Page 1
Radioimmunotherapy with radioactive nanoparticles: Biological doses
and treatment efficiency for vascularized tumors with or without
a central hypoxic area
V. Bouchata?and V. E. Nuttens
Research Center in Physics of Matter and Radiation (PMR), Laboratoire d’Analyses par Réactions
Nucléaires (LARN), University of Namur (FUNDP), Rue de Bruxelles 61, B-5000 Namur, Belgium
C. Michiels
Unité de Recherche en Biologie Cellulaire (URBC), University of Namur (FUNDP),
Rue de Bruxelles 61, B-5000 Namur, Belgium
B. Masereel
Department of Pharmacy (DP), University of Namur (FUNDP), Rue de Bruxelles 61,
B-5000 Namur, Belgium
O. Feron
Unité de Pharmacothérapie (FATH), Université Catholique de Louvain (UCL),
Avenue Mounier 53, B-1200 Brussels, Belgium
B. Gallez
Laboratoire de Resonance Magnétique Biomédicale (CMFA), Université Catholique de Louvain (UCL),
Avenue Mounier 73, B-1200 Brussels, Belgium
T. Vander Borght
Center for Molecular Imaging and Experimental Radiotherapy (IRME), Université Catholique de Louvain
(UCL), Dr. G. Therasse 1, B-5530 Yvoir, Belgium
S. Lucas
Research Center in Physics of Matter and Radiation (PMR), Laboratoire d’Analyses par Réactions
Nucléaires (LARN), University of Namur (FUNDP), Rue de Bruxelles 61, B-5000 Namur, Belgium
?Received 7 September 2009; revised 23 February 2010; accepted for publication 1 March 2010;
published 29 March 2010?
Purpose: Radioactive atoms attached to monoclonal antibodies are used in radioimmunotherapy to
treat cancer while limiting radiation to healthy tissues. One limitation of this method is that only
one radioactive atom is linked to each antibody and the deposited dose is often insufficient to
eradicate solid and radioresistant tumors. In a previous study, simulations with the Monte Carlo
N-Particle eXtended code showed that physical doses up to 50 Gy can be delivered inside tumors
by replacing the single radionuclide by a radioactive nanoparticle of 5 nm diameter containing
hundreds of radioactive atoms. However, tumoral and normal tissues are not equally sensitive to
radiation, and previous works did not take account the biological effects such as cellular repair
processes or the presence of less radiosensitive cells such as hypoxic cells.
Methods: The idea is to adapt the linear-quadratic expression to the tumor model and to determine
biological effective doses ?BEDs? delivered through and around a tumor. This BED is then incor-
porated into a Poisson formula to determine the shell control probability ?SCP? which predicts the
cell cluster-killing efficiency at different distances “r” from the center of the tumor. BED and SCP
models are used to analyze the advantages of injecting radioactive nanoparticles instead of a single
radionuclide per vector in radioimmunotherapy.
Results: Calculations of BED and SCP for different distances r from the center of a solid tumor,
using the non-small-cell lung cancer as an example, were investigated for90Y2O3nanoparticles.
With a total activity of about 3.5 and 20 MBq for tumor radii of 0.5 and 1.0 cm, respectively, results
show that a very high BED is deposited in the well oxygenated part of the spherical carcinoma.
Conclusions: For either small or large solid tumors, BED and SCP calculations highlight the
important benefit in replacing the single ?-emitter90Y attached to each antibody by a90Y2O3
nanoparticle. © 2010 American Association of Physicists in Medicine. ?DOI: 10.1118/1.3368599?
Key words: shell control probability ?SCP?, biological effective dose ?BED?, radioimmunotherapy,
dosimetry, Monte Carlo, tumor model, nanomedicine
18261826Med. Phys. 37 „4…, April 20100094-2405/2010/37„4…/1826/14/$30.00© 2010 Am. Assoc. Phys. Med.
Page 2
I. INTRODUCTION
In radioimmunotherapy ?RIT?, cancer cells are killed thanks
to potential induction of immune response and to ionizing
radiation delivered by single radionuclides coupled to anti-
bodies. The radiation efficacy is mainly influenced by the
choice of the radioactive atom linked to each antibody as
well as the biokinetics and the biodistribution of radiolabeled
antibodies used to target a human tumor antigen. Clinical
studies have, however, shown that doses higher than 60–70
Gy inside tumors are required for treating solid and poorly
vascularized cancers.1Such doses are not easily obtained
with such an approach, in spite of numerous efforts made to
increase antibody accumulation and penetration inside the
tumor.2–5
In a previous paper, we have proposed improving the tu-
mor dose deposition, and therefore, the treatment response
by replacing the single radioactive atom bound to each
monoclonal antibody ?mAb? by a 5 nm diameter inorganic
nanoparticle composed of numerous radioactive and nonra-
dioactive atoms.6The aim of such a treatment is to deliver a
much higher dose to the tumor. Moreover, inorganic nano-
particles can contain different types of radionuclides ??, ?,
?, or x-ray emitters? suited to both diagnostic and therapeutic
applications.7The possible mix between different radiations
will thus represent a practical tool for theragnostics.8This
kind of radiolabeled antibody do not exist yet, but the devel-
opment of both organic and inorganic nanoparticles that spe-
cifically target tumor cells or cancer vasculature has received
considerable interest these past few years. Progress has been
made to improve the stability of these nanoparticles within a
biological microenvironment.7For example, by creating
spherical radioactive nanoparticles whose diameter does not
exceed 5 nm, the radiolabeled antibodies are small enough to
reduce the opsonization process by the reticuloendothelial
system ?RES? responsible for their rapid clearance from
blood circulation.9To avoid that any radioactive atom come
off of the nanoparticle, it is possible to cover the nanopar-
ticles with a thin layer of inert and biocompatible matter,
such as Au or C. These biocompatible surfaces could also be
coated by polymeric macromolecules, such as polyethylene
glycol. This type of macromolecule enhances the chemical
stability of nanoparticles in an aqueous environment and can
act as a protective layer against the RES.7,9–13Finally, nano-
particles of 5 nm diameter possess a large surface capable of
accommodating large number of functional groups so that
more than one antibody can be conjugated per particle. The
more antibodies per nanoparticles there are, the higher will
be the biological half-life and uptake. Indeed, in vivo imag-
ing on animals and humans has shown that targeted nanopar-
ticles can be preferentially distributed in tumor mass after
injection and relatively low accumulation of these nanopar-
ticles is observed in other organs such as the spleen or liver,
which means that antibodies can well be used to target the
nanoparticles to specific anatomical sites.7,14–16
Beta-emitting radioactive nanoparticles have already been
created and investigated with promising results. For ex-
ample, researchers at the University of Missouri-Columbia
have developed an efficient methodology to synthesize radio-
active gold nanoparticles ?12–18 nm? containing
?-emitters ??max=0.96 MeV; half-life of 2.7 days?. Coated
with gum arabic ?polysaccharide glycoprotein?, they did not
observe any aggregation or decomposition of these
nanoparticles in saline solution. Moreover, glycoprotein mol-
ecules have receptors in the liver and biodistribution studies
performed on mice clearly showed a significant localization
of198Au nanoparticles in liver.17,18Finally, therapeutic effi-
cacy was tested on mice bearing a model of human prostate
cancer. An uptake of NPs in prostate cancer cells and a de-
crease in the tumor volume are clearly observed after a direct
injection into the solid tumor.19More recently, Wu and
co-workers20proposed synthesizing radioactive nanopar-
ticles of90Y by using a protein cage of apoferritin. First tests
were performed by diffusing89Y and phosphate ions into the
cavity of apoferritin. The diameter of these phosphate/
apoferritin nanoparticles was around 8 nm after functional-
ization.
Despite these promising results to produce radioactive
nanoparticles for radioimmunotherapy, a question remains:
What would be the benefit of such configuration involving
antibodies labeled with several
nanoparticles in term of dose and tumor control. This paper
attempts to answer to that question with the help of Monte
Carlo simulations and a simple90Y configuration.
Monte Carlo N-Particle eXtended ?MCNPX? simulations
have been used to evaluate the physical dose around and
throughout a spherical solid tumor. Dosimetry calculations
were performed for the beta-emitting radionuclide90Y2O3
and preliminary results showed that viable tumor cells re-
ceive physical doses of up to 50 Gy everywhere inside the
tumor. This observation is still valid even for large nonuni-
form distribution of the total activity inside the tumor. More-
over, dose deposited around the tumor remains sufficiently
weak to avoid affecting the surrounding healthy tissues.6
However, the efficacy of a treatment against cancer does not
depend only on the physical absorbed doses but also on other
radiobiological parameters such as the radiosensitivity of the
targeted tissues, the doubling time of the cancer cells, the
repair process of sublethal damage taking place between two
irradiations, and the effect of hypoxia for which the radiosen-
sitivity changes according to whether cells are anoxic or well
oxygenated.21–23All these biological effects are taken into
account in the biological effective dose ?BED? and tumor
control probability ?TCP? models. Consequently, they offer
interesting tools to evaluate, at least theoretically, the effi-
cacy of a specific treatment. Moreover, these mathematical
models are often used to compare different radiotherapy
techniques and to predict the most appropriate treatment for
individual patients.24–28
In this work, BED and control probability for successive
concentric spherical shells inside and around the tumor ?shell
control probability ?SCP?? have been calculated for the non-
small-cell lung cancer ?NSCLC?. This type of tumor is a
good example of carcinomas for which patients have poor
survival.29,30Indeed, this cancer is relatively radioresistant
and displays important hypoxic areas. Doses larger than
198Au
198Au
90Y atoms configured as
1827 Bouchat et al.: BED and SCP for radioactive nanoparticles1827
Medical Physics, Vol. 37, No. 4, April 2010
Page 3
60–70 Gy are thus required to cure NSCLC.1,30,31In radio-
immunotherapy, doses up to 60 Gy can be delivered within
the tumor after several injections of radiolabeled antibodies
over several days or weeks. Unfortunately, NSCLC is also
well-known to be fast growing, with a cell doubling time
ranging from 2.5 to 3.3 days.1So it is better to deliver a high
total dose during a single injection rather than in small frac-
tions over a longer time. In external beam therapy, such
doses can be deposited at the tumor in one session but a great
part of the surrounding healthy tissues will be also irradiated.
In these conditions, RIT using radioactive nanoparticles
coupled to an antibody seems to be a good method for treat-
ing solid carcinomas such as the NSCLC, since a single in-
jection will be able to deliver doses larger than 60–70 Gy to
the targeted tumor. It is, however, important to verify
whether doses to healthy lung tissue remain lower than 30
Gy to avoid late complications like pneumonitis or
fibrosis.1,22,29In the present paper, the physical doses D?r?
previously simulated with MCNPX 5.0 are converted into
BED and SCP distributions. The main objective is, then, to
analyze the cell cluster-killing efficiency resulting from the
use of antibodies coupled to radioactive nanoparticles and
compare these results to BED and SCP calculations when a
single ?-emitter90Y is coupled to each antibody.
II. BED AND SCP CALCULATIONS
II.A. Tumor model
Absorbed doses as a function of distance from the center
of the tumor were simulated according to the MCNPX 2.5.0
code. This Monte Carlo software requires accurate informa-
tion on the tumor structure and the microscopic distribution
of radioactivity delivered by the radiolabeled antibodies. In
order to accurately provide such information, we developed a
new model for a spherical vascularized tumor in which the
antibody distributions inside the tumor are uniform or het-
erogeneous. This tumor model is described in detail in a
previous publication and consists of a set of spherical cell
clusters of 250 ?m radius arranged in a simple cubic lattice
structure as illustrated in Fig. 1.6The spherical tumor of 0.5
cm radius can contain a maximum number of 3591 cell clus-
ters. When the spherical tumor has a radius of 1.0 cm, the
number of cell clusters increases to a value of 31 071 ?Table
I?. The matter around each cell cluster represents the vascu-
larized stroma containing a pre-existing blood network or
new vessels created during angiogenesis. The radiolabeled
antibodies can penetrate inside the tumor through this vascu-
lature to surround the various cell clusters. The distribution
of radiolabeled antibodies inside the tumor is uniform if all
cell clusters in the cubic lattice have the same probability to
be reached by an antibody. However, it is well-known that
during angiogenesis, the outer region of the tumor is better
vascularized than the center.32–34The density of blood ves-
sels decreases toward the center and the heterogeneity in
blood flow thus generates a nonuniform distribution of radio-
activity in tumors.35In order to take this decrease in vascu-
lature into account, linear and exponential distributions of
radiolabeled antibodies inside the tumor have been model-
ized by subdividing the tumoral sphere into concentric shells
of 0.05 cm thickness, with differing probabilities to be
reached by an antibody. In our model, the probability that an
antibody reaches a cell cluster located near the tumor radius
hits a maximum value of 1.0. Inversely, the probability de-
creases to 0.1 for antibodies which reach the central cell
cluster of the tumor. Between those values, the probability
may decrease linearly ?Eq. ?1?? or exponentially ?Eq. ?2??.
LP?m? = 0.1+?
1.0− 0.1
NbShell− 1?? ?m − 1?,
?1?
(b)(a)
FIG. 1. Spherical tumor of 0.5 cm radius subdivided into 3591 cell clusters.
?a? The first picture is a three-dimensional arrangement of these cell clusters
when 25% of the cell clusters are poorly oxygenated at the center of the
tumor. Picture ?b? corresponds to a cross-section of the center of this mod-
elized tumor with cell clusters inside a cubic lattice of 500 ?m width.
TABLE I. Parameters used for calculating the total activity inside tumors of different radii ?0.5 and 1.0 cm? when
antibodies are linked with radioactive nanoparticles or with single90Y atoms.
ParametersUnits
¯
cm
¯
h
h
mAb/cm2
¯
MBq
RT=0.5 cm
RT=1.0 cm
NP of90Y Single90Y NP of90Y Single90Y
Total # of cell clusters
Hypoxic radius
# of nonhypoxic cell clusters
Physical half-life
Biological half-life
Covering fraction
# of90Y per MAb
Calculated total activity
3591
0.32
2702
64.1
72
3.8?107
1000
3.5
3591
0.32
2702
64.1
72
1010
1
0.9
31 071
0.64
23 342
64.1
72
2.5?107
1000
20
31 071
0.64
23 342
64.1
72
1010
1
7.5
1828Bouchat et al.: BED and SCP for radioactive nanoparticles1828
Medical Physics, Vol. 37, No. 4, April 2010
Page 4
EP?m? = exp?ln?0.1? +?ln?1.0? − ln?0.1?
NbShell− 1?? ?m − 1??,
?2?
where NbShell represents the total number of shells obtained
by subdividing the tumor radius by the thickness of concen-
tric shells. “m” may vary from 1 for the cell cluster located at
the center of the tumor to Nbshell for the cell clusters located
in the vicinity of the tumor surface.
Furthermore, it has to be noted that the center of large
tumors often displays poorly oxygenated or hypoxic cells
caused by the lack of vasculature. This situation can lead to
the formation of a necrosed core. Central hypoxic areas are
introduced in our tumor model by simply considering that
the probability that an antibody reaches this region is null.
The radius of the hypoxic core can vary widely with time
and tumor type. In this work, we have chosen radii of 0.32
and 0.64 cm for both tumor radii of 0.5 and 1.0 cm, respec-
tively. In this case, numbers of hypoxic cell clusters are 889
for the first tumor and 7729 for the second, meaning that
about 25% of the total number of cell clusters are not oxy-
genated ?dark gray cell clusters in Fig. 1?. Radii of hypoxic
cores and numbers of normally oxygenated cell clusters are
given in Table I for tumors of 0.5 and 1.0 cm radii.
II.B. Absorbed dose calculations
This tumor model was used to calculate the deposited
dose inside and around cancer cells as a function of the dis-
tance from the center for two tumor radii ?0.5 and 1.0 cm?. In
these simulations, tumors were irradiated by90Y2O3nano-
particles of 5 nm diameter. A 5 nm diameter nanoparticle of
90Y2O3can contain a maximum of 1.73?103atoms of
yttrium-90, but we assume that the delay time between the
antibodies’ injection and their binding with tumoral antigens
is 2 days, which means that only 60% of radioactive atoms
inside each nanocluster are still radioactive when the nano-
clusters reach the cancer cells.
Energy deposition for different distances “r” from the tu-
mor center was determined by using SMESH tally proposed
in the MCNPX code. The latter is capable of studying the
electron transport through matter by taking into account the
loss of energy, multiple scattering angles and “bremsstrah-
lung.” All these physical processes are considered by using
the photon-electron mode and the default PHYS cards for
electron and photons with a cutoff energy at 0.005 MeV for
both particles. The number of histories ?NPs? was set to
50?106particles and ? spectral data for yttrium-90 was
taken from tables on the RADAR site ?www.doseinfo-
radar.cp/RADARDecay.html?. The SMESH tally builds vir-
tual three-dimensional spherical grids superimposed on the
geometry of our tumor model and gives the energy deposi-
tion, in MeV/g per emitted particle, into each concentric
spherical shell independently of the composition or density
of each material used to modelize the tumor and its sur-
rounding tissues. This energy deposition is then converted
into deposited doses D?r?, in Gy, by the formula ?3? pro-
posed by Nuttens36
D?r? = 21.34? E?r? ? p ? A˜/?eff,
?3?
where E?r? is the energy deposition at a distance r from the
center of the tumor, p is the average number of electrons
emitted per disintegration, ?eff?=ln?2?/T1/2
decay constant, assuming a monoexponential decay.37?effis
given by the sum of the physical decay and the biological
clearance rate constants ??eff=?phy+?biol?.6,36The physical
half-life of yttrium-90 is well-known and corresponds to 64.1
h.38–40Based on pharmacokinetic studies on90Y, Wiseman
and co-workers41estimated that the biological blood half-life
of the antibody varies between 22 and 140 h. For our simu-
lation, we supposed a biological half-life for healthy tissues
of about 72 h.42,43Clearance of the antibodies inside the
tumor must be slower than in healthy tissues. But due to the
short physical half-life of yttrium-90, the biological half-life
in the tumor is mainly determined by the physical half-life of
yttrium-90. So, for our simulations, we also supposed a bio-
logical half-life of 72 h for tumor tissues. In these conditions,
the effective decay constant ??eff? was evaluated at
2.04?10−2h−1both for healthy tissues and tumors. The to-
tal activity A˜was calculated according to the expression ?4?
given in a previous publication6
eff? is the effective
A˜= ?phys? nu? na? nmAb,
?4?
where nuand narepresent, respectively, the number of non-
hypoxic tumor cell clusters and the number of radioactive
atoms per nanoparticle ?Table I?. nmAbis the quantity of
monoclonal antibodies which surrounds each cell cluster. Its
value was calculated by multiplying the surface of the cell
cluster by the covering fraction defined as the number of
bound mAbs per unit of tumor surface. The covering fraction
was adjusted to ensure a maximal dose of 30 Gy around the
tumor surface. In our model, this value is reached if covering
fractions are 3.8?107and 2.5?107mAb/cm2for solid tu-
mors of 0.5 and 1.0 cm radii, respectively. These values are
clearly lower than typical values for covering fractions given
for monoclonal antibodies coupled to a single radionuclide,
which range from 108to 1010mAb/cm2.39With parameters
listed in Table I, we calculated the total activity according to
Eq. ?4? above. The latter represents the activity that would be
injected directly into tumors. When the radioactive nanoclus-
ters are used, the total activities are about 3.5 MBq for tumor
of 0.5 cm radius and 20 MBq for tumor of 1.0 cm radius.
These values are very large if we compare them to cumulated
activities obtained when a single90Y atom is linked to each
antibody. Indeed, despite of a maximal covering fraction of
1010mAb/cm2, total activities for single90Y per mAb de-
crease to 0.9 and to 7.5 MBq for tumor radii of 0.5 and 1.0
cm, respectively. These total activities ?Table I? will be used
to compute the TCP and SCP.
The thickness between each spherical mesh was reduced
to 0.05 cm to increase the number of shells inside and around
the tumor. This value is less than 1 mm, which is the minimal
thickness normally imposed by the software
2.5.0.44,45In order to test the influence of shell thicknesses on
deposited energies simulated by
MCNPX
MCNPX, a comparison
1829Bouchat et al.: BED and SCP for radioactive nanoparticles1829
Medical Physics, Vol. 37, No. 4, April 2010
Page 5
among three different segmentations of concentric spherical
shells ?0.5, 1.0, and 2.0 mm? was performed. As shown in
Fig. 2 for tumors of 0.5 cm radius, the three curves repre-
senting the energy deposition for the three different thick-
nesses display great disparities. When the activity is uni-
formly dispersed throughout the tumor, deposited energies
simulated with MCNPX tend to decrease in tumoral and nor-
mal tissues with the number of concentric spherical shells.
For linear distribution of antibodies, predicted deposited en-
ergy inside the tumor is diminished when the number of
segmentations decreases, whereas it increases in healthy tis-
sues. Finally, curves plotted for the exponential distribution
of antibodies show an increase and a shift in the peak toward
the right when the thickness between meshes decreases. It is
worth noting that these differences in simulated energy depo-
sition according to the choice of the segmentation disappear
for a larger tumor radius. Indeed, as illustrated in Fig. 2 for a
tumor with a radius of 1.0 cm, curves of deposited energies
are similar whatever the thickness of concentric spherical
shells, especially for uniform and linear antibody distribu-
tion. When the antibodies are distributed exponentially, an
increase in the maximal dose deposited near the tumor sur-
face is observed when the thickness between concentric
spherical shells decreases. Consequently, the nature of the
mesh chosen to simulate energy deposition may have an in-
cidence on the shape of the predicted absorbed dose distri-
bution curve for small tumor radii. The segmentation of 0.05
cm was chosen to provide more points on the energy depo-
sition curve and because linear or exponential probability
decreases for each cell cluster to be reached by antibodies
have also been done by steps of 0.05 cm. The latter corre-
sponds to the diameter chosen for cell cluster constituting the
tumor.6
II.C. BED„r…, error, and SCP„r… calculations
BED distribution and TCP are adequate methods to ana-
lyze the radiobiological effects of treatment resulting from
radioactive nanoparticles. Both BED and TCP distributions
are mathematical models often used to predict the response
to irradiation of normal and tumor tissues, which is very
useful for evaluating the best treatment for each individual
patient.25,42,46Absorbed doses D?r? were thus converted into
BED according to Eq. ?5? given by
BED?r? =D?r?
q
??eff+ ??
+
?eff
D?r?2
q2?/?.
?5?
In our model, a spherical tumor is subdivided in cell clusters
and BED?r? is defined as the dose required for killing a cell
unit located at a distance r from the center of the tumor. D?r?
is the absorbed dose computed by our MCNPX simulations.
?eff, ?, ?/?, and q are biological parameters ?see hereunder?.
This equation is valid for both tumors and healthy tissues,
but differences exist between radiobiological factors for tu-
moral and normal tissues. The values of these parameters for
the three antibody distributions are presented in Table II. The
choice of these values is explained in the following two para-
graphs.
All terms in Eq. ?5? have a biological significance. Ioniz-
ing radiation can affect living tissues on a cellular level by
FIG. 2. Effect of the thickness of concentric spherical shells on energy depo-
sition ?per gram and per emitted particle? for tumors with radii of 0.5 and
1.0 cm: 0.5 ?solid lines?, 1.0 ?dotted lines?, and 2.0 mm ?dashed lines?.
Uniform, linear, and exponential distributions of antibodies are taken into
account.
TABLE II. Biological parameters and their references used for BED and SCP calculations for tumor and healthy
tissues.
Biological factors
Tumor Healthy tissues
Range values Tumoral tissues Error Range values Healthy tissuesError
Tbio
?/? ?Gy?
? ?h−1?
? ?#/cm3?
? ?Gy−1?
1/2?h?
22–140a
?5b–d
0.3–2.5b,i
107–108
0.1–1.0l
72
?24
?5
?0.5
¯
¯
22–140a
?5b–d
0.3–2.5b,i
107–108
¯
72
?24
?2
?0.5
…
…
10e–g,b,h
1.39b,h
5?107 k
0.35e
3e–g,b,h
0.46g,b,j
5?107 k
0.031m
aReference 41.
bReference 49.
cReference 58.
dReference 59.
eReference 1.
fReference 22.
gReference 42.
hReference 51.
iReference 53.
jReference 54.
kReference 60.
lReference 37.
mReference 61.
1830Bouchat et al.: BED and SCP for radioactive nanoparticles 1830
Medical Physics, Vol. 37, No. 4, April 2010
Page 6
breaking chemical bonds within DNA molecules. The linear
term in expression ?5? refers to single ionizing events, which
directly provoke double-strand breaks in DNA. This kind of
damage,also called type A damage
co-workers,47,48is necessarily lethal because it is not repair-
able. Inversely, the quadratic component describes the cellu-
lar death as a consequence of two separated sublethal dam-
ages ?type B damage? and these damages can be repaired
when the lapsed time between the two hits is long
enough.26,37,47,49–52The ratio ?eff/??eff+?? was incorporated
in the expression to take into account the reduction in cell
destruction due to repair of sublethal damage during continu-
ous irradiation.26,47,51,52This term is deduced from the dose
protraction factor for continuous irradiation ?T=?? and var-
ies between 0 and 1. ??=ln?2?/T1/2
constant that quantifies the rate of sublethal damage repair.
The half-time of DNA repair ?T1/2
tissues may range from a few minutes to several hours.49,53
In our simulation, calculations have been performed with a
T1/2
time most widely adopted by authors.42,49,54The correspond-
ing repair constant ? is then 0.46 h−1. For a solid tumor, a
lower repair half-time of 0.5 h is generally proposed for
simulations, giving a repair constant ? of 1.4 h−1.49,51This
higher value of ? limits the chance of producing lethal dam-
age by interaction with a second hit, thus reducing the over-
all treatment efficacy. Also called cellular radiosensitivity, ?
and ? are tissue specific parameters expressed in Gy−1and
Gy−2, respectively. Both parameters are determined by a fit
of the cell survival curves.27,49,55–57The ?/? ratio gives an
indication of the relative importance of the linear and qua-
dratic terms and determines the shape of the cell survival
curve. It is well recognized that ?/? ratios less or equal to 5
Gy are generally observed for late-responding tissue. In-
versely, values higher than 5 Gy are observed for a majority
of tumors.49,58,59For our simulations, values of 3 and 10 Gy
were chosen for normal and tumoral tissues, respectively,
because they are the most often used values.1,22,42,49,51
In our tumor model, we have introduced the possibility of
having a hypoxic core. In these conditions, all cell clusters at
the center of the tumor are less radiosensitive than those
which are well oxygenated.21–23,55So, to differentiate ? and
? values for poorly and normally oxygenated cell clusters,
the “q” parameter was introduced. This parameter, also
called hypoxia reduction factor, was first proposed by Jones
and co-workers62to calculate BED for hypoxic cells. They
supposed that the radiosensitivity coefficient ? and ? for a
specific tissue are reduced, respectively, by q and q2when
cells are hypoxic. Indeed, experimental studies have shown
that poorly vascularized areas are up to three times more
resistant to ionizing radiation than proliferating cells.30,62So,
the simplest model is to assume that q is equal to 1 when
cells are well oxygenated and to 3 when cells are hypoxic.
The biological parameters are strongly dependent on the
structure, the shape, and the cellular composition of a tumor.
Experimental evaluations of these radiobiological parameters
often lead to variable values. For our simulations, we simply
byDaleand
Rep? is the exponential rate
Rep? for normal and tumor
Repof 1.5 h for healthy tissues, which is the repair half-
took the most recurrent values proposed in the literature. In
order to evaluate the impact of variation in these biological
parameters on BED distributions, errors in BED were calcu-
lated according to Eq. ?6?
?BED=?BED
???/?????/?? +?BED
??
?? +?BED
?eff
??eff
+?BED
?D
?D.
?6?
The last term ??BED/?D??D is negligible because D is com-
puted to the point that ?D is minimal. Since ??eff=??bio
+??physand ??physis negligible compared to ??bio, then
??eff= −ln 2
Tbio
2?Tbio.
?7?
Values for ???/??, ??, and ?Tbioused to calculate ?BED
are presented in Table II ?column 4 for tumor and column 7
for healthy tissues?. Partial derivatives are determined by
?BED
???/??=
?
? + ?.D˙0
2
?2.
− 1
??/??2,
?8?
?BED
??
=
− ?
?? + ??2.
1
??/??.D˙0
2
?2,
?9?
?BED
??eff
BED?r? distributions calculated according to Eq. ?5? will
be used to determine SCP?r?, which is defined as the prob-
ability that no cell cluster inside each spherical mesh located
at a distance r from the center of the tumor survives irradia-
tion. SCP?r? is based on the TCP-NTCP concept. Indeed,
SCP?r? is capable of predicting the survival rate of cell clus-
ters after irradiation inside the tumor but, also, in the sur-
rounding healthy tissues. The control probability for a single
cell cluster inside a spherical shell located at a distance r
from the center of the tumor defined by the SMESH tally
was first calculated. Cell clusters are assumed to be dead
when all clonogenic cells inside the aggregate are killed by
single or double hit events. As TCP, this probability can be
calculated using the Poissonian form expressed by28,37,49
= −D˙0
2
?2+
− 1
??2+ ???2.
1
??/??. D˙0
2. ?2? + ??.
?10?
CCP?r ? ?r? ? exp?− N · exp?− ? · BED?r???,
?11?
where CCP?r??r? is the cluster control probability of a cell
cluster located at a distance r??r from the center of the
tumor, ?r representing the small variations between the dis-
tance separating the cluster from the tumor center and the
real distance r of the spherical shell defined by the SMESH
tally. N is the number of cells before irradiation inside each
cube defined by the cubic lattice of 500 ?m length sides
used to subdivide the tumor sphere. The cell density is as-
sumed to be uniform throughout the tumor and healthy tis-
sues. So, with a value of 5?107cell/cm3, the number N of
cells in each cube of the cubic lattice corresponds to 6250.60
1831 Bouchat et al.: BED and SCP for radioactive nanoparticles 1831
Medical Physics, Vol. 37, No. 4, April 2010
Page 7
Equation ?11? requires a defined value of ? and not only
the ?/? ratio. This is probably the most difficult radiobio-
logical factor to determine because it is clearly dependent on
the patient and the type of tumor. Atthey and co-workers37
proposed that plausible values for ? may range from 0.1 to
1.0 Gy−1. For non-small-cell lung cancer, ? parameter may
vary between 0.3 and 0.4 Gy−1.1So, we have chosen a mean
value of 0.35 Gy−1for calculating BED and CCP. A lower
value of 0.031 Gy−1was used for the ? parameter of healthy
lung tissues according to Dubray and co-workers.61Finally,
shell control probability for the three different radiolabeled
antibody distributions ?uniform, linear, and exponential? is
defined by the following product:
SCP?r? =?
i
K
CCPi?r ? ?r?,
?12?
where K represents the number of cell clusters in each
spherical shell defined by the SMESH tally. The TCP can be
then calculated by the product of all SCP?r? values, with r
varying from 0 ?center of the tumor? to rT?surface of the
tumor?.
TCP=?
r=0
r=rT
SCP?r?.
?13?
III. RESULTS AND DISCUSSION
Results presented in this work highlight the advantages of
replacing a single radionuclide per antibody with inorganic
nanoparticles containing a high number of radioactive atoms.
BED?r? and SCP?r? were determined according to Eqs. ?5?
and ?12?, which take into account the effects of inhomoge-
neous dose distributions, cellular repair effects between two
single-hit events, and the influence of a radioresistant hy-
poxic core within the tumor. We investigated whether the
nature of the spatial distribution of antibodies and the pres-
ence of a hypoxic center affect the level of damage caused to
cancer cells and to the cells in the surrounding tissue. Effects
of repopulation in normal and tumor tissues will be ignored
because they are less important than damage repair effects
during continuous irradiation.63BED was calculated for two
spherical tumors of 0.5 and 1.0 cm radii irradiated by 5 nm
diameter nanoparticles of90Y2O3. Results are summarized
in Table III for tumor radius of 0.5 cm and in Table IV for
tumor radius of 1.0 cm. They present values for physical
doses D?r? computed with MCNPX, biological effective doses
calculated with Eq. ?5?, and errors on BED?r? due to varia-
tions in biological parameters, obtained from Eq. ?6? and
expressed in %.
Tables III and IV resume the most important values for
the physical and biological doses inside and outside the tu-
mor. The first are the D and the BED values at the center of
the tumor, written down “Cent” in the second column of
tables. When this center is well irradiated with doses of up to
60 Gy, the complete destruction of the tumor would be pos-
sible. In the second column, we can also find “Max” which
gives the maximum values, which can be deposited within
the tumors. To analyze the impact of the radiolabeled nano-
particles on healthy tissues, the value of D and BED at the
surface of the tumor ?Surf? and 1 mm beyond the tumor
surface ?Out? are also given. The best situation is to obtain a
high physical or biological dose at the tumor surface where
the proliferation is probably the most important and a mini-
mum value for D or BED in the surrounding healthy tissues.
Finally, values of D and BED at the center, at the surface and
1 mm beyond the tumor surface, as well as the maximum
physical and biological doses deposited inside the tumor are
TABLE III. Calculated values of D ?in Gy?, BED ?in Gy?, and ?BED ?in %? for a tumor of 0.5 cm radius with or without hypoxia according to data in Tables
I and II. For each antibody distribution ?uniform, linear, and exponential?, the table gives the maximum doses deposited inside the tumor ?Max?, doses at the
center ?Cent?, doses at the surface ?Surf?, and 1 mm beyond the surface ?Out? of the tumor. Data are calculated for a single90Y atom labeled antibody and for
a radioactive nanoparticle labeled antibody.
Tumor of 0.5 cm radius
Single radionuclide total activity: 0.9 MBqRadioactive nanoparticle total activity: 3.5 MBq
No hypoxia
BED
?Gy?
25% hypoxic
BED
?Gy?
No hypoxia
BED
?Gy?
25% hypoxic
BED
?Gy?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
Uniform Cent
Max
Surf
Out
Cent
Max
Surf
Out
Cent
Max
Surf
Out
44
45
11
5
28
34
12
5
28
34
12
5
47
47
11
5
29
35
12
5
29
35
12
5
6
6
2
6
4
5
2
7
4
5
2
7
16
35
12
5
13
33
13
6
12
32
14
6
51
5
2
7
1
5
2
8
1
4
2
8
173
173
42
18
110
132
45
19
67
122
53
22
217
217
45
22
128
157
48
24
73
144
57
28
18
18
6
20
12
14
6
21
8
14
7
23
63
135
48
20
51
127
53
22
48
126
55
23
21
162
51
26
17
150
57
29
16
149
59
30
3
15
6
21
2
14
7
23
2
14
7
23
36
12
6
4
34
14
6
12
34
14
6
Linear
Exponential
1832 Bouchat et al.: BED and SCP for radioactive nanoparticles 1832
Medical Physics, Vol. 37, No. 4, April 2010
Page 8
calculated for a tumor with or without a hypoxic core and for
the three types of antibody distributions: Uniform, linear, and
exponential.
III.A. BED distributions for tumors without hypoxia
III.A.1. Nanoparticle labeled antibody
Figures 3 and 4 show a comparison between absorbed
?solid gray lines? and biological ?solid black lines? dose dis-
tributions for nonhypoxic tumors with a radius of 0.5 or 1.0
cm after injection of radioactive nanoparticles of 5 nm diam-
eter containing90Y2O3distributed uniformly, linearly, or ex-
ponentially. A comparison between the three graphs of Figs.
3 and 4 shows that types of antibody distribution ?uniform,
linear, or exponential? in tumors affect noticeably the shape
of absorbed and biological dose distributions, generating
lower or higher doses at different distances from tumor cen-
ter. However, the overall shape of the physically absorbed
dose curve is similar to that of biological dose and this is true
for each antibody distribution. The conversion of physical
doses into BED shows higher values for doses inside the
tumor, especially at the center when antibodies are dispersed
uniformly. At this position, a difference of about 45 and 30
TABLE IV. Calculated values of D ?in Gy?, BED ?in Gy?, and ?BED ?in %? for a tumor of 1.0 cm radius with or without hypoxia according to data in Tables
I and II. For each antibody distribution ?uniform, linear, and exponential?, the table gives the maximum doses deposited inside the tumor ?Max?, doses at the
center ?Cent?, doses at the surface ?Surf?, and 1 mm beyond the surface ?Out? of the tumor. Data are calculated for a single90Y atom labeled antibody and for
a radioactive nanoparticle labeled antibody.
Tumor of 1.0 cm radius
Single radionuclide total activity: 7.5 MBq Radioactive nanoparticle total activity: 20 MBq
No hypoxia
BED
?Gy?
25% hypoxic
BED
?Gy?
No hypoxia
BED
?Gy?
25% hypoxic
BED
?Gy?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
D
?Gy?
?BED
?%?
Uniform Cent
Max
Surf
Out
Cent
Max
Surf
Out
Cent
Max
Surf
Out
51
51
13
6
25
45
15
7
17
50
22
11
54
56
13
7
26
48
15
12
17
54
23
12
7
7
2
8
4
6
2
9
3
6
3
13
31
55
17
9
0
54
20
11
0
59
25
14
1
7
3
132
135
33
16
49
117
38
19
44
131
57
28
157
162
34
20
52
137
40
24
46
156
62
39
14
15
5
18
6
13
5
20
6
14
7
27
721
14
6
22
?1
14
6
25
?1
15
8
29
51
16
8
1
50
19
10
1
54
24
12
132
42
21
3
131
50
25
2
141
62
30
158
45
27
1
156
54
34
1
170
67
43
10
1
6
3
12
1
7
4
14
Linear
Exponential
FIG. 3. Comparison of D?r? and BED?r? profiles for90Y2O3nanoparticle
labeled antibodies and for single90Y labeled antibodies, in Gray unit, as a
function of the distance r from center for tumor with a radius of 0.5 cm and
for three different antibodies distributions: Uniform, linear, and exponential.
The tumors do not have hypoxic cores and dotted vertical lines represent the
tumor radius. Solid black curves for all spectra are BED?r? and solid gray
curves are D?r? doses. Values for BED?r? were determined according to
parameters given in Table II and Eq. ?5? with q=1 for both tumor and
healthy tissues.
FIG. 4. Comparison of D?r? and BED?r? profiles for90Y2O3nanoparticle
labeled antibodies and for single90Y labeled antibodies, in Gray unit, as a
function of the distance r from center for tumor radius with a radius of 1.0
cm and for three different antibodies distributions: Uniform, linear, and
exponential. The tumors do not have hypoxic cores and dotted vertical lines
represent the tumor radius. Solid black curves for all spectra are BED?r? and
solid gray curves are D?r? doses. Values for BED?r? were determined ac-
cording to parameters given in Table II and Eq. ?1? with q=1 for both tumor
and healthy tissues.
1833Bouchat et al.: BED and SCP for radioactive nanoparticles1833
Medical Physics, Vol. 37, No. 4, April 2010
Page 9
Gy is observed between the absorbed dose and the biological
dose for tumors of 0.5 and 1.0 cm radii, respectively. This
increase is clearly due to the presence of the quadratic com-
ponent of the calculated BED. For the linear or exponential
distributions of antibodies, maximum peaks are observed at
0.25 or 0.40 cm for a tumor radius of 0.5 cm and at 0.70 or
0.90 cm when the tumor radius reaches 1.0 cm. These maxi-
mum doses are clearly located near the tumoral surface
where the cell proliferation is the most important. For both
tumor radii, BED?r? at 1 mm beyond the tumoral surface
?i.e., in healthy tissue? remains inferior to 30 Gy, except for
the exponential distribution of antibodies for the 0.1 cm ra-
dius tumor where the biological dose reaches 39 Gy. This
last result highlights how significantly radiolabeled nanopar-
ticles penetrate deeply inside the tumor rather than staying in
the vicinity of the surface. Indeed, the more the distribution
is exponential, the more that dose deposition inside healthy
tissues is important. It is also possible to use radionuclides
with shorter emission ranges to increase the sharpness of the
falloff near the surface of the tumor on the absorbed dose
and the biological dose curves.
As there exist uncertainties in the values for different bio-
logical parameters proposed in literature, error bars on bio-
logical dose curves have been added to see how the variation
in ? and ?/? can influence initial BED values ?Figs. 3 and
4?. The difference between biological and absorbed doses is
strongly dependent on the choice of radiobiological factors.
The decrease or increase in BED values is mainly due to
variations in the repair half-time ?T?? parameter. For a tumor
of 0.5 cm radius, an increase in T?values from 0.5 to 1.5 h
generates an increase in BED maximal values from 217 to
301 Gy, from 157 to 205 Gy, or from 144 to 185 Gy for
uniform, linear, or exponential antibody distributions, respec-
tively. Such an observation makes sense because cells with
higher repair half-time for sublethal damage have a higher
probability of undergoing cell death after an interaction with
a second radiation. BED values are also weakly reduced
when ?/? increases. If a ?/? ratio of 15 Gy is used in the
model instead of 10 Gy, the maximal BED value for a tumor
of 0.5 cm radius changes from 217 to 203 Gy, from 157 to
148 Gy, and from 144 to 136 Gy for uniform, linear, or
exponential antibody distributions, respectively. The fact that
BED values are reduced is logical because a diminution in
the ?/? ratio induces a decrease in the quadratic term of Eq.
?5?. However, BED values in healthy tissues are lower than
BED inside the tumor, although values of ? and ?/? are
about three times less than in normal tissues.
All these results demonstrate how important it is to know,
with accuracy, the biodistribution of antibodies and the bio-
logical factors when BED is calculated inside the tumor.
However, with values up to 60 Gy everywhere inside the
tumor, biological doses required to treat a cancer remain suf-
ficient even if ?/? or ? varies within a plausible range of
values. Moreover, in most cases, BED values lower than 30
Gy are observed in surrounding healthy tissues indicating
that they will be spared. However, all these values are prob-
ably underestimated because the presence of antibodies in
healthy tissues in this model is assumed to be null. Further-
more, error bars for BED in healthy tissues are small, which
means that large variations in biological parameters induce
small differences of BED. Such findings are important to
ensure the patient safety.
III.A.2. Single atom labeled antibody
Previous results have to be compared to dosimetry calcu-
lations when only a single radionuclide
each antibody. To determine absorbed doses, the maximal
covering fraction of 1010mAbs/cm2has been considered.39
With such a value, total activities correspond to about 0.9
and 7.5 MBq for tumors of 0.5 and 1.0 cm radii, respectively.
As illustrated in Fig. 3 for a tumor of 0.5 cm radius, differ-
ences between D and BED curves are smaller than those
observed for radioactive nanoparticles. Moreover, absorbed
and biological doses are inferior to 60 Gy, which means that
the activity deposited by radiolabeled antibodies is insuffi-
cient to correctly treat solid tumors such as non-small-cell
lung carcinomas. This result remains true independently of
the type of antibody distribution. Similar results are obtained
for a tumor with a radius of 1.0 cm ?Fig. 4? despite the larger
total activity. Without hypoxia, values of absorbed and bio-
logical doses vary between 20 and 60 Gy for the three dif-
ferent antibody distributions, which is again insufficient to
obtain good treatment outcome.
90Y is coupled to
III.B. BED distributions for tumors with hypoxia
The presence of a large central hypoxia in the tumor can
greatly influence clinical outcome in targeted radiotherapy.
As explained earlier, our tumor model is capable of taking
into account two types of cells with different radiosensitivity:
Normally oxygenated ?q=1? and hypoxic cells ?q=3?. BEDs
were modelized for tumors of 0.5 and 1.0 cm radii contain-
ing a hypoxic core ?Figs. 5 and 6?. The percentage of hy-
FIG. 5. Comparison of D?r? and BED?r? profiles for90Y2O3nanoparticle
labeled antibodies and for single90Y labeled antibodies, in Gray unit, as a
function of the distance r from center for a tumor radius with a radius of 0.5
cm, for three different antibodies distribution: Uniform, linear, and exponen-
tial. The gray parts symbolize the hypoxic core of 0.32 cm radius and dotted
vertical lines represent the tumor radius. Values for BED?r? were determined
according to parameters given in Table II and Eq. ?5? with q=1, with the
exception that the value of q changes from 1 to 3 for the hypoxic core.
1834Bouchat et al.: BED and SCP for radioactive nanoparticles1834
Medical Physics, Vol. 37, No. 4, April 2010
Page 10
poxic cell clusters compared to the total number of cell ag-
gregates was chosen to be 25%, corresponding to a spherical
hypoxic core of 0.32 radius for the smaller carcinoma and of
0.64 cm radius for the largest ?cf. Table I?. The absorbed and
biological dose profiles are calculated with the same total
activity as the tumor model without central hypoxia, namely,
3.5 and 20 MBq for 0.5 and 1.0 tumor radii, respectively.
When a single radioactive atom of
antibody, the total activities decrease to values of 0.9 and 7.5
MBq for 0.5 and 1.0 cm tumor radii, respectively. Distribu-
tions of radiolabeled antibodies in the normally oxygenated
part of the spherical solid tumor can be uniform, linear, or
exponential.
90Y is linked to each
III.B.1. Nanoparticle labeled antibody
Figures 5 and 6 show the impact of poorly oxygenated
cells on BED calculation. For the three distributions of ra-
diolabeled antibodies, the shapes between physical dose and
BED curves are different. Indeed, biological doses are higher
than absorbed doses in the normally oxygenated region of
the tumor but lower in the hypoxic core. Maximum values
for BED?r? in a tumor of 0.5 cm radius are 162 Gy for
uniform distribution and 150 Gy for linear or exponential
distribution of radiolabeled antibodies. The aforementioned
biological doses are located at a distance varying between
0.30 and 0.40 cm from the tumor center where the prolifera-
tion of cells is still important. Higher values for maximal
BED are observed when the tumor reaches 1.0 cm radius
with 158, 156, and 170 Gy for uniform, linear, and exponen-
tial distributions, respectively. These values are localized at
0.70 cm from the tumor center for uniform or linear distri-
bution and at 0.90 for the exponential distribution of activity.
As for Figs. 4 and 5, error bars have been added on BED
curves and wide variations in biological doses are observed
only in the living part of the tumor. Changes in BED are
essentially due to fluctuations in the repair half-time since an
increase of 40–55 Gy is observed when T?is 1.5 h rather
than 0.5 h for both tumor radii. Once again, important varia-
tions for ?/? and ? biological parameters do not affect BED
very much: BED?r? remains high inside the nonhypoxic area
of the tumor with doses up to 50 Gy, which are values high
enough to ensure good treatment outcomes. Inversely, BED
values in the hypoxic core are always inferior to 50 Gy with
a minimal value of about 20 Gy at the center of the core for
the tumor of 0.5 cm radius. The latter is still reduced to
values close to zero for larger spherical tumors. BED?r? val-
ues in this region are significantly smaller than physical
doses when we take into account that hypoxic cells are more
radioresistant than oxic cells. Finally, BED values in healthy
tissue are about 30 Gy at a distance of 1 mm from the tumor,
except for the exponential distribution. In this last case, BED
value is higher than 40 Gy, which is too high if we wish to
avoid important damage to the lung tissues ?or surrounding
tissues? in close proximity.
III.B.2. Single atom labeled antibody
Once again, previous results have been compared to D
and BED calculations when only a single atom is linked to
each antibody. For the tumor of 0.5 cm radius in which 25%
of the cell clusters are poorly oxygenated at the center ?Fig.
5?, maximal doses range from 30 to 35 Gy at 0.35 cm from
the tumor center for uniform distribution and at 0.40 cm
from the tumor center for linear or exponential antibody dis-
tribution. Biological doses lower than 10 Gy are also calcu-
lated in the hypoxic core. All these BED values are much too
low to eradicate completely the tumor. For a larger tumor of
1.0 cm radius ?Fig. 6?, maximal doses reached also remain
inferior to 60 Gy whatever the antibody distribution and the
biological doses are close to zero at the tumor center. It has
to be noted that values for absorbed and biological doses
FIG. 7. SCP profiles, in %, as a function of distance r from center of a tumor
of 0.5 cm radius ??a?–?c?? and 1.0 cm radius ??d?–?f?? when 5 nm diameter
nanoparticles containing90Y2O3molecules ?black curves? or when single
90Y ?gray curves? are linked to antibodies distributed uniformly, linearly and
exponentially. Solid and dashed curves correspond, respectively, to BED
calculations applied for tumors without hypoxia ?solid curve? and when 25%
of total cell clusters are hypoxic at the tumor center ?dashed curves?.
FIG. 6. Comparison of D?r? and BED?r? profiles for90Y2O3nanoparticle
labeled antibodies and for single90Y labeled antibodies, in Gray unit, as a
function of the distance r from center for a tumor with a radius of 1.0 cm,
for three different antibodies distribution: Uniform, linear, and exponential.
The gray parts symbolize the hypoxic core of 0.64 cm radius and dotted
vertical lines represent the tumor radius. Values for BED?r? were determined
according to parameters given in Table II and Eq. ?5? with q=1, with the
exception that the value of q changes from 1 to 3 for the hypoxic core.
1835 Bouchat et al.: BED and SCP for radioactive nanoparticles 1835
Medical Physics, Vol. 37, No. 4, April 2010
Page 11
remain inferior to 15 Gy in healthy tissues for both tumor
radii and for the three activity distributions, which means
that the treatment remains harmless for healthy tissues.
III.C. SCP distributions
Up to now, it is not clear which antibody distribution
would be the most efficient to treat spherical solid cancers,
such as NSCLC. The only important difference between the
three distributions we envisaged is the localization of the
maximum of the biologically effective dose inside the tumor
that could influence treatment outcome. For uniform distri-
bution, this maximum is located at the tumor center while
this maximum shifts near the tumor surface when the distri-
bution becomes exponential. Figure 7 shows shell control
probabilities in relation to the distance r for two spherical
tumors with radii of 0.5 cm ?cf. Figs. 7?a?–7?c?? or 1.0 cm
?cf. Figs. 7?d?–7?f??. SCP?r? has been plotted for non-small-
cell lung cancer ??=0.350 Gy−1? surrounded by lung tissues
??=0.031 Gy−1?. Uniform ?Figs. 7?a? and 7?d??, linear ?Figs.
7?b? and 7?e??, or exponential ?Fig. 7?c? and 7?f?? distribu-
tions caused by uniform or nonuniform antibody uptake are
considered.
III.C.1. Nanoparticle labeled antibody
When a NSCLC tumor of 0.5 cm radius does not present
a hypoxic core, and when it is treated with 5 nm diameter
nanoparticles of90Y2O3, the SCP curve displays a plateau
from the center of the tumor toward its surface and this,
independently of the antibody distribution. These results
mean that the probability to observe a cell cluster surviving
irradiation is very weak throughout the whole tumor. The
only difference between the three distributions is the value of
SCP at the tumor surface. Indeed, SCP is maximal for expo-
nential antibody distributions and is a little bit lower when
antibodies are distributed linearly ?SCP of 94%? or uniformly
?SCP of 83%?. Finally, SCP rapidly decreases to zero in lung
healthy tissues, for the three distributions. Tumor control
probabilities for uniform, linear, and exponential distribu-
tions are, respectively, 83%, 94%, and 100%.
Similar results are obtained when the spherical tumor
reaches a radius of 1.0 cm ?Figs. 7?d?–7?f??. SCP values of
100% are calculated inside the tumor, except for the expo-
nential antibody distributions for which a small decrease in
SCP from 100% to 97% is observed halfway between the
center and the surface of the tumor. Inversely, SCP values of
0% are observed in healthy tissues. At the tumor surface,
SCP varies from 100% for the exponential activity to 0%
when the radionuclides contained in the nanoparticles are
distributed uniformly through the tumor. In general, simu-
lated curves plotted on Fig. 7 indicate that a good treatment
outcome could be obtained with the use of radioactive nano-
particles coupled to each antibody, independently of the ac-
tivity distribution ?uniform, linear, or exponential?. With
87%, the best TCP is obtained for exponential distribution of
antibodies.
Figure 7 also shows values of SCP plotted against r when
spherical carcinomas present a hypoxic core, i.e., 25% of the
total number of cell clusters is poorly oxygenated at the cen-
ter of the tumor. In this case, SCP decreases from 100% to
0% in the region of the hypoxic core. This result indicates
that the use of 5 nm diameter nanoparticles containing90Y is
not efficient enough to irradiate three times more radioresis-
tant cell clusters when the antibodies cannot penetrate inside
this part of the tumor.
We have also investigated the variation in SCP when val-
ues of the different biological parameters ??, ?/?, N, and ??
vary. Study was made of a plausible range of values, similar
to those proposed by Atthey and co-workers.37For small
tumors of 0.5 cm radius, variation in ?/? and ? does not
modify SCP values, which means that treatment outcome
does not change even with a reasonable fluctuation of BED.
For a larger tumor of 1.0 cm radius, similar variations in ?/?
and ? provoke only very small differences of SCP at the
tumor surface. When the cell density varies from 107to 108,
N changes, but SCP values remains identical for both tumors.
The fact that SCP values remain unchanged when ?/?, ?,
and N vary is the consequence of the high activity released
by the nanoparticles. However SCP at the tumor surface in-
creases when ? varies from 0.20 to 0.5 Gy−1. For ? larger
than 0.5 Gy−1, SCP reaches a maximum of 100% at the tu-
mor surface, where cellular proliferation is very important.
On the other hand, when ? values are lower than 0.20 Gy−1,
SCP values at the tumor surface remain zero.
III.C.2. Single atom labeled antibody
As presented by the SCP curves in Fig. 7, when a single
90Y is linked to each antibody, the sizes of tumors, antibody
distributions, and the presence of hypoxic cells greatly influ-
ence SCP distribution. For example, no cell clusters will be
killed when the tumor has a radius of 0.5 cm and presents a
central hypoxia of 0.32 cm radius ?Figs. 7?a?–7?c??. Indeed,
SCP values of 0% are calculated for all measures of r. Simi-
lar results are observed when the tumor has no hypoxic core
and an exponential antibody distribution. Consequently,
when tumor has a radius of 0.5 cm and no central hypoxia,
better therapeutic effects are obtained when antibodies are
distributed uniformly or linearly. In these last cases, a SCP of
100% is reached at the tumor center and decreases progres-
sively through the tumor to a value of 0% at 2 mm before the
surface. These results lead to the conclusion that the most
highly proliferating cells are not sufficiently irradiated to
have a chance of a cancer cure.
Figure 7 shows that SCP results for larger tumors of 1.0
cm radius are totally different. Without hypoxia, the shape of
SCP curves varies according to the types of antibody distri-
bution. When antibodies are distributed uniformly ?Fig.
7?d??, SCP displays a plateau in the center of the tumor and
then decreases near the tumor surface which is the region
where the number of proliferating cells is the most impor-
tant. For linear and exponential distributions ?Figs. 7?e? and
7?f??, the maximal values of SCP are located, respectively, at
a distance of 0.70 and 0.90 cm from the center of the tumor,
with a narrower and higher peak for the exponential distri-
bution. Inversely, the shape of SCP curves for the three dif-
1836Bouchat et al.: BED and SCP for radioactive nanoparticles1836
Medical Physics, Vol. 37, No. 4, April 2010
Page 12
ferent antibody distributions is similar when the tumor has a
hypoxic core. A maximal SCP of 100% is reached in the
normally oxygenated part of the tumor, with a deeper radial
position within the tumor when the antibodies are uniformly
distributed through the tumor. Moreover, the more the distri-
bution is exponential, the more the peak is narrow. A better
shell control probability seems to be obtained when the
quantity of antibodies decrease linearly through the nonhy-
poxic part of the 1.0 cm radius tumor.
Variations in the maximal value for SCP were evaluated
for a wide range of biological parameters. Figure 8 shows
that maximal SCP values obtained for a tumor of 1.0 cm
radius without hypoxia decrease when the ratio ?/?, the cel-
lular repair constant and the cell density ? increase. Results
also indicate that shell control probability decreases rapidly
when the intrinsic radiosensitivity ? is lower than 0.35 Gy.
Consequently, due to the lower doses deposited inside the
tumor when single radionuclides coupled to each antibody is
used rather than radioactive nanoparticles, values of SCP de-
pend more on the choice of biological parameters and the
antibody distributions.
IV. CONCLUSIONS
In RIT, dose deposition inside the tumor is performed by
the use of monoclonal antibodies labeled with only one ra-
dioactive atom. In a previous work, the advantage of using
radioactive nanoparticles containing hundreds of radioactive
atoms rather than single radionuclides was modelized.6Do-
simetry calculations were performed with the MCNPX Monte
Carlo code by introducing a new model of tumor in which
radiolabeled antibodies can be uniformly, linearly, or expo-
nentially distributed. However, these deposited doses did not
take into account the radiosensitivity and cellular repair ef-
fects of the targeted tumor and surrounding tissue. Therefore,
BED and SCP formulas were applied in this work to estimate
more properly the tumor response and treatment outcome.
BED and SCP distributions were calculated for advanced
non-small-cell lung cancer for which no efficacious therapy
exists. When only one ?-emitter90Y is coupled to each an-
tibody, the calculated BED is lower than 60 Gy in the overall
tumor. SCP values show clearly that these biological doses
are insufficient to correctly treat NSCLC. When the single
?-emitter is replaced by a 5 nm diameter nanoparticle con-
taining approximately 100090Y atoms, sufficiently high bio-
logical doses can be obtained to completely kill the nonhy-
poxic part of a NSCLC, while limiting radiation in healthy
lung tissues. SCP calculations confirm these results by reach-
ing a maximal value of 100% inside the normally oxygen-
ated part of the tumor and a minimal value of 0% in the
surrounding healthy tissues. However, BED and SCP values
are influenced by the choice of the geometrical factors used
to describe the tumor ?i.e., morphology of the tumor and cell
cluster dimensions, radioactivity distribution throughout the
tumor, and volume of hypoxic core? by the model used to
calculate BED?r? ?i.e., LQ model, cellular repair, and hy-
poxic and repopulation effects? and by biological parameter
values selected for NSCLC and lung tissues. Variability of
both SCP and BED distributions have been analyzed for a
wide range of biological parameter values and the results
confirm their important impact on BED distributions inside
the tumor. Inversely, it is interesting to note that despite large
differences in BED curves, shell control probability remains
relatively unaffected when radioactive nanoparticles are
used. This last result is probably due to the high activity
deposited inside the tumor by the numerous radioactive at-
oms contained in the nanoparticles. To conclude this paper,
for either small or large solid tumors, BED and SCP calcu-
lations clearly confirm the efficacy of radioimmunotherapy
when using radioactive nanoparticles rather than a single ra-
dionuclide coupled to each antibody.
(a)
(b)(c) (d)
FIG. 8. Variation in maximal SCP values, in %, with the different radiobiological factors: ?a? The ratio ?/?, ?b? the intrinsic radiosensitivity ?, ?c? the
exponential cellular repair constant ?, and ?d? the cell density ?. SCP calculations were performed for a tumor of 1.0 cm without hypoxia and for single90Y
labeled antibodies. Activity inside the tumor may be distributed uniformly ?dotted curves?, linearly ?dashed curves?, or exponentially ?solid curves?.
1837Bouchat et al.: BED and SCP for radioactive nanoparticles1837
Medical Physics, Vol. 37, No. 4, April 2010
Page 13
ACKNOWLEDGMENTS
This research ?Targan Project–Convention 0516071? was
supported by the Walloon Region ?Belgium?. Olivier Feron is
senior research associate of FNRS ?Fonds National de la Re-
cherche Scientifique, Belgium?.
a?Author to whom correspondence should be addressed. Electronic mail:
virginie.bouchat@fundp.ac.be; Telephone: 0032-81-725479; Fax: 0032-
81-725474.
1M. Mehta, R. Scrimger, R. Mackie, B. Paliwal, R. Chappell, and J.
Fowler, “A new approach to dose escalation in non-small-cell lung can-
cer,” Int. J. Radiat. Oncol., Biol., Phys. 49, 23–33 ?2001?.
2W. A. Bethge and B. M. Sandmaier, “Targeted cancer therapy using ra-
diolabeled monoclonal antibodies,” Technol. Cancer Res. Treat. 4, 393–
405 ?2005?.
3S. V. Govindan, G. L. Griffiths, H. J. Hansen, I. D. Horak, and D. M.
Goldenberg, “Cancertherapywith
conjugated antibodies,” Technol. Cancer Res. Treat. 4, 375–391 ?2005?.
4R. M. Sharkey and D. M. Goldenberg, “Perspectives on cancer therapy
with radiolabeled monoclonal antibodies,” J. Nucl. Med. 46, 115s–127s
?2005?.
5D. M. Goldenberg, “Advancing role of radiolabeled antibodies in the
therapy of cancer,” Cancer Immunol. Immunother 52, 281–296 ?2003?.
6V. Bouchat, V. E. Nuttens, S. Lucas, C. Michiels, B. Masereel, O. Feron,
B. Gallez, and T. V. Borght, “Radioimmunotherapy with radioactive
nanoparticles: First results of dosimetry for vascularized and necrosed
solid tumors,” Med. Phys. 34, 4504–4513 ?2007?.
7M. J. Welch, C. J. Hawker, and K. L. Wooley, “The advantages of nano-
particles for PET,” J. Nucl. Med. 50, 1743–1746 ?2009?.
8F. Pene, E. Courtine, A. Cariou, and J. P. Mira, “Toward theragnostics,”
Crit. Care Med. 37, S50–S58 ?2009?.
9S. M. Moghimi, A. C. Hunter, and J. C. Murray, “Nanomedicine: Current
status and future prospects,” FASEB J. 19, 311–330 ?2005?.
10S. M. Moghimi and J. Szebeni, “Stealth liposomes and long circulating
nanoparticles: Critical issues in pharmacokinetics, opsonization and
protein-binding properties,” Prog. Lipid Res. 42, 463–478 ?2003?.
11D. E. Owens III and N. A. Peppas, “Opsonization, biodistribution, and
pharmacokinetics of polymeric nanoparticles,” Int. J. Pharm. 307, 93–102
?2006?.
12R. Gref, M. Luck, P. Quellec, M. Marchand, E. Dellacherie, S. Harnisch,
T. Blunk, and R. H. Muller, “‘Stealth’ corona-core nanoparticles surface
modified by polyethylene glycol ?PEG?: Influences of the corona ?PEG
chain length and surface density? and of the core composition on phago-
cytic uptake and plasma protein adsorption,” Colloids Surf., B 18, 301–
313 ?2000?.
13Y. Yi, J. H. Kim, H. W. Kang, H. S. Oh, S. W. Kim, and M. H. Seo, “A
polymeric nanoparticle consisting of mPEG-PLA-Toco and PLMA-
COONa as a drug carrier: Improvements in cellular uptake and biodistri-
bution,” Pharm. Res. 22, 200–208 ?2005?.
14J. Chen, H. Wu, D. Han, and C. Xie, “Using anti-VEGF McAb and
magnetic nanoparticles as double-targeting vector for the radioimmuno-
therapy of liver cancer,” Cancer Lett. 231, 169–175 ?2006?.
15G. Kaul and M. Amiji, “Biodistribution and targeting potential of poly-
?ethylene glycol?-modified gelatin nanoparticles in subcutaneous murine
tumor model,” J. Drug Target. 12, 585–591 ?2004?.
16J. D. Woodward, S. J. Kennel, S. Mirzadeh, S. Dai, J. S. Wall, T. Richey,
J. Avenell, and A. J. Rondinone, “In vivo SPECT/CT imaging and bio-
distribution using radioactive ?CdTe?-Te-125m/ZnS nanoparticles,” Nano-
technology 18, 175103 ?2007?.
17R. Kannan, V. Rahing, C. Cutler, R. Pandrapragada, K. K. Katti, V. Kat-
tumuri, J. D. Robertson, S. J. Casteel, S. Jurisson, C. Smith, E. Boote, and
K. V. Katti, “Nanocompatible chemistry toward fabrication of target-
specific gold nanoparticles,” J. Am. Chem. Soc. 128, 11342–11343
?2006?.
18K. V. Katti, R. Kannan, K. Katti, V. Kattumori, R. Pandrapraganda, V.
Rahing, C. Cutler, E. J. Boote, S. W. Casteel, C. J. Smith, J. D. Robertson,
and S. S. Jurrison, “Hybrid gold nanoparticles in molecular imaging and
radiotherapy,” Czech. J. Phys. 56, D23–D34 ?2006?.
19N. Chanda et al., “Radioactive gold nanoparticles in cancer therapy:
Therapeutic efficacy studies of ?198?AuNP-GA nanoconstruct in prostate
tumor-bearing mice,” Nanomedicine ?in press?.
radiolabeledand drug/toxin-
20H. Wu, J. Wang, Z. Wang, D. R. Fisher, and Y. Lin, “Apoferritin-
templated yttrium phosphate nanoparticle conjugates for radioimmuno-
therapy of cancers,” J. Nanosci. Nanotechnol. 8, 2316–2322 ?2008?.
21D. D. Dionysiou and G. S. Stamatakos, “Applying a 4D multiscale in
vivo tumor growth model to the exploration of radiotherapy scheduling:
The effects of weekend treatment gaps and p53 gene status on the re-
sponse of fast growing solid tumors,” Cancer Inform. 2, 113–121 ?2006?.
22R. Ruggieri, “Hypofractionation in non-small cell lung cancer ?NSCLC?:
Suggestions from modeling both acute and chronic hypoxia,” Phys. Med.
Biol. 49, 4811–4823 ?2004?.
23D. Levin-Plotnik and R. J. Hamilton, “Optimization of tumour control
probability for heterogeneous tumours in fractionated radiotherapy treat-
ment protocols,” Phys. Med. Biol. 49, 407–424 ?2004?.
24M. G. Stabin and G. D. Flux, “Internal dosimetry as a tool for radiation
protection of the patient in nuclear medicine,” Biomed. Imaging Interv. J.
3, e28 ?2007?.
25M. G. Stabin, M. Tagesson, S. R. Thomas, M. Ljungberg, and S. E.
Strand, “Radiation dosimetry in nuclear medicine,” Appl. Radiat. Isot. 50,
73–87 ?1999?.
26R. Barone, F. O. Borson-Chazot, R. Valkerna, S. Walrand, F. Chauvin, L.
Gogou, L. K. Kvols, E. P. Krenning, F. Jamar, and S. Pauwels, “Patient-
specific dosimetry in predicting renal toxicity with Y-90-DOTATOC: Rel-
evance of kidney volume and dose rate in finding a dose-effect relation-
ship,” J. Nucl. Med. 46, 99s–106s ?2005?.
27M. Astrahan, “Some implications of linear-quadratic-linear radiation
dose-response with regard to hypofractionation,” Med. Phys. 35, 4161–
4172 ?2008?.
28B. Warkentin, P. Stavrev, N. Stavreva, C. Field, and B. Fallone, “A TCP-
NTCP estimation module using DVHs and known radiobiological models
and parameter sets,” J. Appl. Clin. Med. Phys. 5, 50–63 ?2004?.
29P. Thirion, O. Holmberg, C. D. Collins, C. O’Shea, M. Moriarty, M.
Pomeroy, C. O’Sullivan, S. Buckney, and J. Armstrong, “Escalated dose
for non-small-cell lung cancer with accelerated hypofractionated three-
dimensional conformal radiation therapy,” Radiother. Oncol. 71, 163–166
?2004?.
30E. Kodym, R. Kodym, A. E. Reis, A. A. Habib, M. D. Story, and D. Saha,
“The small-molecule CDK inhibitor, SNS-032, enhances cellular radi-
osensitivity in quiescent and hypoxic non-small cell lung cancer cells,”
Lung Cancer 66, 37–47 ?2009?.
31M. Engelsman, E. M. Damen, K. De Jaeger, K. M. van Ingen, and B. J.
Mijnheer, “The effect of breathing and set-up errors on the cumulative
dose to a lung tumor,” Radiother. Oncol. 60, 95–105 ?2001?.
32B. Döme, S. Paku, B. Somlai, and J. Timar, “Vascularization of cutaneous
melanoma involves vessel co-option and has clinical significance,” J.
Pathol. 197, 355–362 ?2002?.
33J. A. M. Beliën, P. J. van Diest, and J. P. A. Baak, “Relationships between
vascularization and proliferation in invasive breast cancer,” J. Pathol.
189, 309–318 ?1999?.
34C. Schlueter, H. Weber, B. Meyer, P. Rogalla, K. Roser, S. Hauke, and J.
Bullerdiek, “Angiogenetic signaling through hypoxia-HMGB1: An angio-
genetic switch molecule,” Am. J. Pathol. 166, 1259–1263 ?2005?.
35J. L. Humm and L. M. Cobb, “Nonuniformity of tumor dose in radioim-
munotherapy,” J. Nucl. Med. 31, 75–83 ?1990?.
36V. E. Nuttens, A. C. Wera, V. Bouchat, and S. Lucas, “Determination of
biological vector characteristics and nanoparticle dimensions for radioim-
munotherapy with radioactive nanoparticles,” Appl. Radiat. Isot. 66, 168–
172 ?2008?.
37M. Atthey, A. E. Nahum, M. A. Flower, and V. R. McCready, “Effects of
cellular repair and proliferation on targeted radionuclide therapy: A mod-
eling study,” Phys. Med. Biol. 45, N15–N20 ?2000?.
38M. Cremonesi, M. Ferrari, L. Bodei, G. Tosi, and G. Paganelli, “Systemic
and locoregional dosimetry in receptor radionuclide therapy with pep-
tides,” Q. J. Nucl. Med. Mol. Imaging 50, 288–295 ?2006?.
39R. W. Howell, D. V. Rao, and K. S. R. Sastry, “Macroscopic dosimetry
for radioimmunotherapy-nonuniform activity distributions in solid tu-
mors,” Med. Phys. 16, 66–74 ?1989?.
40R. M. Sharkey and D. M. Goldenberg, “Use of antibodies and immuno-
conjugates for the therapy of more accessible cancers,” Adv. Drug Deliv-
ery Rev. 60, 1407–1420 ?2008?.
41G. A. Wiseman, C. A. White, R. B. Sparks, W. D. Erwin, D. A. Podoloff,
D. Lamonica, N. L. Bartlett, J. A. Parker, W. L. Dunn, S. M. Spies, R.
Belanger, T. E. Witzig, and B. R. Leigh, “Biodistribution and dosimetry
results from a phase III prospectively randomized controlled trial of Zeva-
1838Bouchat et al.: BED and SCP for radioactive nanoparticles 1838
Medical Physics, Vol. 37, No. 4, April 2010
Page 14
lin ?TM? radioimmunotherapy for low-grade, follicular, or transformed
B-cell non-Hodgkin’s lymphoma,” Crit. Rev. Oncol. Hematol. 39, 181–
194 ?2001?.
42R. W. Howell, S. M. Goddu, and D. V. Rao, “Application of the linear-
quadratic model to radioimmunotherapy-further support for the advantage
of longer-lived radionuclides,” J. Nucl. Med. 35, 1861–1869 ?1994?.
43K. Tobinai, Y. Kobayashi, M. Narabayashi, M. Ogura, Y. Kagami, Y.
Morishima, T. Ohtsu, T. Igarashi, Y. Sasaki, T. Kinoshita, and T. Murate,
“‘Feasibility and pharmacokinetic study of a chimeric anti-CD20 mono-
clonal antibody ?IDEC-C2B8, rituximab? in relapsed B-cell lymphoma,’
The IDEC-. C2B8 Study Group,” Ann. Oncol. 9, 527–534 ?1998?.
44N. Reynaert, H. Palmans, H. Thierens, and R. Jeraj, “Parameter depen-
dence of the MCNP electron transport in determining dose distributions,”
Med. Phys. 29, 2446–2454 ?2002?.
45D. R. Schaart, J. T. Jansen, J. Zoetelief, and P. F. de Leege, “A compari-
son of MCNP4C electron transport with ITS 3.0 and experiment at inci-
dent energies between 100 keV and 20 MeV: Influence of voxel size,
substeps and energy indexing algorithm,” Phys. Med. Biol. 47, 1459–
1484 ?2002?.
46B. Brans, L. Bodei, F. Giammarile, O. Linden, M. Luster, W. J. G. Oyen,
and J. Tennvall, “Clinical radionuclide therapy dosimetry: The quest for
the ‘Holy Gray’,” Eur. J. Nucl. Med. Mol. Imaging 34, 772–786 ?2007?.
47R. G. Dale, “The application of the linear-quadratic dose-effect equation
to fractionated and protracted radiotherapy,” Br. J. Radiol. 58, 515–528
?1985?.
48R. Dale and A. Carabe-Fernandez, “The radiobiology of conventional
radiotherapy and its application to radionuclide therapy,” Cancer Biother.
Radiopharm. 20, 47–51 ?2005?.
49R. K. Bodey, P. M. Evans, and G. D. Flux, “Application of the linear-
quadratic model to combined modality radiotherapy,” Int. J. Radiat. On-
col., Biol., Phys. 59, 228–241 ?2004?.
50C. Chiesa, F. Botta, E. Di Betta, A. Coliva, M. Maccauro, G. Aliberti, S.
Bavusi, L. Devizzi, A. Guidetti, E. Seregni, A. M. Gianni, and E. Bom-
bardieri, “Dosimetry in myeloablative Y-90-labeled ibritumomab tiuxetan
therapy: Possibility of increasing administered activity on the base of
biological effective dose evaluation. Preliminary results,” Cancer Biother.
Radiopharm. 22, 113–120 ?2007?.
51S. Baechler, R. F. Hobbs, A. R. Prideaux, R. L. Wahl, and G. Sgouros,
“Extension of the biological effective dose to the MIRD schema and
possible implications in radionuclide therapy dosimetry,” Med. Phys. 35,
1123–1134 ?2008?.
52J. Z. Wang, X. A. Li, W. D. D’Souza, and R. D. Stewart, “Impact of
prolonged fraction delivery times on tumor control: A note of caution for
intensity-modulated radiation therapy ?IMRT?,” Int. J. Radiat. Oncol.,
Biol., Phys. 57, 543–552 ?2003?.
53G. G. Steel, J. M. Deacon, G. M. Duchesne, A. Horwich, L. R. Kelland,
and J. H. Peacock, “The dose-rate effect in human-tumor cells,” Radio-
ther. Oncol. 9, 299–310 ?1987?.
54M. Guerrero and X. A. Li, “Halftime for repair of sublethal damage in
normal bladder and rectum: An analysis of clinical data from cervix
brachytherapy,” Phys. Med. Biol. 51, 4063–4071 ?2006?.
55A. Dawson and T. Hillen, “Derivation of the tumour control probability
?TCP? from a cell cycle model,” Comput. and Math. Meth. in Medicine 7,
121–141 ?2006?.
56N. Matsufuji, T. Kanai, N. Kanematsu, T. Miyamoto, M. Baba, T. Ka-
mada, H. Kato, S. Yamada, J. E. Mizoe, and H. Tsujii, “Specification of
carbon ion dose at the National Institute of Radiological Sciences
?NIRS?,” J. Radiat. Res. ?Tokyo? 48, A81–A86 ?2007?.
57R. G. Dale, “Dose-rate effects in targeted radiotherapy,” Phys. Med. Biol.
41, 1871–1884 ?1996?.
58J. F. Fowler, “Development of radiobiology for oncology-a personal
view,” Phys. Med. Biol. 51, R263–R286 ?2006?.
59R. Dale and C. Deehan, “Brachytherapy,” in Radiobiological Modeling in
Radiation Oncology, edited by R. G. D. B. Jones ?The British Institute of
Radiology, London, 2007?, pp. 113–137.
60S. Webb and A. E. Nahum, “A model for calculating tumour control
probability in radiotherapy including the effects of inhomogeneous distri-
butions of dose and clonogenic cell density,” Phys. Med. Biol. 38, 653–
666 ?1993?.
61B. Dubray, M. Henryamar, J. H. Meerwaldt, E. M. Noordijk, D. O.
Dixon, J. M. Cosset, and H. D. Thames, “Radiation-induced lung damage
after thoracic irradiation for Hodgkin’s disease—The role of fraction-
ation,” Radiother. Oncol. 36, 211–217 ?1995?.
62B. Jones, A. Carabe-Fernandez, and R. Dale, “The oxygen effect,” in
Radiobiological Modeling in Radiation Oncology, edited by R. G. D. B.
Jones ?The British Institute of Radiology, London, 2007?, Vol. 1, pp.
138–157.
63R. D. Stewart and R. J. Traub, “Radiobiological modeling in voxel con-
structs,” presented at the Proceedings of the Monte Carlo 2000 Meeting,
Lisbon, Portugal, 2000, edited by F. B. A. Kling, M. Nakagawa, L.
Tavora, and P. Vaz ?Springer-Verlag, Berlin, 2001?, pp. 285–290.
1839 Bouchat et al.: BED and SCP for radioactive nanoparticles1839
Medical Physics, Vol. 37, No. 4, April 2010
Download full-text