Cargando…
Empirical modeling of the percent depth dose for megavoltage photon beams
INTRODUCTION: This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used...
Autores principales: | , , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2022
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8735605/ https://www.ncbi.nlm.nih.gov/pubmed/34990461 http://dx.doi.org/10.1371/journal.pone.0261042 |
_version_ | 1784628273634869248 |
---|---|
author | Li, Xiao-Jun Ye, Yan-Cheng Zhang, Yan-Shan Wu, Jia-Ming |
author_facet | Li, Xiao-Jun Ye, Yan-Cheng Zhang, Yan-Shan Wu, Jia-Ming |
author_sort | Li, Xiao-Jun |
collection | PubMed |
description | INTRODUCTION: This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (S(c)) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. METHODS AND MATERIALS: The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of [Image: see text] with the main parameter of d (depth in water) and n, while the tail function was in the form of e(−μd) and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = [Image: see text] . The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The S(c) of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. RESULTS: The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of S(c) = n(E)(S)(0.63μ)(E) to get the collimator to scatter factor S(c) for 6 and 10 MV photon beam, while n(E), (μ)(E), S denotes n, μ at photon energy E of field size S, respectively. The calculated S(c) were compared with the measured data and showed agreement at different field sizes to within ±1.5%. CONCLUSIONS: We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the S(c) factors for some clinical requirements. The modeling parameters n and μ can be used to predict the S(c) in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment. |
format | Online Article Text |
id | pubmed-8735605 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-87356052022-01-07 Empirical modeling of the percent depth dose for megavoltage photon beams Li, Xiao-Jun Ye, Yan-Cheng Zhang, Yan-Shan Wu, Jia-Ming PLoS One Research Article INTRODUCTION: This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (S(c)) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. METHODS AND MATERIALS: The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of [Image: see text] with the main parameter of d (depth in water) and n, while the tail function was in the form of e(−μd) and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = [Image: see text] . The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The S(c) of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. RESULTS: The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of S(c) = n(E)(S)(0.63μ)(E) to get the collimator to scatter factor S(c) for 6 and 10 MV photon beam, while n(E), (μ)(E), S denotes n, μ at photon energy E of field size S, respectively. The calculated S(c) were compared with the measured data and showed agreement at different field sizes to within ±1.5%. CONCLUSIONS: We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the S(c) factors for some clinical requirements. The modeling parameters n and μ can be used to predict the S(c) in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment. Public Library of Science 2022-01-06 /pmc/articles/PMC8735605/ /pubmed/34990461 http://dx.doi.org/10.1371/journal.pone.0261042 Text en © 2022 Li et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Li, Xiao-Jun Ye, Yan-Cheng Zhang, Yan-Shan Wu, Jia-Ming Empirical modeling of the percent depth dose for megavoltage photon beams |
title | Empirical modeling of the percent depth dose for megavoltage photon beams |
title_full | Empirical modeling of the percent depth dose for megavoltage photon beams |
title_fullStr | Empirical modeling of the percent depth dose for megavoltage photon beams |
title_full_unstemmed | Empirical modeling of the percent depth dose for megavoltage photon beams |
title_short | Empirical modeling of the percent depth dose for megavoltage photon beams |
title_sort | empirical modeling of the percent depth dose for megavoltage photon beams |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8735605/ https://www.ncbi.nlm.nih.gov/pubmed/34990461 http://dx.doi.org/10.1371/journal.pone.0261042 |
work_keys_str_mv | AT lixiaojun empiricalmodelingofthepercentdepthdoseformegavoltagephotonbeams AT yeyancheng empiricalmodelingofthepercentdepthdoseformegavoltagephotonbeams AT zhangyanshan empiricalmodelingofthepercentdepthdoseformegavoltagephotonbeams AT wujiaming empiricalmodelingofthepercentdepthdoseformegavoltagephotonbeams |