Abstract
In radiation therapy, it is very important to ensure that the radiation dose is correctly delivered to the patient. This is achieved by obtaining quantitative dose measurements for beam calibration in the treatment planning system. Dose calculations should be performed with the required accuracy to a degree of uncertainty of less than 1%. The measurement of the absorbed dose in and around body tissues irradiated with carbon ions requires careful use of materials selected from established phantom and radiation detectors. The main advantage of such materials is that when information on the energy and nature of charged particles at the desired point is incomplete or inaccurate, they can allow determination of the absorbed dose. In general, radiation interactions in a tissue representation caused by carbon ions can be characterized by calculating the linear stopping power. Carbon ions have a limited penetration depth within human tissues that depends on the energy and stopping power of these ions as they penetrate into the body. The purpose of the present study was to calculate the stopping power, range and dose to intestinal and prostate tissues of carbon ions. The stopping power values of these tissues were specified by the effective charge approach method. The 5ZaPa-NR-CV, pcemd-4 and pcSseg-4 sets of Gaussian-type functions were employed for the calculation of electronic charge density. Range calculations were made by means of the Gaussian quadrature method, making use of the continuous slowing down approximation. Flux-based dose calculations were also carried out in accordance with the Bragg–Gray theorem using the Geant4 and FLUKA simulation toolkits. The results were compared with each other and with the SRIM and CasP datasets. Then, depth–dose distributions and range values were verified by positron emission activity using the GATE toolkit. Among the different types of Gaussian functions used here, the best semi-analytical result was found for the 5ZaPa-NR-CV set. The results obtained in the present study can be used for dose verification and dose reconstruction in charged particle radiotherapy and for radiation research on the interaction of radiation with matter. The results calculated here will be useful for quantifying uncertainties associated with stopping power, range, and reconstruction of dose in charged particle therapy.
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References
Agostinelli S, Allison J, Amako K, Apostolakis J, Araujo H, Arce P, Asai M, Axen D, Banerjee S, Barrand G, Behner F, Bellagamba L, Boudreau J, Broglia L, Brunengo A, Burkhardt H, Chauvie S, Chuma J, Chytracek R, Cooperman G, Cosmo G, Degtyarenko P, Dell'Acqua A, Depaola G, Dietrich D, Enami R, Feliciello A, Ferguson C, Fesefeldt H, Folger G, Foppiano F, Forti A, Garelli S, Giani S, Giannitrapani R, Gibin D, Gómez Cadenas JJ, González I, Gracia Abril G, Greeniaus G, Greiner W, Grichine V, Grossheim A, Guatelli S, Gumplinger P, Hamatsu R, Hashimoto K, Hasui H, Heikkinen A, Howard A, Ivanchenko V, Johnson A, Jones FW, Kallenbach J, Kanaya N, Kawabata M, Kawabata Y, Kawaguti M, Kelner S, Kent P, Kimura A, Kodama T, Kokoulin R, Kossov M, Kurashige H, Lamanna E, Lampén T, Lara V, Lefebure V, Lei F, Liendl M, Lockman W, Longo F, Magni S, Maire M, Medernach E, Minamimoto K, Mora de Freitas P, Morita Y, Murakami K, Nagamatu M, Nartallo R, Nieminen P, Nishimura T, Ohtsubo K, Okamura M, O'Neale S, Oohata Y, Paech K, Perl J, Pfeiffer A, Pia MG, Ranjard F, Rybin A, Sadilov S, Di Salvo E, Santin G, Sasaki T, Savvas N, Sawada Y, Scherer S, Sei S, Sirotenko V, Smith D, Starkov N, Stoecker H, Sulkimo J, Takahata M, Tanaka S, Tcherniaev E, Safai Tehrani E, Tropeano M, Truscott P, Uno H, Urban L, Urban P, Verderi M, Walkden A, Wander W, Weber H, Wellisch JP, Wenaus T, Williams DC, Wright D, Yamada T, Yoshida H, Zschiesche D (2003) Geant4—a simulation toolkit. Nucl Instrum Methods Phys Res, Sect A 506(3):250–303. https://doi.org/10.1016/S0168-9002(03)01368-8
Barkas WH, Birnbaum W, Smith FM (1956) Mass-ratio method applied to the measurement of $L$-Meson masses and the energy balance in pion decay. Phys Rev 101(2):778–795. https://doi.org/10.1103/PhysRev.101.778
Battistoni G, Cerutti F, Fassò A, Ferrari A, Muraro S, Ranft J, Roesler S, Sala PR (2007) The FLUKA code: description and benchmarking. AIP Conf Proc 896 (1):31–49. https://doi.org/10.1063/1.2720455
Bethe H (1930) Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie. Ann Phys 397(3):325–400. https://doi.org/10.1002/andp.19303970303
Bloch F (1933) Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie. Ann Phys 408(3):285–320. https://doi.org/10.1002/andp.19334080303
Bragg WH, Kleeman R (1905) On the α particles of radium, and their loss of range in passing through various atoms and molecules. Philos Mag Ser 610(57):318–340. https://doi.org/10.1080/14786440509463378
Bridges D, Kawamura H, Kanai T (2018) Probabilistic dose distribution from interfractional motion in carbon ion radiation therapy for prostate cancer shows rectum sparing with moderate target coverage degradation. PLoS ONE 13(8):e0203289. https://doi.org/10.1371/journal.pone.0203289
Briesmeister JF (2007) MCNP-a general Monte Carlo N-particle transport code. Version 4B, vol LA-12625-M.
Clark T, Chandrasekhar J, Spitznagel GW, Schleyer PVR (1983) Efficient diffuse function-augmented basis sets for anion calculations: III: the 3–21+G basis set for first-row elements, Li–F. J Comput Chem 4(3):294–301. https://doi.org/10.1002/jcc.540040303
Fano U (1963) Penetration of Protons, Alpha Particles, and Mesons. Annual Review of Nuclear Science 13(1):1–66. https://doi.org/10.1146/annurev.ns.13.120163.000245
Farina E, Piersimoni P, Riccardi C, Rimoldi A, Tamborini A, Ciocca M (2015) Geant4 simulation for a study of a possible use of carbon ion pencil beams for the treatment of ocular melanomas with the active scanning system at CNAO. J Phys: Conf Ser 664(7):072048. https://doi.org/10.1088/1742-6596/664/7/072048
Ferlay J SI, Ervik M, Dikshit R, Eser S, Mathers C, Rebelo M, Parkin DM, Forman D, Bray F (2012) GLOBOCAN 2012: estimated cancer incidence, mortality and prevalence worldwide in 2012 v1.0. IARC CancerBase No. 11. IARC Publication
Geithner O, Andreo P, Sobolevsky N, Hartmann G, Jäkel O (2006) Calculation of stopping power ratios for carbon ion dosimetry. Phys Med Biol 51(9):2279
Gray LH (1929) The absorption of penetrating radiation. Proc R Soc Lond Ser A 122(790):647–668. https://doi.org/10.1098/rspa.1929.0050
Gray LH (1936) An ionization method for the absolute measurement of γ-ray energy. Proc R Soc Lond Ser A Math Phys Sci 156(889):578–596. https://doi.org/10.1098/rspa.1936.0169
Haettner E, Iwase H, Kramer M, Kraft G, Schardt D (2013) Experimental study of nuclear fragmentation of 200 and 400 MeV/u (12)C ions in water for applications in particle therapy. Phys Med Biol 58(23):8265–8279. https://doi.org/10.1088/0031-9155/58/23/8265
Hartree DR (1928) The wave mechanics of an atom with a non-coulomb central field: Part I: Theory and methods. Math Proc Cambridge Philos Soc 24(01):89–110. https://doi.org/10.1017/S0305004100011919
Hofmann T, Fochi A, Parodi K, Pinto M (2019a) Prediction of positron emitter distributions for range monitoring in carbon ion therapy: an analytical approach. Phys Med Biol 64(10):105022. https://doi.org/10.1088/1361-6560/ab17f9
Hofmann T, Pinto M, Mohammadi A, Nitta M, Nishikido F, Iwao Y, Tashima H, Yoshida E, Chacon A, Safavi-Naeini M, Rosenfeld A, Yamaya T, Parodi K (2019b) Dose reconstruction from PET images in carbon ion therapy: a deconvolution approach. Phys Med Biol 64(2):025011. https://doi.org/10.1088/1361-6560/aaf676
ICRP (1975) Report of the task group on reference man. ICRP Publication 23. International Commission on Radiological Protection
ICRU (1989) Tissue substitutes in radiation dosimetry and measurements. ICRU Report 44. Bethesda
ICRU (2005) Stopping of ions heavier than helium. ICRU Report 73. Bethesda
Implementation of the International Code of Practice on Dosimetry in Radiotherapy (TRS 398): Review of Testing Results (2010) International Atomic Energy Agency, Vienna
Inaniwa T, Kanematsu N (2016) Effective particle energies for stopping power calculation in radiotherapy treatment planning with protons and helium, carbon, and oxygen ions. Phys Med Biol 61(20):N542–N550. https://doi.org/10.1088/0031-9155/61/20/n542
Jan S, Santin G, Strul D, Staelens S, Assié K, Autret D, Avner S, Barbier R, Bardiès M, Bloomfield PM, Brasse D, Breton V, Bruyndonckx P, Buvat I, Chatziioannou AF, Choi Y, Chung YH, Comtat C, Donnarieix D, Ferrer L, Glick SJ, Groiselle CJ, Guez D, Honore PF, Kerhoas-Cavata S, Kirov AS, Kohli V, Koole M, Krieguer M (2004) GATE: a simulation toolkit for PET and SPECT. Phys Med Biol 49(19):4543–4561. https://doi.org/10.1088/0031-9155/49/19/007
Jensen F (2015) Segmented contracted basis sets optimized for nuclear magnetic shielding. J Chem Theory Comput 11(1):132–138. https://doi.org/10.1021/ct5009526
Gaussian Quadrature Weights and Abscissae (2011) https://pomax.github.io/bezierinfo/legendre-gauss.html
Kubota Y, Sakai M, Tashiro M, Saitoh J-i, Abe T, Ohno T, Nakano T (2018) Technical Note: Predicting dose distribution with replacing stopping power ratio for inter-fractional motion and intra-fractional motion during carbon ion radiotherapy with passive irradiation method for stage I lung cancer. Med Phys 45(7):3435–3441. https://doi.org/10.1002/mp.12966
Lehtola S, Manninen P, Hakala M, Hamalainen K (2013) Contraction of completeness-optimized basis sets: application to ground-state electron momentum densities. J Chem Phys 138(4):044109. https://doi.org/10.1063/1.4788635
Li Z, Fan Y, Dong M, Tong L, Zhao L, Yin Y, Chen X (2018) In-beam PET imaging in carbon therapy for dose verification. IEEE Trans Radiat Plasma Med Sci 2(1):61–67. https://doi.org/10.1109/TRPMS.2017.2769109
Luhr A, Hansen DC, Jakel O, Sobolevsky N, Bassler N (2011) Analytical expressions for water-to-air stopping-power ratios relevant for accurate dosimetry in particle therapy. Phys Med Biol 56(8):2515–2533. https://doi.org/10.1088/0031-9155/56/8/012
Estar stopping-power and range tables for electrons (1999) National Institute of Standards and Technology. https://physics.nist.gov/Star
Ma CMC, Lomax T (2012) Proton and carbon ion therapy. CRC Press, London
Maruyama K, Tsuji H, Nomiya T, Katoh H, Ishikawa H, Kamada T, Wakatsuki M, Akakura K, Shimazaki J, Aoyama H, Tsujii H (2017) Five-year quality of life assessment after carbon ion radiotherapy for prostate cancer. J Radiat Res 58(2):260–266. https://doi.org/10.1093/jrr/rrw122
Mazzucconi D, Agosteo S, Ferrarini M, Fontana L, Lante V, Pullia M, Savazzi S (2018) Mixed particle beam for simultaneous treatment and online range verification in carbon ion therapy: proof-of-concept study. Med Phys 45(11):5234–5243. https://doi.org/10.1002/mp.13219
Mohamad O, Sishc BJ, Saha J, Pompos A, Rahimi A, Story MD, Davis AJ, Kim DWN (2017) Carbon ion radiotherapy: a review of clinical experiences and preclinical research, with an emphasis on DNA damage/repair. Cancers 9(6):1. https://doi.org/10.3390/cancers9060066
Mori S, Zenklusen S, Knopf A-C (2013) Current status and future prospects of multi-dimensional image-guided particle therapy. Radiol Phys Technol 6(2):249–272. https://doi.org/10.1007/s12194-013-0199-0
Namito Y, Hirayama H, Ban S (1998) Improvements of low-energy photon transport in EGS4. Radiat Phys Chem 53(3):283–294. https://doi.org/10.1016/S0969-806X(98)00110-8
Nunes MÁ (2015) Protontherapy versus carbon ion therapy: advantages. Springer International Publishing, Disadvantages and Similarities
Andreo P, Hohlfeld K, Kanai T, Laitano F, Smyth VG, Vynckier S (2001) Absorbed dose determination in external beam radiotherapy. Tech. Report Series. International Atomic Energy Agency, Vienna
Park S-H, Jung W-G, Suh T-S, Jang H-S, Choi B-O, Rah J-E, Park S-G, Lee S-B (2011) Variation of Bragg curve characteristic induced by changing the position of inhomogeneous material: Geant4 simulation study. J Kor Phys Soc 58(2):187–197
Parodi K (2004) On the feasibility of dose quantification with in-beam PET data in radiotherapy with 12C and proton beams. Germany
Parodi K, Enghardt W, Haberer T (2002) In-beam PET measurements of β+ radioactivity induced by proton beams. Phys Med Biol 47(1):21
Paul H, Geithner O, Jäkel O (2007) The influence of stopping powers upon dosimetry for radiation therapy with energetic ions. In: Sabin JR, Brändas E (eds) Advances in quantum chemistry, vol 52. Academic Press, pp 289–306. https://doi.org/10.1016/S0065-3276(06)52013-1
Paz AE, Yamamoto N, Sakama M, Matsufuji N, Kanai T (2018) Tumor control probability analysis for single-fraction carbon-ion radiation therapy of early-stage non-small cell lung cancer. Int J Radiat Oncol Biol Phys 102(5):1551–1559. https://doi.org/10.1016/j.ijrobp.2018.07.2009
Pshenichnov I, Mishustin I, Greiner W (2006) Distributions of positron-emitting nuclei in proton and carbon-ion therapy studied with GEANT4. Phys Med Biol 51(23):6099–6112. https://doi.org/10.1088/0031-9155/51/23/011
Ranasinghe DS, Frisch MJ, Petersson GA (2015) Core-core and core-valence correlation energy atomic and molecular benchmarks for Li through Ar. J Chem Phys 143(21):214110. https://doi.org/10.1063/1.4935972
Roos BO, Lindh R, Malmqvist P-Å, Veryazov V, Widmark P-O (2005) New relativistic ANO basis sets for actinide atoms. Chem Phys Lett 409(4):295–299. https://doi.org/10.1016/j.cplett.2005.05.011
Sánchez-Parcerisa D, Gemmel A, Jäkel O, Parodi K, Rietzel E (2012) Experimental study of the water-to-air stopping power ratio of monoenergetic carbon ion beams for particle therapy. Phys Med Biol 57(11):3629–3641. https://doi.org/10.1088/0031-9155/57/11/3629
Sánchez-Parcerisa D, Gemmel A, Parodi K, Rietzel E (2013) A 3D model to calculate water-to-air stopping power ratio in therapeutic carbon ion fields. J Radiat Res 54(Suppl 1):i143–i146. https://doi.org/10.1093/jrr/rrt035
Schiwietz PLGaG (2011) Convolution approximation for swift Particles (CasP)
Scifoni E, Surdutovich E, Solovyov AV (2010) Spectra of secondary electrons generated in water by energetic ions. Phys Rev E 81(2):021903. https://doi.org/10.1103/PhysRevE.81.021903
Slater JC (1929) The theory of complex spectra. Phys Rev 34(10):1293–1322. https://doi.org/10.1103/PhysRev.34.1293
Sugiyama H (1981) Electronic stopping power formula for intermediate energies. Radiat Effects 56(3–4):205–211. https://doi.org/10.1080/00337578108229892
Tsujii H, Kamada T, Shirai T, Noda K, Tsuji H, Karasawa K (2013) Carbon-ion radiotherapy: principles, practices, and treatment planning. Springer, Japan
Usta M (2019) The calculation of stopping power and range for radium, thorium and uranium using new electronic potential energy function. Appl Radiat Isot 152:193–199. https://doi.org/10.1016/j.apradiso.2019.06.005
Usta M, Tufan MÇ (2017) Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions. Radiat Phys Chem 140(Suppl C):43–50. https://doi.org/10.1016/j.radphyschem.2017.03.005
Usta M, Tufan MÇ, Aydın G, Bozkurt A (2018) Stopping power and dose calculations with analytical and Monte Carlo methods for protons and prompt gamma range verification. Nucl Instrum Methods Phys Res, Sect A 897:106–113. https://doi.org/10.1016/j.nima.2018.04.045
Vlachoudis V (2009) Flair: a powerful but user friendly graphical interface for FLUKA. American Nuclear Society ANS, United States
Walske MC (1952) The Stopping Power of $K$-Electrons. Phys Rev 88(6):1283–1289. https://doi.org/10.1103/PhysRev.88.1283
Ziegler JF, Biersack JP, Ziegler MD (2013) SRIM, the stopping and range of ions in matter. SRIM Company
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This study was supported by the 18.M.098 project within the scope of Mustafa Kemal University Scientific Research Projects (BAP).
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Usta, M., Aydın, G. Use of Gaussian-type functions for flux-based dose calculations in carbon ion therapy. Radiat Environ Biophys 59, 511–522 (2020). https://doi.org/10.1007/s00411-020-00856-9
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DOI: https://doi.org/10.1007/s00411-020-00856-9