Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

Proceedings of the 5th ESTRO Meeting on Radiotherapy and Oncology; 1986

[52] ICRU. ICRU Report 23: Measurement of Absorbed Doses in a Phantom Irradiated by a Single Beam of X or Gamma Rays. Bethesda, MD: ICRU; 1973

[53] Kim S, Zhu TC, Palta JR. An equivalent square field formula for determining head scatter factors of rectangular fields. Medical Physics. 1997;24(11)

[54] Day MJ. A note on the calculation of dose in X-ray fields. The British Journal of Radiology. 1950;23(270): 368-369

[55] Clarkson JR. A note on depth doses in fields of irregular shape. The British Journal of Radiology. 1941;14(164): 265-268

[56] Khan FM. The Physics of Radiation Therapy. Baltimore: Williams and Wilkins; 1984

[57] Sterling TD, Perry H, Katz L. Automation of radiation treatment planning—IV. Derivation of a mathematical expression for the per cent depth dose surface of cobalt 60 beams and visualisation of multiple field dose distributions. The British Journal of Radiology. 1964;37(439):544-550

[58] Greening JR. Fundamentals of Radiation Dosimetry. Bristol: Adam Hilger; 1981

[59] Mayles P, Nahum A, Rosenwald J-C. Handbook of Radiotherapy Physics: Theory and Practice. New York: Franionization Chambers & Taylor; 2007. p. 1432

[60] Gray LH. The experimental determination by ionization methods of the rate of emission of beta- and gamma-ray energy by radioactive

substances. The British Journal of Radiology. 1949;22(264):677-697

[61] Ma C, Nahum AE. Bragg-Gray theory and ion chamber dosimetry for photon beams. Physics in Medicine and Biology. 1991;36(4):413-428

[70] Eklund K, Ahnesjö A. Fast modelling of spectra and stoppingpower ratios using differentiated fluence pencil kernels. Physics in Medicine and Biology. 2008;53(16):

DOI: http://dx.doi.org/10.5772/intechopen.89150

beams. Physics in Medicine and Biology.

[78] Sharma SC, Ott JT, Williams JB, Dickow D. Commissioning and acceptance testing of a CyberKnife linear accelerator. Journal of Applied Clinical Medical Physics. 2007;8:119-125

[79] British Institute of Radiology. Central Axis Depth Dose Data for Use in Radiotherapy Departments: 1996, BJR Supplement 25. London: BIR; 1996

[80] Sauer OA, Wilbert J. Measurement of output factors for small photon beams. Medical Physics. 2007;34:

[81] Alfonso R et al. A new formalism for reference dosimetry of small and nonstandard fields. Medical Physics.

[82] Thomas SD, MacKenzie M, Rogers DWO, Fallone BG. A Monte Carlo derived TG-51 equivalent calibration for helical tomotherapy. Medical Physics. 2005;32:1346-1353

[83] Langen KM et al. QA for helical tomotherapy: Report of the AAPM task group 148. Medical Physics. 2010;37:

[84] Zeverino M, Agostinelli S, Pupillo F,

Taccini G. Determination of the correction factors for different ionization chambers used for the calibration of the helical tomotherapy static beam. Radiotherapy and Oncology. 2011;100:424-428

[85] Sauer OA. Determination of the quality index (Q) for photon beams at arbitrary field sizes. Medical Physics.

[86] Andreo P. On the beam quality specification of high-energy photons for

radiotherapy dosimetry. Medical Physics. 2000;27:434-440

2009;36:4168-4172

2003;48:2081-2099

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field…

1983-1988

4817-4853

2008;35:5179-5186

[71] Eklund K, Ahnesjö A. Modeling silicon diode dose response factors for

[72] Fenwick JD, Kumar S, Scott AJ, Nahum AE. Using cavity theory to describe the dependence on detector density of dosimeter response in nonequilibrium small fields. Physics in Medicine and Biology. 2013;58:

[73] Czarnecki D, Zink K. Monte Carlo calculated correction factors for diodes and ion chambers in small photon fields. Physics in Medicine and Biology. 2013;

[74] Czarnecki D, Zink K. Corrigendum: Monte Carlo calculated correction factors for diodes and ion chambers in small photon fields. Physics in Medicine

[75] Francescon P, Cora S, Satariano N.

detectors and for two linear accelerators using Monte Carlo simulations. Medical

[76] Francescon P, Kilby W, Satariano N,

correction factors for machine specific reference field dose calibration and output factor measurement using fixed and iris collimators on the CyberKnife system. Physics in Medicine and Biology. 2012;57:3741-3758

[77] Sanchez-Doblado F et al. Ionization chamber dosimetry of small photon fields: A Monte Carlo study on stoppingpower ratios for radiosurgery and IMRT

and Biology. 2014;59:791-794

Calculation of for several small

Cora S. Monte Carlo simulated

Physics. 2011;38:6513-6527

75

small photon fields. Physics in Medicine and Biology. 2010;55(24):

4231-4247

7411-7423

2901-2923

58:2431-2444

[62] Spencer LV, Attix FH. A theory of cavity ionization. Radiation Research. 1955;3(3):23-54

[63] Nahum AE. Water/air mass stopping power ratios for megavoltage photon and electron beams. Physics in Medicine and Biology. 1978;23(1): 24-38

[64] Siebers JV, Keall PJ, Nahum AE, Mohan R. Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations. Physics in Medicine and Biology. 2000;45(4):983

[65] Janssens A. Modified energydeposition model, for the computation of the stopping-power ratio for small cavity sizes. Physical Review A. 1981; 23(3):1164-1176

[66] Andreo P. Depth-dose and stopping-power data for monoenergetic electron beams. Nuclear Instruments & Methods in Physics Research Section B Beam Interactions with Materials and Atoms. 1990;51(2): 107-121

[67] Ahnesjö A, Andreo P, Brahme A. Calculation and application of point spread functions for treatment planning with high energy photon beams. Acta Oncologica. 1987;26(1):49-56

[68] Mohan R. Differential pencil beam dose computation model for photons. Medical Physics. 1986;13(1):64

[69] Mackie TR. A convolution method of calculating dose for 15-MV X rays. Medical Physics. 1985;12(2):188

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field… DOI: http://dx.doi.org/10.5772/intechopen.89150

[70] Eklund K, Ahnesjö A. Fast modelling of spectra and stoppingpower ratios using differentiated fluence pencil kernels. Physics in Medicine and Biology. 2008;53(16): 4231-4247

Proceedings of the 5th ESTRO Meeting on Radiotherapy and Oncology; 1986

substances. The British Journal of Radiology. 1949;22(264):677-697

[61] Ma C, Nahum AE. Bragg-Gray theory and ion chamber dosimetry for photon beams. Physics in Medicine and

[62] Spencer LV, Attix FH. A theory of cavity ionization. Radiation Research.

Biology. 1991;36(4):413-428

[63] Nahum AE. Water/air mass stopping power ratios for megavoltage photon and electron beams. Physics in Medicine and Biology. 1978;23(1):

[64] Siebers JV, Keall PJ, Nahum AE, Mohan R. Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations. Physics in Medicine and

Biology. 2000;45(4):983

23(3):1164-1176

107-121

[65] Janssens A. Modified energydeposition model, for the computation of the stopping-power ratio for small cavity sizes. Physical Review A. 1981;

[66] Andreo P. Depth-dose and stopping-power data for monoenergetic electron beams. Nuclear Instruments & Methods in Physics Research Section B Beam Interactions with Materials and Atoms. 1990;51(2):

[67] Ahnesjö A, Andreo P, Brahme A. Calculation and application of point spread functions for treatment planning with high energy photon beams. Acta

[68] Mohan R. Differential pencil beam dose computation model for photons. Medical Physics. 1986;13(1):64

[69] Mackie TR. A convolution method of calculating dose for 15-MV X rays. Medical Physics. 1985;12(2):188

Oncologica. 1987;26(1):49-56

1955;3(3):23-54

24-38

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

Measurement of Absorbed Doses in a Phantom Irradiated by a Single Beam of X or Gamma Rays. Bethesda, MD:

[53] Kim S, Zhu TC, Palta JR. An equivalent square field formula for determining head scatter factors of rectangular fields. Medical Physics.

dose in X-ray fields. The British Journal of Radiology. 1950;23(270):

[54] Day MJ. A note on the calculation of

[55] Clarkson JR. A note on depth doses in fields of irregular shape. The British Journal of Radiology. 1941;14(164):

[56] Khan FM. The Physics of Radiation Therapy. Baltimore: Williams and

[57] Sterling TD, Perry H, Katz L. Automation of radiation treatment planning—IV. Derivation of a mathematical expression for the per cent depth dose surface of cobalt 60 beams and visualisation of multiple field dose distributions. The British Journal of Radiology. 1964;37(439):544-550

[58] Greening JR. Fundamentals of Radiation Dosimetry. Bristol: Adam

[60] Gray LH. The experimental

the rate of emission of beta- and gamma-ray energy by radioactive

[59] Mayles P, Nahum A, Rosenwald J-C. Handbook of Radiotherapy Physics: Theory and Practice. New York: Franionization Chambers & Taylor;

determination by ionization methods of

[52] ICRU. ICRU Report 23:

ICRU; 1973

1997;24(11)

368-369

265-268

Wilkins; 1984

Hilger; 1981

2007. p. 1432

74

[71] Eklund K, Ahnesjö A. Modeling silicon diode dose response factors for small photon fields. Physics in Medicine and Biology. 2010;55(24): 7411-7423

[72] Fenwick JD, Kumar S, Scott AJ, Nahum AE. Using cavity theory to describe the dependence on detector density of dosimeter response in nonequilibrium small fields. Physics in Medicine and Biology. 2013;58: 2901-2923

[73] Czarnecki D, Zink K. Monte Carlo calculated correction factors for diodes and ion chambers in small photon fields. Physics in Medicine and Biology. 2013; 58:2431-2444

[74] Czarnecki D, Zink K. Corrigendum: Monte Carlo calculated correction factors for diodes and ion chambers in small photon fields. Physics in Medicine and Biology. 2014;59:791-794

[75] Francescon P, Cora S, Satariano N. Calculation of for several small detectors and for two linear accelerators using Monte Carlo simulations. Medical Physics. 2011;38:6513-6527

[76] Francescon P, Kilby W, Satariano N, Cora S. Monte Carlo simulated correction factors for machine specific reference field dose calibration and output factor measurement using fixed and iris collimators on the CyberKnife system. Physics in Medicine and Biology. 2012;57:3741-3758

[77] Sanchez-Doblado F et al. Ionization chamber dosimetry of small photon fields: A Monte Carlo study on stoppingpower ratios for radiosurgery and IMRT

beams. Physics in Medicine and Biology. 2003;48:2081-2099

[78] Sharma SC, Ott JT, Williams JB, Dickow D. Commissioning and acceptance testing of a CyberKnife linear accelerator. Journal of Applied Clinical Medical Physics. 2007;8:119-125

[79] British Institute of Radiology. Central Axis Depth Dose Data for Use in Radiotherapy Departments: 1996, BJR Supplement 25. London: BIR; 1996

[80] Sauer OA, Wilbert J. Measurement of output factors for small photon beams. Medical Physics. 2007;34: 1983-1988

[81] Alfonso R et al. A new formalism for reference dosimetry of small and nonstandard fields. Medical Physics. 2008;35:5179-5186

[82] Thomas SD, MacKenzie M, Rogers DWO, Fallone BG. A Monte Carlo derived TG-51 equivalent calibration for helical tomotherapy. Medical Physics. 2005;32:1346-1353

[83] Langen KM et al. QA for helical tomotherapy: Report of the AAPM task group 148. Medical Physics. 2010;37: 4817-4853

[84] Zeverino M, Agostinelli S, Pupillo F, Taccini G. Determination of the correction factors for different ionization chambers used for the calibration of the helical tomotherapy static beam. Radiotherapy and Oncology. 2011;100:424-428

[85] Sauer OA. Determination of the quality index (Q) for photon beams at arbitrary field sizes. Medical Physics. 2009;36:4168-4172

[86] Andreo P. On the beam quality specification of high-energy photons for radiotherapy dosimetry. Medical Physics. 2000;27:434-440

[87] Xiong G, Rogers DWO. Relationship between %dd(10)x and stopping-power ratios for flattening filter free accelerators: A Monte Carlo study. Medical Physics. 2008;35:2104-2109

[88] Palmans H, National Physical Laboratory. Personal Communication; 2015

[89] Dalaryd M, Knöös T, Ceberg C. Combining tissue-phantom ratios to provide a beam-quality specifier for flattening filter free photon beams. Medical Physics. 2014;41:111716

[90] Palmans H. Determination of the beam quality index of high-energy photon beams under nonstandard reference conditions. Medical Physics. 2012;39:5513-5519

[91] Podgorsak EB. External photon beams: Physical aspects. In: Radiation Oncology Physics: A Handbook.

[92] Verhaegen F, Das IJ, Palmans H. Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit. Physics in Medicine & Biology. 1998;43(10): 2755

[93] Ding GX, Duggan DM, Coffey CW. Comment on "Testing of the analytical anisotropic algorithm for photon dose calculation" [Med. Phys. 33, 4130-4148 (2006)]. Medical Physics. 2007;34(8): 3414

[94] Kijewski PK, Bjärngard BE, Petti PL. Monte Carlo calculations of scatter dose for small field sizes in a 60Co beam. Medical Physics. 1986;13(1):74-77

[95] Ding GX, Duggan DM, Coffey CW. Commissioning stereotactic radiosurgery beams using both experimental and theoretical methods. Physics in Medicine & Biology. 2006; 51(10):2549

[96] Ding GX. Dose discrepancies between Monte Carlo calculations and measurements in the buildup region for a high-energy photon beam. Medical Physics. 2002;29(11): 2459-2463

[105] Chetty IJ, Charland PM, Tyagi N, McShan DL, Fraass BA, Bielajew AF. Photon beam relative dose validation of the DPM Monte Carlo code in lungequivalent media. Medical Physics.

DOI: http://dx.doi.org/10.5772/intechopen.89150

[113] Westermark M, Arndt J, Nilsson B, Brahme A. Comparative dosimetry in narrow high-energy photon beams. Physics in Medicine & Biology. 2000;

[114] Deng J, Ma CM, Hai J, Nath R. Commissioning 6 MV photon beams of a stereotactic radiosurgery system for Monte Carlo treatment planning. Medical Physics. 2003;30(12):3124-3134

[115] Paskalev KA, Seuntjens JP, Patrocinio HJ, Podgorsak EB. Physical aspects of dynamic stereotactic radiosurgery with very small photon beams (1.5 and 3 mm in diameter). Medical Physics. 2003;30(2):111-118

[116] Tsougos I, Theodorou K,

with experimental dosimetric techniques for a 6 MV stereotactic radiotherapy unit. Journal of BUON.

2004;9:451-564

504-513

Bazioglou M, Stathakis S. Kappas C. a comparison of Monte Carlo simulation

[117] Francescon P, Cora S, Cavedon C. Total scatter factors of small beams: A multidetector and Monte Carlo study. Medical Physics. 2008;35(2):

[118] Heydarian M, Asnaashari K, Allahverdi M, Jaffray DA. Dosimetric evaluation of a dedicated stereotactic linear accelerator using measurement and Monte Carlo simulation. Medical Physics. 2008;35(9):3943-3954

[119] Cranmer-Sargison G, Charles PH,

methodological approach to reporting corrected small field relative outputs. Radiotherapy and Oncology. 2013;

[120] Charles PH, Cranmer-Sargison G, Thwaites DI, Crowe SB, Kairn T, Knight RT, et al. A practical and

theoretical definition of very small field size for radiotherapy output factor measurements. Medical Physics. 2014;

Trapp JV, Thwaites DI. A

109(3):350-355

41(4):041707

45(3):685

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field…

[106] Rogers DWO, Kawrakow I, Seuntjens JP, Walters BRB, Mainegra-

EGSnrc. NRCC Report PIRS-702 (Rev.

Agostinelli S. GEANT4—A simulation toolkit. Nuclear Instruments and Methods A. 2003;506(25)

[108] MCNP—A General Monte Carlo. N-Particle Transport Code. Vol. I: Overview and Theory. Los Alamos, NM: Los Alamos National Laboratory; 2003.

Beddoe AH. A comparison of dosimetry techniques in stereotactic radiosurgery. Physics in Medicine & Biology. 1996;

[110] Scielzo G, Grillo FR, Schwarz M, Rivolta A, Brunelli B, Surridge M, et al. The Monte Carlo method and parallel estimation in the drawing up of radiosurgery treatment plans. La Radiologia Medica. 1998;95(6):

[111] De Vlamynck K, Palmans H, Verhaegen F, De Wagter C, De Neve W,

Thierens H. Dose measurements

[112] Cheung YC, Yu KN, Ho RTK, Yu CP. Stereotactic dose planning system used in Leksell gamma knife model-B: EGS4 Monte Carlo versus GafChromic films MD-55. Applied Radiation and Isotopes. 2000;53(3):

1999;26(9):1874-1882

compared with Monte Carlo simulations of narrow 6 MV multileaf collimator shaped photon beams. Medical Physics.

[109] Heydarian M, Hoban PW,

Hing E. NRC user codes for

[107] GEANT Collaboration,

2003;30(4):563-573

B). 2003

LA-UR-03-1987

41(1):93

647-655

427-430

77

[97] Ding GX. Using Monte Carlo simulations to commission photon beam output factors—A feasibility study. Physics in Medicine & Biology. 2003; 48(23):3865

[98] Ahnesjö A. Collimator scatter in photon therapy beams. Medical Physics. 1995;22(3):267-278

[99] Jones AO, Das IJ, Jones FL Jr. A Monte Carlo study of IMRT beamlets in inhomogeneous media. Medical Physics. 2003;30(3):296-300

[100] Jones AO, Das IJ. Comparison of inhomogeneity correction algorithms in small photon fields. Medical Physics. 2005;32(3):766-776

[101] Saitoh H, Fujisaki T, Sakai R, Kunieda E. Dose distribution of narrow beam irradiation for small lung tumor. International Journal of Radiation Oncology Biology Physics. 2002;53(5): 1380-1387

[102] Al-Hallaq HA, Reft CS, Roeske JC. The dosimetric effects of tissue heterogeneities in intensity-modulated radiation therapy (IMRT) of the head and neck. Physics in Medicine & Biology. 2006;51(5):1145

[103] Paelinck L, Reynaert N, Thierens H, De Neve W, De Wagter C. Experimental verification of lung dose with radiochromic film: Comparison with Monte Carlo simulations and commercially available treatment planning systems. Physics in Medicine & Biology. 2005;50(9):2055

[104] Krieger T, Sauer OA. Monte Carloversus pencil-beam/collapsed-conedose calculation in a heterogeneous multi-layer phantom. Physics in Medicine & Biology. 2005;50(5):859

Prospective Monte Carlo Simulation for Choosing High Efficient Detectors for Small-Field… DOI: http://dx.doi.org/10.5772/intechopen.89150

[105] Chetty IJ, Charland PM, Tyagi N, McShan DL, Fraass BA, Bielajew AF. Photon beam relative dose validation of the DPM Monte Carlo code in lungequivalent media. Medical Physics. 2003;30(4):563-573

[87] Xiong G, Rogers DWO. Relationship between %dd(10)x and stopping-power

and measurements in the buildup region for a high-energy photon beam. Medical Physics. 2002;29(11):

[97] Ding GX. Using Monte Carlo simulations to commission photon beam output factors—A feasibility study. Physics in Medicine & Biology. 2003;

[98] Ahnesjö A. Collimator scatter in photon therapy beams. Medical Physics.

[99] Jones AO, Das IJ, Jones FL Jr. A Monte Carlo study of IMRT beamlets in inhomogeneous media. Medical Physics.

[100] Jones AO, Das IJ. Comparison of inhomogeneity correction algorithms in small photon fields. Medical Physics.

[101] Saitoh H, Fujisaki T, Sakai R, Kunieda E. Dose distribution of narrow beam irradiation for small lung tumor. International Journal of Radiation Oncology Biology Physics. 2002;53(5):

[102] Al-Hallaq HA, Reft CS, Roeske JC.

heterogeneities in intensity-modulated radiation therapy (IMRT) of the head and neck. Physics in Medicine &

Thierens H, De Neve W, De Wagter C. Experimental verification of lung dose with radiochromic film: Comparison with Monte Carlo simulations and commercially available treatment planning systems. Physics in Medicine

[104] Krieger T, Sauer OA. Monte Carloversus pencil-beam/collapsed-conedose calculation in a heterogeneous multi-layer phantom. Physics in Medicine & Biology. 2005;50(5):859

The dosimetric effects of tissue

Biology. 2006;51(5):1145

[103] Paelinck L, Reynaert N,

& Biology. 2005;50(9):2055

2459-2463

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

48(23):3865

1995;22(3):267-278

2003;30(3):296-300

2005;32(3):766-776

1380-1387

ratios for flattening filter free accelerators: A Monte Carlo study. Medical Physics. 2008;35:2104-2109

[88] Palmans H, National Physical Laboratory. Personal Communication;

[89] Dalaryd M, Knöös T, Ceberg C. Combining tissue-phantom ratios to provide a beam-quality specifier for flattening filter free photon beams. Medical Physics. 2014;41:111716

[90] Palmans H. Determination of the beam quality index of high-energy photon beams under nonstandard reference conditions. Medical Physics.

[91] Podgorsak EB. External photon beams: Physical aspects. In: Radiation Oncology Physics: A Handbook.

[92] Verhaegen F, Das IJ, Palmans H. Monte Carlo dosimetry study of a 6 MV stereotactic radiosurgery unit. Physics in Medicine & Biology. 1998;43(10):

[93] Ding GX, Duggan DM, Coffey CW. Comment on "Testing of the analytical anisotropic algorithm for photon dose calculation" [Med. Phys. 33, 4130-4148 (2006)]. Medical Physics. 2007;34(8):

[94] Kijewski PK, Bjärngard BE, Petti PL. Monte Carlo calculations of scatter dose for small field sizes in a 60Co beam. Medical Physics. 1986;13(1):74-77

[95] Ding GX, Duggan DM, Coffey CW.

experimental and theoretical methods. Physics in Medicine & Biology. 2006;

[96] Ding GX. Dose discrepancies between Monte Carlo calculations

Commissioning stereotactic radiosurgery beams using both

51(10):2549

76

2012;39:5513-5519

2755

3414

2015

[106] Rogers DWO, Kawrakow I, Seuntjens JP, Walters BRB, Mainegra-Hing E. NRC user codes for EGSnrc. NRCC Report PIRS-702 (Rev. B). 2003

[107] GEANT Collaboration, Agostinelli S. GEANT4—A simulation toolkit. Nuclear Instruments and Methods A. 2003;506(25)

[108] MCNP—A General Monte Carlo. N-Particle Transport Code. Vol. I: Overview and Theory. Los Alamos, NM: Los Alamos National Laboratory; 2003. LA-UR-03-1987

[109] Heydarian M, Hoban PW, Beddoe AH. A comparison of dosimetry techniques in stereotactic radiosurgery. Physics in Medicine & Biology. 1996; 41(1):93

[110] Scielzo G, Grillo FR, Schwarz M, Rivolta A, Brunelli B, Surridge M, et al. The Monte Carlo method and parallel estimation in the drawing up of radiosurgery treatment plans. La Radiologia Medica. 1998;95(6): 647-655

[111] De Vlamynck K, Palmans H, Verhaegen F, De Wagter C, De Neve W, Thierens H. Dose measurements compared with Monte Carlo simulations of narrow 6 MV multileaf collimator shaped photon beams. Medical Physics. 1999;26(9):1874-1882

[112] Cheung YC, Yu KN, Ho RTK, Yu CP. Stereotactic dose planning system used in Leksell gamma knife model-B: EGS4 Monte Carlo versus GafChromic films MD-55. Applied Radiation and Isotopes. 2000;53(3): 427-430

[113] Westermark M, Arndt J, Nilsson B, Brahme A. Comparative dosimetry in narrow high-energy photon beams. Physics in Medicine & Biology. 2000; 45(3):685

[114] Deng J, Ma CM, Hai J, Nath R. Commissioning 6 MV photon beams of a stereotactic radiosurgery system for Monte Carlo treatment planning. Medical Physics. 2003;30(12):3124-3134

[115] Paskalev KA, Seuntjens JP, Patrocinio HJ, Podgorsak EB. Physical aspects of dynamic stereotactic radiosurgery with very small photon beams (1.5 and 3 mm in diameter). Medical Physics. 2003;30(2):111-118

[116] Tsougos I, Theodorou K, Bazioglou M, Stathakis S. Kappas C. a comparison of Monte Carlo simulation with experimental dosimetric techniques for a 6 MV stereotactic radiotherapy unit. Journal of BUON. 2004;9:451-564

[117] Francescon P, Cora S, Cavedon C. Total scatter factors of small beams: A multidetector and Monte Carlo study. Medical Physics. 2008;35(2): 504-513

[118] Heydarian M, Asnaashari K, Allahverdi M, Jaffray DA. Dosimetric evaluation of a dedicated stereotactic linear accelerator using measurement and Monte Carlo simulation. Medical Physics. 2008;35(9):3943-3954

[119] Cranmer-Sargison G, Charles PH, Trapp JV, Thwaites DI. A methodological approach to reporting corrected small field relative outputs. Radiotherapy and Oncology. 2013; 109(3):350-355

[120] Charles PH, Cranmer-Sargison G, Thwaites DI, Crowe SB, Kairn T, Knight RT, et al. A practical and theoretical definition of very small field size for radiotherapy output factor measurements. Medical Physics. 2014; 41(4):041707

[121] Francescon P, Kilby W, Satariano N, Orlandi C, Elshamndy SK. The impact of inter-unit variations on small field dosimetry correction factors, with application to the CyberKnife system. Physics in Medicine and Biology. 2018

[122] Casar B, Gershkevitsh E, Mendez I, Jurković S, Huq MS. A novel method for the determination of field output factors and output correction factors for small static fields for six diodes and a microdiamond detector in megavoltage photon beams. Medical Physics. 2019; 46(2):944-963

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[124] Freud N, Letang JM, Mary C, Boudou C, Ferrero C, Elleaume H, et al. Fast dose calculation for stereotactic synchrotron radiotherapy. In: 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE; 2007. pp. 3914-3917

[125] Chetty IJ, Curran B, Cygler JE, DeMarco JJ, Ezzell G, Faddegon BA, et al. Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo-based photon and electron external beam treatment planning. Medical Physics. 2007;34(12):4818-4853

[126] Jang SY, Liu HH, Mohan R. Underestimation of low-dose radiation in treatment planning of intensitymodulated radiotherapy. International Journal of Radiation Oncology Biology Physics. 2008;71(5):1537-1546

[127] Petti PL, Chuang CF, Smith V, Larson DA. Peripheral doses in CyberKnife radiosurgery. Medical Physics. 2006;33(6 Part 1):1770-1779 [128] Chuang CF, Larson DA, Zytkovicz A, Smith V, Petti PL. Peripheral dose measurement for CyberKnife radiosurgery with upgraded linac shielding. Medical Physics. 2008; 35(4):1494-1496

Chapter 4

Validation

and Viviana Fanti

specific MC toolkit are commented too.

Abstract

1. Introduction

enunciated as:

79

or, translated to English:

specific board?

Monte Carlo's Core and Tests for

Application Developers: Geant4

In this chapter, the Monte Carlo (MC) core is presented, particularly its cross-sectional libraries and random generators. The main idea is to introduce validation and reliability of MC applications and to explore its limitations. As an example, a comparison between two MC toolkits, namely XRMC (version 6.5.0–2) and Geant4 (version 10.02.p02), and a validation between each of them and experimental data applied to mammography (external dosimetry) are presented. The simulated quantities compared are exposure, kerma, half-value layer, and backscattering. Limitations, advantages, and disadvantages of using a general and

Keywords: Monte Carlo, mammography, medical physics, XRMC, Geant4

The Monte Carlo (MC) method history began two centuries before its computational implementation that happened in the period of World War II (1939–1945). The MC method conception starts in 1733 with the Probléme de l'aiguille (Needle's problem) by Georges-Louis Leclerc, known as the Comte de Buffon [1], which is

Sur un plancher qui n est formé que de planches égales & parallèles, on jette une Baguette d'une certaine longueur, & qu'on suppose sans largeur. Quand tombera-t-

On the floor formed only of equal boards placed in parallel, one throws a needle of a certain length which and supposed without width. When will this needle fall on one

elle franchement íùr une seule planche? Leclerc [1], p. 44

and XRMC Comparison and

Gabriela Hoff, Bruno Golosio, Elaine E. Streck

[129] Di Betta E, Fariselli L, Bergantin A, Locatelli F, Del Vecchio A, Broggi S, et al. Evaluation of the peripheral dose in stereotactic radiotherapy and radiosurgery treatments. Medical Physics. 2010;37(7 Part 1):3587-3594
