References
- Agostinelli , S. , Allison , J. , Amako , K. Apostolakis , J. 2003 . Geant4-a simulation toolkit . Nucl. Instrum. Methods B , 506 : 250 – 303 .
- Ahnesjö , A. , Saxner , M. and Trepp , A. 1992 . A pencil beam model for photon dose calculation . Med. Phys. , 19 : 263 – 273 .
- Allison , J. 2006 . Geant4 developments and applications . IEEE Trans. Nucl. Sci. , 53 : 270 – 278 .
- Andreo , P. 1991 . Monte Carlo techniques in medical radiation physics . Phys. Med. Biol. , 36 : 861 – 920 .
- Balsara , D. 2001 . Fast and accurate discrete ordinates methods for multidimensional radiative transfer. Part I, basic methods . J. Quant. Spectrosc. Radiat. Transfer , 69 : 671 – 707 .
- Boman , E. , Tervo , J. and Vauhkonen , M. 2005 . Modelling the transport of ionizing radiation using the finite element method . Phys. Med. Biol. , 50 : 265 – 280 .
- Börgers , C. 1998 . Complexity of Monte Carlo and deterministic dose calculation methods . Phys. Med. Biol. , 43 : 517 – 528 .
- Brunner , T.A. 2002 . Forms of application radiation transport Sandia Report, sand2002-1778, Sandia National Laboratories, Albuquerque
- Cheong , W. , Prahl , S.A. and Welch , A.J. 1990 . A review of the optical properties of biological tissues . IEEE J. Quant. Electron. , 26 : 2166 – 2185 .
- Coppa , G.G.M. and Ravetto , P. 1995 . Quasi-singular angular finite element methods in neutron transport problems . Trans. Theory Stat. Phys. , 24 : 155 – 172 .
- Cygler , J. 2005 . Clinical use of a commercial Monte Carlo treatment planning system for electron beams . Phys. Med. Biol. , 50 : 1029 – 1034 .
- Datta , R.P. 1996 . Computational model for coupled electron–photon transport in two dimensions . Phys. Rev. E , 53 : 6514 – 6522 .
- Duclous , R. 2010 . Reduced multi-scale kinetic model for the relativistic electron transport in solid targets: Effects related to secondary electrons . Laser Particle Beams , 28 ( 1 ) : 165 – 177 .
- Edström , P. 2005 . A fast and stable solution method for the radiative transfer problem . SIAM Rev. , 47 : 447 – 468 .
- Eyges , L. 1948 . Multiple scattering with energy loss . Phys. Rev. , 74 : 1534 – 1535 .
- Fermi , E. 1940 . The ionization loss of energy in gases and in condensed materials . Phys. Rev. , 57 : 485 – 493 .
- Frank , M. , Hensel , H. and Klar , A. 2007 . A fast and accurate moment method for the Fokker–Planck equation and applications to electron radiotherapy . SIAM J. Appl. Math. , 67 : 582 – 603 .
- M. Frank, M. Herty, and A.N. Sandjo, Optimal treatment planning governed by kinetic equations, to appear in Math. Mod. Meth. Appl. Sci. Available at http://www.worldscinet.com/m3as/00/forthcoming.shtml (preprint 2009)
- Frank , M. , Herty , M. and Schäfer , M. 2008 . Optimal treatment planning in radiotherapy based on Boltzmann transport calculations . Math. Mod. Meth. Appl. Sci. , 18 : 573 – 592 .
- Garth , J.C. 2004 . Electron/photon transport – a key technology to radiation physics? A review . Trans. Amer. Nucl. Soc. , 90 : 289 – 291 .
- J.C. Garth, Electron/photon transport and its applications, The Monte Carlo Method: Versatility Unbounded in a Dynamic Computing World, Chattanooga, Tennessee, 17–21 April, 2005
- Gifford , K.A. 2006 . Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations . Phys. Med. Biol. , 51 : 2253 – 2265 .
- González-Rodríguez , P. and Kim , A.D. 2008 . Light propagation in tissues with forward-peaked and large-angle scattering . Appl. Opt. , 47 : 2599 – 2609 .
- Hensel , H. , Iza-Teran , R. and Siedow , N. 2006 . Deterministic model for dose calculation in photon radiotherapy . Phys. Med. Biol. , 51 : 675 – 693 .
- Henyey , L.G. and Greenstein , J.L. 1941 . Diffuse radiation in the galaxy . Astrophys. J. , 93 : 70 – 83 .
- Hogstrom , K.R. , Mills , M.D. and Almond , P.R. 1981 . Electron beam dose calculations . Phys. Med. Biol. , 26 : 445 – 459 .
- Huizenga , H. and Storchi , P. 1989 . Numerical calculation of energy deposition by broad high-energy electron beams . Phys. Med. Biol. , 34 : 1371 – 1396 .
- Berger , M.J. , Jablonski , A. , Bronic , I.K. , Powell , C.J. , Salvat , F. and Sanche , L. 2007 . Elastic scattering of electrons and positrons, report 77 . J. ICRU , 7
- Itikawa , Y. and Mason , N. 2005 . Cross sections for electron collisions with water molecules . J. Phys. Chem. Ref. Data , 34 ( 1 ) : 1 – 22 .
- Janssen , J. 1994 . Numerical calculation of energy deposition by high-energy electron beams: III. Three-dimensional heterogeneous media . Phys. Med. Biol. , 39 : 1351 – 1366 .
- Janssen , J. 1997 . Numerical calculation of energy deposition by high-energy electron beams: III-B. Improvements to the 6D phase space evolution model . Phys. Med. Biol. , 42 : 1441 – 1449 .
- Jette , D. 1988 . Electron dose calculation using multiple-scattering theory. A. Gaussian multiple-scattering theory . Med. Phys. , 15 : 123 – 137 .
- Jette , D. and Bielajew , A. 1989 . Electron dose calculation using multiple-scattering theory: Second-order multiple-scattering theory . Med. Phys. , 16 : 698 – 711 .
- Korevaar , E. 2000 . Accuracy of the phase space evolution dose calculation model for clinical 25 MeV electron beams . Phys. Med. Biol. , 45 : 2931 – 2945 .
- Krieger , H. 2007 . Grundlagen der Strahlungsphysik und des Strahlenschutzes , 2nd ed. , Wiesbaden : Teubner Verlag .
- Larsen , E. 1997 . Electron dose calculations using the method of moments . Med. Phys. , 24 : 111 – 125 .
- LaVerne , J.A. and Pimblott , S.M. 1997 . Effect of elastic collisions on energy deposition by electrons in water . J. Phys. Chem. A , 101 : 4504 – 4510 .
- Leakeas , C.L. and Larsen , E.W. 2001 . Generalized Fokker–Planck approximations of particle transport with highly forward-peaked scattering . Nucl. Sci. Eng. , 137 : 236 – 250 .
- Lewis , H.W. 1950 . Multiple scattering in an infinite medium . Phys. Rev. , 78 : 526 – 529 .
- Martens , C. 2002 . Underdosage of the upper-airway mucosa for small fields as used in intensity-modulated radiation therapy: A comparison between radiochromic film measurements, Monte Carlo simulations, and collapsed cone convolution calculations . Med. Phys. , 29 : 1528 – 1535 .
- Morawska-Kaczyńska , M. and Huizenga , H. 1992 . Numerical calculation of energy deposition by broad high-energy electron beams: II. Multi-layered geometry . Phys. Med. Biol. , 37 : 2103 – 2116 .
- Morel , J.E. 1985 . An improved Fokker–Planck angular differencing scheme . Nucl. Sci. Eng. , 89 : 131 – 136 .
- N. Papanikolau, et al., Tissue inhomogeneity corrections for megavoltage photon beams, Medical Physics Publishing, Madison, AAPM Report No. 85 (2004)
- Pomraning , G.C. 1992 . The Fokker–Planck operator as an asymptotic limit . Math. Models Methods Appl. Sci. , 2 ( 1 ) : 21 – 36 .
- Rossi , B. and Greisen , K. 1941 . Cosmic-ray theory . Rev. Med. Phys. , 13 : 240 – 309 .
- F. Salvat, J.M. Fernández-Varea, and J. Sempau, PENELOPE-2008: A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD, 2009
- Schwoerer , H. 2006 . Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets . Nature , 439 : 445 – 448 .
- Shiu , A.S. and Hogstrom , K.R. 1991 . Pencil-beam redefinition algorithm for electron dose distributions . Med. Phys. , 18 : 7 – 18 .
- Siantar , C. 2001 . Description and dosimetric verification of the peregrine Monte Carlo dose calculation system for photon beams incident on a water phantom . Med. Phys. , 28 : 1322 – 1337 .
- Spezi , E. and Lewis , G. 2008 . An overview of Monte Carlo treatment planning for radiotherapy . Radiat. Prot. Dos. , 131 : 123 – 129 .
- Tervo , J. 1999 . A finite-element model of electron transport in radiation therapy and a related inverse problem . Inverse Probl. , 15 : 1345 – 1361 .
- Vassiliev , O.N. 2008 . Feasibility of a multigroup deterministic solution method for 3D radiotherapy dose calculations . Int. J. Radiat. Oncol. Biol. Phys. , 72 : 220 – 227 .
- Venselaar , J. , Welleweerd , H. and Mijnheer , B. 2001 . Tolerances for the accuracy of photon beam dose calculations of treatment planning systems . Radiother. Oncol. , 60 : 191 – 201 .