1. M. Sadeghi, O. Kiavar, P. Saidi and R. Fatehi
Novel dose calculation and characterization
of 32
P intravascular brachytherapy stent
source
Derived from AAPM task group No. 60/149 protocol, applica-
ble in treatment planning In this study, the two-dimensional
dose distributions in water for a 32
P intravascular brachyther-
apy stent have been calculated. The pure beta emitter source
32
P which has been coated on Palmaz-Schatz stent is discussed.
The dosimetric parameters required by the AAPM TG-60/149
formalism are discussed and calculated. Version 5 of the
(MCNP) Monte Carlo radiation transport code was used to
calculate the dosimetry parameters around the source. The
Monte Carlo calculated dose rate at the reference point is
found to be 2.8 Gy/lCi. Also in this study, the geometry func-
tion, G(r,h), radial dose function, g(r), and the anisotropy func-
tion, F(r,h), have been calculated at distances from 1.8 to
9 mm. The results of these calculations have been compared
with other published calculated and measured values for an ac-
tual same source. High dose variants were visible near the 32
P
stent surface, but these values decreased with depth in water
rapidly. There is an acceptable agreement between the calcu-
lated data in this study and other published data for the same
source, which validate our simulations method.
Neue Dosisberechnungen und Charakteristika in der intra-
vaskulären Brachytherapie mit 32
P. In der vorliegenden Stu-
die wurden die zweidimensionalen Dosisverteilungen in Was-
ser für die intravaskulären Brachytherapie mit 32
P berechnet.
Als Strahlenquelle werden Palmaz-Schatz Stents mit dem
reinen Betaemitter 32
P beschichtet verwendet. Die dosimetri-
schen Parameter, die nach dem AAPM TG-60/149 Formalis-
mus erforderlich sind werden diskutiert und berechnet. Ver-
sion 5 des (MCNP) Monte Carlo Strahlungstransportcodes
zur Berechnung der dosimetrischen Parameter um die Quelle
herum verwendet. Die so berechnete Dosisleistung am Refe-
renzpunkt liegt bei 2,8 Gy/lCi. Ebenfalls in dieser Studie wur-
de die Geometriefunktion G(r,h), die radiale Dosisfunktion
g(r) und die Anisotropiefunktion F(r, h) berechnet für Abstän-
de von 1,8 bis 9 mm. Die Ergebnisse dieser Berechnungen wur-
den verglichen mit anderen veröffentlichten Berechnungen und
mit gemessenen Werten für die gleiche Quelle. Große Dosis-
schwankungen zeigten sich nahe der 32
P Stentoberfläche, nah-
men aber mit der Tiefe in Wasser sehr schnell ab. Die Überein-
stimmung zwischen den in dieser Studie berechneten Werten
und anderen veröffentlichten Daten für die gleiche Quelle ist
akzeptabel, wodurch die gewählte Simulationsmethode vali-
diert wird.
1 Introduction
Restenosis is the major limitation of angioplasty. The impact
of restenosis is highlighted by studies that compared coronary
angioplasty to bypass surgery as a treatment strategy for cor-
onary artery disease [1]. Treatment with angioplasty had low-
er initial costs and fewer major complications. However, the
six month to three years follow-up of patients with more angi-
na required more revascularization procedures and lost most
of the benefit of angioplasty [1, 2]. Coronary stent placement
in conjunction with angioplasty can reduce the restenosis rate
to 22%–32% [3]. Recent preclinical studies indicate that irra-
diation using ionizing radiations in the dose range of 15–
30 Gy may reduce substantially the problem of restenosis in
patients who have undergone an angioplasty [6].
Randomized, controlled clinical trials have shown that bra-
chytherapy using beta or gamma emitters is highly effective in
reducing the incidence of recurrent in-stent restenosis as mea-
sured angiographically and by intravascular ultrasound [4, 5].
Brachytherapy also reduces the incidence of major adverse
cardiac events (primarily the need for further revasculariza-
tion), compared with placebo [4]. In the case of using intra-
vascular brachytherapy, radiation doses can be delivered with
minimal normal tissue toxicity due to the high localization of
dose to the immediate vicinity of radioactive sources. It is
estimated that the restenosis rate may drop from roughly 35–
40% to well below 10% if radiation is delivered to the ob-
struction site during or after angioplasty [5]. Therefore, the
potential of intravascular brachytherapy in reducing resteno-
sis has aroused a tremendous interest in the cardiology com-
munity [6, 7].
Based on these studies, three brachytherapy systems one
gamma and two beta emitters have been approved by the
Food and Drug Administration (FDA) for the treatment of
in-stent restenosis. These three systems are based on radionu-
clides 192
Ir, 90
Sr/90
Y, and 32
P and have been used in more than
30,000 patients [5, 9]. To understand the results of various
preclinical studies using a variety of radionuclides and deliv-
ery systems for IVBT (Intravascular Brachytherapy) Ameri-
can Association of Physicists in Medicine (AAPM) in 1999
published a protocol Task Group-60 introducing the recom-
mendations and dosimetry studies for intravascular bra-
chytherapy [6].
One of the sources subjected to preclinical and clinical
testing is beta particle emitting 32
P radionuclide source which
was initially used in radioactive stents in IVBT [7, 16]. 32
P is a
pure beta emitter with mean energy of 0.693 MeV and the
half-life of 14.262 days [9]. This report presents Monte Carlo
(MC) simulation results for the dosimetry parameters of the
32
P radioactive Palmaz-Shatz stent. To evaluate the simula-
M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
76 (2011) 5 Ó Carl Hanser Verlag, München 367
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2. tion accuracy in this study, the Monte Carlo simulation meth-
od was benchmarked with GDT-P32-1 20 mm 32
P source [19].
Also the Monte Carlo calculation results used in this study
has been compared with measured values for the same type
of stent [7].
Three-dimensional dose distribution data and the corre-
sponding American Association of Physicists in Medicine
TG-60/149 [6, 8] dosimetric quantities are necessary for char-
acterization of the dose received by both the target tissue,
and surrounding normal tissues. Hence, this work is dedicated
to the Monte Carlo method to calculated dosimetric parame-
ters by MCNP5 code, according to TG-60/149 guidelines for
the 32
P brachytherapy stent.
2 Materials and methods
2.1 Stent description
An arbitrary stent design, closely matching that of a commer-
cial stent (Palmaz-Schatz) was used for this work [6]. The
physical parameters of the stent, defined in TG-60 [6] were
used to model the stent. Fig. 1 shows a schematic diagram of
the source. In addition acquiring much more accurate results,
the MCNP5 which has more cross sections in its library in
comparison with previous versions was selected. The Palmaz-
Schatz stent [6] of 14 mm length, 0.5 and 1.75 mm internal
and external radius respectively is made of stainless steel with
the composition of (by weight percent), [Cr (17%), Ni (13%),
Mo (2.5%), Fe (64.5%), Si (1%), Mn (2%)] and the density
of 6.2 g/cm3
which is coated with 1 lm layer of radioactive
32
P [9, 10] obtained from the following equation:
31
P þ n ! 32
P ð1Þ
2.2 Monte Carlo evaluation
Version 5 of Monte Carlo (MC) radiation transport code was
used to calculate the dose distribution of 32
P active stent [11].
The geometry of this stent was developed in the form of a
square lattice on a cylindrical surface in MCNP assuming
the outer and inner radius of the active stent source to be
1.5 and 1.75 mm after-expanded with 1 lm coating layer and
14 mm length. Fig. 2 portrays the model and dimensions used
for the Monte Carlo simulations. To obtain the TG-60/149
dosimetric quantities such as, G(r, h), F(r, h) and g(r) [12]
scoring voxels, consisted of joint gyrate disk shells, were con-
sidered at radial distances from 1.8 to 9 mm in 0.2 mm incre-
ment away from the source along the longitudinal axis and at
polar angles from 08 to 908 in 10 degree increments. Particle
fluxes and energy deposited tallies, F4 and *F8 respectively
were applied to calculate kerma and the net energy (MeV)
deposited in the detectors around the source in this study
[13, 14]. Deposited energy (MeV) in the detectors was di-
vided by scoring region mass, yields the raw Monte Carlo cal-
culated dose per starting particle. The dose rate is then calcu-
lated by multiplying the dose per starting particle, the source
activity (dps) and 32
P beta emission intensity [5, 15, 18]. The
simulations were performed up to 3 · 107
histories and deliv-
ered absolute doses to voxels were calculated by the follow-
ing Eq. (1).
Where: t = treatment time and A0 = whole Activity (lCi).
2.3 AAPM TG-60/149 formalism
According to the protocols described in TG-60/149; [6, 8] do-
simetric parameters have been calculated using the Monte
Carlo method by MCNP5 [11]. The detectors were defined
at polar angles of 08–908 in 108 increments and at radial dis-
tances of r = 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.5,
5, 6, 7, 8 and 9 mm away from center of stent. F4 tally was em-
ployed to calculate G(r, h), with the mass densities of all ma-
terials within the entire computational geometry set equal to
zero so there were no interaction and particles streamed
through the stent and phantom geometry [13, 14]. According
to TG-43U1 protocol for calculating G(r, h) the source sup-
posed to be line source [12].
M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
368 76 (2011) 5
Fig. 1. Palmaz-Schatz 32
P stent used in coronary artery brachytherapy Fig. 2. A schematic diagram of simulated 32
P stent in the water phantom
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3. The anisotropy function, F(r, h), accounts for the angular
dependence of beta absorption and scatter. In order to calcu-
lation of the anisotropy function, the *F8 tally was used to ob-
tain dose per particle in detectors by using beta emitters for-
mula for lattice cylindrical source (Eq. (2)) [12–14].
DoseðGyÞ ¼
EðjÞ
mðkgÞ
Â
Intensityð%Þ
100
Â
Z t
0
A0eÀkt
dt ð2Þ
The radial dose function, g(r), accounts for radial dependence
of beta absorption and scatter in the medium along the trans-
verse axis [12]. According to the methodology described in
TG-60/149; g(r) was calculated by using line-source geometry
for the stent by the following equation (Eq. (3)) [6, 8].
gðrÞ ¼
Dðr; h0ÞGðr0; h0Þ
Dðr0; h0ÞGðr; h0Þ
ð3Þ
For beta radiation sources, the radial dose function is deter-
mined using a least squares fit of a sixth order logarithmic
polynomial. Thus, where ai are the coefficients of the sixth
function, and r is in mm. This function is normalized at r0
(2 mm from surface of stent).
gðrÞ ¼ ða0 þ a1r1
þ a2r2
þ a3r3
þ a4r4
þ a5r5
þ a6r6
Þ ð4Þ
3 Results and discussion
The MCNP simulation method in this work was benchmarked
with GDT-P32-1 20 mm 32
P source [19]. The comparison of
MCNP-calculated value of the dose rate at reference point r0
(2.841E-01 cGy/s mCi), with the previously published data
for the sources [19] (3.004E-01 cGy/s mCi), demonstrate the
accuracy of our simulation method.
Table 1 shows the calculated dose rate of the 32
Pstent at
the distances of r = 0.5, 1 and 2 mm away from the stent using
MCNP5 code. For the purpose of comparison, the measured
values obtained by Carter et al. [7] (clinical) using radio-
chromic film are also presented at Table 1. The comparison
between the measured and calculated values shows that the
differences between these two data sets are large depending
on the distance [15, 16]. These differences are also a function
of the phantom size used in MC and measurement condition,
respectively. Measurements may have uncertainty due to in-
adequate energy response of the radiochromic dosimeter.
The differences between the average doses calculated using
MCNP5 and TG-60 measured data at radial distances of
r = 0.5, 1 and 2 mm from stent surface were 0.7%, 4% and
13% respectively.
Fig. 3. shows the variation of dose with radial distance of
6.0 lCi 32
P stent at reference angle (h0 = 908) over 28 days
[20–22]. Also Fig. 3 presents the comparison between the cal-
culated results in this study with the measured and calculated
data by Prestwitch et al. [16] and Duggan et al. [17] respec-
tively. The axial dependence of the dose at a fixed radial
distance can be calculated by the cylindrical shell method of
Prestwich et al. [16].
The line source approximation of the geometry function,
G(r, h),values for the 32
P stent has For easier calculation and
for convenience to compare with other published data the
form r2
G(r, h) is used instead of G(r, h) [13, 14]. The calcu-
lated values of G(r, h) times r2
are shown in Table 2.
The anisotropy function, F(r, h), accounts for the variation
of dose distribution around the source as a function of dis-
tance and angle from the center of the source [11]. The values
are presented in Table 3. The steep dose gradient in the radial
direction causes high values of F(r, h) encountered at small
angles and large distances from the source center.
In terms of the TG-60 parameters, the radial dose function,
g(r), was defined to characterize the effects of absorption and
scatter in the medium along the transverse axis of the source
and Fig. 4 demonstrates its fall-off curve. The calculated line
source radial dose function, g(r), for the 32
P stent in water in
this work and the calculated by Mourtada et al. [19] for 32
P
segment source are shown in Fig. 4. The difference between
these two data mainly derives from the different source de-
M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
76 (2011) 5 369
Table 1. Monte Carlo calculated dose of the 32
P coated stent with 1, 6, 14 lCi activity at three selected points in compare with the clinical results
(pig coronary artery) of Carter et al. [7]
Distance from
source surface
(mm)
Dose (Gy)
(1 lCi)
Dose (Gy)
(6 lCi)
Dose (Gy)
(14 lCi)
Measured [7] MCNP5 Measured [7] MCNP5 Measured [7] MCNP5
0.5 18 17.86 107.9 107.16 251.9 250.04
1 9.7 10.12 58.4 60.72 13.64 14.68
2 3.3 2.86 19.7 17.16 46.1 40.04
Fig. 3. Radial dose distribution of 6.0 lCi 32
P stent with MCNP5 calcu-
lations at reference angle (h0 = 908) from surface of the stent over 28 days
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4. M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
370 76 (2011) 5
Table 2. The r2
G(r, h) for 32
P coated stent calculated by MCNP5
r(mm) r2
G(r ,h) for 32
P coated stent
108 208 308 408 508 608 708 808 908
1.8 – – – – – 0.007 0.006 0.006 0.006
2.0 – – – – 0.009 0.008 0.007 0.007 0.006
2.2 – – – – 0.009 0.008 0.007 0.007 0.007
2.4 – – – 0.012 0.010 0.009 0.008 0.008 0.007
2.6 – – – 0.013 0.011 0.009 0.008 0.008 0.008
2.8 – – – 0.014 0.011 0.010 0.009 0.008 0.008
3.0 – – – 0.015 0.012 0.010 0.009 0.009 0.009
3.2 – – 0.021 0.016 0.013 0.011 0.010 0.009 0.009
3.4 – – 0.022 0.016 0.013 0.011 0.010 0.010 0.009
3.6 – – 0.023 0.017 0.014 0.012 0.011 0.010 0.010
3.8 – – 0.024 0.017 0.014 0.012 0.011 0.010 0.010
4.0 – – 0.024 0.018 0.014 0.012 0.011 0.011 0.010
4.5 – 0.041 0.026 0.019 0.015 0.013 0.012 0.011 0.011
5.0 – 0.043 0.027 0.020 0.016 0.014 0.013 0.012 0.012
6.0 – 0.044 0.028 0.021 0.017 0.015 0.014 0.013 0.013
7.0 – 0.040 0.027 0.021 0.018 0.016 0.015 0.014 0.014
8.0 – 0.035 0.026 0.021 0.018 0.016 0.015 0.015 0.014
9.0 0.039 0.031 0.025 0.021 0.018 0.017 0.016 0.015 0.015
Table 3. The anisotropy functions F(r, h) for 32
P stent calculated by MCNP5
r(mm) F(r, h) for 32
P stent
108 208 308 408 508 608 708 808 908
1.8 – – – – – 1.076 0.992 0.978 1
2.0 – – – – 0.965 1.001 1.002 0.997 1
2.2 – – – – 1.011 1.006 1.014 1.005 1
2.4 – – – 1.056 1.061 1.046 1.032 1.013 1
2.6 – – – 1.110 1.138 1.111 1.069 1.022 1
2.8 – – – 1.279 1.280 1.218 1.119 1.027 1
3.0 – – – 1.561 1.516 1.377 1.198 1.051 1
3.2 – – 2.056 2.060 1.952 1.650 1.301 1.076 1
3.4 – – 3.032 3.038 2.731 2.107 1.500 1.102 1
3.6 – – 5.395 5.226 4.277 2.965 1.794 1.141 1
3.8 – – 10.899 10.256 7.618 4.422 2.218 1.221 1
4.0 – – 29.627 26.716 17.624 8.389 3.063 1.355 1
4.5 – 1087.211 1071.824 793.389 323.230 64.385 7.355 1.165 1
5.0 – 2012.464 1853.226 972.446 167.710 6.095 0.757 0.728 1
6.0 – 2917.190 2056.737 244.467 1.248 0.954 0.993 1.230 1
7.0 – 1057.315 434.640 1.393 0.501 0.759 0.429 0.578 1
8.0 – 257.905 20.072 0.412 0.434 1.110 0.503 0.594 1
9.0 3.294 3.373 0.529 0.608 0.391 0.640 0.453 0.670 1
2011CarlHanserVerlag,Munich,Germanywww.nuclear-engineering-journal.comNotforuseininternetorintranetsites.Notforelectronicdistribution.

5. scription, different methods for simulation, and different ver-
sions of MCNP code. The radial dose function is usually given
in the form of a polynomial function which can be evaluated
at the desired radial distance r.
The sixth order polynomial fitting function for g(r) is re-
ported in Fig. 4.
Figure 5 depicts the standard errors for the doses calcu-
lated along the transverse axis of the stent. The average of
the standard errors reported by MCNP5 was 0.2% in nearest
detectors and largest standard error was 20% (in furthest
voxels from the stent surface).
Figure 6 displays the isodose contours for the 32
P stent in
water which were calculated by MCNP5 in longitudinal and
transverse plans. As shown in the figure, the isodose curves
of the 32
P stent, appears isotropic dose distribution around
the source.
M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
76 (2011) 5 371
Fig. 4. Radial dose function, g(r), values for 32
P stent and 32
P segment
sources (Ref. 19)
Fig. 5. Standard errors calculated by MCNP5 along the transverse axis
of the 32
P stent
(a) (b)
Fig. 6. Isodose curves (Gy),
around the 32
P stent, calculated
and plotted from the dose re-
sults of present work with the
activity of 1.0 lCi for 28 days
treatment times at (a) longitu-
dinal plane, (b) transverse
plane
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6. 4 Conclusions
In this work, the 2D dose distributions have been calculated
for a 32
P IVBT source stent in water using the MCNP5 Monte
Carlo code. The dose parameters required by the AAPM TG-
60/149 formalism are discussed and calculated based on the
2D dose distribution. For the beta source stent studied, dose
distribution is uniform along the axial direction of the stent.
By and large only the practical clinical trials exactly will
answer the questions of whether or not radioactive stents re-
duce restenosis in human arteries and what activities and
doses are optimal for achieving this reduction. Nevertheless,
the dose distribution surrounding stents used in intravascular
brachytherapy is needed for confident treatment planning.
The results were in good agreement with previously pub-
lished paper results. High dose variants were visible near the
32
P stent surface, but these values decreased with increasing
in depth at vessel layers. The results show that, 32
P stent with
1.0 lCi activity, can deliver almost 18 Gy expected dose value
to 0.5 mm thick vessel wall as well as measured values. It can
be infered from the isodose curves that the isodose curves
surrounding the stent at vessel wall are significantly homo-
geneous. It shows the suitability of using this unique source.
Matching the animal clinical and calculated results would
help us to have more reliable treatment, but still clinical use
of this stent is pending upon more biological scrutinizes.
(Received on 13 February 2011)
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The authors of this contribution
Mahdi Sadeghi
Agricultural, Medical Industrial Research School
Nuclear Science and Technology Research Institute
P.O. Box 31485-498, Karaj, Iran
E-mail: msadeghi@nrcam.org
Omid Kiavar and Pooneh Saidi
Department of Nuclear Engineering, Islamic Azad University
Science and Research Branch, Tehran, Iran
E-mail: o.kiavar@gmail.com, poonehsaidi@gmail.com
Rozhin Fatehi
Department of Chemistry, Islamic Azad University
North branch, Tehran, Iran
E-mail: r.fatehy@yahoo.com
You will find the article and additional material by entering
the document number KT110166 on our website at
www.nuclear-engineering-journal.com
M. Sadeghi et al.: Novel dose calculation and characterization of 32
P intravascular brachytherapy stent source
372 76 (2011) 5
2011CarlHanserVerlag,Munich,Germanywww.nuclear-engineering-journal.comNotforuseininternetorintranetsites.Notforelectronicdistribution.