On the scattering power of radiotherapy protons

Medical Physics

Volumn 37, Issue 1, 2010, Pages 352-367

  Gottschalk, Bernard ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Fermi Eyges theory; Protons; Radiotherapy; Scattering power

Indexed keywords

ANGULAR DISTRIBUTION; GAUSSIAN BEAMS; MONTE CARLO METHODS; NUMERICAL METHODS; PROTONS; RADIOTHERAPY;

ACCURATE FORMULAS; CORRECTION FACTORS; DETERMINISTIC TRANSPORT; FERMI-EYGES THEORY; NUMERICAL DERIVATIVES; POINT OF INTEREST; RADIATION LENGTHS; SINGLE SCATTERING;

PROTON BEAM THERAPY;

EID: 73649125487     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.3264177     Document Type: Article

References (31)

1. M. J. Berger, " Stopping powers and ranges for protons and alpha particles.," ICRU Report No. 49, 1993.
2. G. Molìre, " Theorie der Streuung schneller geladener Teilchen II Mehrfach- und Vielfachstreuung-streuung.," Z. Naturforsch. B 0044-3174 3A, 78-97 (1948).
3. H. A. Bethe, " Molìre's theory of multiple scattering.," Phys. Rev. 0096-8250 89, 1256-1266 (1953) 10.1103/PhysRev.89.1256.
4. Four entries in the second column (the Gaussian) of Table are slightly incorrect but the error (corrected in our programs) is at worst 1%. (A. Cormack, personal communication (1990)).
5. c2 should read × 106. 10.1016/0168-583X(93)95944-Z
6. H. Svensson, " Radiation dosimetry: Electron beams with energies between 1 and 50 MeV.," ICRU Report No. 35, 1984.
7. M. Hollmark, " Influence of multiple scattering and energy loss straggling on the absorbed dose distributions of therapeutic light ion beams: I. Analytical pencil beam model.," Phys. Med. Biol. 0031-9155 49, 3247-3265 (2004). 10.1088/0031-9155/49/14/016 (Pubitemid 39140010)
8. N. Kanematsu, " Alternative scattering power for Gaussian beam model of heavy charged particles.," Nucl. Instrum. Methods Phys. Res. B 0168-583X 266, 5056-5062 (2008). 10.1016/j.nimb.2008.09.004
9. X. A. Li and D. W. O. Rogers, " Electron mass scattering powers: Monte Carlo and analytical calculations.," Med. Phys. 0094-2405 22 (5), 531-541 (1995). 10.1118/1.597582
10. K. R. Russell, E. Grusell, and A. Montelius, " Dose calculations in proton beams: Range straggling corrections and energy scaling.," Phys. Med. Biol. 0031-9155 40, 1031-1043 (1995). 10.1088/0031-9155/40/6/005
11. E. Pedroni, " Experimental characterization and physical modeling of the dose distribution of scanned proton pencil beams.," Phys. Med. Biol. 0031-9155 50, 541-561 (2005). 10.1088/0031-9155/50/3/011 (Pubitemid 40297924)
12. M. Hollmark, " An analytical model for light ion pencil beam dose distributions: Multiple scattering of primary and secondary ions.," Phys. Med. Biol. 0031-9155 53, 3477-3491 (2008). 10.1088/0031-9155/53/13/005 (Pubitemid 352020034)
13. B. Gottschalk, in Proton and Charged Particle Radiotherapy, edited by, T. F. Delaney, and, H. M. Kooy, (Lippincott Williams and Wilkins, Philadelphia, 2008), Chap..
14. E. Grusell, " A general solution to charged particle beam flattening using an optimized dual scattering foil technique, with application to proton therapy beams.," Phys. Med. Biol. 0031-9155 39, 2201-2216 (1994). 10.1088/0031-9155/39/12/005
15. H. vers, " On small angle multiple scattering in confined bodies.," CERN Yellow Report No. 60-18, 1960.
16. U. Schneider, J. Besserer, and P. Pemler, " On small angle multiple Coulomb scattering of protons in the Gaussian approximation.," Z. Med. Phys. 0939-3889 11, 110-118 (2001).
17. V. L. Highland, " Some practical remarks on multiple scattering.," Nucl. Instrum. Methods 0029-554X 129, 497-499 (1975) 10.1016/0029-554X(75)90743-0; V. L. Highland, " Erratum.," Nucl. Instrum. Methods 0029-554X 161, 171 (1979). 10.1016/0029-554X(79)90379-3
18. B. Rossi, High-Energy Particles (Prentice-Hall, New York, 1952).
19. A. Brahme, " On the optimal choice of scattering foils for electron therapy.," Royal Institute of Technology Technical Report TRITA-EPP-17, 1972.
20. G. Kraft, " Tumor therapy with heavy charged particles.," Prog. Part. Nucl. Phys. 0146-6410 45, S473-S544 (2000). 10.1016/S0146-6410(00)00112-5 (Pubitemid 32076531)
21. H. W. Barkas, Nuclear Research Emulsions (Academic Press, Inc., New York, 1963).
22. N. Kanematsu, " Semi-empirical formulation of multiple scattering for Gaussian beam model of heavy charged particles stopping in tissue-like matter.," Phys. Med. Biol. 0031-9155 54, 2015-2027 (2009). 10.1088/0031-9155/54/7/010
23. M. Soukup, M. Fippel, and M. Alber, " A pencil beam algorithm for intensity modulated proton therapy derived from Monte Carlo simulations.," Phys. Med. Biol. 0031-9155 50, 5089-5104 (2005). 10.1088/0031-9155/50/21/010 (Pubitemid 41503992)
24. W. M. Preston and A. M. Koehler, " The effects of scattering on small proton beams.," unpublished manuscript, Harvard Cyclotron Laboratory (1968). A facsimile is available in \BGdocs.zip at http://physics.harvard.edu/ ~gottschalk.
25. B. Gottschalk, " Passive beam spreading in proton radiation therapy.," unpublished book (2004). Available in PDF format at http://physics.harvard.edu/~gottschalk.
26. H. Paganetti, " Accurate Monte Carlo simulations for nozzle design, commissioning and quality assurance for a proton radiation therapy facility.," Med. Phys. 0094-2405 31 (7), 2107-2118 (2004). 10.1118/1.1762792 (Pubitemid 38924832)
27. Geant4 Physics Reference Manual (2008). Download from http://geant4.cern.ch/G4UsersDocuments/UsersGuides/PhysicsReferenceManual/html/ PhysicsReferenceManual.html.
28. M. F. Moyers, " Calibration of a proton beam energy monitor.," Med. Phys. 0094-2405 34 (6), 1952-1966 (2007). 10.1118/1.2717382 (Pubitemid 47055730)
29. J. F. Janni, Proton Range-Energy Tables, 1 KeV-10 GeV (Academic Press, Inc., New York, 1982).
30. J. F. Janni, " Calculations of energy loss, range, path length, straggling, multiple scattering, and the probability of inelastic nuclear collisions for 0.1 to 1000 MeV protons.," Air Force Weapons Laboratory Technical Report No. AFWL-TR-65-150, 1966.
31. H. A. Bethe and J. Ashkin, in Experimental Nuclear Physics, edited by, E. Segr̀, (Wiley, New York, 1953), p. 283.