Dosimetry method based on a two-parametric model of electrons beam for radiation processing
The work is devoted to development of electron dosimetry methods for radiation technologies. In authors previous work it was shown that use of two parametric models of electron beam makes it possible to correctly approximate the measurements results of depth dose distributions. In this paper, we des...
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nasplib_isofts_kiev_ua-123456789-1361812025-02-10T00:21:45Z Dosimetry method based on a two-parametric model of electrons beam for radiation processing Метод дозиметрії на основі двопараметричної моделі електронного пучка для радіаційних технологій Метод дозиметрии на основе двухпараметрической модели электронного пучка для радиационных технологий Lazurik, V.T. Lazurik, V.M. Popov, G.Ph. Zimek, Z. Применение ядерных методов The work is devoted to development of electron dosimetry methods for radiation technologies. In authors previous work it was shown that use of two parametric models of electron beam makes it possible to correctly approximate the measurements results of depth dose distributions. In this paper, we describe the method of electron radiation based on a two-parameter electron beam model and basic semiempirical relations of this method. Approbation of proposed methods of radiation dosimetry based on measurements was performed in the sterilization center of the Institute of Nuclear Chemistry and Technology, Warsaw, Poland. Робота присвячена розробці методів дозиметрії електронів для радіаційних технологій. У попередній роботі авторів показано, що використання двопараметричних моделей електронного пучка дозволяє правильно аппроксимірувати результати вимірів розподілів глибинних доз. В даній роботі описується метод електронного випромінювання на основі двопараметричної моделі електронного пучка та основних напівемпіричних співвідношень цього методу. Проведена апробація запропонованих методів дозиметрії електронного випромінювання на основі вимірювань, проведених у центрі стерилізації Інституту ядерної хімії та технологій, Варшава, Польща. Работа посвящена разработке методов дозиметрии электронов для радиационных технологий. В предыдущей работе авторов показано, что использование двухпараметрических моделей электронного пучка позволяет правильно аппроксимировать результаты измерений распределений глубинных доз. В настоящей работе описывается метод электронного излучения на основе двухпараметрической модели электронного пучка и основных полуэмпирических соотношений этого метода. Проведена апробация предложенных методов дозиметрии электронного излучения на основании измерений, проведенных в центре стерилизации Института Ядерной Химии и Технологий, Варшава, Польша. 2017 Article Dosimetry method based on a two-parametric model of electrons beam for radiation processing / V.T. Lazurik, V.M. Lazurik, G.Ph. Popov, Z. Zimek // Вопросы атомной науки и техники. — 2017. — № 6. — С. 137-141. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 61.80.Сb https://nasplib.isofts.kiev.ua/handle/123456789/136181 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Применение ядерных методов Применение ядерных методов |
| spellingShingle |
Применение ядерных методов Применение ядерных методов Lazurik, V.T. Lazurik, V.M. Popov, G.Ph. Zimek, Z. Dosimetry method based on a two-parametric model of electrons beam for radiation processing Вопросы атомной науки и техники |
| description |
The work is devoted to development of electron dosimetry methods for radiation technologies. In authors previous work it was shown that use of two parametric models of electron beam makes it possible to correctly approximate the measurements results of depth dose distributions. In this paper, we describe the method of electron radiation based on a two-parameter electron beam model and basic semiempirical relations of this method. Approbation of proposed methods of radiation dosimetry based on measurements was performed in the sterilization center of the Institute of Nuclear Chemistry and Technology, Warsaw, Poland. |
| format |
Article |
| author |
Lazurik, V.T. Lazurik, V.M. Popov, G.Ph. Zimek, Z. |
| author_facet |
Lazurik, V.T. Lazurik, V.M. Popov, G.Ph. Zimek, Z. |
| author_sort |
Lazurik, V.T. |
| title |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| title_short |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| title_full |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| title_fullStr |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| title_full_unstemmed |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| title_sort |
dosimetry method based on a two-parametric model of electrons beam for radiation processing |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2017 |
| topic_facet |
Применение ядерных методов |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/136181 |
| citation_txt |
Dosimetry method based on a two-parametric model of electrons beam for radiation processing / V.T. Lazurik, V.M. Lazurik, G.Ph. Popov, Z. Zimek // Вопросы атомной науки и техники. — 2017. — № 6. — С. 137-141. — Бібліогр.: 9 назв. — англ. |
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Вопросы атомной науки и техники |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2017. №6(112) 137
DOSIMETRY METHOD BASED ON A TWO-PARAMETRIC MODEL
OF ELECTRONS BEAM FOR RADIATION PROCESSING
V.T. Lazurik
1
, V.M. Lazurik
1
, G.Ph. 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: popov_gen@yahoo.com
The work is devoted to development of electron dosimetry methods for radiation technologies. In authors previ-
ous work it was shown that use of two parametric models of electron beam makes it possible to correctly approxi-
mate the measurements results of depth dose distributions. In this paper, we describe the method of electron radia-
tion based on a two-parameter electron beam model and basic semiempirical relations of this method. Approbation
of proposed methods of radiation dosimetry based on measurements was performed in the sterilization center of the
Institute of Nuclear Chemistry and Technology, Warsaw, Poland.
PACS: 61.80.Сb
INTRODUCTION
One of the problems of electron radiation dosimetry
in radiation technologies is determination of electrons
energy in the process of radiation treatment. The prob-
lem is that when implementing optimal irradiation re-
gimes, it is necessary to control the electron energy with
high accuracy. In international standards [1, 2], formal
procedures for monitoring the electrons energy in pro-
cess irradiation are determined on basis of use a dosi-
metric wedge or stack. However, when performing the-
se procedures, it is necessary to obtain solutions incor-
rect mathematical problems. Quasi-solutions of these
tasks are obtained by approximating results of meas-
urements using various mathematical methods and types
of functions [3, 4].
In the authors papers [5, 6] it was showen that two-
parameters model of electron beam makes it possible
correctly approximate the results of measurements of
depth dose distributions obtained with use of dosimetric
wedge or stack.
Therefore, it is of interest of relations, connecting
parameters (E0, X0) of the electron beam model with
standard characteristics (EP, EAv) of electrons radiation
energy. Since these relationships will allow us to realize
the computer dosimetry method, that does not contain
errors in traditionally used empirical formulas, which
are given, for example, in the standard [2].
1. METHODS OF PROCESSING
MEASUREMENTS
1.1. RESULTS OF MEASUREMENTS
The results of measurements of depth dose distribu-
tion performed using an aluminum dosimetric wedge
from RISO [4] are shown in Fig. 1. The results of meas-
urements are a set of discrete data ),( ii Dl , where il is
distance from a certain initial point of reference (marked
by a marker) to first point i of dose measurement iD on
the dosimetric film. In this dataset, you should select
four areas, which are separated in the Fig. 1 by vertical
dashed curves.
The results of measurements of depth dose distribu-
tion, performed using an aluminum dosimetric wedge
from RISO [4], are shown in Fig. 1. The measurement
results are a set of discrete data, where is the distance
from a certain initial point of reference (marked by a
marker) to the dots of the dose measurement point on
the dosimetric film. In this data set, four areas should be
selected, which are separated in the Fig. 1 by vertical
dashed curves.
The measurement results are a set of discrete data
),( ii Dl , where il is the distance from a certain initial
point of reference (marked by a marker) to i dots of
the dose measurement point
iD on the dosimetric film.
In this data set, four areas should be selected, which are
separated in Fig. 1 by vertical dashed curves.
21 3 4
0
10
20
30
40
-2 0 2 4 6 Length, cm.
Dose, KGy
Fig. 1. Results of measurements performed
by the method of dosimetric wedge
Area 1 the dose value in dosimetric film located
on entrance surface of dosimetric wedge.
Area 2 the results of measurements in area where
dosimetric film enters into dosimetric wedge. The area
contains a marker a point at which dose value is sub-
stantially larger than in neighboring ones. Data in this
area are distorted by design of device and application of
a marker on film.
Area 3 the results of measurements of electron ra-
diation dose iD , depending on spatial position of
measurement point in dosimetric wedge.
Area 4 the dose values in dosimetric film, located
on exit surface of dosimetric wedge. The data can sig-
nificantly depend on design elements, on which the do-
simetric wedge is located.
mailto:popov_gen@yahoo.com
ISSN 1562-6016. ВАНТ. 2017. №6(112) 138
1.2. STANDARD PROCESSING
OF MEASUREMENT RESULTS
In the first stage, characteristics of depth dose distri-
bution of electron dose, such as practical range of elec-
trons Rp and depth of half the maximum dose reduction
R50, were determined. To do this, it was determine the
maximum value of dose distribution Dmax based on the
least-squares fit using a polynomial of third degree. The
data, chosen for approximation, are marked in Fig. 2 by
filled triangular markers.
y = -16.726x + 99.331
R2 = 0.9965
y = 0.0762x3 - 3.9615x2 + 16.651x + 29.048
Rp
0
10
20
30
40
0 2 4 6Length, cm.
Dose, kGy
Fig. 2. Standard procedures for processing the depth
dose distribution of electron radiation, measured
with dosimetric wedge method
To determine value of the practical range of elec-
trons Rp, it was selected data on decline of depth dose
distribution, where a dose-to-depth curve is observed
that is close to linear. In practice, a range of dose values
from 0.8 to 0.2 of maximum dose value Dmax is used.
The data on decline in depth dose distribution are cho-
sen to determine the practical range of electrons Rp, are
marked in Fig. 2 by filled triangular markers.
The value of practical range of electrons Rp is de-
termined based on approximation of selected data using
a linear function as shown in Fig. 2. The third-degree
polynomial and linear function, which approximate the
measurement results are shown in Fig. 2.
The depth of half-reduction of maximum dose value
R50, is calculated from value of the maximum dose dis-
tribution Dmax based on linear function, that is used to
determine value of Rp.
In the second stage, empirical formulas connecting
characteristics of depth dose distribution (Rp, R50,) with
characteristics of electron energy are used to determine
characteristics of the electron energy, such as most
probable energy EP and average energy EAv of the elec-
trons source [1]. According to standard [2], empirical
formulas for values of EP, EAv (expressed in MeV) and
Rp, R50 (expressed in centimeters in an aluminum target)
are the following:
Ep =0.423+ 4.69* Rp +0.0532* R
2
p,
EAv =0.734+5.78* R50+0.0504* R
2
50. (1)
1.3. MEASUREMENT PROCESSING IN TWO-
PARAMETER ELECTRON BEAM MODEL
A parametric adjustment of the semiempirical elec-
tron energy absorption model (PFSEM method [7]) to
measurements of depth dose distribution of electron
radiation performed by the dosimeter wedge method.
Solid curve shown in Fig. 3 calculation according to the
semiempirical model of electron energy absorption [8, 9].
X0
0
10
20
30
40
-1 0 1 2 3 4 5 6 Length
Dose
Fig. 3. Parametric adjustment of semi-empirical model
to measurements the depth dose distribution
of electron radiation
Model parameters are as follows: electron energy
E0 = 9.37 MeV, displacement of dose distribution in the
film, X0 = 0.8 cm. The dose distribution characteristics
(Rp, R50) are connected to parameters of electron beam
model (E0, X0)) with the following relations [6]:
R
*
p (E0) = Rp + X0, (2)
R
*
50 (E0) = R50 + X0, (3)
where R
*
p (E0) means practical penetration range and
R
*
50 (E0) range for which the deposited dose is twice
smaller than the max value for electron energy level
marked as E0. Those parameters must be calculated on
the base of semi-empirical model for depth dose distri-
bution of mono-energetic electron beam.
Linear approximation of calculated data leads to
formulas for R
*
p (E) and R
*
50 (E) as electron energy
function:
R
*
p (E) = 0.2092* E -0.0687, (4)
R
*
50 (E) = 0.1691* E -0.0965. (5)
From the above relations (2) - (5) it follows that:
Rp=0.2092* E0 -0.0687- X0 * Kw, (6)
R50=0.1691* E0 -0.0965- X0 * Kw, (7)
here X0 displacement of depth dose distribution rela-
tive to position of marker on the film. Kw ratio of film
distance to depth in dosimeter wedge substance. For
standard aluminum dosimetric wedge, this ratio is
Kw =0.28 [4].
In this method, determination of the energy charac-
teristics of source electrons, such as EP and EAv, can be
performed in accordance with second stage of standard
measurement processing.
Empirical formulas, presented in the reports and
standards, do not have descriptions of methods for pro-
cessing depth dose distributions on basis of which these
formulas were obtained. Therefore, an estimation of
accuracy of the electron radiation dosimetry performed
on basis of standard methods of processing measure-
ments is not possible.
In this connection, it is of interest, within the frame-
work of a two-parameter electron beam model, to derive
relationships for calculating characteristics of the elec-
tron energy of a source directly from parameters of elec-
tron beam model: E0 and X0.
ISSN 1562-6016. ВАНТ. 2017. №6(112) 139
To obtain the relations, we take into account the fol-
lowing:
- empirical relations R
*
p (E) and R
*
50 (E) (see (2) and
(3)), are the dependences of practical range of electrons
Rp and the depth of a half dose reduction R50 on energy
E for a monoenergetic electron beam;
- the empirical dependencies of most probable ener-
gy EP(Rp) and average energy EAv(R50) of the source
electrons on the values of Rp and R50 (see (1)) are ob-
tained on basis of the depth dose distribution of mo-
noenergetic electron beams;
- in case of monoenergetic beams, values EP and EAv
are equal to electron energy Е.
It follows from above facts, that in case when two-
parameter electron beam model satisfactorily describes
the depth dose distribution, functions EP(Rp) and
EAv(R50) can be assumed to be inverse functions to R
*
p
(E) and R
*
50 (E), respectively.
On the basis of this assumption, from relations (6) -
(7) we obtain:
Ep(E0,X0) = E0 - Kw*X0 /0.2092, (8)
EAv(E0,X0) = E0 - Kw*X0 /0.1691. (9)
Table shows the calculation results, which were per-
formed by the standard method (column M0), using
two-parameter electron beam model, using the values of
Rp,, and R50 (column M1) and by direct calculation using
parameters E0 and X0 of the model electron beam (col-
umn M2)). Calculations of values of Ep and EAv are per-
formed on basis of measurement results shown in Fig. 1.
The values of most probable energy Ep and average
energy EAv of electrons, calculated using various
computational methods
Electrons energy M0 M1 M2
EP, MeV 8.37 8.40 8.30
EAv, MeV
8.15 8.10 8.05
As can be seen from comparison of presented data,
results calculations of standard energy characteristics of
the electron source have a small spread of values (less
than 1%) and are in good agreement with each other.
2. MODIFIED METHOD OF ELECTRON
RADIATION DOSIMETRY
The methods of processing the measurement results
considered in previous sections are essentially based on
fact, that boundary of dosimetric device, as point of the
depth dose distribution, is strictly defined on dosimetric
film. However, when measuring by the dosimeter
wedge method, this point is located in area 2 (see
Fig. 1), where the data can be significantly distorted due
to construction heterogeneity and the marker application
on the film. In this connection, it is of interest to refine
the point coordinate, which corresponds to the boundary
of dosimetric device.
The procedure for specifying coordinate of dosimet-
ric device boundary was developed on the basis of a
two-parameter model of electron beam. According to
this model, the depth dose distribution D(E0, X0 + x)
well approximates the measurement results in the data
area 3, presented in Fig. 1.
At the border of dosimetric device, dose value
should be equal to dose value on surface of device DB,,
i.e. coincide with average value of the dose in region 1
(see Fig. 1). This condition can be represented as an
equation and allows you to determine the XB coordinate
of the device boundary.
DB = D(E0, X0 + XB). (10)
The procedure for specifying coordinate of dosimet-
ric device boundary is illustrated in Fig. 4.
Triangular markers marked the measurement results,
which are used to parametrically fit the semi-empirical
model. The solid curve is the depth dose distribution
D(E0, X0 + x) calculated in a semiempirical model. The
horizontal dashed curve is the dose value on the surface
of the DB device.
As can be seen from Fig. 4, position XB, determined
according to described procedure, can significantly dif-
fer from marker point, whose position is shown by a
vertical dashed curve. Calculation of the most probable
energy Ep and the average energy EAv of the source elec-
trons relative to boundary of dosimetric device XB can
be performed using equations (8) and (9) according to
the expressions:
Ep = Ep(E0, X0 + XB), (11)
EAv = EAv(E0, X0 + XB). (12)
From the formulas (11) and (12) we obtain EP =
8.64 MeV and EAv = 8.46 MeV. Comparison of these
values with given in the Table shows, that change in
values of electron energy characteristics, due to refine-
ment of the dosimeter device boundary, significantly
exceeds differences in results of calculations, obtained
using various methods of processing measurements (see
Table).
XB
0
10
20
30
40
-1 1 3 5 Length
Dose
Fig. 4. Modified method for processing the depth dose
distribution of electron radiation, measured using
a standard dosimeter wedge
The described procedure for processing measure-
ments and presented relations (8) - (12) allow us to cal-
culate characteristics of the electron energy source, tak-
ing into account refined coordinate of dosimeter wedge
boundary.
When determining the coordinate of boundary of a
dosimetry device, using modified method of processing
the measurements, the value of XB is significantly de-
pendent on the dose value on surface of device DB.
It is well known, that results of dose measurements
at the interfaces of dissimilar media can contain signifi-
cant errors due to the boundary effects that arise when
ionizing radiation passes through heterogeneous struc-
tures.
ISSN 1562-6016. ВАНТ. 2017. №6(112) 140
In this regard, one of the significant sources of error
a modified method for processing measurements is de-
termination of the dose value at boundaries of a dosi-
metric device.
To eliminate this component of error in method of
dosimetry of electron radiation, it is proposed a modifi-
cation of a dosimeter device design in which an alumi-
num plate is placed in front of a wedge. The plate
should provide a balance of secondary electron radiation
at boundary between plate and construction of the do-
simeter wedge, which eliminates "boundary effects"
when measuring dose values at this boundary.
To test proposed method of dosimetry, measurements
of depth dose distribution were performed using the mod-
ified design of dosimetric device. A standard dosimetric
wedge was used for measurements [4] on which a 2 mm
aluminum plate was placed. A standard dosimetric PVC
film was placed in the dosimetric wedge at interface be-
tween plate and wedge. The measurement results are
represented by triangular markers in Fig. 5.
For processing with PFSEM method, it was selected
measurement results marked with filled triangular mark-
ers. The solid curves depth dose distributions calculated
in a semi-empirical model on the basis of parameters ob-
tained by the PFSEM method. Horizontal dotted curves
the doses values on surface of dosimetric wedge.
21
0
10
20
30
40
50
-2 0 2 4 6Length, cm
Dose, kGy
Fig. 5. Processing of depth dose distributions
of electron radiation, measured with a modified
dosimetric device
The vertical solid straight line 2 border of dosimet-
ric wedge Xw, which is determined according to equa-
tion (10) on basis of dose values on the dosimeter
wedge surface. Vertical solid straight line 1 border of
modified structure of dosimeter XB. Coordinates of this
boundary are shifted on plate thickness h and calculated
from relation XB = Xw + h.
Calculation of most probable energy Ep and average
energy EAv of the source electrons relative to boundary
of modified structure of dosimetric device XB can be
performed according to expressions (11) and (12).
Comparison of calculation results of most probable
energy Ep and average energy EAv of the source elec-
trons relative to XB boundary of standard dosimetric
wedge and modified dosimetric device allows us to con-
clude, that dosimetry methods based on two-parameter
electron beam model provide determination the standard
energy characteristics of electron radiation with an un-
certainty not exceeding 2%.
CONCLUSIONS
It was obtained relations, that binding model param-
eters of the electron beam model directly to the standard
electron energy characteristics. This makes it possible to
use the dosimetry method on basis of two-parameter
electron beam model without calculation stage using
standard empirical formulas, that reduces errors of do-
simetry method.
It was performed procedure for processing meas-
urements on the basis of a two-parameter electron beam
model, and obtained relationships, which allow us to
calculate the characteristics of electron energy of the
source with allowance for the refined coordinate of do-
simetric wedge boundary.
It was proposed modification of the dosimetric
wedge construction, in which the equilibrium of the
secondary electron radiation at the boundary of the do-
simeter wedge is ensured, which eliminates "boundary
effects" at measuring the dose value.
It was presented relations that make it possible to
calculate characteristics the energy of electrons source
on basis of processing the measurements results per-
formed using modified construction of the dosimetric
wedge.
It was carried out approbation of the proposed meth-
ods of electron radiation dosimetry on the basis of
measurements, performed in the sterilization center of
Institute of Nuclear Chemistry and Technology, War-
saw, Poland.
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Article received 11.10.2017
ISSN 1562-6016. ВАНТ. 2017. №6(112) 141
МЕТОД ДОЗИМЕТРИИ НА ОСНОВЕ ДВУХПАРАМЕТРИЧЕСКОЙ МОДЕЛИ ЭЛЕКТРОННОГО
ПУЧКА ДЛЯ РАДИАЦИОННЫХ ТЕХНОЛОГИЙ
В.Т. Лазурик, В.М. Лазурик, Г.Ф. Попов, З. Зимек
Работа посвящена разработке методов дозиметрии электронов для радиационных технологий. В преды-
дущей работе авторов показано, что использование двухпараметрических моделей электронного пучка поз-
воляет правильно аппроксимировать результаты измерений распределений глубинных доз. В настоящей
работе описывается метод электронного излучения на основе двухпараметрической модели электронного
пучка и основных полуэмпирических соотношений этого метода. Проведена апробация предложенных ме-
тодов дозиметрии электронного излучения на основании измерений, проведенных в центре стерилизации
Института Ядерной Химии и Технологий, Варшава, Польша.
МЕТОД ДОЗИМЕТРІЇ НА ОСНОВІ ДВОПАРАМЕТРИЧНОЇ МОДЕЛІ ЕЛЕКТРОННОГО ПУЧКА
ДЛЯ РАДІАЦІЙНИХ ТЕХНОЛОГІЙ
В.Т. Лазурик, В.М. Лазурик, Г.Ф. Попов, З. Зімек
Робота присвячена розробці методів дозиметрії електронів для радіаційних технологій. У попередній ро-
боті авторів показано, що використання двопараметричних моделей електронного пучка дозволяє правильно
аппроксимірувати результати вимірів розподілів глибинних доз. В даній роботі описується метод електрон-
ного випромінювання на основі двопараметричної моделі електронного пучка та основних напівемпіричних
співвідношень цього методу. Проведена апробація запропонованих методів дозиметрії електронного випро-
мінювання на основі вимірювань, проведених у центрі стерилізації Інституту ядерної хімії та технологій,
Варшава, Польща.
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