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A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production
While the dose deposition of charged hadrons has received much attention over the last decades starting in 1930 with the publication of the Bethe equation, there are still practical obstacles in implementing it in fields like radiotherapy and isotope production on cyclotrons. This is especially true...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6879469/ https://www.ncbi.nlm.nih.gov/pubmed/31772348 http://dx.doi.org/10.1038/s41598-019-54103-3 |
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author | Martinez, D. M. Rahmani, M. Burbadge, C. Hoehr, C. |
author_facet | Martinez, D. M. Rahmani, M. Burbadge, C. Hoehr, C. |
author_sort | Martinez, D. M. |
collection | PubMed |
description | While the dose deposition of charged hadrons has received much attention over the last decades starting in 1930 with the publication of the Bethe equation, there are still practical obstacles in implementing it in fields like radiotherapy and isotope production on cyclotrons. This is especially true if the target material consists of non-homogeneous materials, either consisting of a mixture of different elements or experiencing phase changes during irradiation. While Monte-Carlo methods have had great success in describing these more difficult target materials, they come at a computational cost, especially if the problem is time-dependent. This can greatly hinder optimal advancement in therapy and isotope targetry. Here, a regular perturbation method is used to solve the Bethe equation in the limit of small relativistic effects. Particular focus is given to incident energy level relevant to radionuclide production and radiotherapy applications, i.e. 10–200 MeV. We present a series solution for the range and dose distribution in terms of elementary functions, as opposed to special functions which will aid in uptake by practitioners. |
format | Online Article Text |
id | pubmed-6879469 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-68794692019-12-05 A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production Martinez, D. M. Rahmani, M. Burbadge, C. Hoehr, C. Sci Rep Article While the dose deposition of charged hadrons has received much attention over the last decades starting in 1930 with the publication of the Bethe equation, there are still practical obstacles in implementing it in fields like radiotherapy and isotope production on cyclotrons. This is especially true if the target material consists of non-homogeneous materials, either consisting of a mixture of different elements or experiencing phase changes during irradiation. While Monte-Carlo methods have had great success in describing these more difficult target materials, they come at a computational cost, especially if the problem is time-dependent. This can greatly hinder optimal advancement in therapy and isotope targetry. Here, a regular perturbation method is used to solve the Bethe equation in the limit of small relativistic effects. Particular focus is given to incident energy level relevant to radionuclide production and radiotherapy applications, i.e. 10–200 MeV. We present a series solution for the range and dose distribution in terms of elementary functions, as opposed to special functions which will aid in uptake by practitioners. Nature Publishing Group UK 2019-11-26 /pmc/articles/PMC6879469/ /pubmed/31772348 http://dx.doi.org/10.1038/s41598-019-54103-3 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Martinez, D. M. Rahmani, M. Burbadge, C. Hoehr, C. A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title | A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title_full | A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title_fullStr | A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title_full_unstemmed | A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title_short | A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production |
title_sort | practical solution of the bethe equation in the energy range applicable to radiotherapy and radionuclide production |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6879469/ https://www.ncbi.nlm.nih.gov/pubmed/31772348 http://dx.doi.org/10.1038/s41598-019-54103-3 |
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