Sei, V. Sirotenko, D. Smith, N. Starkov, H. Stoecker, J. Sulkimo, M. Takahata, S. Tanaka, E. Tcherniaev, E. S. Tehrani, M. Tropeano, P. Truscott, H. Uno, L. Urban, P. Urban, M. Verderi, A. Walkden, W. Wander, H. Weber, J. P. Wellisch, T. Wenaus, D. C. Williams, D. Wright, T. Yamada, H. Yoshida and D. Zschiesche, "Geant4—a simulation toolkit," Nucl. Instr. Meth. Phys. Res. A, vol. 506, no. 3, pp. 250-303, 2003.
[39] J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. A. Dubois, M. Asai, G. Barrand, R. Capra, S. Chauvie, R. Chytracek, G. A. P. Cirrone, G. Cooperman, G. Cosmo, G. Cuttone, G. G. Daquino, M. Donszelmann, M. Dressel, G. Folger, F. Foppiano, J. Generowicz, V. Grichine, S. Guatelli, P. Gumplinger, A. Heikkinen, I. Hrivnacova, A. Howard, S. Incerti, V. Ivanchenko, T. Johnson, F. Jones, T. Koi, R. Kokoulin, M. Kossov, H. Kurashige, V. Lara, S. Larsson, F. Lei, O. Link, F. Longo, M. Maire, A. Mantero, B. Mascialino, I. McLaren, P. M. Lorenzo, K. Minamimoto, K. Murakami, P. Nieminen, L. Pandola, S. Parlati, L. Peralta, J. Perl, A. Pfeiffer, M. G. Pia, A. Ribon, P. Rodrigues, G. Russo, S. Sadilov, G. Santin, T. Sasaki, D. Smith, N. Starkov, S. Tanaka, E. Tcherniaev, B. Tomé, A. Trindade, P. Truscott, L. Urban, M. Verderi, A. Walkden, J. P. Wellisch, D. C. Williams, D. Wright, and H. Yoshida, "Geant4 Developments and Applications," IEEE Trans. Nucl. Sci., vol. 53, no. 1, 2006.
[40] C. Z. Jarlskog and H. Paganetti, "Physics Settings for Using the Geant4 Toolkit in Proton Therapy," IEEE Trans. Nucl. Sci., vol. 55, no. 3, pp. 1018-1025, 2008.
[41] S. Keiichi, I. Osamu, N. Tsuneo, I. Nobuyuki, I. Akira, K. Satoshi, C. Satoshi, F. Kazuyoshi, O. Naohiko, O. Takaaki, M. Toru, M. Hiroyuki, Z. Atsushi, K. So, and K. Jun-ichi, "JENDL-4.0: A New Library for Nuclear Science and Engineering," Journal of Nuclear Science and Technology, vol. 48, no. 1, pp. 1-30, 2011/01/01 2011.
[42] Zebra, https://www.iba-dosimetry.com/product/zebra/. (1/16).
[43] D. A. Low, W. B. Harms, S. Mutic, and J. A. Purdy, "A technique for the quantitative evaluation of dose distributions," Med. Phys., vol. 25, no. 5, pp. 656-661, 1998.
[44] P. YEPES, S. RANDENIYA, P. J. TADDEI, and W. D. NEWHAUSER, "A track-repeating algorithm for fast Monte Carlo dose calculations of proton radiotherapy," Nucl. Technol., vol. 168, no. 3, pp. 736-740, 2009.
[45] S. D. Randeniya, P. J. Taddei, and W. D. Newhauser, "Intercomparision of Monte Carlo Radiation Transport Codes MCNPX, GEANT4, and FLUKA for Simulating Proton Radiotherapy of the Eye," Nucl. Technol., vol. 168, no. 3, pp. 810-814, 2009.
[46] A. Dotti, V. D. Elvira, G. Folger, K. Genser, S. Y. Jun, J. B. Kowalkowski, and M. Paterno, "Geant4 Computing Performance Benchmarking and Monitoring," in 21st International Conference on Computing in High Energy and Nuclear Physics (CHEP), PARTS 1-9, Okinawa, JAPAN, 2015, vol. 664: IOP.
[47] Z. Y. Yang, P. E. Tsai, S. C. Lee, Y. C. Liu, C. C. Chen, T. Sato, and R. J. Sheu, "Inter-comparison of Dose Distributions Calculated by FLUKA, GEANT4, MCNP, and PHITS for Proton Therapy," presented at the 13th International Conference on Radiation Shielding (ICRS) / 19th Topical Meeting of the Radiation-Protection-and-Shielding-Division-of-the-American-Nuclear-Society (RPSD), Paris, FRANCE, OCT 03-06, 2016, 2017.
[48] B. Schaffner, "Proton dose calculation based on in-air fluence measurements," Phys. Med. Biol., vol. 55, no. 6, pp. 1545-1562, 2008.
[49] M. A. Cortés-Giraldo and A. Carabe, "A critical study of different Monte Carlo scoring methods of dose average linear-energy-transfer maps calculated in voxelized geometries irradiated with clinical proton beams," Phys. Med. Biol., vol. 60, no. 7, pp. 2645-2669, 2015.
[50] D. Czarnecki, B. Poppe, and K. Zink, "Impact of new ICRU Report 90 recommendations on calculated correction factors for reference dosimetry," Phys. Med. Biol., vol. 63, no. 15, 2018, Art. no. 155015.