Department of Mathematics,
Chalmers University of Technology,
and
Göteborg University
I supervise in
ECMI Modelling week 2001, Klagenfurt, Aug. 31-Sept. 9 I suggest the following topics:
A pencil beam model for charged particles
This is an interdisciplinary problem in particle/medical physics concerning electron and photon dose calculations of radiative transfer/radiation treatment.
The project is to model a forward-peaked scattering process in the
linear transport equation and study both asymptotic behavior
and numerical approximations for the such obtained beam particles.
A front line application is, e.g. in radiation therapy where the
objective is twofold: (i) To maximize the deposit of electron dose
(energy) inside seek cells (ii) To minimize the deposit of energy
in surrounding healthy tissue. In this way one has an optimization
(max-min) problem with many challenging and interesting aspects.
A more detailed abstract can be found in the following file:
abstract (ps-file) ,
abstract (pdf-file) .
Implementations are easily done writing MatLab codes. However,
knowledge in the following programing/software may be very much useful:
Mathematica, Fortran, PDE tool-box, and
if possible DSMC (Direct Simulated Monte-Carlo).
Here are some relevant literature:
M. Asadzadeh,
Streamline diffusion methods for the Fermi and
Fokker-Planck equations,
Transport Theory and Statistical Physics, (1997), 319--340.
M. Asadzadeh,
Characteristic Methods for Fokker-Planck and Fermi Pencil Beam
Equations,
Proceedings of 21th International Symposium on Rarefied Gas
Dynamics,
ed. by R. Brun et al , Vol II, 205--212, Marseille 1998.
M. Asadzadeh,
A posteriori error estimates for the Fokker-Planck and Fermi
pencil beam equations,
Math. Models and Methods in Appl. Sci.,
10(2000), 737--769.
C. Borgers and E. W. Larsen,
The trasversely integrated scalar flux for a norrowly focused particle
beam,
SIAM J. Appl. Math. 55(1955), 1--22.
C. Borgers and E. W. Larsen,
On the accuracy of the Fokker-Planck and Fermi pencil beam equations
for charged particle transport,
Med. Phys. 23 (1996), nr. 10, 1749--1759.
C. Borgers and E. W. Larsen,
Asymptotic derivation of the Fermi pencil beam approximation,
Nucl. Sci. Eng. 123(1996), 343--357
D. Jette
Electron Beam Dose Calculations,
Radiation therapy physics,
ed by A. Smith, Springer (1995), 95--121
D. Jette,
Electron dose calculation using multiple-scattering theory.
A. Guassian multiple-scattering theory.
Med. Phys. 15 (1988), 123--137.
J. Lang,
Adaptive Multilevel Solution of Nonlinear Parabolic PDE System,
Lecture Notes in Computational Science and Engineering, Springer
, 16 (2000).
E. W. Larsen,
The amplitude and radius of a radiation beam,
Proceedings of the International Conference on Latest Developments
and Fundamental Advances in Radiative Transfer (Los Angeles, CA,
1996). Transport Theory Statist. Phys.
26 (1997), no. 4-5, 533--554.
G. C. Pomraning,
The Fokker-Planck operator as an asymptotic limit,
Math. Models and Methods in Appl. Sci.,
2(1992), 21--36.
G. C. Pomraning and A. Prinja,
High-order multiple scattering theories for charged particle
transport,
Med. Phys. 23 (1996), nr. 10, 1761--1744.