1. M. Sadeghi and O. Kiavar
Dosimetric aspects of 103
Pd radioactive
stent source
This study aims to determine AAPM TG-60 dosimetric quanti-
ties in regions surrounding the 103
Pd stent wall by MCNP5
Monte Carlo code. The Palmaz-Schatz stent was modeled by
a hollow cylinder of 17.89 mm length (2 mm diameter) with
net surface very similar to real stent. The Dose deposited per
photon (Gy), relative dose, Anisotropy function, F(r,h), and ra-
dial dose function, gL(r), were described at AAPM TG-60 pro-
tocol were generated from these values and listed in tabular
format. For benchmarking, the relative dose values were veri-
fied with TG-43 and EGS4 code results at identical conditions,
relative to the radial distances from surface of the stent. There
were noticeable results. These physical dosimetric parameters
can be used in future treatment planning systems for IVBT.
Dosimetrische Aspekte radioaktiver 103
Pd Stents. Ziel dieser
Arbeit war die Bestimmung dosimetrischer Größen in der Um-
gebung von 103
Pd Stents gemäß den AAPM TG-60-Empfeh-
lungen mit Hilfe des MCNP5 Monte Carlo Rechencodes. Der
Palmaz-Schatz Stent wurde dabei modelliert durch einen
Hohlzylinder von 17.89 mm Länge (2 mm Durchmesser) mit
einer Netzoberfläche ähnlich der des realen Stents. Die pro
Photon erzeugte Dosis (Gy), die relative Dosis, die Anisotro-
piefunktion, F(r,h), und die radiale Dosisfunktion, gL(r), wur-
den wie im AAPM TG-60-Protokoll beschrieben aus diesen
Werten erzeugt und tabellarisch dargestellt. Zu Benchmarking-
zwecken wurden die relativen Dosiswerte verifiziert mit TG-43
und EGS4 Rechenergebnissen bei gleichen Bedingungen, rela-
tive zur radialen Entfernung von der Stentoberfläche. Die Er-
gebnisse sind bemerkenswert. Die dosimetrischen Parameters
können bei zukünftigen Therapieplanungssystemen für IVBT
verwendet werden.
1 Introduction
The doses given to the vessel wall are very crucial quantities
in intravascular brachytherapy (IVBT). When the concept of
using radiation to reduce the incidence of restenosis following
angioplasty was introduced, preclinical studies revealed pro-
mising results for both temporary catheter implants and per-
manently implanted radioactive stents [1]. The purpose of in-
travascular brachytherapy is to safely deliver a sufficient
radiation dose to the vessel wall while limiting dose to normal
tissues surrounding the vessel [2]. Current clinical trials are
showing that intravascular brachytherapy techniques effec-
tively reduce the occurrence of restenosis in humans [3, 4].
In addition, many dosimetry studies are being conducted to
determine which isotopes and delivery methods are best sui-
ted for inhibiting restenosis in human arteries.
This paper is a new study in which Monte Carlo code
(MCNP5) is employed to investigate the dosimetric character-
istics of a 103
Pd-implanted stent for the purpose of assessing
its potential use in IVBT [4, 5]. Because of the characteristic
low-energy X-rays that 103
Pd emits and the low activity re-
quired for intravascular brachytherapy, a 103Pd stent can be
handled safely with minimal shielding requirements. In addi-
tion, the short half-life of 103
Pd (T1/2 = 16.97 days) allows it
to deliver > 90% of its radiation over 2 months and also gives
it a reasonable shelf life [6]. Numerous other characteristics of
103
Pd make it an attractive choice for intravascular bra-
chytherapy.
By and large, the main aim of this study is to determine do-
simetric parameters of TG-60 protocol [7]. For benchmarking,
the relative doses around the stent are calculated by MCNP5
and the results are verified with previously published papers
data [8, 9]. It is worth noting that the all conditions in this re-
search are identical with the mentioned articles.
2 Methods
2.1 Stent description
An arbitrary stent design, closely matching that of a commer-
cial stent (Palmaz-Schatz) [8] was used for this work. The
stent was composed of 201 identical (316L) stainless steel
struts with a thin layer of 103
Pd on the stent. The stainless
steel had a density of 7.861 g/cm3
and was composed of 17%
Cr, 13% Ni, 2.5% Mo, 64.5% Fe and allowable maximums
of 1% Si and 2% Mn (Table 1) [10]. The 103
Pd is a photon
emitter and has a half life of almost 17 days with density of
12.023 g/cm3
(Table 2) [11–14]. Fig. 1 shows the diagram of
half stent geometry in simulation. To model the stent as it
might appear in a blood vessel, the stent was expanded to an
outer diameter of 2 mm and a length of 17.89 mm (18-mm un-
expanded length) [9, 17].
2.2 Monte Carlo calculation technique
The Monte Carlo N-Particle code (MCNP version 5) was used
for the dose calculations [15]. In this article it was tried to
KT_kt-110222 – 17.9.12/stm media köthen
M. Sadeghi and O. Kiavar: Dosimetric aspects of 103
Pd radioactive stent source
77 (2012) 5 Ó Carl Hanser Verlag, München 1
Table 1. Atomic numbers for 103
Pd, 316L stainless steel and a 1:1 mix-
ture [10, 11]
Material Z or Zeff
a)
103
Pd 46
Stainless steel 316L [Cr (17%), Ni (13%), Mo (2.5%),
Fe (64.5%), Si (1%), Mn (2%)]b)
27
1:1 Mixture of stainless steel and 103
Pd 39
a)
Zeff = (a1Z1
m
+ a2Z2
m
+ ... anZn
m
)1/m
; (m = 3.5)

2. KT_kt-110222 – 17.9.12/stm media köthen
simulate the geometry which is approximately similar to phys-
ical parameters of real stent, but simplification was inevitable
(Fig. 1). For geometry simulation the stent was covered longi-
tudinally and radially by 2 cm and 4.0 cm of water voxels, re-
spectively. The water detectors were also simulated in the
form of shells with 0.1 mm thickness and 0.2 mm height
(Fig. 1). The outputs of Monte Carlo simulation were the en-
ergy deposited (MeV) per photon, calculated by *F8 tallies.
Dose values can multiply by intensity factor (the number of
photons emitted per disintegration) and divided on mass of
each detector (kg) to give dose deposited per disintegration
(Gy). The number of photon histories was set at 4 · 107
in or-
der to obtain a relative statistical error not greater than 0.7%
for each of the tallies placed at angles of 08 and 908.
In this study the relative dose were obtained by volume-
averaging the dose values in the detectors only along the
transverse axis at radial distances of r = 0.5, 1, 1.5, 2, 2.5, 3,
3.5 and 4 cm from surface of stent and then normalizing them
by the volume-averaged dose value at 1 cm. For benchmark-
ing, the relative dose calculated by MCNP5, were compared
to those data at TG43 [16] and EGS4 (Monte Carlo) [9]. Ac-
cording to the protocol described in TG-60; F(r, h), gL(r) were
acquired in water using gamma emitter’s formula (Eq. (1) and
(2)). Ultimately, treatment planning and dose fall-off curves
were also calculated [7].
Fðt; hÞ ¼ Dðr; p=2ÞGðr; hÞ ð1Þ
gLðrÞ ¼
Dðr; p=2ÞGðr0; p=2Þ
Dðr0; p=2ÞGðr; p=2Þ
ð2Þ
Where: r = the distance from center of stent, r0= the reference
point for photons (1 cm), G(r, h) = geometry factor resulting
from spatial distribution of the radioactivity within the source.
For calculating G(r, h), employed the Monte Carlo F4 tally
with the mass densities of all materials within the entire com-
putational geometry set equal to zero so there were no inter-
action and particles streamed through the stent and water
geometry. This parameter based on TG-43 protocol was used
for removing the inverse square law, in computations of stated
F(r, h) and gL(r) factors [8].
3 Results and discussion
In this investigation, the dose distributions were calculated by
MCNP5 Monte Carlo code at definite points in transverse
M. Sadeghi and O. Kiavar: Dosimetric aspects of 103
Pd radioactive stent source
2 77 (2012) 5
Table 2. Statistical decay of 103
Pd radioisotope [16]
No Half life Rad. Type Energy
(keV)
Intensity
(%)
1 16.991 days Gamma 39.7480 0.0683
2 " " 53.2900 0
3 " " 62.410 0.001038
4 " " 241.880 0
5 " " 294.98 0.0028
6 " " 317.720 0
7 " " 357.450 0.02206
8 " " 443.790 0
9 " " 497.080 0.003961
10 " X L 2.7 8.80
11 " X KA2 20.0737 22.06
12 " X KA1 20.2161 41.93
13 " X KB 22.7 13.05
Fig. 1. The geometry and detectors simulations
with MCNP5 for half expanded stent (MCNP
plot)
Fig. 2. The dose fall-off of a 103
Pd stent per photon at the distance from
surface (Gy)

3. cross sections for per photon. Dose maps were plotted for dis-
tances ranging from contact to 0.7 cm radially out from the
stent surface (Fig. 2) and showed the fast dose fall-off of
photons. The curve decreases exponentially from surface
slightly and ultimately acquires the least value.
Table 3 shows our calculated relative-dose values com-
pared to the corresponding values calculated from tabulated
TG43 [8] and EGS4 data [9]. Regarding to the acquired dose
results, the mean averaged error, reported by MCNP5 was
less than 0.7%. The percent error between the previous calcu-
lated TG43 and EGS4 (Monte Carlo) data and MCNP5 (pres-
ent work) are also shown in Table 3.
According to American Association of Physicists in Medi-
cine (AAPM) Task Group No.60 recommendation, the an-
isotropy function (F(r, h)), the radial dose function, gL(r),
were calculated in water for gamma photons [7]. The detec-
tors were simulated at polar angles of 0–908 in 108 increase
and at radial distances of r = 0.18 to 0.9 cm relative to the
stent center (Fig. 1).
The 2-D anisotropy function describes the variation of
dose in the longitudinal plane of a brachytherapy source. For
calculation of the anisotropy function, the *F8 tally was used
to obtain dose per photon in contiguous annular disk shells
detectors by using gamma emitters formula (Eq. (1)) and the
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M. Sadeghi and O. Kiavar: Dosimetric aspects of 103
Pd radioactive stent source
77 (2012) 5 3
Table 3. MCNP5 calculated relative dose versus TG-43 and EGS4 (Monte Carlo) along the transverse axis of a 103
Pd stent
Distance from surface
(cm)
TG-43
Relative dose [16]
Monte Carlo
Relative dose [9]
MCNP5
Relative dose
(present work)
MCNP5
error by TG-43
(%) [9]
MCNP5
error by MCNP5
(%) (present work)
0.50 4.97 4.90 4.821 2.9 –1.6
1.00 1.00 1.00 1.00 – –
1.50 0.343 0.333 0.351 2.3 5
2.00 0.145 0.146 0.149 2.7 2
2.50 0.069 0.071 0.066 –4.3 –7.02
3.00 0.035 0.036 0.034 –2.85 –5.5
3.50 0.019 0.0193 0.0198 4 2.5
4.00 0.010 0.0107 0.0106 5 –0.9
Table 4. Anisotropy function, F(r, h), for 103
Pd stent, used at coronary arteries
r (cm) 108 208 308 408 508 608 708 808 908
0.18 – – – – – 2.854 1.940 1.979 1
0.20 – – – – 2.815 2.909 1.965 1.988 1
0.22 – – – – 1.866 1.956 1.996 1.006 1
0.24 – – – 1.796 1.939 1.998 1.016 1.002 1
0.26 – – – 1.912 1.985 1.992 1.881 1.024 1
0.28 – – – 1.078 1.180 1.169 1.111 1.028 1
0.30 – – – 1.344 1.408 1.326 1.182 1.043 1
0.32 – – 1.491 1.856 1.862 1.618 1.311 1.081 1
0.34 – – 1.351 1.774 1.891 1.958 1.087 1.007 1
0.36 – – 1.345 1.829 1.926 1.896 1.796 1.167 1
0.38 – – 0.937 0.947 0.983 0.998 1.184 1.113 1
0.40 – – 0.600 0.788 0.852 0.892 0.931 1.168 1
0.45 – 0.825 0.98 0.991 1.002 1.038 1.231 1.033 1
0.50 – 0.652 0.823 0.906 0.941 0.964 0.994 1.012 1
0.60 – 0.515 0.728 0.865 0.916 0.964 0.982 1.052 1
0.70 – 0.504 0.721 0.854 0.930 0.960 0.955 0.987 1
0.80 – 0.505 0.722 0.854 0.91 0.964 0.945 0.985 1
0.90 0.418 0.612 0.754 0.857 0.921 0.954 0.978 1.012 1

4. KT_kt-110222 – 17.9.12/stm media köthen
results were presented in Table 4 [8, 13]. The anisotropy func-
tion, F(r, h), table, showed homogeneous doses scores near
the surface of stent. Notwithstanding, it is considerable that,
at some deep angles and near distances from surface of stent,
the F(r, h) values show variants values near 2.
The radial dose function, gL(r), was determined in order to
characterize the effects of absorption and scatter in the med-
ium along the reference radial (h0 = 908) axis of the source
(Eq. 2) [8]. Fig. 3 shows the radial dose function curve with
respect to the distance from surface of stent. It is clear from
the Fig. 3 that by increasing the distance from surface, the
gL(r) increases sharply and reaches the peak at 0.5 cm point.
This event can be because of the huge amount of energy
which the gamma photons deposit at nearby the source. At
the second step the gL(r) decreases steeply for the points be-
tween 0.5 and 1.5 and keeps its exponential fall-off after
1.5 cm. Regarding Fig. 3 it is obvious that g(r) = 1 where
r = 1 (reference point for gamma emitters). It can be justified
by considering the equivalence of the numerator and denomi-
nator of the mentioned fraction (Eq. (2)).
Finally the isodose curves plotted on transverse cross sec-
tion and the values of them demonstrated in percent scale
(Fig. 4). The isodose curves showed the detailed dose distribu-
tion in the arterial wall surrounding the stent. These curves
revealed the homogeneous treatment planning curves. The er-
rors of these points located at transverse cross section were
also reported (Fig. 5). It also should be added that all statisti-
cal uncertainness was less than 0.7% for this unique gamma
emitting source.
The American Association of Physicists in Medicine Task
Group No. 60 [7] has recommended specific radioactive-stent
dose prescriptions so that various studies can be compared.
Their recommendations, based on past preclinical studies
and the intimal proliferation mechanism of restenosis, specify
the dose delivered over 28 days at a depth of 0.5 mm along
the perpendicular bisector to the long axis of the stent from
its outer surface [7].
Our study showed well results in dose and comparative
dose rate computation by following the mentioned protocol
and these data were compared with both previous TG-43
and EGS4. From Table 3 it is conspicuous that the mean per-
cent error between the calculated relative doses by MCNP5
and TG43 values is almost 3.4% and for MCNP5 and EGS4
is about 3.5%. By considering Fig. 2, the curve decreases ex-
ponentially from surface slightly and ultimately acquires the
least value and this event is quite relevant by gamma behavior
through the tissue [4]. The anisotropy function according to
the TG-43 was calculated and listed in the Table 4. The men-
tioned occurrence of high values at some detectors must be
due to the natural behavior of photons which in these points
near to the stent deposit much more energy. This high dose
value (at numerator) compare with the dose at reference
angle (at denominator) can affect on the fraction of Eq. (1)
and increase it.
Owing to the complex geometry of stents, the ability to
model it in dose distributions using Monte Carlo calculations
is limited. The calculation technique we used to model a stent
and calculate the 3-D dose distribution surrounding it may
not perfectly match that of a commercial stent. Nevertheless,
at distances at least 0.5 mm from the surface of the stent, the
differences in calculation should be small and were showed.
4 Conclusions
Our technique provides a reasonable method for acquiring
the 3-D dose distribution around a stent and visualizing the
effects that the discrete stent structure has on the dose distri-
bution. Dosimetric parameters, including dose per photon,
relative dose, radial dose function, gL(r), and anisotropy func-
tion, F(r, h) of the 103
Pd stent have been calculated by using
M. Sadeghi and O. Kiavar: Dosimetric aspects of 103
Pd radioactive stent source
4 77 (2012) 5
Fig. 3. The radial dose function, gL(r), of a 103
Pd active stent from the
surface of stent
Fig. 4. The isodose curves (Percent scale) of a 103
Pd stent (X-Y cross sec-
tion)
Fig. 5. The standard errors calculated by MCNP5 at located detectors
(radial distances) (h0 = 90)

5. the MCNP5 Monte Carlo code [18, 19]. These calculations
were performed following the AAPM TG-60 task group re-
commendations. These values need to be determined inde-
pendently by several investigators to routinely calculate dose
in an artery in the clinical setting. More experimental dosime-
try is also essential to support these results. Future work, in-
cluding measuring dosimetry on a 103
Pd implanted stent, de-
termining the self-absorption of a 103
Pd implanted stent and
expanding the calculation to include plaque buildup in the ar-
tery wall, needs to be performed to fully assess the applicabil-
ity of a 103
Pd-implanted stent in intravascular brachytherapy.
These data by future experimental works lead us to have
promising results and plan more confident treatment [20, 21].
However, the use of this stent is still pending upon more bio-
logical scrutinizes.
Acknowledgement
The authors are thankful for all supports of Prof. Dr. Ali
S. Meigooni (Comprehensive Cancer Center of Nevada, Las
Vegas, Nevada, USA), and Prof. Dr. Claudio Tenreiro (De-
partment of Energy Science, SungKyunKwan University, Su-
won, Republic of Korea), and Milad Enferadi.
(Received on 28 December 2011)
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The authors of this contribution
Mahdi Sadeghi
Agricultural, Medical and Industrial Research School
Nuclear Science and Technology Research Institute
P.O. Box: 31485/498
Karaj, Iran
* Corresponding author. E-mail: msadeghi@nrcam.org
Omid Kiavar
Department of Biomedical Radiation Engineering
Science and Research Branch, Islamic Azad University
Tehran, Iran
You will find the article and additional material by entering
the document number KT110222 on our website at
www.nuclear-engineering-journal.com
KT_kt-110222 – 17.9.12/stm media köthen
M. Sadeghi and O. Kiavar: Dosimetric aspects of 103
Pd radioactive stent source
77 (2012) 5 5