Journal of Radiological Protection
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Monte-Carlo simulation of beta particle induced bremsstrahlung doses To cite this article before publication: Dusan Mrdja et al 2017 J. Radiol. Prot. in press https://doi.org/10.1088/1361-6498/aa928f
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Monte-Carlo simulation of beta particle induced bremsstrahlung doses
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D. Mrdja, K. Bikit, I. Bikit, J. Slivka, S.Forkapic, J.Knezevic
University of Novi Sad, Faculty of Sciences, Department of Physics
*Corresponding author: Kristina Bikit, University of Novi Sad, Faculty of Sciences, Department of Physics, Trg Dositeja Obradovica 4, 21000 Novi Sad
Tel.+381 21 459 368, Fax.+381 21 459 367, e-mail: [email protected]
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Abstract
It is well known that the protection from external irradiation produced by beta emitters is simpler than
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the corresponding shielding of radioactive sources that emit gamma radiation. This is caused by relatively strong absorption (i.e. short range) of electrons in different materials. However, for strong beta sources specific attention should be devoted to the bremsstrahlung radiation induced in the source encapsulation (matrix), especially for emitters with relatively high beta-endpoint energy ( 1 MeV ), that are frequently used in nuclear medicine. In the present work, the bremsstrahlung spectra produced in daughter Y-90), P-32,
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various materials by the following beta emitters Sr-90 (together with its
and Bi-210 were investigated by Monte-Carlo simulations, using Geant4 software. In these simulations, it is supposed that the point radioactive sources are surrounded by cylindrically shaped capsules made from different materials: Pb, Cu, Al, glass, and plastic. For the case of Sr-90(Y-90) in cylindrical lead
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and aluminum capsules, the dimensions of these capsules have also been varied. The absorbed dose rates from bremsstrahlung radiation were calculated for cases where the encapsulated point source is placed at the distance of 30 mm from the surface of a water cylinder with a mass of 75 kg (approximately
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representing the human body). The bremsstrahlung dose rate and bremsstrahlung spectrum from the Y-90(Sr-90) point source encapsulated in an Al capsule, were also measured experimentally and
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compared with the corresponding simulation results. In addition, the bremsstrahlung radiation risk for medical staff in therapies using Y-90 was considered in simulations, relating to finger dose as well as
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whole body dose during preparation and injection of this radioisotope. The corresponding annual doses were obtained for medical workers for specified numbers of Y-90 applications to patients.
Keywords: beta emitters, Monte-Carlo simulations, bremsstrahlung spectra, absorbed doses, overexposure
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Introduction
The bremsstrahlung radiation spectrum, produced by the deceleration of electrons passing through matter, is continuous. It is well known that besides external bremsstrahlung [1, 2] which
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is investigated in this work, an internal bremsstrahlung spectra resulting from electron interactions with their parent nuclei, is produced [3]. Energetic electrons, causing bremsstrahlung radiation within a specific material (matrix), can be emitted from beta radioactive sources, as well as from x-ray tubes, or the beamlines of electron
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accelerator facilities [4, 5, 6], including high-energy electron beams used in external radiotherapy [7]. The maximum energy of the bremsstrahlung spectrum from a beta emitter is determined by the maximum energy of electrons produced in the beta decay process, with the average energy of this spectrum being significantly lower than the maximum energy. The
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probability of bremsstrahlung emission increases with electron energy, as well as with the atomic number of the absorber. Thus, for beta sources with electron endpoint energies less than approximately 0.1 MeV, the absorbed dose from bremsstrahlung radiation can be neglected.
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However, for beta emitters with higher endpoint energies, especially for those placed within materials of relatively high atomic number, the bremsstrahlung intensity and corresponding 2
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induced dose, needs to be analyzed. Some of these high-energy beta emitters can be used as nuclear therapy sources (such as Yttrium-90), or as tracers in nuclear medicine (e.g. P-32).
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There are some empirical equations that can be used for the estimation of bremsstrahlung
intensity. For example, the starting point in such estimations can be the following equation: F = 3.5 × 10-4 Z Eβmax, representing the fraction (F) of beta-particle energy converted to bremsstrahlung (where Z is the atomic number of the matrix (absorber) and Eβmax is the maximum beta energy in MeV). Very often, as a result of such assessments, only the order of magnitude of expected bremsstrahlung dose rate can be calculated. A more detailed method of
Sr-90+Y-90 is presented in [8].
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calculating the lead shielding requirement for radioactive bremsstrahlung sources incorporating
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Besides analysis of bremsstrahlung from beta sources, a model for predicting the absolute bremsstrahlung intensity spectrum produced by x-ray tube technology for different incident electron angles on different target materials and at different tube voltages can be developed [9]. On the other hand, for more precise determination of the expected bremsstrahlung intensity and the corresponding dose rate caused by this radiation in the vicinity of a beta radioactive source,
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Monte-Carlo simulations should be performed. The use of simulation software provides the possibility to take into account the actual energy distribution of the beta particles emitted from the beta source, the geometry and composition of the source encapsulation material, and the
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production and self-absorption of bremsstrahlung in the encapsulation material. Monte-Carlo simulations can be also useful for analyses of bremsstrahlung production by x-ray machines used in radiography and radiotherapy [10].
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Simulations of bremsstrahlung spectra by Geant4 software In the present work, we used Geant4 software (Version 4.9.5.) [11] to obtain the bremsstrahlung
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spectra of the following beta emitters: Sr-90 (together with its daughter Y-90), P-32 and Bi-210. The validation of Geant4 code for determination of attenuation properties and bremsstrahlung radiation yield of different types of plastic materials and aluminum used as shields for Sr-90 and Y-90 sources is presented in [12].
We applied G4 standard electromagnetic package in our simulations with following MC
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simulation parameters: 1 μm for tracking cut and 250 eV for energy cut.
The reason why we simulated Sr-90/Y-90, instead of Y-90 alone, was the experimental possibility to check results of simulations by Sr-90/Y-90 source, but knowing that the
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bremsstrahlung dose rate contribution of Sr-90 itself is far lower than the bremsstrahlung dose rate from Y-90, due to differences in their beta-endpoint energies. Detailed descriptions of beta decay, as well as bremsstrahlung emission, modeled by Geant4 software are given in
. These radionuclides were chosen due to their relatively high beta-
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endpoint energies, Eβmax: 546.2 keV for Sr-90, 2281.5 keV for Y-90, 1710.3 keV for P-32 and 1161.5 keV for Bi-210. The almost two times lower endpoint energy of Bi-210 relative to Y-90, provides the possibility of observing the influence of endpoint energy on induced bremsstrahlung
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dose rate. In all these simulations, the point radioactive source was placed in the center of a cylindrically shaped capsule. The simulations were performed for different matrices: Pb, Cu, Al, glass and plastic. Initial parameters for each simulation were the dimensions of the cylindrical capsule that contained the point source. These dimensions were adjusted to be nearly equal to the
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range of most energetic electrons from beta decay in the specified matrix, thus minimizing the probability that some electrons could escape from matrix, but simultaneously, by not using too 4
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thick layer of capsule material, minimizing the effects of self-absorption of bremsstrahlung. Thus, maximum values of bremsstrahlung emission from the encapsulated sources are obtained.
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The simple empirical formula given by Katz and Penfold [14] can be used for the calculation of the maximum range,𝑅𝑚𝑎𝑥 , of a beta particle in units [g/cm2] : 𝑔
𝑅max [𝑐𝑚2 ] = {
1.265−0.0954 ln(𝐸𝛽 )
0.412 𝐸𝛽
0.530 𝐸𝛽 − 0.106
0.01 ≤ 𝐸𝛽 ≤ 2.5 MeV 𝐸𝛽 > 2.5 MeV
(1)
Here, Eβ represents the maximum beta energy in MeV. For, example if matrix is Pb (ρ = 11.34 g·cm−3), we obtain the range of electron of 0.96 mm for the maximum electron energy from
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Y-90 decay (Eβmax = 2281.5 keV). More precise calculations of range for electrons of different energies in various materials can be done using the ESTAR program [15].
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(Y-90) shown in Fig.1.
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According to previous calculation, we started from the geometry for Pb encapsulation of Sr-90
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Fig.1. Simulation of Sr-90(Y-90) source in lead encapsulation with dimensions1.9 mm height x
1.9 mm diameter. The bremsstrahlung emission is visualized by green lines, whereas the electron 5
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paths are given in red. The minimum distance of the source from the surface of the capsule (0.95 mm) corresponds approximately to the range of electrons with the maximum energy of
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2.28 MeV.
This Pb capsule with a Sr-90 (Y-90) source was, in simulation, placed at a distance of 30 mm from the surface of a water cylinder representing the human body (Fig.2a). The height, diameter and mass of water cylinder were 1.7 m, 0.237 m and 75 kg, respectively (Fig.2.b). The number of generated decays of Sr-90 was N=500000, followed by the same number of decays of its
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the water cylinder was obtained (Fig.2.c).
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daughter (Y-90). In the next step, the spectrum of deposited energies of bremsstrahlung events in
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Fig.2.Position of the radioactive source near a water cylinder representing the human body, (a), (b), and corresponding bremsstrahlung spectrum deposited in this water cylinder (c)
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By integration of this spectrum, the following data were found: the total number of counts (Nc=12713) and the total deposited energy (Ebremss= 2399 MeV).
Then, we decreased the dimensions of Pb matrix to be 1 mm height x 1 mm diameter, resulting in a significant increase of bremsstrahlung spectral intensity (Nc=23078, Ebremss=3990 MeV). The procedure described here was further applied in simulations of bremsstrahlung production
It
should
be
noted
that
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for different capsule dimensions, as well as for other beta emitters. P-32
decays
into
a
stable
isotope
and
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Bi-210 into a pure alpha emitter, whereas Sr-90 has a radioactive daughter (Y-90) which is a pure beta emitter that makes the dominant contribution to bremsstrahlung intensity. Calculation of the dose rate from bremsstrahlung radiation for a given activity of Sr-90 in a Pb matrix The average absorbed dose in water cylinder for N decays of Sr-90 (followed by the same
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number N of Y-90 decays) from bremsstrahlung radiation is:
where ΔEbremss
∆𝐸𝑏𝑟𝑒𝑚𝑠𝑠 , ∆𝑚 represents the deposited energy of bremsstrahlung radiation within the water 𝐷=
cylinder of mass Δm. Having in mind the penetration ability of bremsstrahlung photons with the
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deposited energy distribution given in Fig.2.c, the absorbed dose is calculated taking into account the total mass of the water cylinder. This is because the photons are effective at penetrating the cylinder, as illustrated in Fig.2.b.
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If the activity of the Sr-90 source is A[s-1], then the time (in seconds) required for N decays of Sr-90 is t = N/A. Within this time, N decays of Y-90 will also occur, since Sr-90 and Y-90 are in
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secular equilibrium in our simulations. Finally, the dose rate caused by bremsstrahlung radiation
can be expressed as D' = D/t. Thus the relation between number of decays in our simulations and corresponding dose rate caused by specified source activity is established.
For 0.37 GBq activity of Sr-90 (Y-90), we obtained the following values of dose rate from bremsstrahlung radiation originating from a Pb matrix: 23 μGy/h (from a 1 mm x 1 mm capsule)
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and 14 μGy/h (from a 1.9 mm x 1.9 mm capsule).
Simulations of bremsstrahlung dose rates induced by beta sources within Cu, Al, glass, and polyethylene matrices The dimensions of cylindrically shaped matrices were successively increased in comparison with
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the size of Pb matrix (Table 1), due to the greater range of electrons within these matrices. Table 1. Characteristics of Sr-90+Y-90 encapsulation
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Matrix
Dimensions of cylindrical matrix (diameter x height) [mm]
Cu
2x2
Al
7x7
Glass
8x8
Polyethylene
20 x 20
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(Al 0.53% - Si 34.82% - Mg 0.6% - Ca 7.15% Na 9.65% - K 0.415% - O 46.835%, 2.5 g/cm3)
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The number of generated decays of Sr-90 was N = 500 000 for each matrix, followed with the same number of decays of its daughter (Y-90). Also, we simulated 500 000 decays of P-32, 8
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as well as Bi-210 within 7 x 7 mm Al matrix. The comparisons of bremsstrahlung spectra induced by Sr-90 (Y-90), P-32, Bi-210 sources, absorbed within the water cylinder, are presented
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in Fig.3a-b. The simulated distributions induced by Sr-90 are similar to the experimental bremsstrahlung spectra, presented in [16], which were obtained using a HPGe detector and a
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Sr-90 source encapsulated within different absorbing materials.
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Fig.3.Simulated energy distributions of bremsstrahlung radiation deposited within the water cylinder, originating from different Sr-90 (Y-90) source matrices (a). The comparison of
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bremsstrahlung spectral distributions originated from Sr-90 (Y-90), P-32 and Bi-210 sources within the same encapsulation (b). The dependence of dose rate on capsule matrices for 0.37 GBq Sr-90 (Y-90) source (c)
The deposited energy in the water phantom is much higher for the Cu capsule than for the
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polyethylene one.
The bremsstrahlung dose rates induced by a Sr-90 (Y-90) source of 0.37 GBq activity placed
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within different matrices are compared in Fig.3.c. Dimensions of these cylindrical matrices for Cu, Al, glass and polyethylene are indicated above the rectangular bars of the histogram. For capsules that fully absorb electrons, the dose rate for Pb is about 20 times bigger than for polyethylene.
By increasing the dimensions of the aluminum capsule for Sr-90 (Y-90) source, from 7 x 7 mm
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to 20 x 20 mm we obtained about a 30% lower dose rate (dose rate decreased from 3.55 μGy/h to 2.57 μGy/h for a 0.37 GBq source). In addition, the dose rates from P-32 and Bi-210 placed within the 7 x 7 mm Al matrix were
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found to be 1.53 μGy/h and 0.54 μGy/h, respectively, for a 0.37 GBq source. Energy density within the water cylinder and experimental measurements of dose rate and bremsstrahlung spectrum
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In the calculations reported above, the bremsstrahlung dose rates averaged over whole water cylinder representing the human body were found. However, for the given position of the 10
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bremsstrahlung source relative to the water cylinder presented in Fig. 2.b, there are differences in deposited bremsstrahlung energy in different volume elements of cylinder, depending of their
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relative position to the source. We can expect the highest values of deposited energy density (i.e. bremsstrahlung hit distribution) to be found in volume elements located near the position of the source. In order to find distribution of deposited energy density (that is related to dose rate) over the water cylinder volume, Geant4 simulations were performed.
In Fig.4. can be seen darker regions of water cylinder which represent volume elements with
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higher number of bremsstrahlung interactions and consequently of higher dose rates. The results in Fig.4 are related to the Sr-90 (Y-90) source inside Al matrix (30 mm diameter, 13.5 mm height), the same radionuclide and encapsulation which were also used in experimental
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measurements.
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Fig.4. Distribution of deposited energy density within water cylinder for Sr-90 (Y-90) source
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inside Al capsule (30 mm diameter, 13.5 mm height): a) side projection b) front projection c) top projection
Clearly, the highest dose rate is found for the region labeled “1”, whereas significantly lower
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values correspond to regions “2” on Fig.4. For the cylindrical segment “1” the average absorbed dose rate calculated from simulations was 13 µGy/h (corresponding to an equivalent dose rate of 13 µSv/h ) for the Sr-90 source of 0.37 GBq activity, placed within an Al matrix (30 mm diameter, 13.5 mm height) , Fig.5, at
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3 cm from the surface of the water cylinder. For regions marked “2”, the calculated average equivalent dose rates were 3.53 µSv/h.
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The Sr-90 source which is schematically shown in Fig.5, was also used to measure the bremsstrahlung dose rate in order to compare the experimental value with simulation result, as described below. However, the activity of Sr-90/Y-90 source which we used in experiment was relatively small: 63 300 Bq. For dose rate measurements, we used a portable NaI(Tl) detector
[17], operating in dose rate mode, calibrated by the manufacturer to show ambient dose
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equivalent rate, H*(10). This detector can be also used in spectroscopy mode.
Fig.5. Sr-90 source within an Al matrix that was simulated and also used in an experiment as a
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source of bremsstrahlung radiation
Having in mind relatively small activity of our Sr-90 source, the measurements of bremsstrahlung dose rate were conducted inside an iron chamber of 25 cm wall thickness, where
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the background ambient dose equivalent rate is significantly reduced: from ≈ 90 nSv/h outside the chamber, to ≈ 3 nSv/h inside the chamber . The measurements of bremsstrahlung ambient dose equivalent rate were done in the geometry
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shown in Fig.6.
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Fig.6.Measurement of bremsstrahlung dose rate from Sr-90 within an Al matrix using a portable NaI(Tl) detector. The activity of Sr-90 was 63 300 Bq. The distance between Sr-90/Y-90 point
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source and surface of NaI(Tl) crystal was 4.5 cm.
The total ambient dose equivalent rate measured inside the iron chamber for this source-detector geometry was
≈ 15 nSv/h, thus when we subtract the background dose rate of about
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3 nSv/h, the Sr-90 induced ambient dose equivalent rate was 12 nSv/h. Our simulation was performed in such way that Sr-90/Y-90 source is placed near water cylindrical volume element (Fig.7.a) which has the same dimensions like NaI crystal of gamma
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detector we used for measurement, whereas the distance between Sr-90/Y-90 source and water
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element was the same like the distance between NaI crystal and Sr-90/Y-90 source in experiment, i.e. 4.5 cm, Fig.6. This volume element can be imagined as voxel, which belongs to
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the big cylinder representing human body, Fig.7b, positioned at 4.5 cm from Sr-90/Y-90 source.
Fig.7. Sr-90/Y-90 source placed in simulation near water cylindrical volume element (a), which is supposed to be a voxel belonging to the big cylinder representing human body (b). From simulations we obtained dose rate of 9.5 nSv/h for water voxel shown on Fig.7, taking into
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account the Sr-90 source activity identical to the experimental conditions, i.e. ASr-90=63 300 Bq. This dose rate value is 20% lower than experimental value, indicating reasonable good quantitative agreement of simulation results with experiment.
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The reasons for relatively small discrepancy of 20% between dose rate measurements by calibrated detector, and simulated dose rate were: 1) detector dose rate calibration in a “far field“ geometry, instead of measurements close
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to the radiation source, where the finite size of detector and source become important;
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2) manufacturer calibration using Cs-137, Co-60 and Am-241 sources, which have emission spectra that do not correspond to the bremsstrahlung spectral distribution;
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3) calculation of the equivalent dose rate for a segment of the water cylinder, whereas the ambient dose equivalent H*(10) rate, a quantity in which our NaI (Tl) detector was
calibrated, is defined for slightly different material - tissue-equivalent plastic, for a reference depth of 10 mm for strongly penetrating radiation
Independently from dose rate measurements and dose rate simulations, the comparison of
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measured and simulated bremsstrahlung spectra is the most appropriate way to validate simulation approach for investigation of bremsstrahlung emission induced by beta emitters. In order to show more directly the reliability of our simulations, we also measured experimental
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bremsstrahlung spectrum by NaI (Tl) detector operating in spectroscopy mode (again in geometry given in Fig.6),
and compared it with simulated spectrum, Fig.8. Thus we found
almost identical measured and simulated spectral distributions ( Fig.8b), while relative difference between measured and simulated bremsstrahlung spectral intensities was 30% ( for spectral
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region 5 keV – 1000 keV ) .
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Fig.8.Simulation of bremsstrahlung spectrum of Sr-90/Y-90 source in Al matrix positioned near
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NaI detector (a).Comparison of measured and simulated bremsstrahlung spectral intensities (b) This difference can be due to existing layers of materials around NaI crystal, as well as additional effects of light collection from NaI crystal in real detector, which are not incorporated in simulations.
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The quantitative and qualitative agreement between the simulated and measured values for this case, justifies the validity of the simulation results for other sources and capsules. Bremsstrahlung radiation risk for medical staff in therapies with Y-90
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Our simulations showed the highest dose-rate from the source studied is due to bremsstrahlung radiation from Y-90. A pure Y-90 source produces only a 2.3 % lower bremsstrahlung dose-rate than a Sr-90/Y-90 source of the same activity (where Sr-90 and Y-90 are in secular equilibrium). In other words, the contribution of Sr-90 to bremsstrahlung production compared with the Y-90
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contribution is negligible.
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Having in mind that, in practice, Y-90 is widely used, it is important to find expected whole body doses, as well as corresponding doses to fingers, received by medical staff working with
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this radionuclide during application procedures to patients. Since our simulations were based on a beta source positioned at 30 mm distance from the body of person working with the source, the doses obtained from simulations can be reduced in practice by increasing the distance between operator and source.
The typical activity of Y-90 for medical application is 1 GBq – 3 GBq [18], while the time of a
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manual application procedure is approximately 10 minutes [19]. Even relatively short times of application can lead to the overexposure of the hands and fingers of medical staff [19]. In order to find the dose to the fingers in contact with a glass matrix containing Y-90, we
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performed simulations, as presented in Fig.9.
Fig.9.Simulation of bremsstrahlung emission for contact geometry of a Y-90 source within a glass matrix (“S”) and a model of a finger based on a water matrix (“F”). The dimensions of the
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finger model (“F”) and source glass cylindrical capsule (“S”) are given in centimeters.
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The spectrum of absorbed energies within the model of a finger is presented in Fig.10. It is qualitatively different from the corresponding spectrum of absorbed energies for the whole body
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(Fig.3a)] due to the very small volume of the finger model in which only low-energy bremsstrahlung photons (E ≲ 20 keV) can efficiently deposit their energies, whereas the whole
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body model can absorb higher energies (E ≲ 90 keV) with significant probability.
Fig.10.Distribution of absorbed energies for model of finger (Y-90 source within glass matrix) The absorbed dose found for the model of a finger is 5 mGy during a single 10 minute
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application of 3 GBq activity of Y-90 (therapy doses should be given slowly [18]).This result is in a good agreement with reported experimental mean values for absorbed dose to the fingertips during injection [18]. Consequently, 150 such applications will cause a total absorbed finger
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dose of 750 mGy (750 mSv equivalent dose), which is 50% higher than the annual finger dose limit of 500 mSv [20],[21], implying overexposure of medical staff fingers. This further means that expected annual finger doses should be reduced in appropriate way. Since it is not possible to significantly decrease the time required for preparation and application of Y-90 solution, the
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number of applications performed by a single person over the year must be decreased. In 19
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addition, by use of manual shielded injector, the received dose per single injection can be reduced.
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Besides finger dose calculations, we demonstrated in our simulations that the whole body
bremsstrahlung doses for medical personnel are non-negligible. Thus, 3 GBq activity of Y-90 placed within glass will produce 20 µGy/h absorbed dose rate averaged over the whole body, corresponding to 3.4 µGy of whole-body absorbed dose during a 10 minute application time. On this basis, 150 applications will cause the total absorbed dose of about 0.51 mGy. This value is
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significantly lower than whole body annual dose limit of 20 mSv for professional exposure [20],[21].
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Conclusions
The bremsstrahlung emission from encapsulated pure beta emitters was studied by detailed Monte-Carlo calculations. Real energy distributions of emitted beta particles are included in the simulation processes. Production of bremsstrahlung as well as self-absorption of this radiation in encapsulation matrices was taken into account. Some of the Monte-Carlo estimations have been
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verified experimentally, i.e. the bremsstrahlung dose rate, together with bremsstrahlung spectrum from the Y-90(Sr-90) point source encapsulated in an Al capsule, were measured and compared with the simulation results. By using capsule thicknesses that completely stop the beta rays, the difference in bremsstrahlung intensity in different materials is quantitatively determined. Thus,
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the dose rate from Pb is found to be about 20 times bigger than from polyethylene, 6.5 times bigger than from Al, and almost 3.5 times bigger than from Cu. Since the energy distribution of electrons from beta decay is important for bremsstrahlung production, the bremsstrahlung dose
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rate from Sr-90 (Y-90) in the same matrix (i.e. aluminum) is 2.3 times higher than the dose rate from P-32, and 6.5 times higher than the dose rate from Bi-210. 20
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Our Monte-Carlo simulations showed that annual finger doses for medical staff involved in application procedures of Y-90 can exceed the finger dose limit for professional exposure. Based
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on these results, we suggested possible ways to reduce potential overexposure. We found that although non-negligible, the whole body annual doses for medical workers caused by the application of Y-90 are much lower than the whole body annual dose limit for professional exposure.
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Acknowledgments: The authors acknowledge the financial support of the Ministry of Education, Science and Technological Development of Serbia, within the project Nuclear
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[6] Haridas G, Verma D, Sahani PK, Nayak MK, Thakkar KK, Sarkar PK. Experimental determination of Bremsstrahlung dose rate due to accidental beam loss in Indus-1 storage
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[10] Taleei R, Shahriari M. Monte Carlo simulation of X-ray spectra and evaluation of filter effect using MCNP4C and FLUKA code. Appl Radiat Isotopes 2009; 67: 266–271. [11] Agostinelli S, Allison J, Amako K, Apostolakis J, Araujo H, Arce P., et al. Geant4— a simulation toolkit. Nucl Instrum Meth A 2003; 506: 250–303. [12] Amato E, Lizio D. Plastic materials as a radiation shield for β- sources: a
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[14] Katz L, Penfold AS. Range-Energy Relations for Electrons and the Determination of Beta-Ray End-Point Energies by Absorption. Rev Mod Phys 1952; 24: 28-44. [15] NIST ESTAR Database Program,
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[16] Mietelski JW, Meczynski W. Application of a low-background gamma-ray spectrometer to the determination of 90Sr. Appl Radiat Isotopes 2000; 53: 121-126.
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[17] SAIC Exploranium – GR-135 System Manual. Part 87317-1 Rev.3.4., Mississauga, Ontario 2004.
[18] Cremonesi M, Ferrari M, Paganelli G, Rossi A, Chinol M, Bartolomei M, Prisco G, Tosi G. Radiation protection in radionuclide therapies with
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[20] ICRP 60. 1990 Recommendations of the International Commission on Radiological Protection. Ann ICRP 1991; 21:1-201.
[21] ICRP 103. The 2007 Recommendations of the International Commission on
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ACCEPTED MANUSCRIPT
Monte-Carlo simulation of beta particle induced bremsstrahlung doses To cite this article before publication: Dusan Mrdja et al 2017 J. Radiol. Prot. in press https://doi.org/10.1088/1361-6498/aa928f
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Monte-Carlo simulation of beta particle induced bremsstrahlung doses
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D. Mrdja, K. Bikit, I. Bikit, J. Slivka, S.Forkapic, J.Knezevic
University of Novi Sad, Faculty of Sciences, Department of Physics
*Corresponding author: Kristina Bikit, University of Novi Sad, Faculty of Sciences, Department of Physics, Trg Dositeja Obradovica 4, 21000 Novi Sad
Tel.+381 21 459 368, Fax.+381 21 459 367, e-mail: [email protected]
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Abstract
It is well known that the protection from external irradiation produced by beta emitters is simpler than
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the corresponding shielding of radioactive sources that emit gamma radiation. This is caused by relatively strong absorption (i.e. short range) of electrons in different materials. However, for strong beta sources specific attention should be devoted to the bremsstrahlung radiation induced in the source encapsulation (matrix), especially for emitters with relatively high beta-endpoint energy ( 1 MeV ), that are frequently used in nuclear medicine. In the present work, the bremsstrahlung spectra produced in daughter Y-90), P-32,
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various materials by the following beta emitters Sr-90 (together with its
and Bi-210 were investigated by Monte-Carlo simulations, using Geant4 software. In these simulations, it is supposed that the point radioactive sources are surrounded by cylindrically shaped capsules made from different materials: Pb, Cu, Al, glass, and plastic. For the case of Sr-90(Y-90) in cylindrical lead
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and aluminum capsules, the dimensions of these capsules have also been varied. The absorbed dose rates from bremsstrahlung radiation were calculated for cases where the encapsulated point source is placed at the distance of 30 mm from the surface of a water cylinder with a mass of 75 kg (approximately
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representing the human body). The bremsstrahlung dose rate and bremsstrahlung spectrum from the Y-90(Sr-90) point source encapsulated in an Al capsule, were also measured experimentally and
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compared with the corresponding simulation results. In addition, the bremsstrahlung radiation risk for medical staff in therapies using Y-90 was considered in simulations, relating to finger dose as well as
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whole body dose during preparation and injection of this radioisotope. The corresponding annual doses were obtained for medical workers for specified numbers of Y-90 applications to patients.
Keywords: beta emitters, Monte-Carlo simulations, bremsstrahlung spectra, absorbed doses, overexposure
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Introduction
The bremsstrahlung radiation spectrum, produced by the deceleration of electrons passing through matter, is continuous. It is well known that besides external bremsstrahlung [1, 2] which
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is investigated in this work, an internal bremsstrahlung spectra resulting from electron interactions with their parent nuclei, is produced [3]. Energetic electrons, causing bremsstrahlung radiation within a specific material (matrix), can be emitted from beta radioactive sources, as well as from x-ray tubes, or the beamlines of electron
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accelerator facilities [4, 5, 6], including high-energy electron beams used in external radiotherapy [7]. The maximum energy of the bremsstrahlung spectrum from a beta emitter is determined by the maximum energy of electrons produced in the beta decay process, with the average energy of this spectrum being significantly lower than the maximum energy. The
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probability of bremsstrahlung emission increases with electron energy, as well as with the atomic number of the absorber. Thus, for beta sources with electron endpoint energies less than approximately 0.1 MeV, the absorbed dose from bremsstrahlung radiation can be neglected.
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However, for beta emitters with higher endpoint energies, especially for those placed within materials of relatively high atomic number, the bremsstrahlung intensity and corresponding 2
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induced dose, needs to be analyzed. Some of these high-energy beta emitters can be used as nuclear therapy sources (such as Yttrium-90), or as tracers in nuclear medicine (e.g. P-32).
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There are some empirical equations that can be used for the estimation of bremsstrahlung
intensity. For example, the starting point in such estimations can be the following equation: F = 3.5 × 10-4 Z Eβmax, representing the fraction (F) of beta-particle energy converted to bremsstrahlung (where Z is the atomic number of the matrix (absorber) and Eβmax is the maximum beta energy in MeV). Very often, as a result of such assessments, only the order of magnitude of expected bremsstrahlung dose rate can be calculated. A more detailed method of
Sr-90+Y-90 is presented in [8].
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calculating the lead shielding requirement for radioactive bremsstrahlung sources incorporating
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Besides analysis of bremsstrahlung from beta sources, a model for predicting the absolute bremsstrahlung intensity spectrum produced by x-ray tube technology for different incident electron angles on different target materials and at different tube voltages can be developed [9]. On the other hand, for more precise determination of the expected bremsstrahlung intensity and the corresponding dose rate caused by this radiation in the vicinity of a beta radioactive source,
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Monte-Carlo simulations should be performed. The use of simulation software provides the possibility to take into account the actual energy distribution of the beta particles emitted from the beta source, the geometry and composition of the source encapsulation material, and the
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production and self-absorption of bremsstrahlung in the encapsulation material. Monte-Carlo simulations can be also useful for analyses of bremsstrahlung production by x-ray machines used in radiography and radiotherapy [10].
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Simulations of bremsstrahlung spectra by Geant4 software In the present work, we used Geant4 software (Version 4.9.5.) [11] to obtain the bremsstrahlung
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spectra of the following beta emitters: Sr-90 (together with its daughter Y-90), P-32 and Bi-210. The validation of Geant4 code for determination of attenuation properties and bremsstrahlung radiation yield of different types of plastic materials and aluminum used as shields for Sr-90 and Y-90 sources is presented in [12].
We applied G4 standard electromagnetic package in our simulations with following MC
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simulation parameters: 1 μm for tracking cut and 250 eV for energy cut.
The reason why we simulated Sr-90/Y-90, instead of Y-90 alone, was the experimental possibility to check results of simulations by Sr-90/Y-90 source, but knowing that the
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bremsstrahlung dose rate contribution of Sr-90 itself is far lower than the bremsstrahlung dose rate from Y-90, due to differences in their beta-endpoint energies. Detailed descriptions of beta decay, as well as bremsstrahlung emission, modeled by Geant4 software are given in
. These radionuclides were chosen due to their relatively high beta-
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endpoint energies, Eβmax: 546.2 keV for Sr-90, 2281.5 keV for Y-90, 1710.3 keV for P-32 and 1161.5 keV for Bi-210. The almost two times lower endpoint energy of Bi-210 relative to Y-90, provides the possibility of observing the influence of endpoint energy on induced bremsstrahlung
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dose rate. In all these simulations, the point radioactive source was placed in the center of a cylindrically shaped capsule. The simulations were performed for different matrices: Pb, Cu, Al, glass and plastic. Initial parameters for each simulation were the dimensions of the cylindrical capsule that contained the point source. These dimensions were adjusted to be nearly equal to the
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range of most energetic electrons from beta decay in the specified matrix, thus minimizing the probability that some electrons could escape from matrix, but simultaneously, by not using too 4
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thick layer of capsule material, minimizing the effects of self-absorption of bremsstrahlung. Thus, maximum values of bremsstrahlung emission from the encapsulated sources are obtained.
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The simple empirical formula given by Katz and Penfold [14] can be used for the calculation of the maximum range,𝑅𝑚𝑎𝑥 , of a beta particle in units [g/cm2] : 𝑔
𝑅max [𝑐𝑚2 ] = {
1.265−0.0954 ln(𝐸𝛽 )
0.412 𝐸𝛽
0.530 𝐸𝛽 − 0.106
0.01 ≤ 𝐸𝛽 ≤ 2.5 MeV 𝐸𝛽 > 2.5 MeV
(1)
Here, Eβ represents the maximum beta energy in MeV. For, example if matrix is Pb (ρ = 11.34 g·cm−3), we obtain the range of electron of 0.96 mm for the maximum electron energy from
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Y-90 decay (Eβmax = 2281.5 keV). More precise calculations of range for electrons of different energies in various materials can be done using the ESTAR program [15].
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(Y-90) shown in Fig.1.
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According to previous calculation, we started from the geometry for Pb encapsulation of Sr-90
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Fig.1. Simulation of Sr-90(Y-90) source in lead encapsulation with dimensions1.9 mm height x
1.9 mm diameter. The bremsstrahlung emission is visualized by green lines, whereas the electron 5
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paths are given in red. The minimum distance of the source from the surface of the capsule (0.95 mm) corresponds approximately to the range of electrons with the maximum energy of
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2.28 MeV.
This Pb capsule with a Sr-90 (Y-90) source was, in simulation, placed at a distance of 30 mm from the surface of a water cylinder representing the human body (Fig.2a). The height, diameter and mass of water cylinder were 1.7 m, 0.237 m and 75 kg, respectively (Fig.2.b). The number of generated decays of Sr-90 was N=500000, followed by the same number of decays of its
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the water cylinder was obtained (Fig.2.c).
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daughter (Y-90). In the next step, the spectrum of deposited energies of bremsstrahlung events in
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Fig.2.Position of the radioactive source near a water cylinder representing the human body, (a), (b), and corresponding bremsstrahlung spectrum deposited in this water cylinder (c)
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By integration of this spectrum, the following data were found: the total number of counts (Nc=12713) and the total deposited energy (Ebremss= 2399 MeV).
Then, we decreased the dimensions of Pb matrix to be 1 mm height x 1 mm diameter, resulting in a significant increase of bremsstrahlung spectral intensity (Nc=23078, Ebremss=3990 MeV). The procedure described here was further applied in simulations of bremsstrahlung production
It
should
be
noted
that
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for different capsule dimensions, as well as for other beta emitters. P-32
decays
into
a
stable
isotope
and
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Bi-210 into a pure alpha emitter, whereas Sr-90 has a radioactive daughter (Y-90) which is a pure beta emitter that makes the dominant contribution to bremsstrahlung intensity. Calculation of the dose rate from bremsstrahlung radiation for a given activity of Sr-90 in a Pb matrix The average absorbed dose in water cylinder for N decays of Sr-90 (followed by the same
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number N of Y-90 decays) from bremsstrahlung radiation is:
where ΔEbremss
∆𝐸𝑏𝑟𝑒𝑚𝑠𝑠 , ∆𝑚 represents the deposited energy of bremsstrahlung radiation within the water 𝐷=
cylinder of mass Δm. Having in mind the penetration ability of bremsstrahlung photons with the
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deposited energy distribution given in Fig.2.c, the absorbed dose is calculated taking into account the total mass of the water cylinder. This is because the photons are effective at penetrating the cylinder, as illustrated in Fig.2.b.
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If the activity of the Sr-90 source is A[s-1], then the time (in seconds) required for N decays of Sr-90 is t = N/A. Within this time, N decays of Y-90 will also occur, since Sr-90 and Y-90 are in
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secular equilibrium in our simulations. Finally, the dose rate caused by bremsstrahlung radiation
can be expressed as D' = D/t. Thus the relation between number of decays in our simulations and corresponding dose rate caused by specified source activity is established.
For 0.37 GBq activity of Sr-90 (Y-90), we obtained the following values of dose rate from bremsstrahlung radiation originating from a Pb matrix: 23 μGy/h (from a 1 mm x 1 mm capsule)
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and 14 μGy/h (from a 1.9 mm x 1.9 mm capsule).
Simulations of bremsstrahlung dose rates induced by beta sources within Cu, Al, glass, and polyethylene matrices The dimensions of cylindrically shaped matrices were successively increased in comparison with
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the size of Pb matrix (Table 1), due to the greater range of electrons within these matrices. Table 1. Characteristics of Sr-90+Y-90 encapsulation
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Matrix
Dimensions of cylindrical matrix (diameter x height) [mm]
Cu
2x2
Al
7x7
Glass
8x8
Polyethylene
20 x 20
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(Al 0.53% - Si 34.82% - Mg 0.6% - Ca 7.15% Na 9.65% - K 0.415% - O 46.835%, 2.5 g/cm3)
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The number of generated decays of Sr-90 was N = 500 000 for each matrix, followed with the same number of decays of its daughter (Y-90). Also, we simulated 500 000 decays of P-32, 8
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as well as Bi-210 within 7 x 7 mm Al matrix. The comparisons of bremsstrahlung spectra induced by Sr-90 (Y-90), P-32, Bi-210 sources, absorbed within the water cylinder, are presented
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in Fig.3a-b. The simulated distributions induced by Sr-90 are similar to the experimental bremsstrahlung spectra, presented in [16], which were obtained using a HPGe detector and a
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Sr-90 source encapsulated within different absorbing materials.
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Fig.3.Simulated energy distributions of bremsstrahlung radiation deposited within the water cylinder, originating from different Sr-90 (Y-90) source matrices (a). The comparison of
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bremsstrahlung spectral distributions originated from Sr-90 (Y-90), P-32 and Bi-210 sources within the same encapsulation (b). The dependence of dose rate on capsule matrices for 0.37 GBq Sr-90 (Y-90) source (c)
The deposited energy in the water phantom is much higher for the Cu capsule than for the
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polyethylene one.
The bremsstrahlung dose rates induced by a Sr-90 (Y-90) source of 0.37 GBq activity placed
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within different matrices are compared in Fig.3.c. Dimensions of these cylindrical matrices for Cu, Al, glass and polyethylene are indicated above the rectangular bars of the histogram. For capsules that fully absorb electrons, the dose rate for Pb is about 20 times bigger than for polyethylene.
By increasing the dimensions of the aluminum capsule for Sr-90 (Y-90) source, from 7 x 7 mm
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to 20 x 20 mm we obtained about a 30% lower dose rate (dose rate decreased from 3.55 μGy/h to 2.57 μGy/h for a 0.37 GBq source). In addition, the dose rates from P-32 and Bi-210 placed within the 7 x 7 mm Al matrix were
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found to be 1.53 μGy/h and 0.54 μGy/h, respectively, for a 0.37 GBq source. Energy density within the water cylinder and experimental measurements of dose rate and bremsstrahlung spectrum
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In the calculations reported above, the bremsstrahlung dose rates averaged over whole water cylinder representing the human body were found. However, for the given position of the 10
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bremsstrahlung source relative to the water cylinder presented in Fig. 2.b, there are differences in deposited bremsstrahlung energy in different volume elements of cylinder, depending of their
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relative position to the source. We can expect the highest values of deposited energy density (i.e. bremsstrahlung hit distribution) to be found in volume elements located near the position of the source. In order to find distribution of deposited energy density (that is related to dose rate) over the water cylinder volume, Geant4 simulations were performed.
In Fig.4. can be seen darker regions of water cylinder which represent volume elements with
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higher number of bremsstrahlung interactions and consequently of higher dose rates. The results in Fig.4 are related to the Sr-90 (Y-90) source inside Al matrix (30 mm diameter, 13.5 mm height), the same radionuclide and encapsulation which were also used in experimental
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measurements.
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Fig.4. Distribution of deposited energy density within water cylinder for Sr-90 (Y-90) source
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inside Al capsule (30 mm diameter, 13.5 mm height): a) side projection b) front projection c) top projection
Clearly, the highest dose rate is found for the region labeled “1”, whereas significantly lower
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values correspond to regions “2” on Fig.4. For the cylindrical segment “1” the average absorbed dose rate calculated from simulations was 13 µGy/h (corresponding to an equivalent dose rate of 13 µSv/h ) for the Sr-90 source of 0.37 GBq activity, placed within an Al matrix (30 mm diameter, 13.5 mm height) , Fig.5, at
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3 cm from the surface of the water cylinder. For regions marked “2”, the calculated average equivalent dose rates were 3.53 µSv/h.
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The Sr-90 source which is schematically shown in Fig.5, was also used to measure the bremsstrahlung dose rate in order to compare the experimental value with simulation result, as described below. However, the activity of Sr-90/Y-90 source which we used in experiment was relatively small: 63 300 Bq. For dose rate measurements, we used a portable NaI(Tl) detector
[17], operating in dose rate mode, calibrated by the manufacturer to show ambient dose
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equivalent rate, H*(10). This detector can be also used in spectroscopy mode.
Fig.5. Sr-90 source within an Al matrix that was simulated and also used in an experiment as a
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source of bremsstrahlung radiation
Having in mind relatively small activity of our Sr-90 source, the measurements of bremsstrahlung dose rate were conducted inside an iron chamber of 25 cm wall thickness, where
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the background ambient dose equivalent rate is significantly reduced: from ≈ 90 nSv/h outside the chamber, to ≈ 3 nSv/h inside the chamber . The measurements of bremsstrahlung ambient dose equivalent rate were done in the geometry
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shown in Fig.6.
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Fig.6.Measurement of bremsstrahlung dose rate from Sr-90 within an Al matrix using a portable NaI(Tl) detector. The activity of Sr-90 was 63 300 Bq. The distance between Sr-90/Y-90 point
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source and surface of NaI(Tl) crystal was 4.5 cm.
The total ambient dose equivalent rate measured inside the iron chamber for this source-detector geometry was
≈ 15 nSv/h, thus when we subtract the background dose rate of about
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3 nSv/h, the Sr-90 induced ambient dose equivalent rate was 12 nSv/h. Our simulation was performed in such way that Sr-90/Y-90 source is placed near water cylindrical volume element (Fig.7.a) which has the same dimensions like NaI crystal of gamma
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detector we used for measurement, whereas the distance between Sr-90/Y-90 source and water
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element was the same like the distance between NaI crystal and Sr-90/Y-90 source in experiment, i.e. 4.5 cm, Fig.6. This volume element can be imagined as voxel, which belongs to
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the big cylinder representing human body, Fig.7b, positioned at 4.5 cm from Sr-90/Y-90 source.
Fig.7. Sr-90/Y-90 source placed in simulation near water cylindrical volume element (a), which is supposed to be a voxel belonging to the big cylinder representing human body (b). From simulations we obtained dose rate of 9.5 nSv/h for water voxel shown on Fig.7, taking into
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account the Sr-90 source activity identical to the experimental conditions, i.e. ASr-90=63 300 Bq. This dose rate value is 20% lower than experimental value, indicating reasonable good quantitative agreement of simulation results with experiment.
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The reasons for relatively small discrepancy of 20% between dose rate measurements by calibrated detector, and simulated dose rate were: 1) detector dose rate calibration in a “far field“ geometry, instead of measurements close
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to the radiation source, where the finite size of detector and source become important;
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2) manufacturer calibration using Cs-137, Co-60 and Am-241 sources, which have emission spectra that do not correspond to the bremsstrahlung spectral distribution;
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3) calculation of the equivalent dose rate for a segment of the water cylinder, whereas the ambient dose equivalent H*(10) rate, a quantity in which our NaI (Tl) detector was
calibrated, is defined for slightly different material - tissue-equivalent plastic, for a reference depth of 10 mm for strongly penetrating radiation
Independently from dose rate measurements and dose rate simulations, the comparison of
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measured and simulated bremsstrahlung spectra is the most appropriate way to validate simulation approach for investigation of bremsstrahlung emission induced by beta emitters. In order to show more directly the reliability of our simulations, we also measured experimental
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bremsstrahlung spectrum by NaI (Tl) detector operating in spectroscopy mode (again in geometry given in Fig.6),
and compared it with simulated spectrum, Fig.8. Thus we found
almost identical measured and simulated spectral distributions ( Fig.8b), while relative difference between measured and simulated bremsstrahlung spectral intensities was 30% ( for spectral
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region 5 keV – 1000 keV ) .
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Fig.8.Simulation of bremsstrahlung spectrum of Sr-90/Y-90 source in Al matrix positioned near
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NaI detector (a).Comparison of measured and simulated bremsstrahlung spectral intensities (b) This difference can be due to existing layers of materials around NaI crystal, as well as additional effects of light collection from NaI crystal in real detector, which are not incorporated in simulations.
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The quantitative and qualitative agreement between the simulated and measured values for this case, justifies the validity of the simulation results for other sources and capsules. Bremsstrahlung radiation risk for medical staff in therapies with Y-90
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Our simulations showed the highest dose-rate from the source studied is due to bremsstrahlung radiation from Y-90. A pure Y-90 source produces only a 2.3 % lower bremsstrahlung dose-rate than a Sr-90/Y-90 source of the same activity (where Sr-90 and Y-90 are in secular equilibrium). In other words, the contribution of Sr-90 to bremsstrahlung production compared with the Y-90
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contribution is negligible.
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Having in mind that, in practice, Y-90 is widely used, it is important to find expected whole body doses, as well as corresponding doses to fingers, received by medical staff working with
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this radionuclide during application procedures to patients. Since our simulations were based on a beta source positioned at 30 mm distance from the body of person working with the source, the doses obtained from simulations can be reduced in practice by increasing the distance between operator and source.
The typical activity of Y-90 for medical application is 1 GBq – 3 GBq [18], while the time of a
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manual application procedure is approximately 10 minutes [19]. Even relatively short times of application can lead to the overexposure of the hands and fingers of medical staff [19]. In order to find the dose to the fingers in contact with a glass matrix containing Y-90, we
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performed simulations, as presented in Fig.9.
Fig.9.Simulation of bremsstrahlung emission for contact geometry of a Y-90 source within a glass matrix (“S”) and a model of a finger based on a water matrix (“F”). The dimensions of the
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finger model (“F”) and source glass cylindrical capsule (“S”) are given in centimeters.
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The spectrum of absorbed energies within the model of a finger is presented in Fig.10. It is qualitatively different from the corresponding spectrum of absorbed energies for the whole body
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(Fig.3a)] due to the very small volume of the finger model in which only low-energy bremsstrahlung photons (E ≲ 20 keV) can efficiently deposit their energies, whereas the whole
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body model can absorb higher energies (E ≲ 90 keV) with significant probability.
Fig.10.Distribution of absorbed energies for model of finger (Y-90 source within glass matrix) The absorbed dose found for the model of a finger is 5 mGy during a single 10 minute
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application of 3 GBq activity of Y-90 (therapy doses should be given slowly [18]).This result is in a good agreement with reported experimental mean values for absorbed dose to the fingertips during injection [18]. Consequently, 150 such applications will cause a total absorbed finger
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dose of 750 mGy (750 mSv equivalent dose), which is 50% higher than the annual finger dose limit of 500 mSv [20],[21], implying overexposure of medical staff fingers. This further means that expected annual finger doses should be reduced in appropriate way. Since it is not possible to significantly decrease the time required for preparation and application of Y-90 solution, the
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number of applications performed by a single person over the year must be decreased. In 19
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addition, by use of manual shielded injector, the received dose per single injection can be reduced.
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Besides finger dose calculations, we demonstrated in our simulations that the whole body
bremsstrahlung doses for medical personnel are non-negligible. Thus, 3 GBq activity of Y-90 placed within glass will produce 20 µGy/h absorbed dose rate averaged over the whole body, corresponding to 3.4 µGy of whole-body absorbed dose during a 10 minute application time. On this basis, 150 applications will cause the total absorbed dose of about 0.51 mGy. This value is
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significantly lower than whole body annual dose limit of 20 mSv for professional exposure [20],[21].
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Conclusions
The bremsstrahlung emission from encapsulated pure beta emitters was studied by detailed Monte-Carlo calculations. Real energy distributions of emitted beta particles are included in the simulation processes. Production of bremsstrahlung as well as self-absorption of this radiation in encapsulation matrices was taken into account. Some of the Monte-Carlo estimations have been
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verified experimentally, i.e. the bremsstrahlung dose rate, together with bremsstrahlung spectrum from the Y-90(Sr-90) point source encapsulated in an Al capsule, were measured and compared with the simulation results. By using capsule thicknesses that completely stop the beta rays, the difference in bremsstrahlung intensity in different materials is quantitatively determined. Thus,
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the dose rate from Pb is found to be about 20 times bigger than from polyethylene, 6.5 times bigger than from Al, and almost 3.5 times bigger than from Cu. Since the energy distribution of electrons from beta decay is important for bremsstrahlung production, the bremsstrahlung dose
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rate from Sr-90 (Y-90) in the same matrix (i.e. aluminum) is 2.3 times higher than the dose rate from P-32, and 6.5 times higher than the dose rate from Bi-210. 20
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Our Monte-Carlo simulations showed that annual finger doses for medical staff involved in application procedures of Y-90 can exceed the finger dose limit for professional exposure. Based
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on these results, we suggested possible ways to reduce potential overexposure. We found that although non-negligible, the whole body annual doses for medical workers caused by the application of Y-90 are much lower than the whole body annual dose limit for professional exposure.
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Acknowledgments: The authors acknowledge the financial support of the Ministry of Education, Science and Technological Development of Serbia, within the project Nuclear
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