Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation
By means of Monte Carlo computer modeling the effects of heterogeneity and spatial arrangement of irradiated disposable syringes on the absorbed dose deposition profiles has been studied for different kinds of irradiation. Substantial deviations from the predictions of conventional approximation of...
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irk-123456789-1103932017-01-05T03:02:21Z Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation Dyuldya, S.V. Bratchenko, M.I. Ядернo-физические методы и обработка данных By means of Monte Carlo computer modeling the effects of heterogeneity and spatial arrangement of irradiated disposable syringes on the absorbed dose deposition profiles has been studied for different kinds of irradiation. Substantial deviations from the predictions of conventional approximation of homogenized medium have been found for electron beam irradiation. The dependencies of irradiation process parameters on the orientation and the regularity/stochasticity of the product loading pattern, the variations of dose accumulation in component parts of a syringe and the non-equilibrium dose effects on the internal surface of a syringe needle have been investigated. Шляхом моделювання методом Монте-Карло вивчено вплив гетерогенності та просторового розташування одноразових шприців під опроміненням на профілі поглиненої дози за різних видів опромінення. Для електронного опромінювання знайдені суттєві відхилення від передбачень звичайного наближення гомогенізованого середовища. Виявлені залежності технологічних параметрів опромінювання від орієнтації та регулярності/стохастичності розташування шприців під опроміненням, різниці в накопиченні дози у різних деталях шприцу та нерівноважні дозові ефекти на внутрішній поверхні його голки. Путем моделирования методом Монте-Карло изучено влияние гетерогенности и пространственного размещения облучаемых одноразовых шприцов на профили поглощенной дозы при различных видах облучения. Для электронного облучения обнаружены существенные отклонения от предсказаний обычного приближения гомогенизированной среды. Выявлены зависимости технологических параметров облучения от ориентации и регулярности/стохастичности расположения шприцов под облучением, различия в накоплении дозы в различных деталях шприца и неравновесные дозовые эффекты на внутренней поверхности его иглы. 2007 Article Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation / S.V. Dyuldya, M.I. Bratchenko // Вопросы атомной науки и техники. — 2007. — № 5. — С. 81-89. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 02.70.Uu, 02.70.Uu, 61.82.Pv, 81.40.Wx, 87.66.Jj, 89.20.Bb http://dspace.nbuv.gov.ua/handle/123456789/110393 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ядернo-физические методы и обработка данных Ядернo-физические методы и обработка данных |
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Ядернo-физические методы и обработка данных Ядернo-физические методы и обработка данных Dyuldya, S.V. Bratchenko, M.I. Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation Вопросы атомной науки и техники |
| description |
By means of Monte Carlo computer modeling the effects of heterogeneity and spatial arrangement of irradiated disposable syringes on the absorbed dose deposition profiles has been studied for different kinds of irradiation. Substantial deviations from the predictions of conventional approximation of homogenized medium have been found for electron beam irradiation. The dependencies of irradiation process parameters on the orientation and the regularity/stochasticity of the product loading pattern, the variations of dose accumulation in component parts of a syringe and the non-equilibrium dose effects on the internal surface of a syringe needle have been investigated. |
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Article |
| author |
Dyuldya, S.V. Bratchenko, M.I. |
| author_facet |
Dyuldya, S.V. Bratchenko, M.I. |
| author_sort |
Dyuldya, S.V. |
| title |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation |
| title_short |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation |
| title_full |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation |
| title_fullStr |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation |
| title_full_unstemmed |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation |
| title_sort |
effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, x-ray and gamma irradiation |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2007 |
| topic_facet |
Ядернo-физические методы и обработка данных |
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http://dspace.nbuv.gov.ua/handle/123456789/110393 |
| citation_txt |
Effect of heterogeneity of subjects of industrial irradiation processes on spatial distributions of absorbed doses upon electron beam, X-ray and gamma irradiation / S.V. Dyuldya, M.I. Bratchenko // Вопросы атомной науки и техники. — 2007. — № 5. — С. 81-89. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T00:33:47Z |
| last_indexed |
2025-07-08T00:33:47Z |
| _version_ |
1837036813797031936 |
| fulltext |
EFFECT OF HETEROGENEITY OF SUBJECTS
OF INDUSTRIAL IRRADIATION PROCESSES ON
SPATIAL DISTRIBUTIONS OF ABSORBED DOSES UPON
ELECTRON BEAM, X-RAY AND GAMMA IRRADIATION
S.V. Dyuldya∗, M.I. Bratchenko
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received May 23, 2006)
By means of Monte Carlo computer modeling the effects of heterogeneity and spatial arrangement of irradiated
disposable syringes on the absorbed dose deposition profiles has been studied for different kinds of irradiation. Sub-
stantial deviations from the predictions of conventional approximation of homogenized medium have been found for
electron beam irradiation. The dependencies of irradiation process parameters on the orientation and the regular-
ity/stochasticity of the product loading pattern, the variations of dose accumulation in component parts of a syringe
and the non-equilibrium dose effects on the internal surface of a syringe needle have been investigated.
PACS: 02.70.Uu, 02.70.Uu, 61.82.Pv, 81.40.Wx, 87.66.Jj, 89.20.Bb
Relativistic beams of electron accelerators and
gamma quanta from nuclear decay of radionuclides
are extensively used worldwide in various industrial
irradiation processes. Among them the most impor-
tant are the radiation sterilization of medical items
(syringes, blood transfusion systems etc.), food irra-
diation and so on [1].
Certain kinds of irradiated products (medical
items, packaged food, electric cables etc.) are sub-
stantially heterogeneous. The effects of products het-
erogeneity on the absorbed dose deposition are of
keen interest for operators and users of industrial ir-
radiation processes from the point of view of their
reliability and optimality. Besides for such an ap-
plied problem the heterogeneity effects are valuable
for mainstream directions of the developments in the-
oretical dosimetry and experimental techniques based
on interaction of radiation with solid.
Currently the tendency of application of quantita-
tive methods of mathematical modeling of the trans-
port of electrons and photons in condensed media
is exhibited in the irradiation industry [2, 3, 4, 5].
Being validated by the intercomparison with exper-
imental dosimetry they become a constituent of in-
ternational regulatory documents that establish the
standard practices of industrial irradiation processes
development and support [6, 7]. The most adequate
for these applications are the Monte Carlo methods
due to their capability to take into account the com-
plex structure and composition of irradiated products
and to provide precise calculation of beam energy de-
position in heterogeneous systems.
The present paper deals with the study of the
heterogeneity effects in representative subjects of in-
dustrial irradiation by means of the in-house devel-
oped Monte Carlo computer code RaT based on the
CERN Geant4 OO Toolkit class library [8]. The RaT
code inherits the extensively validated Geant4 physi-
cal models of electromagnetic interactions of charged
particles and photons with media, provides a user-
friendly framework for development of complex 3D
models of radiation sources and irradiated products
and effective algorithms of handling with large arrays
of these models, the tools for deep analysis of mod-
eling results as well as advanced features such as the
capability to deal with stochastic 3D geometries for
simulation of radiation transport in random media
[9].
We recognize the modeling methods to supple-
ment experimental qualification and routine dosime-
try and to obtain valuable information especially in
cases of intractable problems of direct experimental
measurements [2]. Hence this work is focused on the
pure effects of product heterogeneity concerning the
role of spatial and directional loading patterns of ir-
radiated products, effects of the randomness of their
arrangement and variations of the dose accumulation
in different component parts of the product unit.
1. MODELING SETUP
As a representative type of product we have chosen
disposable syringes, a typical subject of electrophys-
ical technologies of radiation sterilization [1]. Using
actual specimen of one of syringe models, the 2 ml
insulin syringe, we have developed its detailed 3D
model (see Fig.1 that is the VRML output from the
RaT code 3D geometry engine) to be used in Monte
Carlo modeling.
∗Corresponding author. E-mail address: sdul@kipt.kharkov.ua
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2007, N5.
Series: Nuclear Physics Investigations (48), p.81-89.
81
Polymeric details of a syringe model consist of
0.9 g/cm3 dense (CH2)n polypropylene (PP). The
syringe needle (40 mm long and ®0.65 mm across
diameter) is made of stainless steel with density
7.9 g/cm3. It has a ®0.32 mm concentric hole. The
overall spatial dimensions of a syringe unit as it is
packaged into the cartridge-belt-like bands are about
8×2.5×1.5 cm.
In industrial sterilization processes plenty of sy-
ringes are irradiated simultaneously being placed in
cartons according to the more of less fixed loading
pattern.
From the computational point of view the devel-
opment of mathematical model of the dense place-
ment of syringes in containers (the product loading
pattern) is non-trivial. The problem arises from the
fact that product loading patterns are not completely
deterministic and fluctuate from one packaging box
to another whereas the deductions made from the re-
sults of modeling have to bear relation to the whole
irradiation process rather then to the irradiation of
specific carton [9].
Fig.1. 3D computer model of disposable syringe
This problem does not spring up in the commonly
used approximation of homogenized medium [2, 9]
with effective density and composition. For syringes
such a mix (incl. the environmental air) contains 14
chemical elements (H, C, O, Fe, etc.) and, for accept-
able degree of unit packaging, has effective density of
0.11 g/cm3.
To study effects of the product heterogeneity more
sophisticated approximations have to be introduced.
The simplest one is the assumption of regular load-
ing pattern when syringe units are supposed to form
regular 3D lattice. Within the RaT code it is imple-
mented using the spatial replication of 3D volumes
(see, e.g., Fig.2).
Another characteristic feature of product loading
patterns is the orientation of product units with re-
spect to the direction of beam. We considered two
limiting cases: the collinear longitudinal orientation
(see Fig.2) and the transversal loading when syringe
axes are orthogonal to the beam axis direction. In
the former case syringes are irradiated from the face
while in the latter one the beam exposes flank sur-
faces of barrels.
The stochastic perturbations of loading patterns
at this stage have been introduced in the approxi-
mation of random shifts of laterally regular layers of
syringes. This algorithm is quite enough to uncouple
long-range spatial correlations such as open channels
in regular lattices.
Both regular and randomized loading patterns ex-
actly preserve the product unit heterogeneity and
conserve the mean density of irradiated medium to
be equal to the density of the effective homogenized
medium.
To model the radiation transport in randomized
loading patterns the advanced double Monte Carlo
method proposed in Ref. [9] was used. The stochas-
tic reconstruction of the problem 3D geometry was
performed for each primary particle history using the
technique of random replications implemented for the
first time in the current version of the RaT code.
In the present work we have limited ourselves with
investigation of the effects of heterogeneity on depth-
dose dependencies knowingly neglecting the effects
[5] arising at lateral edges of product boxes. For the
same reason the packaging box itself also was not in-
cluded in the computer model. Finally, we did not
ventured to model definite industrial irradiators and
in order to obtain some general results systematically
applied the approximation of a broad beam for all
kinds of irradiation.
Fig.2. RaT screenshot of the perspective
projection of the regular longitudinal loading pattern
of syringes
Within this approximation the beam was uni-
formly aimed to the representative unit cell of the
transversal plane that falls on one syringe. Other
requirements of the broad beam approximation is
the sufficient transversal dimensions of the irradiated
medium to eliminate all lateral edge effects and the
normalization of calculated quantities per unit of pri-
mary particles flux.
In view of these requirements in our model the lat-
eral dimensions of product loading patterns spread to
6−8 m. In longitudinal (depth z) direction the thick-
ness of product layer was 80−120 cm subject to the
pattern orientation. Thus the whole 3D geometry of
the product model contained about 5.7 × 106 of sy-
ringe models.
Three kinds of the broad beam irradiation have
been considered. The first one represents the direct
82
irradiation by 5 MeV parallel electron beam (EB).
We expected the heterogeneity effects to be the most
pronounced in this case because the calculated CSDA
range of electrons in polypropylene (2.456 g/cm2 or
2.729 cm at 5 MeV) is much less then the length of a
syringe barrel.
The second case is the irradiation by X-ray beam
from (e−, X)-converter driven by the same 5 MeV
electron beam. The X-ray production in converter
was simulated in detail i.e. the heterogeneous con-
verter model was included into the problem geometry
and accelerated electrons were considered as primary
radiation. The multilayer model of the optimized
water-cooled converter included 50 µm thick Tita-
nium foil of the accelerator beam exit window, 12 cm
wide air gap and the converter itself: the 1.2 mm
thick Tantalum plate, 2 mm thick layer of liquid water
coolant followed by 2 mm of Iron that simulates the
cooler casing. In a series of preliminary calculations
the photon yields and energy spectra from the con-
verter had been simulated and benchmarked against
the manufacturer modeling data as well as against
the independent modeling by means of the XR-Soft
code [4]. The obtained energy conversion efficiency
reaches 8.697% (0.9% relative deviation from data of
Ref. [4]). The photon spectrum has a broad maxi-
mum at 300 keV and agrees quantitatively with the
results both of ITS3 and XR-Soft [4] codes simula-
tions.
The last case corresponds to the irradiation by
the γ-radiation with bare spectrum of the mix of Eu-
ropium radionuclides (47% of 152Eu, 51% of 154Eu
and 2% of 155Eu). These nuclides have complex
broad spectra of decay gammas (photon energies from
121 keV up to 1.408 MeV with mean energy of about
800 keV) and are considered as candidate nuclides for
prospective industrial gamma sources [10]. Concern-
ing the penetration capability of gamma radiation the
Europium radionuclides are quite comparable with
conventional industrial radionuclides 60Co and 137Cs
[11]. Unlike for X-ray and EB irradiation the broad
isotropic gamma beam was simulated that is closer to
the actual angular distribution of radiation of typical
gamma irradiators.
In course of RaT modeling the depth dependen-
cies of energy fluxes of all sorts of primary and sec-
ondary particles and the absorbed dose deposition
profiles were scored and normalized per one primary
electron (or photon for γ-irradiation) incident onto
the transversal plane unit area per unit of time.
These data can be easily scaled to the absorbed dose
rates at certain beam current density (or gamma
source activity).
For heterogeneous modeling setups depth depen-
dencies of fluxes and doses were scored separately for
syringe barrels, needles and their air filled holes as
well as for environmental air. For comparison the
modeling of dose deposition in the homogenized ef-
fective medium also were carried out for all kinds of
irradiation.
2. EFFECT OF THE PRODUCT
LOADING PATTERN ON THE
ABSORBED DOSE SPATIAL
DISTRIBUTIONS
The dose absorbed inside the material of the poly-
meric syringe barrel is supposed to be representative
and close to the readings of technological film dosime-
ters and dose indicators [1]. The modeling results
obtained for barrel dose depth dependencies at dif-
ferent product loading patterns are depicted in Fig.3.
In general they indicate that the product heterogene-
ity becomes crucial namely for direct electron beam
irradiation.
0 20 40 60 80 100 120
0.010
0.015
0.020
0.025
0.030
0.035
0.040
(a)
2 ml Helm disposable syringes
5 MeV X-ray irradiation
Dose in syringe barrel (PP)
RaT (Geant4)
Syringes loading pattern:
regular: longitudinal transversal
random: longitudinal transversal
effective homogenized mediumA
bs
or
be
d
do
se
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Depth in product, cm
0 5 10 15 20 25 30 35 40 45 50
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
(b)
Syringes loading pattern:
regular: longitudinal
transversal
random: longitudinal
transversal
effective medium
2 ml Helm disposable syringes
5 MeV EB irradiation
Dose in syringe barrel (PP)
RaT (Geant4)
A
bs
or
be
d
do
se
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Depth in product, cm
Fig.3. Depth dependencies of absorbed dose in
syringe barrels at X-ray (a) and EB (b) irradiation
for different product loading patterns. Solid curves
represent the modeling results obtained in the
approximation of effective homogenized medium
For X-ray irradiation (see Fig.3,a) the dose pro-
files are practically independent of the type and ori-
entation of the product loading pattern and in par-
ticular of its regularity or stochasticity. All curves
coincide with the depth-dose curve for effective ho-
mogenized medium. Similar behavior has been found
for γ-irradiation having harder spectrum and larger
penetrating capability.
On the contrary for EB irradiation the depth-dose
curves in heterogeneous product substantially differ
from those in the effectively homogenized medium
(see Fig.3,b). One can see that the homogenization
of medium results in considerable underestimation
83
of the effective range of electrons down to ∼25 cm
as compared to 35−50 cm for heterogeneous media.
As a result all dose profiles in heterogeneous me-
dia demonstrate overextended tails spread to large
depths.
However we expect these tails to have somewhat
different nature in the cases of regular and ran-
domized loading patterns. Namely for the former
case the directional effects of regular lattices trans-
parency dominates that leads to enhanced transmis-
sion through aligned voids between syringes (a kind
of particle ”channeling”) and to the growth of en-
ergy deposition at large depths. On the other hand
for loading patterns randomized on a layer-by-layer
basis the probability to find transparent voids is sup-
pressed and the large-depth dose enhancement effect
is of complex stochastic nature. Qualitatively simi-
lar effect of the stochastic blooming of random media
(as compare to the averaged homogeneous medium)
had been found in computer experiments concerning
gamma irradiation of one-dimensional random lay-
ered structures and studied analytically in Ref. [9].
Among intrinsic heterogeneity effects at EB ir-
radiation one should also distinguish the directional
effects of the product unit orientation and the effects
of loading pattern randomization.
The effect of syringes orientation is considerable
for all kinds of loading patterns but changes its sign
as the penetration depth increases. For small depths
transversal loading patterns demonstrate higher dose
deposition then the longitudinal patterns. At large
depths the effect is completely adverse.
The dose profile for the regular transversal load-
ing pattern demonstrates the unforeseen feature, the
minimum at small depth z ≈ 5 cm, that is absent
for homogenized medium and randomized patterns.
This feature is not peculiar for conventional unimodal
profiles of EB dose deposition in homogeneous media.
To clarify its nature the depth profiles of the electron
energy fluxes are shown in Fig. 4.
0 20 40 60 80 100 120
10-3
10-2
10-1
100
0 5 10 15 20 25 30
0
1
2
3
4
5 RaT
(Geant4)
2 ml Helm syringe
5 MeV EBeam
flux in barrel
(PP)
Longitudinal
loading pattern:
regular
random
Transversal
loading pattern:
regular
random
El
ec
tro
n
en
er
gy
fl
ux
, M
eV
/c
m
2 p
er
e
- /c
m
2
Depth in product, cm
RaT
(Geant4)
E
le
ct
ro
n
en
er
gy
fl
ux
, M
eV
/c
m
2 p
er
e
- /c
m
2
Depth in product, cm
Fig.4. Depth dependencies of the particle energy
fluxes in syringe barrels for different loading
patterns under EB irradiation. The inset plot
illustrates the small-depth behavior of the same
curves
It is clear from the Fig.4 inset plot that near the
outer surface of the lattice of transversally arranged
syringes the enhanced stopping of initially parallel
electron beam takes place and a kind of particle flux
blocking occurs. Consequently the surface peak of
energy deposition is observed in Fig.3,b at depths
less then the CSDA range in polypropylene (its value
at surface is close to the value for the homogenized
medium). It is due to the electrons stopped in the
near-surface layers.
However certain beam fraction reaches larger
depths through open channels and gradually expe-
riences lateral scattering. At z > 5 cm the beam an-
gular spreading becomes the dominating factor that
forms the peak at z ≈ 10 cm, the same depth where
the energy deposition maximum is located for ran-
domized transversal loading pattern that prohibits
the long-range directional effects.
At the depth-dose dependencies of Fig.3,b no ap-
preciable effects of syringe layers randomization are
observed for the longitudinal pattern while for the
transversal patterns the presence of stochastic effect
is evident and results in the smallest effective range of
electrons among all versions of heterogeneous media.
It is explained by the reason that, similarly to the
amplitude of the stochastic blooming effect [9], the
amplitude of the randomization effects has to increase
with the increase of the number N of the fluctuating
layers (for our model of independent randomly shifted
layers it is expected to be roughly proportional to√
N).
For longitudinal orientation the unit of depth con-
tains about fourfold smaller number of layers then
that for the transversal one. Hence in the former case
the randomization effects really have not time to be-
come apparent at depths where the energy deposition
is significant.
It is confirmed by the Fig.4 flux data where at
z > 40 cm in the longitudinal patterns stochastic ef-
fects also begin to perturb the flux profiles; but the
dose at such depths is marginal.
On the other hand for the transversal randomized
loading pattern the stochastic enhancement of elec-
tron stopping and scattering leads to the complete
elimination of primary beam electrons at z > 50 cm
where the electron energy flux practically is not depth
dependent. It is formed by Compton electrons pro-
duced by weakly absorbed bremsstrahlung photons.
For regular patterns and for longitudinal randomized
pattern similar effect is observed at doubled depth of
about 1 m.
In general one can conclude that due to the combi-
nation of heterogeneity and stochasticity of EB irradi-
ated medium the uniformity of absorbed dose delivery
across the depth in irradiated product is improved as
compared with the homogeneous medium of effective
density and composition. The modeling also allows to
expect the longitudinal loading patterns to be more
stable with respect to the effects of random variations
of product units loading in packaging boxes.
84
3. DOSES IN VARIOUS COMPONENT
PARTS OF IRRADIATED SYRINGES
Other valuable effects of the irradiated product
heterogeneity concern the differences of absorbed
dose values in different component parts of the prod-
uct unit. They can be of great importance for the
optimization of irradiation processes and the evalua-
tion of achievement of irradiation goals (e.g. steril-
ization). In general these effects are hard to estimate
in the homogenized medium approximation and to
measure experimentally.
Results of modeling of depth-dose dependencies
in various component parts of syringes for different
kinds of irradiation are illustrated by Figs.5 and 6.
0 8 16 24 32 40 48 56 64 72 80 88 96
0
1
2
3
4
5
6
7
8
2 ml Helm syringes Eu gamma irradiation
Regular longitudinal loading pattern
RaT (Geant4)
environment (air)
needle (steel)
needle hole (air)
syringe barrel (PP)
homogenized
effective medium
G
am
m
a
en
er
gy
fl
ux
, 1
013
M
eV
/(s
·k
C
i)
Depth in the product loading pattern, cm
(a)
0 8 16 24 32 40 48 56 64 72 80 88 96
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
(b)
2 ml Helm syringes Eu gamma irradiation
Regular longitudinal loading pattern
RaT (Geant4)
environment (air)
needle (steel)
needle hole (air)
syringe barrel (PP)
homogenized
effective medium
A
bs
or
be
d
do
se
ra
te
, k
G
y·
m
2 /(h
r·k
C
i)
Depth in the product loading pattern, cm
Fig.5. Depth dependencies of the gamma quanta
energy fluxes (a) and absorbed doses (b) in various
component parts of syringes for regular longitudinal
product loading pattern irradiated by γ-radiation of
a mix of Europium radionuclides. Dashed curves
represent the profiles in the effective homogenized
medium
Concerning the gamma irradiation one should
note that the product unit heterogeneity only weakly
perturbs the energy flux IE of hard gamma quanta
(see Fig.5,a).
Supposing that the electronic equilibrium is
reached in the bulk of product layer the absorbed
dose D is close to photon kerma K and can be cal-
culated by the formula:
D ≈ K ∝
∫
Eγ
µen(Eγ)
ρ
· IE(Eγ)dEγ , (1)
where (µen/ρ) is the mass-energy absorption coeffi-
cient at photon energy Eγ and the unessential di-
mensional factor is omitted.
Since IE(Eγ) is practically common to all syringe
components the differences of absorbed doses in dif-
ferent component parts are mainly determined by the
differences in µen/ρ for different materials. The doses
are maximal in the heavy material of the syringe nee-
dle. The dose in the polymeric barrel is representa-
tive as compared with the averaged dose in effective
medium. The dose in the needle hole is minimal even
in comparison with the dose averaged over the envi-
ronmental air; this is due to the holes shielding by
the steel body of needles.
0 20 40 60 80 100 120
0.00
0.01
0.02
0.03
0.04
0.05
2 ml Helm syringes
Longitudinal randomized
loading pattern
5 MeV X-ray irradiation
Dose deposition in:
syringe barrel (PP) needle (steel)
needle hole (air) environment (air)
homogenized effective medium
RaT (Geant4)
A
bs
or
be
d
do
se
, 1
0-1
3 k
G
y
pe
r e
- /c
m
2
Depth in product loading pattern, cm
(a)
0 5 10 15 20 25 30 35 40
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
(b)
2 ml Helm syringes
Transversal randomized
loading pattern
5 MeV EB irradiation
RaT (Geant4)
Dose deposition in:
syringe barrel (PP)
syringe needle (steel)
needle hole (air)
environment (air)
homogenized eff. mediumA
bs
or
be
d
do
se
, 1
0-1
3 k
G
y
pe
r e
- /c
m
2
Depth in product loading pattern, cm
Fig.6. Depth dependencies of absorbed doses in
various component parts of syringes for randomized
transversal product loading pattern at X-ray (a) and
EB (b) irradiation. Dashed curves represent the
profiles in the effective homogenized medium
Exactly the same interrelation of doses absorbed
in different component parts is observed for softer X-
ray beam (see Fig.6,a) though the shapes of depth-
dose curves are different for another kind of beam
(mainly due to different initial angular distribution
of photons).
For EB irradiation (see Fig.6,b) right up to the
effective range of electrons the dose in the syringe
barrel dominates over doses in other component parts
85
and particularly in the needle (the latter is opposite
to the cases of X-ray and gamma irradiation). The
dose absorbed in the needle hole is again the small-
est one. One should note that at large z > 30 cm
the interrelation between the component parts doses
becomes similar to that observed for photon irra-
diation; this is due to the contribution of electron
bremsstrahlung.
The decontamination of internal surfaces of sy-
ringe needles is the critical moment of the process of
radiation sterilization of this medical item. Since it
is hard to apply the experimental dosimetry methods
for measurements inside the needle hole the model-
ing provides a unique tool to clarify the dose accu-
mulation within the needle. This problem is hard
for Monte Carlo modeling too because it requires the
achievement of good statistics of energy deposition
events inside small 3D objects.
For EB irradiation we have studied in detail the
interrelation of the mean doses absorbed in the nee-
dle material and in the air inside the hole. In Fig.7
the ”needle-to-hole” dose ratios are plotted as func-
tions of depth for different orientations of syringes in
a loading pattern.
0 5 10 15 20 25 30 35 40
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2 ml Helm syringes
5 MeV EB irradiation
Randomized loading patterns:
RaT (Geant4)
N
ee
dl
e-
to
-h
ol
e
do
se
ra
tio
, r
el
.u
n.
Depth in product loading pattern, cm
transversal orientation
longitudinal orientation
Fig.7. Depth dependencies of the ratio of mean
doses absorbed in the needle material and in the
air-filled needle hole for different product loading
patterns
One can see from Fig.7 that at depths z < 25 cm
where dose rates are significant the transversal load-
ing pattern in which needles are directed orthogonally
to the beam axis provides better uniformity of dose
fields inside needles and holes. At deeper z both ra-
tios grow.
Even finer computer experiment has been carried
out for gamma irradiation. Namely the radial distri-
bution of absorbed dose and photon kerma has been
calculated inside the syringe needle with radial reso-
lution of 10 µm. For this calculation the solitary sy-
ringe model embedded into the homogenized medium
to take into account scattered photons and secondary
particles was irradiated isotropically by γ-radiation of
the mixture of Europium radionuclides. The model-
ing results are shown in Fig.8.
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0.00
0.25
0.50
0.75
1.00
1.25
1.50
2 ml Helm syringe needle
Eu gamma irradiation
needle (steel)
absorbed dose
photon kerma
A
bs
or
be
d
do
se
ra
te
, a
rb
. u
n.
Distance from needle axis, mm
needle hole (air)
RaT (Geant4)
Fig.8. Fine structure of the distribution of photon
kerma and absorbed dose over the syringe needle
radius for the syringe embedded into the
homogenized product medium irradiated by the
isotropic gamma radiation of Europium
radionuclides
One can see that inside the needle material the ab-
sorbed dose is close to photon kerma; hence for steel
the electronic equilibrium is reached. Inside the nee-
dle hole the kerma is constant due to the constancy of
photon flux in air. On the contrary the absorbed dose
has strong radial variation that is completely due to
the non-equilibrium effects in view of the proximity
of dense material. The mean value of absorbed dose
in the needle hole is 5% lower then the photon kerma
level. However due to the surface buildup effect the
dose in air near the surface is close to the average
dose in the needle material.
Therefore one can conclude that the dose ab-
sorbed in the syringe needle material is representative
from the point of view of the needle surface decon-
tamination.
Guardedly extrapolating this conclusion onto the
case of EB irradiation one should notice that in this
case the estimation of the achievement of decontami-
nation dose using the dose absorbed in the polymeric
components of syringes can result in certain under-
irradiation of the needle surfaces (see Fig.6,b). For
gamma and X-ray irradiation this estimation is con-
servative because the dose in a syringe barrel is the
highest one.
4. CALCULATIONS OF PARAMETERS
OF IRRADIATION PROCESSES
Indispensable standard parameters of irradiation
pro-cesses are the regulated minimal absorbed dose
Dmin in a product that is required to achieve the
desired irradiation effect (e.g. the product steriliza-
tion; for this purpose typically Dmin = 25 kGy) and
the lowest achievable dose uniformity ratio (DUR)
δ = Dmax/Dmin where Dmax is the maximal dose
absorbed in the irradiated product stack.
To improve the dose field uniformity the two-sided
irradiation from the opposite directions is commonly
applied till equal dose values are delivered by each
86
side irradiation. In this case the total dose D2 at dis-
tance z from the edge of the product stack of thick-
ness L is a sum of one-side irradiation depth-dose
curves D1(z):
D2(z;L) = D1(z) + D1(L− z). (2)
It has been shown in Ref. [11] that for any spe-
cific value of the DUR δ the maximal allowed product
thickness Lmax(δ) of the product stack is determined
by the maximal root of the non-linear equation:
max{D2(z;Lmax)} = δ ×min{D2(z; Lmax)}, (3)
where the search of maximum and minimum is car-
ried out upon the variable z. It can be accomplished
using the depth-dose dependencies D1(z) obtained
by the computer simulation methods. We have per-
formed such a procedure for all kinds of irradiation
using the dose profiles obtained for syringe barrels.
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 20 40 60 80 100 120
1.00
1.05
1.10
1.15
1.20
RaT (Geant4)
2 ml Helm disposable syringes
Transversal randomized loading pattern
5 MeV X-ray two-side irradiation
D
m
in
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Product stack thickness, cm
D
U
R
=
D
m
ax
/D
m
in
,
re
l.
un
.
Fig.9. The dependencies of the minimal dose rate
Ḋmin and the dose uniformity ratio on the product
stack thickness for two-sided X-ray irradiation
As it can be seen from Fig.9 for X-ray irradia-
tion the minimal absorbed dose rate Ḋmin gradually
decreases with L except for the thin surface buildup
layer. For this case the function δ(L) is monotone in-
creasing and the equation (3) has only one root. The
very acceptable values of DUR δ < 1.15 are achieved
at all values of product stack thickness L < 1.2 m
considered in our modeling. Therefore at X-ray ir-
radiation (as well as at irradiation by harder gamma
quanta) of such a low-density medium the issues of
dose uniformity can arise only at much greater prod-
uct thickness.
The case of EB irradiation is much more complex
due to smaller ranges of electrons and non-monotonic
profiles of absorbed dose. In Fig.10 dose profiles de-
rived from Eq. (2) for two-sided EB irradiation at
increasing syringe layer thickness L are shown.
One can see that the shape of profile changes qual-
itatively as L increases. At small L the maximum is
located in the layer symmetry plane. At greater L it
splits into two separated maxima while a broad min-
imum appears near the symmetry plane. Other local
minima are observed at layer surfaces. Such a multi-
modal behavior complicates the solving of Eq. (3)
that can have multiple roots. The best way is to per-
form it graphically.
Fig.10. Symmetric depth profiles of absorbed dose
in syringe barrels at two-sided EB irradiation of
product layers of different thickness
The results of quantitative analysis are illustrated
by Fig.11. It is clear that at large L the DUR rapidly
grows to inadmissible large values. Obviously DUR
is good for thin layers (L < 10 cm) but they are un-
acceptable on the subject of the irradiation process
throughput capacity.
The optimal thickness corresponds to the sharp
minimum of the dependency δ(L). For all product
loading patterns it is located at thickness Lmax ≈
40 − 45 cm that is close to the thickness of one eu-
robox. One can notice that it slightly greater then
the doubled characteristic depth R50 for EB dose de-
position profile in the effective homogenized medium
(see Fig.3,b; R50 is the depth where the dose on the
decaying part of the profile equals to the half of max-
imal dose). The optimal thickness is characterized by
the definite value of minimal dose rate that in general
decreases as L increases.
Further comparative analysis of Fig.11,a,b shows
that the optimal value δ ≈ 1.2 is practically inde-
pendent on the kind of the product loading pattern.
The application of the homogenized medium approx-
imation (see Fig.11,c) results in greater optimal dose
uniformity ratio δ = 1.32 that is overestimated by
8%.
At longitudinal product orientation the optimal
DUR value is reached at somewhat greater (by
4−5 cm) thickness that allows irradiating of larger
amount of syringes in a container. However it has to
be noticed that the corresponding minimal dose rate
Ḋmin(Lmax) is 15% higher at the transversal orien-
tation of syringes. It is a competitive factor that
controls the speed of the desired dose delivery and in
conjunction with the product amount irradiated per
unit of time determines the throughput capacity P of
a process under optimization.
This integral quantity can be estimated as follows
(we omit the factor inessential for comparative anal-
ysis):
P (L) ∝ Ḋmin(L)
Dmin
· L. (4)
87
Far from the optimal product stack thickness the
functions P (L) shown in Fig.12 substantially depend
on the product loading pattern and drastically differ
from the prediction of homogenized medium model.
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70 80
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2 ml Helm disposable syringes
Longitudinal randomized loading pattern
5 MeV EB two-sided irradiation
RaT (Geant4)
D
m
in
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Product stack thickness, cm
(a)
D
U
R
=
D
m
ax
/D
m
in
,
re
l.
un
.
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70 80
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
(b)
RaT (Geant4)
2 ml Helm syringes
Transversal randomized
loading pattern
5 MeV EB
two-sided irradiation
D
m
in
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Product stack thickness, cm
D
U
R
=
D
m
ax
/D
m
in
,
re
l.
un
.
0
1
2
3
4
5
6
7
0 10 20 30 40 50 60 70 80
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
(c)
RaT (Geant4)
2 ml Helm syringes
Homogenized effective
medium (0.11 g/cm3)
5 MeV EB
two-sided irradiation
D
m
in
,
10
-1
3 k
G
y
pe
r e
- /c
m
2
Product stack thickness, cm
D
U
R
=
D
m
ax
/D
m
in
,
re
l.
un
.
Fig.11. The L-dependencies of Ḋmin and DUR
for two-sided EB irradiation of different loading
patterns of syringes (a,b) and the homogenized
medium (c)
Near the optimal thickness Lmax ≈ 40 cm the
P -curves differ only quantitatively and have close
optimal values for all kinds of product loading pat-
terns. It means that L = Lmax corresponds to the
case when practically the whole electron beam energy
contributes to the dose deposition irrespective of the
details of the dose profile.
However the highest throughput capacity at opti-
mal thickness is observed for the transversal random-
ized loading pattern. The value derived from the ho-
mogenized medium approximation is about 6% lower.
Thus the arrangement of syringes under irradiation
opens the possibility to optimize the process produc-
tivity that is especially important for large-scale con-
tract irradiators.
One can conclude that using advanced technique
of Monte Carlo modeling of energy deposition in
complex heterogeneous media we have demonstrated
the complete cycle of calculations of technological
parameters of the process of radiation sterilization of
medical items at electron beam, X-ray and gamma
irradiation. The capabilities of the RaT code allow
to perform such calculations for arbitrary sorts of ir-
radiated products taking into account their complex
geometry and composition.
0 10 20 30 40 50 60 70 80
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
2 ml Helm syringes
5 MeV EB two-sided
irradiation
RaT (Geant4)
Ir
ra
di
at
io
n
th
ro
ug
hp
ut
c
ap
ac
ity
, a
rb
. u
n.
Product stack thickness, cm
Product loading pattern:
transversal random
regular
longitudinal random
regular
homogenized medium (0.11 g/cm3)
Fig.12. The L-dependencies of the normalized
throughput capacity P of two-sided EB irradiation
process for different loading patterns of syringes and
for the effective homogenized medium
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ВЛИЯНИЕ ГЕТЕРОГЕННОСТИ ОБЪЕКТОВ ОБРАБОТКИ
ПРОМЫШЛЕННЫХ РАДИАЦИОННЫХ ТЕХНОЛОГИЙ
НА ПРОСТРАНСТВЕННЫЕ РАСПРЕДЕЛЕНИЯ ПОГЛОЩЕННЫХ ДОЗ
ПРИ ЭЛЕКТРОННОМ, РЕНТГЕНОВСКОМ И ГАММА-ОБЛУЧЕНИИ
С.В. Дюльдя, М.И. Братченко
Путем моделирования методом Монте-Карло изучено влияние гетерогенности и пространственного
размещения облучаемых одноразовых шприцов на профили поглощенной дозы при различных ви-
дах облучения. Для электронного облучения обнаружены существенные отклонения от предсказаний
обычного приближения гомогенизированной среды. Выявлены зависимости технологических парамет-
ров облучения от ориентации и регулярности/стохастичности расположения шприцов под облучением,
различия в накоплении дозы в различных деталях шприца и неравновесные дозовые эффекты на внут-
ренней поверхности его иглы.
ВПЛИВ ГЕТЕРОГЕННОСТI ОБ’ЄКТIВ ОБРОБКИ
ПРОМИСЛОВИХ РАДIАЦIЙНИХ ТЕХНОЛОГIЙ
НА ПРОСТОРОВI РОЗПОДIЛИ ПОГЛИНЕНИХ ДОЗ ЗА УМОВ
ЕЛЕКТРОННОГО, РЕНТГЕНIВСЬКОГО ТА ГАММА-ОПРОМIНЮВАННЯ
С.В. Дюльдя, М.I. Братченко
Шляхом моделювання методом Монте-Карло вивчено вплив гетерогенностi та просторового розта-
шування одноразових шприцiв пiд опромiненням на профiлi поглиненої дози за рiзних видiв опро-
мiнення. Для електронного опромiнювання знайденi суттєвi вiдхилення вiд передбачень звичайного
наближення гомогенiзованого середовища. Виявленi залежностi технологiчних параметрiв опромiню-
вання вiд орiєнтацiї та регулярностi/стохастичностi розташування шприцiв пiд опромiненням, рiзницi
в накопиченнi дози у рiзних деталях шприцу та нерiвноважнi дозовi ефекти на внутрiшнiй поверхнi
його голки.
89
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