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The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy

INTRODUCTION: This study presents an empirical method to model the curve of electron beam percent depth dose (PDD) by using the primary-tail function in electron beam radiation therapy. The modeling parameters N and n can be used to predict the minimal side length when the field size is reduced belo...

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Autores principales: Ma, You-Guo, Zhang, Yan-Shan, Ye, Yan-Cheng, Wu, Jia-Ming
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8519681/
https://www.ncbi.nlm.nih.gov/pubmed/34660785
http://dx.doi.org/10.1155/2021/3397350
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author Ma, You-Guo
Zhang, Yan-Shan
Ye, Yan-Cheng
Wu, Jia-Ming
author_facet Ma, You-Guo
Zhang, Yan-Shan
Ye, Yan-Cheng
Wu, Jia-Ming
author_sort Ma, You-Guo
collection PubMed
description INTRODUCTION: This study presents an empirical method to model the curve of electron beam percent depth dose (PDD) by using the primary-tail function in electron beam radiation therapy. The modeling parameters N and n can be used to predict the minimal side length when the field size is reduced below that required for lateral scatter equilibrium (LSE) in electron radiation therapy. METHODS AND MATERIALS: The electrons' PDD curves were modeled by the primary-tail function in this study. The primary function included the exponential function and the main parameters of N and μ, while the tail function was composed of a sigmoid function with the main parameter of n. The PDD of five electron energies was modeled by the primary and tail function by adjusting the parameters of N, μ, and n. The R(50) and R(p) can be derived from the modeled straight line of 80% to 20% region of PDD. The same electron energy with different cone sizes was also modeled by the primary-tail function. The stopping power of different electron energies in different depths can also be derived from the parameters N, μ, and n. RESULTS: The main parameters N and n increase but μ decreases in the primary-tail function for characterizing the electron beam PDD when the electron energy increased. The relationship of parameter n, N, and ln(−μ) with electron energy are n = 31.667E(0) − 88, N = 0.9975E(0) − 2.8535, and ln(−μ) = −0.1355E(0) − 6.0986, respectively. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at a certain electron energy. The stopping power of different electron energies can be derived from n and N with the following equation: stopping power = (−0.042ln(N(E(0))) + 1.072)e((−n(E(0)) · 5 · 10(−5) + 0.0381)·x), where x is the depth in water. The lateral scatter equivalence (LSE) of the clinical electron beam can be described by the parameters E(0), n, and N in the equation of S(eq) = (n(E(0)) − N(E(0)))(0.288)/(E(0)/n(E(0)))(0.0195). The LSE was compared with the root mean square scatter angular distribution method and shows the agreement of depth dose distributions within ±2%. CONCLUSIONS: The PDD of the electron beam at different energies and cone sizes can be modeled with an empirical model to deal with what is the minimal field size without changing the percent depth dose when approximate LSE is given in centimeters of water.
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spelling pubmed-85196812021-10-16 The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy Ma, You-Guo Zhang, Yan-Shan Ye, Yan-Cheng Wu, Jia-Ming Biomed Res Int Research Article INTRODUCTION: This study presents an empirical method to model the curve of electron beam percent depth dose (PDD) by using the primary-tail function in electron beam radiation therapy. The modeling parameters N and n can be used to predict the minimal side length when the field size is reduced below that required for lateral scatter equilibrium (LSE) in electron radiation therapy. METHODS AND MATERIALS: The electrons' PDD curves were modeled by the primary-tail function in this study. The primary function included the exponential function and the main parameters of N and μ, while the tail function was composed of a sigmoid function with the main parameter of n. The PDD of five electron energies was modeled by the primary and tail function by adjusting the parameters of N, μ, and n. The R(50) and R(p) can be derived from the modeled straight line of 80% to 20% region of PDD. The same electron energy with different cone sizes was also modeled by the primary-tail function. The stopping power of different electron energies in different depths can also be derived from the parameters N, μ, and n. RESULTS: The main parameters N and n increase but μ decreases in the primary-tail function for characterizing the electron beam PDD when the electron energy increased. The relationship of parameter n, N, and ln(−μ) with electron energy are n = 31.667E(0) − 88, N = 0.9975E(0) − 2.8535, and ln(−μ) = −0.1355E(0) − 6.0986, respectively. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at a certain electron energy. The stopping power of different electron energies can be derived from n and N with the following equation: stopping power = (−0.042ln(N(E(0))) + 1.072)e((−n(E(0)) · 5 · 10(−5) + 0.0381)·x), where x is the depth in water. The lateral scatter equivalence (LSE) of the clinical electron beam can be described by the parameters E(0), n, and N in the equation of S(eq) = (n(E(0)) − N(E(0)))(0.288)/(E(0)/n(E(0)))(0.0195). The LSE was compared with the root mean square scatter angular distribution method and shows the agreement of depth dose distributions within ±2%. CONCLUSIONS: The PDD of the electron beam at different energies and cone sizes can be modeled with an empirical model to deal with what is the minimal field size without changing the percent depth dose when approximate LSE is given in centimeters of water. Hindawi 2021-10-08 /pmc/articles/PMC8519681/ /pubmed/34660785 http://dx.doi.org/10.1155/2021/3397350 Text en Copyright © 2021 You-Guo Ma et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Ma, You-Guo
Zhang, Yan-Shan
Ye, Yan-Cheng
Wu, Jia-Ming
The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title_full The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title_fullStr The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title_full_unstemmed The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title_short The Study of Field Equivalence Determined by the Modeled Percentage Depth Dose in Electron Beam Radiation Therapy
title_sort study of field equivalence determined by the modeled percentage depth dose in electron beam radiation therapy
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8519681/
https://www.ncbi.nlm.nih.gov/pubmed/34660785
http://dx.doi.org/10.1155/2021/3397350
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