Publication Cover
Computational and Mathematical Methods in Medicine
An Interdisciplinary Journal of Mathematical, Theoretical and Clinical Aspects of Medicine
Volume 11, 2010 - Issue 4
32
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Generalized Fokker–Planck theory for electron and photon transport in biological tissues: application to radiotherapy

&
Pages 313-339 | Received 09 Dec 2009, Accepted 21 Apr 2010, Published online: 30 Sep 2010

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 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.