Volume 10, Issue 5
Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation

Christophe Berthon, Martin Frank, Céline Sarazin & Rodolphe Turpault

Commun. Comput. Phys., 10 (2011), pp. 1184-1210.

Published online: 2011-10

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  • Abstract

The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy. To address this issue, we consider a moment approximation of radiative transfer, closed by an entropy minimization principle. The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms. The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function. Indeed, this dependence will be seen to be stiff and specific numerical strategies must be derived in order to obtain the needed accuracy. A first approach is developed considering the 1D case, where a judicious change of variables allows to eliminate the space dependence in the flux function. This is not possible in multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, and generalize this to 2D by alternating transformations between separate meshes. We call this procedure projection method. Several numerical experiments, coming from medical physics, illustrate the potential applicability of the developed method.

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@Article{CiCP-10-1184, author = {}, title = {Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {5}, pages = {1184--1210}, abstract = {

The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy. To address this issue, we consider a moment approximation of radiative transfer, closed by an entropy minimization principle. The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms. The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function. Indeed, this dependence will be seen to be stiff and specific numerical strategies must be derived in order to obtain the needed accuracy. A first approach is developed considering the 1D case, where a judicious change of variables allows to eliminate the space dependence in the flux function. This is not possible in multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, and generalize this to 2D by alternating transformations between separate meshes. We call this procedure projection method. Several numerical experiments, coming from medical physics, illustrate the potential applicability of the developed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020810.171210a}, url = {http://global-sci.org/intro/article_detail/cicp/7480.html} }
TY - JOUR T1 - Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation JO - Communications in Computational Physics VL - 5 SP - 1184 EP - 1210 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.020810.171210a UR - https://global-sci.org/intro/article_detail/cicp/7480.html KW - AB -

The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy. To address this issue, we consider a moment approximation of radiative transfer, closed by an entropy minimization principle. The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms. The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function. Indeed, this dependence will be seen to be stiff and specific numerical strategies must be derived in order to obtain the needed accuracy. A first approach is developed considering the 1D case, where a judicious change of variables allows to eliminate the space dependence in the flux function. This is not possible in multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, and generalize this to 2D by alternating transformations between separate meshes. We call this procedure projection method. Several numerical experiments, coming from medical physics, illustrate the potential applicability of the developed method.

Christophe Berthon, Martin Frank, Céline Sarazin & Rodolphe Turpault. (2020). Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation. Communications in Computational Physics. 10 (5). 1184-1210. doi:10.4208/cicp.020810.171210a
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