On the transverse diffusion of beams of photons in radiation therapy

S. Brull; B. Dubroca; M. Frank; T. Pichard

doi:10.1007/978-3-319-91548-7_35

On the transverse diffusion of beams of photons in radiation therapy

S. Brull
, B. Dubroca
, M. Frank
, T. Pichard

Univ. Bordeaux
RWTH Aachen University
UPMC Université de Paris VI

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Typical external radiotherapy treatments consist in emitting beams of energetic photons targeting the tumor cells. Those photons are transported through the medium and interact with it. Such interactions affect the motion of the photons but they are typically weakly deflected which is not well modeled by standard numerical methods. The present work deals with the transport of photons in water. The motion of those particles is modeled by an entropy-based moment model, i.e., the M₁ model. The main difficulty when constructing numerical approaches for photon beam modeling emerges from the significant difference of magnitude between the diffusion effects in the forward and transverse directions. A numerical method for the M₁ equations is proposed with a special focus on the numerical diffusion effects.

Original language	English
Title of host publication	Theory, Numerics and Applications of Hyperbolic Problems II
Editors	Michael Westdickenberg, Christian Klingenberg
Publisher	Springer New York LLC
Pages	465-477
Number of pages	13
ISBN (Print)	9783319915470
DOIs	https://doi.org/10.1007/978-3-319-91548-7_35
Publication status	Published - 1 Jan 2018
Externally published	Yes
Event	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 - Aachen, Germany Duration: 1 Aug 2016 → 5 Aug 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	237
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Country/Territory	Germany
City	Aachen
Period	1/08/16 → 5/08/16

Keywords

Entropy-based moment model
Photon beam modeling Transverse diffusion

Access to Document

10.1007/978-3-319-91548-7_35

Cite this

Brull, S., Dubroca, B., Frank, M., & Pichard, T. (2018). On the transverse diffusion of beams of photons in radiation therapy. In M. Westdickenberg, & C. Klingenberg (Eds.), Theory, Numerics and Applications of Hyperbolic Problems II (pp. 465-477). (Springer Proceedings in Mathematics and Statistics; Vol. 237). Springer New York LLC. https://doi.org/10.1007/978-3-319-91548-7_35

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title = "On the transverse diffusion of beams of photons in radiation therapy",

abstract = "Typical external radiotherapy treatments consist in emitting beams of energetic photons targeting the tumor cells. Those photons are transported through the medium and interact with it. Such interactions affect the motion of the photons but they are typically weakly deflected which is not well modeled by standard numerical methods. The present work deals with the transport of photons in water. The motion of those particles is modeled by an entropy-based moment model, i.e., the M1 model. The main difficulty when constructing numerical approaches for photon beam modeling emerges from the significant difference of magnitude between the diffusion effects in the forward and transverse directions. A numerical method for the M1 equations is proposed with a special focus on the numerical diffusion effects.",

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Brull, S, Dubroca, B, Frank, M & Pichard, T 2018, On the transverse diffusion of beams of photons in radiation therapy. in M Westdickenberg & C Klingenberg (eds), Theory, Numerics and Applications of Hyperbolic Problems II. Springer Proceedings in Mathematics and Statistics, vol. 237, Springer New York LLC, pp. 465-477, 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016, Aachen, Germany, 1/08/16. https://doi.org/10.1007/978-3-319-91548-7_35

On the transverse diffusion of beams of photons in radiation therapy. / Brull, S.; Dubroca, B.; Frank, M. et al.
Theory, Numerics and Applications of Hyperbolic Problems II. ed. / Michael Westdickenberg; Christian Klingenberg. Springer New York LLC, 2018. p. 465-477 (Springer Proceedings in Mathematics and Statistics; Vol. 237).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Dubroca, B.

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AU - Pichard, T.

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N2 - Typical external radiotherapy treatments consist in emitting beams of energetic photons targeting the tumor cells. Those photons are transported through the medium and interact with it. Such interactions affect the motion of the photons but they are typically weakly deflected which is not well modeled by standard numerical methods. The present work deals with the transport of photons in water. The motion of those particles is modeled by an entropy-based moment model, i.e., the M1 model. The main difficulty when constructing numerical approaches for photon beam modeling emerges from the significant difference of magnitude between the diffusion effects in the forward and transverse directions. A numerical method for the M1 equations is proposed with a special focus on the numerical diffusion effects.

AB - Typical external radiotherapy treatments consist in emitting beams of energetic photons targeting the tumor cells. Those photons are transported through the medium and interact with it. Such interactions affect the motion of the photons but they are typically weakly deflected which is not well modeled by standard numerical methods. The present work deals with the transport of photons in water. The motion of those particles is modeled by an entropy-based moment model, i.e., the M1 model. The main difficulty when constructing numerical approaches for photon beam modeling emerges from the significant difference of magnitude between the diffusion effects in the forward and transverse directions. A numerical method for the M1 equations is proposed with a special focus on the numerical diffusion effects.

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DO - 10.1007/978-3-319-91548-7_35

M3 - Conference contribution

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BT - Theory, Numerics and Applications of Hyperbolic Problems II

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On the transverse diffusion of beams of photons in radiation therapy

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