Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number
The work is devoted to studying the possibility of using a two-parametric model of an electron beam to describe the depth distributions of the electron dose in materials with a low density and an effective atomic number. In this model, the parameters are determined by fitting the semi-empirical mode...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2021
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nasplib_isofts_kiev_ua-123456789-1954642025-02-23T17:58:26Z Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number Двопараметрична модель пучка для дозиметрії процесу електронного опромінення матеріалів з низькою щільністю і атомним номером Двухпараметрическая модель пучка для дозиметрии процесса электронного облучения материалов с малыми плотностью и атомным номером Lazurik, V.T. Lazurik, V.M. Popov, G. Zimek, Z. Interaction of relativistic particles with crystals and matter The work is devoted to studying the possibility of using a two-parametric model of an electron beam to describe the depth distributions of the electron dose in materials with a low density and an effective atomic number. In this model, the parameters are determined by fitting the semi-empirical model (PFSEM-method) to the results of measurements of the depth-dose distribution in a dosimetric wedge. The depth-dose distributions in a birchwood wedge were measured at the Institute of Nuclear Chemistry and Technology in Warsaw, Poland. The parameters of the electron beam incident on the wedge were determined by the PFSEM method. The Monte Carlo simulations of the depth-dose distribution in the wedge for the process of electron irradiation, the characteristics of which are determined by the PFSEM method, have been carried out. It is shown that there is a satisfactory agreement between the measurement results and the Monte Carlo simulation of the depth-dose distribution. The advantages of describing depth-dose distributions in a wedge based on a two-parametric model of an electron beam in comparison with traditional methods of polynomial approximation of measurement results are discussed. Робота присвячена дослідженню можливості використання двопараметричної моделі електронного пучка для опису розподілу дози електронів по глибині в матеріалах з низькою щільністю і ефективним атомним номером. У цій моделі параметри визначаються шляхом підгонки напівемпіричної моделі (PFSEM-метод) до результатів вимірювань розподілу дози по глибині в дозиметричному клині. Розподіл дози по глибині в клині з березової деревини було виміряно в Інституті ядерної хімії та технологій в Варшаві, Польща. Параметри падаючого на клин електронного пучка визначалися методом PFSEM. Проведено моделювання методом Монте-Карло розподілу дози по глибині в клині для процесу електронного опромінення, характеристики якого визначені методом PFSEM. Показано, що існує згода між результатами вимірювань і моделюванням методом Монте-Карло розподілу дози по глибині. Обговорюються переваги опису розподілу дози по глибині в клині на основі двопараметричної моделі електронного пучка в порівнянні з традиційними методами поліноміальної апроксимації результатів вимірювань. Работа посвящена исследованию возможности использования двухпараметрической модели электронного пучка для описания распределения дозы электронов по глубине в материалах с низкой плотностью и эффективным атомным номером. В этой модели параметры определяются путем подгонки полуэмпирической модели (PFSEM-метод) к результатам измерений распределения дозы по глубине в дозиметрическом клине. Распределение дозы по глубине в клине из березовой древесины было измерено в Институте ядерной химии и технологий в Варшаве, Польша. Параметры падающего на клин электронного пучка определялись методом PFSEM. Проведено моделирование методом Монте-Карло распределения дозы по глубине в клине для процесса электронного облучения, характеристики которого определены методом PFSEM. Показано, что существует удовлетворительное согласие между результатами измерений и моделированием методом Монте-Карло распределения дозы по глубине. Обсуждаются преимущества описания распределения дозы по глубине в клине на основе двухпараметрической модели электронного пучка по сравнению с традиционными методами полиномиальной аппроксимации результатов измерений. 2021 Article Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number / V.T. Lazurik, V.M. Lazurik, G. Popov, Z. Zimek // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 34-37. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 87.53.Bn DOI: https://doi.org/10.46813/2021-136-034 https://nasplib.isofts.kiev.ua/handle/123456789/195464 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Interaction of relativistic particles with crystals and matter Interaction of relativistic particles with crystals and matter |
| spellingShingle |
Interaction of relativistic particles with crystals and matter Interaction of relativistic particles with crystals and matter Lazurik, V.T. Lazurik, V.M. Popov, G. Zimek, Z. Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number Вопросы атомной науки и техники |
| description |
The work is devoted to studying the possibility of using a two-parametric model of an electron beam to describe the depth distributions of the electron dose in materials with a low density and an effective atomic number. In this model, the parameters are determined by fitting the semi-empirical model (PFSEM-method) to the results of measurements of the depth-dose distribution in a dosimetric wedge. The depth-dose distributions in a birchwood wedge were measured at the Institute of Nuclear Chemistry and Technology in Warsaw, Poland. The parameters of the electron beam incident on the wedge were determined by the PFSEM method. The Monte Carlo simulations of the depth-dose distribution in the wedge for the process of electron irradiation, the characteristics of which are determined by the PFSEM method, have been carried out. It is shown that there is a satisfactory agreement between the measurement results and the Monte Carlo simulation of the depth-dose distribution. The advantages of describing depth-dose distributions in a wedge based on a two-parametric model of an electron beam in comparison with traditional methods of polynomial approximation of measurement results are discussed. |
| format |
Article |
| author |
Lazurik, V.T. Lazurik, V.M. Popov, G. Zimek, Z. |
| author_facet |
Lazurik, V.T. Lazurik, V.M. Popov, G. Zimek, Z. |
| author_sort |
Lazurik, V.T. |
| title |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| title_short |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| title_full |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| title_fullStr |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| title_full_unstemmed |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| title_sort |
two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2021 |
| topic_facet |
Interaction of relativistic particles with crystals and matter |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195464 |
| citation_txt |
Two-parametric beam model for dosimetry of the process of electron irradiation of materials with low density and atomic number / V.T. Lazurik, V.M. Lazurik, G. Popov, Z. Zimek // Problems of Atomic Science and Technology. — 2021. — № 6. — С. 34-37. — Бібліогр.: 11 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2021. № 6(136) 34
https://doi.org/10.46813/2021-136-034
TWO-PARAMETRIC BEAM MODEL FOR DOSIMETRY
OF THE PROCESS OF ELECTRON IRRADIATION OF MATERIALS
WITH LOW DENSITY AND ATOMIC NUMBER
V.T. Lazurik
1
, V.M. Lazurik
1
, G. Popov
1
, Z. Zimek
2
1
V.N. Karasin Kharkiv National University, Kharkov, Ukraine;
2
Institute of Nuclear Chemistry and Technology, Warsaw, Poland
E-mail: lazurik@hotmail.com
The work is devoted to studying the possibility of using a two-parametric model of an electron beam to describe
the depth distributions of the electron dose in materials with a low density and an effective atomic number. In this
model, the parameters are determined by fitting the semi-empirical model (PFSEM-method) to the results of meas-
urements of the depth-dose distribution in a dosimetric wedge. The depth-dose distributions in a birchwood wedge
were measured at the Institute of Nuclear Chemistry and Technology in Warsaw, Poland. The parameters of the
electron beam incident on the wedge were determined by the PFSEM method. The Monte Carlo simulations of the
depth-dose distribution in the wedge for the process of electron irradiation, the characteristics of which are deter-
mined by the PFSEM method, have been carried out. It is shown that there is a satisfactory agreement between the
measurement results and the Monte Carlo simulation of the depth-dose distribution. The advantages of describing
depth-dose distributions in a wedge based on a two-parametric model of an electron beam in comparison with tradi-
tional methods of polynomial approximation of measurement results are discussed.
PACS: 87.53.Bn
INTRODUCTION
The practical use of a dosimetric wedge in radiation
technologies is regulated by international standards,
which define the procedures for measuring the depth
distribution of the dose in the wedge, methods for pro-
cessing the measurements and interpreting the results of
processing measurements [1, 2]. The standards propose
to determine the most probable energy EP and the aver-
age energy EAv of electrons in the beam using the
dosimetric wedge method. These characteristics of elec-
trons in a beam are widely used to control the stability
of the electron radiation flux in radiation-technological
processes. However, the characteristics of electron radi-
ation obtained using a standard dosimetric wedge, in
some cases, are unsuitable for describing the spatial
distribution of the dose in irradiated objects. Indeed, the
spatial distribution of the dose substantially depends on
the density and the effective atomic number of the mate-
rials of the irradiated objects. As a rule, during radiation
sterilization of medical devices and foodstuffs, the den-
sity and effective atomic number of materials of irradi-
ated objects are several times lower than for aluminum,
on the basis of which a standard dosimetric wedge is
made. In addition, for materials with low density, the
spatial distribution of the dose in the irradiated objects
depends significantly on the angular distribution of elec-
trons in the beam. Therefore, for the further develop-
ment of radiation technologies, dosimetric wedges cre-
ated on the basis of materials with low density and ef-
fective atomic number are of interest.
A modern method for determining the characteristics
of electron radiation is based on measurements of the
depth distribution of the dose in a dosimetric wedge and
using the parametric fitting method of the semi-
empirical model (PFSEM method) [3 - 5]. This method
has proven itself well in radiation sterilization technolo-
gies in which aluminum dosimetric wedges are used [6 -
9]. In connection with the above, an urgent scientific
and practical task is to test the PFSEM method using the
results of measurements in dosimetric wedges created
from materials with low density and effective atomic
number.
Therefore, for the further development of radiation
technologies, dosimetric wedges created on the basis of
materials with low density and effective atomic number
are of interest, which was carried out at the radiation
sterilization line of the Institute of Nuclear Chemistry
and Technology in Warsaw, Poland [10]. The ad-
vantages of describing depth dose distributions in a
wedge on the basis of a semiempirical model with pa-
rameters calculated by the PFSEM method in compari-
son with traditional methods of polynomial approxima-
tion of measurement results are discussed.
1. DEPTH-DOSE CURVE OF ELECTRON
RADIATION IN A BIRCH WEDGE
Measurements of the depth-dose curve of electron
radiation were carried out using dosimetric films located
in a wedge made of birch wood. The characteristics of
the wedge are as follows:
- density of birch wood: 0.536 g/cm
3
;
- effective atomic number: 6.28;
- effective atomic weight: 11.86;
- dimensions: 12.546.545.5 cm;
- slope factor: 0.265.
The method of irradiation and processing of
dosimetric films is described in [6, 7].
The measurement results are shown in Fig. 1. The
dose value D(x) is normalized to the calculated dose
value D(0) on the wedge surface onto which the elec-
tron beam falls. The depth in the wedge X is indicated in
standard mass units of length [g/cm
2
]. The vertical
dashed lines indicate the boundaries of the depth regions
that are used in the radiation sterilization process. Mark
X1 indicates the depth range that is used for single-sided
irradiation and X2 for double-sided irradiation. For com-
mailto:lazurik@hotmail.com
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 35
parison, in Fig. 1 shows the depth-dose curve of elec-
trons in the birch wedge, calculated using a semi-
empirical model [5], the parameters of which were de-
termined by the PFSEM method.
X2
X1
0
0.5
1
1.5
0 1 2 3 4 5X, g/cm2
D(x)/D(0)
Fig. 1. Dose distribution by depth in a wedge of birch.
Points results of measurements, a continuous curve
approximation of measurements by the PFSEM method
When characterizing electron radiation by the
PFSEM method, the absolute values of the measured
dose are not used and, therefore, the method error is
determined only by the reproducibility of measurement.
Estimates of the reproducibility standard deviation of
measurements Δ were made on the basis of calculating
the standard deviation of the dose values measured on
the first D1(xi) and second D2(xi) dosimetry films, for
each of the recorded depths xi. For the areas of depths
defined by marks X1 and X2, the estimates of the root-
mean-square measurement errors are close and do not
exceed values of 2%. As seen from Fig. 1, the error in
approximating the measurement results using the
PFSEM method is comparable to the error in the meas-
urements
2. PROCESSING OF MEASUREMENT
RESULTS BY USING THE PARAMETRIC
FITTING METHOD OF THE SEMI-
EMPIRICAL MODEL
The processing of the results of dose measurements
on two dosimetric films by the PFSEM method was
carried out. For each of the films, using the PFSEM
method, the model parameters of the electron beam of
the radiation sterilization line, corresponding to the
measurement results, were calculated. Model parame-
ters of the electron beam calculated from the measure-
ment data for the first Ex1 and the second Ex2 films are
presented in Table. The line Av_Ex shows the model
parameters of the electron beam obtained for the aver-
aged data from these two measurements.
The results of fitting the parameters
of the semi-empirical model of the depth distribution
of the dose of electron beam to the measurement results
E1
[MeV]
E0
[MeV]
X0
[g/cm
2
]
Ex1 8.67 8.71 0.016
Ex2 8.7 8.82 0.056
Av_Ex 8.69 8.77 0.037
As can be seen from Table and Fig. 1, the model pa-
rameter of the displacement X0 is small in comparison
with the depths and the use of dose distributions in radi-
ation technologies. This indicates the correct choice of
the starting point when processing the depth distribution
of the dose on the films. Note, that there is a small dif-
ference in the model energy parameters for the one-
parameter fit E1 and two-parameter fit E0 of the data
obtained in these two measurements.
The test results of the PFSEM method are illustrated
in Fig. 2. In the figure, the dots show the values of the
dose distribution averaged over two measurements. The
solid curve is an approximation of the averaged values
of the dose distribution using the PFSEM method and
computer visualization of the semi-empirical model of
the depth distribution of the absorbed energy of an elec-
tron beam in matter [5]. Histogram calculation using
the ModeRTL software module of the RT-Office system
[11] in accordance with the values of the characteristics
of electron radiation E0 = 8.77 and X0 = 0.037 deter-
mined by the PFSEM method (see Table 1) within the
framework of the two-parameter model of the electron
beam [7].
X1
X2
0
0.5
1
1.5
0 1 2 3 4 5X, g/cm2
D(x)/D(0)
Fig. 2. Comparison of measurement and calculation
results using the PFSEM method. Points average
depth distribution of the dose over two measurement
results, a continuous curve approximation of meas-
urements by the PFSEM method, histogram calcula-
tion using ModeRTL module of the RT-Office system
As seen in Fig. 2 satisfactory agreement:
- between the measurement values and the calcula-
tion results, using a computer visualization of a semi-
empirical model [5] of the depth dose distribution in a
wedge of birch wood irradiated with an electron beam,
the parameters of which were determined by the
PFSEM method;
- between the measurement values and the calcula-
tion results, using Monte Carlo simulation [11] of the
depth dose distribution in a wedge of birch wood irradi-
ated with an electron beam, the parameters of which
were determined by the PFSEM method.
3. POLYNOMIAL APPROXIMATION
OF MEASUREMENT RESULTS
A numerical study of the possibilities of determining
the dependences of the depth dose distribution on the
basis of traditional methods of polynomial approxima-
tion of the measurement results was carried out. Some
ISSN 1562-6016. ВАНТ. 2021. № 6(136) 36
results of the numerical study of the polynomial approx-
imation of measurements of the depth distributions of
the electron radiation dose in a wedge made of birch
wood are shown in Figs. 3 and 4.
As can be find in Fig. 3 the dashed curve is the ap-
proximation by a polynomial of the 2nd degree, the
dashed-dotted curve is the approximation by the poly-
nomial of the 3rd degree and the dashed curve is the
approximation by the polynomial of the 4th degree. Sol-
id curve according approximation by the PFSEM meth-
od.
X1
X2
0
0.5
1
1.5
0 1 2 3 4 5X, g/cm
2
D(x)/D(0)
Fig. 3. Comparison of approximations of measurement
results by polynomials of different degrees
X1
X2
y2 (x)= -0.0734x
3
+ 0.2863x
2
- 0.1217x + 1.1047
R
2
= 0.9869
y1 (x)= -0.0605x
3
+ 0.2249x
2
- 0.0444x + 1.0835
R
2
= 0.9675
0
0.5
1
1.5
0 1 2 3 4 5X, g/cm2
D(x)/D(0)
Fig. 4. Comparison of approximations of measurement
results by degree 3 polynomials and using the PFSEM
method. Points measurement results, continuous
curves approximation by polynomials of degree 3,
a dashed curve approximation of measurements
by the PFSEM method
According to that:
- the results of measurements of dose distributions in
the depth ranges (0-X1) and (0-X2) cannot be approxi-
mated by polynomials below the 3rd degree with an
accuracy comparable to the accuracy of the measure-
ments;
- polynomial approximation of measurement results
cannot provide correct extrapolation to determine the
dose value on the wedge surface, on which the electron
beam falls.
CONCLUSIONS
Comparison of the depth dose distributions obtained
as a result of measurements and calculations based on
the parameters of the electron beam determined by the
using the parametric fitting method of the semi-
empirical modelallows us to draw the following conclu-
sions:
- the error in approximating the results of measure-
ments of the depth dose distribution in a birch wood
dosimetric wedge, made by the PFSEM method, is
comparable to the error in the measurements;
- there is satisfactory agreement between the results
of measurements and Monte Carlo calculation of the
depth distribution of the dose of electron radiation, the
characteristics of which were determined by the PFSEM
method;
- in the depth ranges of practical interest, approxima-
tion of the results of measurements of the depth distri-
bution of the dose by polynomials above the 3rd degree
allows us to describe the depth distribution of the dose
with an accuracy comparable to the accuracy of the
measurements;
- the approximation of the results of measurements
of the depth dose distribution performed by the PFSEM
method coincides with the accuracy comparable with
the accuracy of the polynomial approximation of these
measurement results.
Thus, the using the parametric fitting method of the
semi-empirical model allows one to satisfactorily de-
scribe the results of measurements of depth dose distri-
butions using only two characteristics of the electron
beam, in contrast to the polynomial approximation for
which at least four formal parameters are required.
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Energies between 300 keV and 25 MeV, Annual
Book of ASTM Standards. 2005, v. 12.02.
2. Radiation Dosimetry: Electron Beams with Energies
between 1 and 50 MeV, International Commission
on Radiation Units and Measurements. 1984, report
35, Bethesda, MD, USA.
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dose distribution of irradiation, Journal of Kharkiv
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Article received 12.10.2021
ДВУХПАРАМЕТРИЧЕСКАЯ МОДЕЛЬ ПУЧКА ДЛЯ ДОЗИМЕТРИИ ПРОЦЕССА
ЭЛЕКТРОННОГО ОБЛУЧЕНИЯ МАТЕРИАЛОВ С МАЛЫМИ ПЛОТНОСТЬЮ
И АТОМНЫМ НОМЕРОМ
В.Т. Лазурик., В.М. Лазурик, Г. Попов, З. Зимек
Работа посвящена исследованию возможности использования двухпараметрической модели электронно-
го пучка для описания распределения дозы электронов по глубине в материалах с низкой плотностью и
эффективным атомным номером. В этой модели параметры определяются путем подгонки полуэмпириче-
ской модели (PFSEM-метод) к результатам измерений распределения дозы по глубине в дозиметрическом
клине. Распределение дозы по глубине в клине из березовой древесины было измерено в Институте ядерной
химии и технологий в Варшаве, Польша. Параметры падающего на клин электронного пучка определялись
методом PFSEM. Проведено моделирование методом Монте-Карло распределения дозы по глубине в клине
для процесса электронного облучения, характеристики которого определены методом PFSEM. Показано, что
существует удовлетворительное согласие между результатами измерений и моделированием методом Мон-
те-Карло распределения дозы по глубине. Обсуждаются преимущества описания распределения дозы по
глубине в клине на основе двухпараметрической модели электронного пучка по сравнению с традиционны-
ми методами полиномиальной аппроксимации результатов измерений.
ДВОПАРАМЕТРИЧНА МОДЕЛЬ ПУЧКА ДЛЯ ДОЗИМЕТРІЇ ПРОЦЕСУ ЕЛЕКТРОННОГО
ОПРОМІНЕННЯ МАТЕРІАЛІВ З НИЗЬКИМИ ЩІЛЬНІСТЮ І АТОМНИМ НОМЕРОМ
В.Т. Лазурик, В.М. Лазурик, Г. Попов, З. Зимек
Робота присвячена дослідженню можливості використання двопараметричної моделі електронного пучка
для опису розподілу дози електронів по глибині в матеріалах з низькою щільністю і ефективним атомним
номером. У цій моделі параметри визначаються шляхом підгонки напівемпіричної моделі (PFSEM-метод) до
результатів вимірювань розподілу дози по глибині в дозиметричному клині. Розподіл дози по глибині в кли-
ні з березової деревини було виміряно в Інституті ядерної хімії та технологій в Варшаві, Польща. Параметри
падаючого на клин електронного пучка визначалися методом PFSEM. Проведено моделювання методом
Монте-Карло розподілу дози по глибині в клині для процесу електронного опромінення, характеристики
якого визначені методом PFSEM. Показано, що існує згода між результатами вимірювань і моделюванням
методом Монте-Карло розподілу дози по глибині. Обговорюються переваги опису розподілу дози по глиби-
ні в клині на основі двопараметричної моделі електронного пучка в порівнянні з традиційними методами
полиномиальной апроксимації результатів вимірювань.
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