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On the biologically effective dose (BED)-using convolution for calculating the effects of repair: I. Analytical considerations.

Gustafsson, Johan Ruben LU ; Nilsson, Per LU orcid and Sjögreen Gleisner, Katarina LU (2013) In Physics in Medicine and Biology 58(5). p.1507-1527
Abstract
This work presents a new mathematical formulation of biologically effective dose (BED) for radiation therapy where effects of repair need to be considered. The formulation is based on the observation that the effects of repair, both during protracted irradiation and of incomplete repair between fractions, can be written using a convolution, i.e. [Formula: see text] where T is the total irradiation time, R(T)(t) is the absorbed dose rate as a function of time t and I(t) is the function describing repair. To validate this formulation, the previously published expressions for instant and protracted irradiation are first summarized. Then, by analytical derivation, it is shown that the new formulation gives identical results. The calculation of... (More)
This work presents a new mathematical formulation of biologically effective dose (BED) for radiation therapy where effects of repair need to be considered. The formulation is based on the observation that the effects of repair, both during protracted irradiation and of incomplete repair between fractions, can be written using a convolution, i.e. [Formula: see text] where T is the total irradiation time, R(T)(t) is the absorbed dose rate as a function of time t and I(t) is the function describing repair. To validate this formulation, the previously published expressions for instant and protracted irradiation are first summarized. Then, by analytical derivation, it is shown that the new formulation gives identical results. The calculation of BED can thus be treated within one single mathematical framework, applicable in external beam therapy, brachytherapy, radionuclide therapy, or a combination of these treatment modalities. Moreover, the new formulation allows for a straightforward incorporation of different repair models and has the advantage of being numerically applicable. (Less)
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publishing date
type
Contribution to journal
publication status
published
subject
in
Physics in Medicine and Biology
volume
58
issue
5
pages
1507 - 1527
publisher
IOP Publishing
external identifiers
  • wos:000315191400022
  • pmid:23403468
  • scopus:84880957341
  • pmid:23403468
ISSN
1361-6560
DOI
10.1088/0031-9155/58/5/1507
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Radiation Physics, Lund (013034000), Reconstructive Surgery (013240300)
id
d4b1532e-35c7-4535-90a8-f81f3591bc41 (old id 3559877)
alternative location
http://www.ncbi.nlm.nih.gov/pubmed/23403468?dopt=Abstract
date added to LUP
2016-04-01 10:57:15
date last changed
2022-03-20 01:32:37
@article{d4b1532e-35c7-4535-90a8-f81f3591bc41,
  abstract     = {{This work presents a new mathematical formulation of biologically effective dose (BED) for radiation therapy where effects of repair need to be considered. The formulation is based on the observation that the effects of repair, both during protracted irradiation and of incomplete repair between fractions, can be written using a convolution, i.e. [Formula: see text] where T is the total irradiation time, R(T)(t) is the absorbed dose rate as a function of time t and I(t) is the function describing repair. To validate this formulation, the previously published expressions for instant and protracted irradiation are first summarized. Then, by analytical derivation, it is shown that the new formulation gives identical results. The calculation of BED can thus be treated within one single mathematical framework, applicable in external beam therapy, brachytherapy, radionuclide therapy, or a combination of these treatment modalities. Moreover, the new formulation allows for a straightforward incorporation of different repair models and has the advantage of being numerically applicable.}},
  author       = {{Gustafsson, Johan Ruben and Nilsson, Per and Sjögreen Gleisner, Katarina}},
  issn         = {{1361-6560}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1507--1527}},
  publisher    = {{IOP Publishing}},
  series       = {{Physics in Medicine and Biology}},
  title        = {{On the biologically effective dose (BED)-using convolution for calculating the effects of repair: I. Analytical considerations.}},
  url          = {{http://dx.doi.org/10.1088/0031-9155/58/5/1507}},
  doi          = {{10.1088/0031-9155/58/5/1507}},
  volume       = {{58}},
  year         = {{2013}},
}