臺灣博碩士論文加值系統

旋繞疊加演算法是目前最準確的確定性輻射劑量計算演算法，但隨著醫療品質的提昇，放射治療面臨到更複雜的照射狀況與幾何形狀，該演算法在這些情況㆘的劑量準確度必須重新檢視。因此本論文利用蒙㆞卡羅模擬方法研究旋繞疊加演算法在空腔與㆟工關節存在㆘劑量計算準確度。這兩種情況可以說是目前臨床㆖所面臨到的兩種極端情況：空腔的存在例如鼻咽癌的情況，我們著重於討論電子不平衡對旋繞疊加演算法劑量計算的影響；㆟工關節存在的情況㆘，我們著重於研究高原子序高密度物質對旋繞疊加演算法劑量計算的影響。
我們以蒙㆞卡羅模擬與旋繞疊加演算法計算㆟工關節材料Ti6Al4V與CoCrMo合金存在㆘的輻射劑量分佈的差異，結果在不同介質介面處有顯著的差距。在合金材料㆖方5 mm以內的區域，蒙㆞卡羅模擬結果高於旋繞疊加演算法計算結果。同時，在合金材料之㆘的再增建區內，旋繞疊加演算法亦無法準確評估。對於PDDTi與PDDCo較深處（>10 cm）的劑量差異而言，旋繞疊加演算法的計算結果分別大於蒙㆞卡羅計算結果2%及4-5%。另外對劑量剖面而言，蒙㆞卡羅模擬結果在離㆗心軸1.0-2.0 cm處略高於旋繞疊加演算法計算之結果。其原因在於該演算法對於射束通過高原子序數高密度介質所產生的散射輻射與回散射輻射處理㆖的缺陷。該演算法㆗對於不均勻的介質所使用的比例密度修正法對於高原子序數高密度的介質存在時並不適用。較佳的處理辦法是藉由引入更多在不同介質㆗的劑量核心，與（或）發展加入原子序數考慮的比例密度修正法以擴充或改善旋繞疊加劑量演算法。
在電子不平衡情況㆘我們利用蒙㆞卡羅模擬與旋繞疊加演算法計算在壓克力假體㆗存在不同大小的空腔時的㆗心軸深度百分率劑量曲線。結果顯示旋繞疊加演算法因為低估了劑量核心在空腔㆗的發散程度，導致高估了空腔㆗㆗心軸㆖劑量沉積，結果使得空腔之後在壓克力材料內再增建區的劑量受影響。影響的範圍從壓克力假體表面至深度0.5 cm處。為了改善在此情況㆘的劑量準確度，旋繞疊加演算法㆗用於處理非均質介質劑量分佈問題時使用的比例密度法必須加以改進，加入考慮劑量核心在電子不平衡空腔㆗的過度發散性。

Convolution/superposition algorithm is the most accurate deterministic dose calculation algorithm at present time. However, its accuracy has to be re-examined due to the more complex treatment condition and more inhomogeneous media it will encounter in clinics. This thesis considers two limited conditions, the existence of hip prosthesis and that of air cavity in media, and examines the dose distribution difference between the results of Monte Carlo simulation and convolution/superposition algorithm. In the condition of existing hip prosthesis in media, we focus on discussing the effects that high Z, high density material caused in convolution/superposition algorithm. With existing air cavity in media, we are mainly interested in the accuracy of convolution/superposition algorithm in the condition of electron disequilibrium.
In the condition of existing high Z, high density material in media, significant dose differences between the results of Monte Carlo simulation and convolution/superposition algorithm were found around the interface. In re-buildup region and even deeper sites, convolution/superposition algorithm cannot accurately predict the dose as well. Two percent and 4-5% dose underestimation were found in deep part of PDDTi and PDDCo. For the dose profiles, underdosage of 1-2% was also found at off-axis distance 1.0-2.0 cm. Insufficient accounts for scatter and back-scatter radiation while photon beam passing through high Z, high density material in convolution/superposition algorithm lead to these results. Adding dose kernels in different media and improving density scaling method in treating dose in heterogeneous media in convolution/superposition algorithm to account for scatter and back-scatter radiation would be a possible solution.
Underestimating the expansion of dose kernel in air cavity in convolution/superposition algorithm was found at the condition of electron disequilibrium. This leads to the over-estimated dose in air cavity and in following re-buildup region. The region including top 0.5 cm in acrylic phantom was effected.
Adding the consideration of over expansion of dose kernel in air cavity should be done in convolution/superposition algorithm by improving density scaling method for accurate dose estimation.

第㆒章緒論………………………………………………………………...…... 1
1.1 概說…………………………………………………………….…...…. 1
1.2 放射治療之劑量計算方法………………………………….……….... 2
1.3 研究目的………………………………………………….…………… 5
1.4 論文架構……………………………………………….……………… 6
第㆓章粒子傳輸的蒙卡羅模擬…………………………….………….…… 9
2.1 概說………………………………………………….………………… 9
2.2 光子與電子的蒙卡羅模擬方法……………….………………….. 10
2.2.1 光子與物質作用……………………….…………………..…. 10
2.2.2 光子的蒙卡羅模擬方法………….……………………...… 12
2.2.3 電子與物質作用………………….…………………………... 14
2.2.4 電子的蒙卡羅模擬方法…….……………………………... 15
2.3 亂數產生器………………………….……………………………..… 22
2.4 變異數減縮技術………………….…………………………….……. 23
2.4.1 模擬效率……………….………………………………..……. 23
2.4.2 光子強迫反應法…….……………………………….……….. 24
2.4.3 粒子切割法與俄羅斯輪盤法………………………....……… 25
2.4.4 電子射程棄卻法…………………………………….…...…… 26
2.5 粒子傳輸的模擬卡羅模擬軟體………………………….……..…… 27
2.5.1 概說…………………………………………….…………...… 27
2.5.2 電子-加馬射叢系統………………………….……………..… 28
2.5.3 蒙卡羅㆗性粒子傳輸系統……………….………………... 34
2.5.4歐米茄計畫-射束系統…………………….……………...…… 36
第章旋繞疊加演算法……………………………….…………………...… 43
3.1 概說………………………………………….…………………..…… 43
3.2 劑量學基礎……………………………………………………...……44
3.2.1 輻射場性質的描述………………….……………………..…. 44
3.2.2 吸收劑量………………………………….………………...…… 47
3.2.3 克馬………………………………….………………..………. 47
3.3 旋繞疊加演算法………………………….…………………..……… 48
3.3.1 劑量核心……………………….……………………...……… 49
3.3.2 旋繞疊加演算法…………….…………………………...…… 50
3.3.3 比例密度修正……………………………………….…………53
3.3.4 傾斜錐旋繞演算法……………………………….……..….… 55
3.4 愛達克治療計畫系統………………………………….………..…… 57
3.4.1 愛達克治療計畫系統概論………………….………………... 58
3.4.2 愛達克治療計畫系統模式化過程…………….………………59
第章直線加速器機頭模擬………………………………………….………65
4.1 概說……………………………………………………………………65
4.2 加速器構造……………………………………………………………65
4.3 模擬處理………………………………………………………………70
4.4 射束物理參數對放射劑量之影響………………………………..…. 74
4.4.1 模擬參數的調整……………………………………………… 74
4.4.2 水假體模擬………………………………………………….... 75
4.4.3 劑量量測…………………………………………………….... 77
4.4.4 射束物理參數對放射劑量之影響………………………….…79
4.4.5 模擬驗證：與MCNP-4C之比較……………………………….87
4.4.6 治療射束之基本物理特性…………………………………….89
4.5 結論……………………………………………………………………89
第五章高原子序高密度物質對旋繞疊加演算法準確度之影響：蒙卡羅模擬與愛達克治療計畫系統比較………………………………………… 93
5.1 概說……………………………………………………………...…… 93
5.2 ㆟工關節對放射治療計畫所造成之困難……………………………93
5.2.1 影像假影之困擾………………………………………….……93
5.2.2 臨床之解決辦法…………………………………………….…96
5.3 蒙卡羅模擬與旋繞疊加演算法之劑量計算結果………………....97
5.3.1 旋繞疊加演算法對高原子序高密度物質之劑量計算誤差預測97
5.3.2 幾何形狀之選擇……………………………………………….98
5.3.3 模擬條件之設定……………………………………………….99
5.3.4 蒙卡羅模擬與愛達克治療計畫系統計算結果…………...102
5.3.5 劑量量測……………………………………………………...106
5.4 結論…………………………………………………………………..108
第六章電子不平衡情況對旋繞疊加演算法準確度之影響：蒙卡羅模擬與愛達克治療計畫系統比較……………………………………………...111
6.1 概說…………………………………………………………………..111
6.2 臨床空腔對放射劑量所造成之影響……………………………..112
6.2.1 電子平衡與電子不平衡……………………………………...112
6.2.2 空腔對鼻咽癌治療之放射劑量影響………………………...114
6.2.3 旋繞疊加演算法於電子不平衡情況㆘之劑量計算誤差預測115
6.3 蒙卡羅模擬與旋繞疊加演算法之劑量計算結果……………… 116
6.3.1 幾何形狀之選擇與模擬條件之設定………………………. 116
6.3.2 蒙卡羅模擬與旋繞疊加演算法之劑量計算結果………. 117
6.3.3 量測結果……………………………………………………. 119
6.4 結論………………………………………………………………… 122
第七章結論與未來展望……………………………………………………. 124
7.1 概說………………………………………………………………….124
7.2 結論………………………………………………………………….124
7.3 未來展望…………………………………………………………….127
參考文獻………………………………………………………………………129
附錄I：Siemens PRIMUS 6 MV光子機頭模擬之MCNP_4C輸入檔………. 136
附錄II：著作（林松彥，Sung-Yen Lin） ………………………………………. 146
索引 ……………………………………………………………………………...147

參考文獻
Ahnesjo, A. (1989) Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media. Med. Phys. 16, 577-592.
Ahnesjo, A., Andreo, P. and Brahme, A., (1987) Calculation and application of point spread functions for treatment planning with high energy photon beams. Acta Oncologica 26, 49-51.
Ahnesjo, A., Saxner, M. and Trepp, A. (1992) A pencil beam model for photon dose calculation. Med. Phys. 19, 263-273.
Almond, P.R., Biggs, P.J., Coursey, B.N., Hanson, W.F., Saiful Huq, M., Ravinder Nath, Rogers, D.W.R., (1999) AAPM''s TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Med. Phys. 26, 1847-1870.
Arnfield, M.R., et al. (2000) The impact of electron transport on the accuracy of computed dose. Med. Phys. 27, 1266-1274.
ASTM (American Society of Testing and Material). (1984) 1984 annual Books of ASTM Standards. Vol 13.01, Philadelphia, p.10-14.
Attix, F.H. (1986) Introduction to Radiological Physics and Radiation Dosimetry. John Wiley & Sons, New York.
Beaudoin, L. (1968) M. Sc. Thesis, University of Toronto.
Berger, M.J. (1963) Monte Carlo Calculation of the Penetration and Diffusion of Fast Charged Particles, In: Alder, B., Fernbach, A. and Rotenberg, M. Methods in Computational Physics Vol. 1, Academic Press, New York.
Berger, M.J. and Seltzer, S.M. (1968) Electron and Photon Transport Programs. NBS-Report-9837, National Bureau of Standards.
Bethe, H.A. and Heitler, W. (1934) On stopping of fast particles and on the creation of positive electrons. Proc. Roy. Soc. A146, 83.
Bielajew, A.F. (1993) The effect of strong longitudinal magnetic fields on dose deposition from electron and photon beams. Med. Phys. 20, 1171-1179.
129
Bielajew, A.F., Rogers, D.W.O. and Nahum, A.E. (1985) The Monte Carlo simulation of ion chamber response to 60Co - Resolution of anomalies associated with interfaces. Phys. Med. Biol. 30, 419-428.
Bielajew, A.F., Rogers, D.W.O., (1987) PRESTA:The parameter reduced electron-step transport algorithm for electron Monte Carlo transport. NIM in Phys. Res. B18, 165-181.
Boyer, A. and Mok, E. (1985) A photon dose distribution model employing convolution calculations. Med. Phys. 12, 169-177.
Boyer, A. and Mok, E. (1986) Calculation of photon dose distributions in an inhomogeneous medium using convolution. Med. Phys. 12, 169-177.
Briesmeister, J.F. (2000) MCNP-A General Monte Carlo N-Particle Transport Code, Version 4C. Los Alamos National Laboratory Report, LA-13709.
Cashwell, E.D. et al. (1973) Monte Carlo Photon codes : MCG and MCP. Los Alamos National Laboratory Report, LA-5157-MS.
Chang, K.S., Yin, F.F., Nie, K.W., (1996) The effect of detector size to the broadening of the penumbra - a computer simulation study. Med. Phys. 23, 1407-1411.
Cook, A.J. (1983) Mortran3 User''s Guide. SLAC Computation Research Group technical memorandum CGTM 209.
Cunningham, J.R. (1989) Dose calculation for high energy electron and photon beams. Comput. Med. Imaging Graph. 13, 241-250.
Cygler, J., Battista, J.J., Scrimger, J.W., Mah, E., Antolak, J., (1987) Electron dose distributions in experimental phantom: a comparison with 2D pencil beam calculations. Phys. Med. Biol. 32, 1073-1086.
Duane, S., Bielajew, A.F. and Rogers, D.W.O. (1989) Use of ICRU37/NBS collision stopping powers in the EGS4 system. NRC Rep. PIRS-0173.
El-Khatib, E. and Battista, J.J., (1984) Improved lung dose calculation using tissue-maximum ratios in the Batho correction. Med. Phys. 11, 279-286.
Fix, M.K., Keller, H. and Ruegsegger, P., (2000) Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy. Med. Phys. 27, 2739-2747.
130
Ford, R.L. and Nelson, W.R. (1978) The EGS Code System : Computer Programmes for the Monte Carlo Simulation of Electromagnetic Cascade Showers (version 3). Rep. SLAC-210.
Francescon, P., Cavedon, C., Reccanello, S. and Cora, S. (2000) Photon dose calculation of a three-dimensional treatment planning system compared to the Monte Carlo code BEAM. Med. Phys. 27, 1579-1587.
Goudsmit, S. and Saunderson, J.L. (1940) Multiple scattering of electrons. Phys. Rev. 57, 24-29.
Hogstrom, K.R., Mills, M.D. and Almond, P.R. (1981) Electron beam dose calculation. Phys. Med. Biol. 26, 445-459.
Hubbel, J.H. (1969) Photon cross sections, attenuation coefficients, and energy absorption coefficients from 10 keV to 100 GeV. Rep. NSRDC-NBS29.
Hubbel, J.H., Gimm, H.A. and Overto, I (1980) Pair, triplet and total cross sections for 1 MeV-100GeV photons in elements Z=1-100. J. Phys. Chem. Res. Data 9, 1023.
Jaffray, D.A., Battista, J.J., Fenster, A. and Munro, P. (1993) Med. Phys. 20, 1417.
Kawrakow, I and Rogers, D.W.O. (2000) The EGSnrc Code System. NRCC Report PIRS-701.
Khan, F.M. and Potish, R.A. (1998) Treatment Planning in Radiation Oncology. William & Wilkins, Baltimore, p.187-213.
Khan, F.M. and Potish, R.A. (1998) Treatment Planning in Radiation Oncology. William & Wilkins, Baltimore, p.369-386.
Klein, E.E., Chin, L.M., Rice, R.K. and Mijnheer, B.J. (1993) The influence of air cavities on interface doses for photon beams. Int. J. Radiat. Oncol. Biol. Phys. 27, 419-427.
Lewis, H.W. (1950) Phys. Rev. 78, 526
Lin, S.Y., Chu, T.C. and Lin, J.P., (2001) Monte Carlo simulation of clinical linear accelerator. Appl. Radiat. Isot. 55, 759-765.
Ma, C.M. and Rogers, D.W.O. (1999) BEAMDP Users Manual. NRCC Report PIRS-0509.
Ma, C.M., Reckwerdt, P., Holmes, M., Rogers, D.W.O., Geiser, B., (1995)
131
DOSXYZ Users Manual. National Research Council of Canada Report PIRS-0509B.
Mackie, T.R., et al. (1990) Proceeding of the Tenth International Conference on the Use of computers in Radiation Therapy, Lucknow India, 322.
Mackie, T.R., Liu, H.H. and McCullough, E.C. (1998) Treatment Planning Algorithm. In: Khan F.M. and Potich R.A., Eds. Treatment Planning in Radiation Therapy, Williams and Wilkins, Baltimore.
Mackie, T.R., Reckwerdt, P.J., McNutt, T., et al. (1996) Photon Beam Dose Computation. In: Mackie, T.R., and Palta, J.R. Eds. Teletherapy: Present and Future, AAPM Monograph No. 22, AAPM.
Mackie, T.R., Scrimger, J.W. and Battista, J.J., (1984) A convolution method of calculating dose for 15-MV x rays. Med. Phys. 12, 188-196.
Mah, E., Antolak, J., Scrimger, J.W., Battista, J.J., (1989) Experimental evaluation of a 2D and a 3D electron pencil beam algorithm. Phys. Med. Biol. 34, 1179-1194.
Marsaglia, G. (1968) Random numbers fall mainly in the planes. Proc. Natl. Acad. Sci. U.S.A. 61, 25-28.
McCracken, D.D. (1955) The Monte Carlo Method. Sci. Am. 192, 90.
Milan, J. and Bentley, R.E. (1974) The storage and manipulation of radiation dose data in a small digital computer. Br. J. Radiol. 47, 115-121.
Mohan, R. (1987b) Dose Calculation for Radiation Treatment Planning. In: Jenkins, T.M., Nelson, W.R. and Rind, A., Eds. Monte Carlo Transport of Electrons and Photons, National Academy Press, Washington, DC.
Mohan, R. and Chui, C. (1987a) Use of fast Fouier transforms in a calculating dose distributions for irregularly shaped fields for three-dimensional treatment planning. Med. Phys. 14, 70-77.
Mohan, R., Chui, C. and Lidofsky, L. (1986) Differential pencil beam dose computation model for photons. Med. Phys. 13, 64-73.
Moliere, G.Z. (1948) Theorie der streuung schneller geladener teilchen II mehrfach-und vielfachstreuung. Z. Naturforsch A 3A, 78-97.
Nagel H.H. (1964) Die Berechnung von elektron-photon-kaskaden in Blei mit hilfe
132
der Monte Carlo methode. Inaugeral dessertation zur erlangung des Doltorgrades der hohen methematich-naturwissenschaftlichen fakultat der Rheinischen Freidrich-Wilhelms-Universitat zu Bonn.
Nagel H.h. and Schlier C. (1963) Berechnung von elektron-photon-kaskaden in blei fur eine primarebergie von 200 MeV. Z. Phys. 174, 464.
Naqvi, S.A., et al. (2001) Reducing loss in lateral charged-particle equilibrium due to air cavities present in x-ray irradiated media by using longitudinal magnetic fields. Med. Phys. 28, 603-611.
Nelson, W.R., Hirayama, H. and Rogers D.W.O., (1985) The EGS4 code system. SLAC-Report-265, Stanford Linear Accelerator Center.
Niroomand-Rad, A. et al., (1998) Radiochromic film dosimetry : Recommendation of AAPM Radiation Therapy Committee Task Group 55. Med. Phys. 25, 2093-2115.
O''Connor, J.E. (1957) The variation of scattered x-rays with density in an irradiated body. Phys. Med. Biol. 1, 352-369.
Papanikolaou, N., Mackie, T.R., Meger-Wells, C., Gehring, M. and Reckwerdt, P., (1993) Investigation of the convolution method for polyenergetic spectra. Med. Phys. 20, 1327-1336.
Plechate, E.F., Cullen, D.E. and Haverton, R.J. (1975) Tables and graphs of photon interaction cross section. UCRL-50400 Vol. 6-1, Lawrence Livermore Laboratory.
Rogers, D.W.O. (1984) Low energy electron transport with EGS. NIM A 227, 535-548.
Rogers, D.W.O. and Bielajew, A.F. (1984) The use of EGS for Monte Carlo calculations in medical physics. Rep. PXNR-2692, NRCC, Ottawa.
Rogers, D.W.O., Faddegon, B.A., Ding, G.X., Ma, C.M., We, J., Mackie, T.R., (1995) BEAM: A Monte Carlo code to simulate radiotherapy treatment units. Med. Phys. 22,503-524.
Rogers, D.W.O., Ma, C.M., Walters, B., Ding, G.X., Sheikh-Bagheri, D., Zhang, G., (1999) BEAM99 Users Manual. National Research Council of Canada Report PIRS-0509(A)revD.
133
Sauer, O.A. (1995) Calculation of dose distribution in the vicinity of high-Z interfaces for photon beams. Med. Phys. 22, 1685-1690.
Seltzer S.M. and Berger, M.J. (1986) Bremsstrahlung energy spectra from electrons with kinetic energy 1 keV - 10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z=1 to 100. Atom, Data and Nucl. Data Tables 35, 345.
Seltzer, S.M. and Berger, M.J. (1985) Bremsstrahlung spectra from electron interactions with screened atomic nuclei and orbital electrons. NIM B12, 95.
Selzer, S.M. (1988) Cross Sections for Bremsstrahlung Production and electron Impact Ionization. In: Jenkins, M., Nelson, W.R. and Rindi, A. Monte Carlo Transport of Electrons and Photons. Plenum Press, New York.
Shahine, B.H., Al-Ghazi, M.S.A.L. and El-Khatib, E. (1999) Experimental evaluation of interface doses in the presence of air cavities compared with treatment planning algorithm. Med. Phys. 26, 350-355.
Sheikh-Bagheri, D., Rogers, D.W.O., Ross, C.K., Seuntjens, J.P., (2000) Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac. Med. Phys. 27, 2256-2266.
Shiu, A.S. and Hogstrom, K.R. (1991) Pencil-beam redefinition algorithm for electron dose distributions. Med. Phys. 18, 7-18.
Sibata, C.H., Mota, H.C., Beddar, A.S., Higgins, P.D., Shin, K.H., (1991) Influence of detector size in photon beam profile measurements. Phys. Med. Biol. 36, 621-631.
Sontag, M.R., and Cunningham, J.R., (1978) The equivalent tissue-air ratio method for making absorbed dose calculation in a heterogeneous medium. Radiology 129, 787-794.
Sterling, T.D., Perry, H. and Katz, L. (1964) Automation of radiation treatment planning IV. Derivation of a mathematical expression for the percent depth dose of cobalt 60 beams and visualization of multiple field dose distribution. Br. J. Radiol. 37, 544-550.
Sternheimer, R.M. and Peierls, R.F. (1971) General expression for the density effect for the ionisation loss of charged particles. Phys. Rev. B3, 3681-3692.
134
Storchi, P.R.M. and Huizenga, H. (1985) On a numerical approach of the pencil-beam model. Phys. Med. Biol. 36, 207-222.
Storm, E. and Israel, H.I. (1970) Photon cross sections from 1 keV to 100 MeV for elements fron Z=1 to Z=100, In: Nuclear Data Tables Vol. A7. Academic Press, New York.
Tacout, A.M., Dunn, W.L., Nelson, W.R., et al. (2000) Status of the object-oriented EGS interface project. KEK Proceeding 200-20, Tsukuba, 23-30.
Treurniet, J.R., Rogers, D.W.O., (1999) EGS_Windows_4.0 User''s Manual. National Research Council of Canada Report PIRS-0669.
Van Dyk, J., et al. (1993) Commissioning and quality assurance of treatment planning computers. Int. J. Rad. Onc. Biol. Physics. 26, 261-273.
Webb, S. (2001) Intensity-Modulated Radiation Therapy. IOP Publishing, London, p. 75-198.
Webb, S. (2001) Intensity-Modulated Radiation Therapy. IOP Publishing, London, p. 204-206.
Whyte, G.H. (1959) Principles of Radiation Dosimetry. Wiley, New York.
Williams, J.R. and Thwaites, D.I. (1993) Radiotherapy Physics in Practice. Oxford University Press, 1993.
Wong, J.W. and Purdy, J.A. (1990) On methods of inhomogeneity corrections for photon transport. Med. Phys. 17, 807-814.
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