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Implantable magnetic nanocomposites for the localized treatment of breast
cancer
Article  in  Journal of Applied Physics · December 2014
DOI: 10.1063/1.4903736
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Implantable magnetic nanocomposites for the localized treatment of breast cancer
Kwabena Kan-Dapaah, Nima Rahbar, and Wole Soboyejo 
 
Citation: Journal of Applied Physics 116, 233505 (2014); doi: 10.1063/1.4903736 
View online: http://dx.doi.org/10.1063/1.4903736 
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/23?ver=pdfcov 
Published by the AIP Publishing 
 
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JOURNAL OF APPLIED PHYSICS 116, 233505 (2014)
Implantable magnetic nanocomposites for the localized treatment of breast
cancer
Kwabena Kan-Dapaah,1 Nima Rahbar,2,a) and Wole Soboyejo3
1Department of Materials Science and Engineering, African University of Science and Technology, Abuja,
Federal Capital Territory, Nigeria and Department of Biomedical Engineering, University of Ghana, Accra,
Ghana
2Department of Civil and Environmental Engineering, Worcester Polytechnic Institute, Worcester,
Massachusetts 01609, USA
3Department of Materials Science and Engineering, African University of Science and Technology, Abuja,
Federal Capital Territory, Nigeria; Department of Mechanical and Aerospace Engineering,
Princeton University, Princeton, New Jersey 08544, USA; and Princeton Institute for Science
and Technology of Materials (PRISM), Princeton University, Princeton, New Jersey 08544, USA
(Received 23 September 2014; accepted 24 November 2014; published online 18 December 2014)
This paper explores the potential of implantable magnetic nanocomposites for the localized
treatment of breast cancer via hyperthermia. Magnetite (Fe3O4)-reinforced polydimethylsiloxane
composites were fabricated and characterized to determine their structural, magnetic, and thermal
properties. The thermal properties and degree of optimization were shown to be strongly dependent
on material properties of magnetic nanoparticles (MNPs). The in-vivo temperature profiles and
thermal doses were investigated by the use of a 3D finite element method (FEM) model to simulate
the heating of breast tissue. Heat generation was calculated using the linear response theory model.
The 3D FEM model was used to investigate the effects of MNP volume fraction, nanocomposite
geometry, and treatment parameters on thermal profiles. The implications of the results were then
discussed for the development of implantable devices for the localized treatment of breast cancer.
VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903736]
I. INTRODUCTION potentially overcome the drawbacks associated with metallic
alloys.
The treatment of early stage breast cancer typically
More than 50 yr ago, Gilchrist and co-workers10 pub-
involves mastectomy (surgical removal of whole breast) or
lished their classical work on localized heating with MNPs.
lumpectomy (breast conservation) followed by radiation ther-
Since then, several fundamental studies have been carried
apy to remove any residual cancer cells. Although mastec-
out in an effort to understand the physical and chemical
tomy has a low recurrence rate,1 it is an aggressive form of
properties of MNPs.11–16 In the case of iron oxide nanopar-
treatment for early stage breast cancer. Therefore, treatment
ticles,13,14,16 their attractive combinations of high magnetic
modalities that could enhance the use of lumpectomy by elim-
susceptibility, biocompatibility, and low toxicity, coupled
inating residual breast cancer cells with limited side effects
with the penetration depth of the AMF, are the motivation
are needed. Interest in hyperthermia has increased recently,
for the recent interest in MNP heating for applications in
due to its minimal side effects and potential to enhance the 17,18
2–5 hyperthermia. However, problems related to aggregationtherapeutic efficacy of conventional cancer therapies.
and instability due to the rapid biodegradation of bare MNPs
Interstitial magnetic hyperthermia using implantable heat gen-
in biological media, continue to hinder the transition to clini-
erators, can be considered as one of the most advanced treat-
cal applications.
ment modalities in terms of fundamental research and clinical
In order to overcome these challenges, nanocomposites
research.6–8
(NCs) consisting of polymers (mostly elastomers and
In implantable heat generators, heat is generated by the
hydrogels)19,20 and MNPs have been proposed for the local-
remote application of an external alternating magnetic field
ized treatment of tumor tissue via localized hyperther-
(AMF). The mechanism of heat generation depends on mate-
mia.19,21 These materials offer new opportunities for the
rial properties such as the chemical composition, magnetic
development of novel cancer treatment modalities. They
structure, and size of the heat generator. Metallic alloy ther-
have also been combined with materials for the controlled
moseeds, such as nickel-silicon, dissipate heat due to eddy
9 release of therapeutic drugs to synergistically treat cancer bycurrents induced by the AMF. Although these kinds of ther-
the combined effects of localized drug release and heat.19,20
moseeds have been shown to generate high power output,
In this paper, a biocompatible magnetic NC, consisting
issues related to biocompatibility, corrosion, fibrous encap-
of magnetite (Fe3O4) nanoparticles and polydimethylsilox-sulation, and migration across the tissues still remain a
9 ane (PDMS), is explored. The NCs were fabricated usingchallenge. Magnetic nanoparticle (MNP) based heating can
soft lithography and the effects of MNP content on their
structure, magnetic, and thermal properties were then inves-
a)Author to whom correspondence should be addressed. Electronic mail: tigated. Furthermore, in an effort to investigate the in-vivo
nrahbar@wpi.edu thermal profile, a 3D finite element method (FEM) model
0021-8979/2014/116(23)/233505/11/$30.00 116, 233505-1 VC 2014 AIP Publishing LLC
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233505-2 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
was used to simulate the heating of breast tissue. Heat gener- microscope (FEI, Hillsboro OR, USA). All samples were
ation was calculated using the linear response theory (LRT) coated with carbon to prevent charging during scanning elec-
model. The FEM model was used to study the effect of NC tron microscopy (SEM) examinations. The SEM photomicro-
volume fraction on thermal profiles. The models were then graphs were obtained with a constant magnification (1000)
validated by comparing the results from the simulations with at an operating voltage of 10 kV.
the experimental results. The implications of the results were Bonding: The functional groups of plain PDMS and its
then discussed for the development of implantable devices NCs were characterized using a Tensor 27 Fourier trans-
for the localized hyperthermic treatment of breast cancer. form infrared spectroscope (Bruker, Inc., Madison WI,
USA). For each test run of the Fourier transform infrared
II. EXPERIMENTAL spectroscopy (FT-IR) examination, a background spectrum
was first measured (without any sample mounted) at the
A. Materials
ZnSe crystal spot of the sample plate. Then, a solid slab
Commercially available Fe3O4 nano-powder (high purity, sample was placed on the ZnSe crystal spot. The lever arm
99.5þ%, 15–20 mm) was purchased from US Research was then moved over to snap it into place above the crystal.
Nanomaterials, Inc., Houston, TX, USA, while PDMS The top handle was turned downward to press the tip of the
Sylgard 184 silicone elastomer kit was purchased from Dow sample onto the crystal face. The scan wave number was in
1
Corning Corporation, Auburn, MI, USA. These were used to the range of 600–3500 cm .
prepare the NC samples. All the chemicals were used in the Magnetic properties: The magnetic properties of the
as-received condition. Fe3O4 powder and the Fe3O4 NCs containing 5 and 10 wt. %
of Fe3O4 were measured using an MPMS XL-5 semi-con-
B. Fabrication of nanocomposites duction quantum interface device (SQUID) magnetometer
(Quantum Design, San Diego CA, USA). The Fe3O4 powder
Three types of MNP-PDMS NC samples, designated as
sample was mounted in capsules, while the solid NC samples
MNP-0, MNP-5, and MNP-10, were prepared. MNP-0 was a
were mounted in drinking straws. The magnetization curves
Fe3O4-free NC. It was studied as a control. The MNP-5 sam- were obtained by varying the magnetic fields between
ple contained 5 wt. % Fe3O4 while the MNP-10 sample con- 500 mT and 500 mT at temperatures of 25 C. The resulting
tained 10 wt. % Fe3O4, as summarized in Table I. A simple magnetization values were normalized with the sample
soft lithography technique was used to fabricate the Fe3O4- masses to obtain the specific magnetization values.
PDMS samples. PDMS elastomer kit (base) and its curing
Thermal properties: Thermal characterization was car-
agent were mixed at a weight ratio of 10:1. The mixture was
ried out using samples that were immersed in water within a
whisked vigorously with a spatula to produce a uniform mix-
glass sample holder. The sample holder was positioned in an
ture with adequate cross-linking. Fe3O4 nano-powder was induction system that generated an AMF. The induction
then added into the PDMS mixture. The resulting mixtures
heating system, DM100 (nanoScale Biomagnetics, Zaragoza,
were stirred thoroughly for 15 min to ensure uniform distri-
Spain), consisted of an alternating current power supply, a
butions of the Fe3O4 nanoparticles. The mixtures were then controller, a cylindrical sample holder, a Dewar flask, a fiber
placed in a desiccator for 1 h to ensure that the air bubbles
optic sensor, and a solenoid coil. The change in the tempera-
were completely removed. The resulting Fe3O4-PDMS nano- ture of water was measured using an in-built fiber optic sen-
particle mixtures were poured into cubic moulds with a side
 sor. This was done as a function of time in the AMF. Thelength of 4 mm. After baking in an oven at 100 C for 35
measurements were made every 200 ms with a resolution of
min, the PDMS replica was removed and peeled off.
0.2 C. The experimentally measured specific absorption rate
(SARexp) values were calculated using the expression
C. Material characterization X
Crystal structure: The crystal structure of the Fe3O4 Cpimi
nano-powder that was used in this study was verified using a SAR exp ¼ i
DT
; (1)
DB Focus X-ray diffractometer (XRD, Bruker, Inc., Madison mFe 0 Dt3 4
WI, USA). This was done using the following experimental
conditions: X-ray source¼Ni-filtered Cu Ka radiation; X-ray where Cpi and mi are the respective specific heat capacity
¼ 1 1power 40 kV, 40 mA; sampling angle¼ 0.05 and 2h scan- and mass for each component (Cpi¼ 4186 J Kg K for
ning rate¼ 2 s step1. The microstructure of the NC samples water) and mFe 0 is the mass of the magnetite nanoparticles.3 4
was studied using a Quanta 200 FEG MKII scanning electron T and t are temperature and time, respectively.
Finally, the degree of optimization, a, that can be
TABLE I. Compositions of the samples. achieved from our thermal experiments is explored by com-
paring the theoretical maximum hysteresis loops with experi-
Weight percentages (%)
mentally determined hysteresis loops. Note that a is a
Sample Fe3O4 PDMS dimensionless parameter that characterizes the relative area
of the hysteresis loops with respect to the ideal square.22,23
MNP-0 0 100
Also, a¼ 1 represents a perfectly optimized system (easy
MNP-5 5 95
MNP-10 10 90 axis of all the MNPs align along the magnetic field) and for
the case where the easy axis of the MNPs are randomly
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233505-3 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
oriented, a¼ 0.39.23 The theoretical maximum hysteresis The physical properties of the MNPs that were used
area, Amax, is then defined by were: MS¼ 446 kA m1,25 density¼ 5.18 g cm3,25 and heat
capacity¼ 670 J Kg1K1.25 Additionally, the AMF parame-
Amax ¼ 4l0Hmaxrs; (2) ters used were T¼ 300 K, f¼ 100 kHz, and H ¼ 5 kA m1max .
The physical properties of PDMS were obtained from Ref. 26.
where l0 is the permeability of free space, Hmax is the AMF
strength, and rs is the saturation magnetization. Combining
Eqs. (1) and (2), a is calculated as B. Tissue heating by MNP-PDMS nanocomposites
In order to study temperature profile and thermal dose
¼ SAR exp 1 ¼ Aa exp ; (3) coverage in biological media, a 3D FEM model of breast tis-
f Amax Amax sue was developed.
where Aexp is the experimentally measured hysteresis loop
and f is the AMF frequency. 1. Problem formulation
The geometric model that was used in our study was simi-
III. IN-VIVO PREDICTIONS
lar to that employed by Reynoso et al.27 for modeling gold-
A. Calculation of optimum parameters of MNPs nanoparticle mediated heating. Breast tissue was modeled as a
semi-ellipsoidal block with long and short axes diameters of
When constrained super-paramagnetic MNPs are placed
12 cm and 5 cm, respectively. The model is shown schemati-
in an AMF with given parameters (Hmax, f), the amount of cally in Fig. 1(a). The NC (blue) was embedded within a cavity
heat dissipated (specific losses), A, during one cycle of the
created after the tumor is surgically removed. The dimensions
AMF is equal to the area of their hysteresis loop. Using the
22,24,25 of the breast were chosen to represent a computational domainLRT model, A, is defined as
that was large enough to reduce the numerical errors due to
pl2M2V xs boundary conditions. Two different NC geometries were used
A ¼ 0 S M 2ð ÞHmax; (4)þ 2 2 in our model [Fig. 1(b)]: a cubic block with side length, L3k T 1 x s nc,B
with its lowest value set at 0.25 cm and a cylindrical block with
where M is the spontaneous magnetization, V is the vol- a radius of 0.125 cm and height of 0.32 cm. The cubic NCS M
ume, x (2pf) is the angular frequency, s is the Neel-Brown was similar to the one that was used in our prior in-vitro
28
relaxation time, and kB is the Boltzmann constant. Details on experiments. For both geometries, we assumed that the
the origin and derivation of this equation can be found in MNPs are uniformly distributed within the PDMS matrix.
Appendix A. The temperature distribution in solids, due to an external
The volumetric power output, P, is given by heat source, can be determined by the Fourier heat conduc-
tion equation. This is given by
P ¼ /Af; (5)
where / is the volume fraction of MNPs in the polymer. To
calculate the optimum size of the MNPs, the evolution of the
SAR was determined as a function of the diameter at fixed
AMF parameters. The SAR was obtained from
¼ PSAR ; (6)
qNC
where qNC is the effective density of the NC, and P is the
volumetric power output (Eq. (5)). Note that qNC was esti-
mated using simple rule-of-mixtures.
According to Ref. 22, maximum area of the hysteresis
loop for the LRT model occurs when the condition xs¼ 1 is
met. Therefore, assuming that the shape of MNPs is spheri-
cal, the optimum nanopasrtifficffiffilffieffiffiffiffirffiaffiffidffiffiffiiffiuffiffiffisffi isffiffiffiffiffiffi
gffiffiiffiffi
vffiffien by
¼ 3 3 kBT 1ropt ln ; (7)
4p Keff xs
where Keff is the effective anisotropy constant. Using
Eq. (7), the SAR of Fe3O4 MNPs with optimum radius was
calculated as a function of anisotropy. The domain of valid-
ity of the LRT model was determined by plotting the condi-
FIG. 1. (a) Schematic of breast phantom with a long axis diameter of 12 cm
tion, n< 1, where n is the reduced magnetic field defined as: and a short axis diameter of 5 cm. A spherical cavity illustrates tumor region
n¼ l0MSVMHmax/(kBT). where NC (blue) is inserted. (b) MNP-PDMS NCs used for FEM modeling.
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233505-4 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
TABLE II. Physical properties of tissue.
Material(Ref.32) k (W m1K1) q (kg m3) c (kJ kg1K1) x (s1) Qm (W m
3)
Breast 0.48 1080 3000 0.00018 450
Blood … 1060 4200 … …
8  !
@T 2
qcp ¼ kr2 >T þ Q <gen; (8) ðT  45Þ@t SF ðTÞ ¼ >: 1 þ exp  if T  45
C;
b 12 (11)

where q is the density, cp is the specific heat capacity at con- 2 if T > 45 C:
stant pressure, k is the thermal conductivity, and Qgen is the
heat generation term, which is defined differently for each Also, the temperature dependent thermal conductivity was
domain. In the case of the NC, the result from Eq. (5) was obtained from Ref. 35 to be
used. It was set to zero for all other domains. kðTÞ ¼ 0:48½1 þ 0:0028ðT  293:15KÞ: (12)
For biological media, Pennes model29 modifies Eq. (8)
by including effects of heat generation due to constant blood The constant physical properties of the tissue, which were
perfusion, Qp, and metabolic heat, Qm. Qp is defined as obtained from Bezerra et al.,32 are summarized in Table II.
The MNPs were assumed to be homogeneously distrib-
Qp ¼ qbcbxbðTb  TÞ; (9) uted within PDMS. This assumption was acceptable
although Fig. 3 shows evidence of the formation of MNP
where qb, xb, cb, and Tb are the density, blood perfusion clusters. These clusters have been shown to affect some ther-
rate, specific heat capacity, and temperature of blood, respec- mal properties.36,37 However, the number of clusters formed
tively. Qm is defined in Table II. at relatively low volume are low.38 Therefore, its effects can
The assessment of the lesion predicted by our model be considered negligible for the range of volume fraction
was described using the method developed by Sapareto and used in this study. The properties of NC were calculated
Dewey,30 which expresses the thermal dose as a cumulative using a method described in Sec. III A. Thermal conductivity
equivalent minutes of exposure at 43 C (CEM43). CEM43 is of PDMS was taken as 0.15 Wm1 from Ref. 26. Effective
defined as ð thermal conductivity of NCs was computed using the follow-t ing expression:f
CEM ¼ R½43TðtÞ43 dt; (10)
0 1=k ¼ ð1  /Þ=k1 þ /=k2; (13)
where tf is the treatment duration and R has a value of 0.25 where subscripts 1 and 2 denote PDMS and MNP conductiv-
when the temperature as a function of time, T(t), is less than ity values, respectively.
43 C or 0.5 otherwise. We considered the tissue with a The boundary conditions for Eq. (8) were: a prescribed
CEM43 value of 28 min to be necrosed.
31
temperature, T¼ 37 C, at the chest wall; heat transfer by
The properties of the materials that were used in the convection between the surface of the breast and the external
simulations were based on data reported in the literature.26,32 environment, n  (krT)¼ h  (TextT); where the heat
Due to the pronounced changes in blood perfusion (BP) and transfer coefficient h¼ 3.5 Wm2K1, external temperature,
thermal conductivity of tissues, it is appropriate to use T ¼ 20 ext C, and continuity, n  (k1rT1 k2rT2)¼ 0,
temperature-dependent values.33 To account for temperature were enforced on all the interior boundaries. Initial tempera-
dependence of BP, Eq. (9) was multiplied by a scaling factor tures in all domains of the model were set to the normal
(SF). SF for breast tissue, SFb, can be expressed as
34
body temperature of 37 C.
FIG. 2. (a) XRD profile of the Fe3O4
powder used in our study and (b) FT-
IR spectra of plain PDMS and its NCs
with different weight fractions.
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FIG. 3. SEM images of PDMS-MNP
NC containing: (a) 5 wt. % Fe3O4 and
(b) 10 wt. % Fe3O4.
2. FEM model validation Fe3O
1
4 powder had an MS value of 33 emu g . The MS
value for NC containing 5 wt. % of Fe3O4 was 1.2 emu g
1.
In order to validate the model, we simulate the case
This is about 4% of the M value obtained for the pure
where a NC containing 10 wt. % (2 vol. %) MNP was S
¼ Fe3O4 powder. Similarly, the sample containing 10 wt. %placed in water and exposed to AMF with Hmax 11.94 kA
1 ¼ had an MS value of 2 emu g
1. This is about 6% of the M
m (15 mT) at f 298 kHz. In the simulation, blood perfu- S
value obtained for pure Fe
sion and metabolic heat terms were omitted, since they are 3
O4 powder. The NC samples
exhibited hysteresis loops, with defined areas for
not applicable under in-vitro conditions. All other experi-
H ¼ 11.94 kA m1.
mental conditions were implemented in the model, as they max
were in the experiments. The heat generation term needed in
the simulation was calculated from 2. Thermal property characterization
¼ mFe 0
The thermal experiments explored the dependence of
Q SAR 3 4exp ; (14)
V heat generation on MNP content and magnetic field strength.NC
The measurements were obtained from the PDMS and the
where mFe 0 . is the mass of MNPs in the NCs and VNC is3 4 Fe3O4-PDMS NCs at three different field strengths (3.98,
the volume of the NC. 6.76, and 11.94 kA m1) and a frequency of 298 kHz. In Fig.
4(a), the time dependence of temperature is presented. This
IV. RESULTS AND DISCUSSION is shown for three different weight percentages of MNPs, for
an AMF field strength of 11.94 kA m1 at a frequency of
A. Experimental 298 kHz. Plain PDMS exhibited no increase in the applied
1. Structural and magnetic properties field. The temperature changes associated with heating from
the NCs containing 10 wt. % Fe304 were greater than those
A typical XRD pattern of the magnetic nanoparticle associated with NCs containing 5 wt. % Fe304. Hence, the
(Fe3O4) that was used in this study is presented in Fig. 2(a). The heat generation increased with nanoparticle weight fraction.
peaks confirmed the presence of the cubic system of Fe3O4. Fig. Fig. 4(b) presents the dependence of SAR on magnetic
2(b) presents the FT-IR spectra of plain PDMS and its NCs con- field. This is shown for NCs containing 5 and 10 wt. %
taining 5 and 10 wt. % of Fe3O4. The FT-IR spectra of plain
 Fe304. The results show that, for a given field strength, thePDMS includes a rocking peak, ranging from 785 to 815 cm 1;
 SAR increases with increasing weight percentage of Fe 0 .a wide multi-component peak ranging from 1000 cm 1
3 4
to
 Furthermore, the SAR values for the NCs had small ampli-1100 cm 1, related to Si-O-Si symmetrical stretching modes;
  tudes at low magnetic fields. They also exhibit a sharp risetwo peaks at approximately 1410 cm 1 and 1258 cm 1, related
to –CH wagging and a peak at 2960 cm
above a critical field strength, which is usually taken to be
1
3 , related to asymmet- the coercive field of the MNPs. This behavior, which has
ric stretching of –CH3. For the two NCs, the chemical structure been analyzed in a previous study,23 is exhibited by
of PDMS was well maintained as shown by the unaffected char-
acteristic peaks of the PDMS matrix presented in Fig. 2(b). This
suggests that the Fe O nanoparticles were physically adsorbed TABLE III. Summary of results from magnetization and thermal experi-3 4
ments: A was calculated using Eq. (2); A was measured at f¼ 298 kHz
by the PDMS molecules, instead of forming primary chemical max exp
and a was calculated using Eq. (3).
bonding during the fabrication process.
Fig. 3 presents SEM photomicrographs of the cross- Samples H (kA m1max ) rs (Am
2 kg1) Amax (mJ g
1) Aexp (mJ g
1) a
sectional area of NC containing 5 and 10 wt. % Fe3O4. The
MNP-0 11.94 0 0 0 0
results show Fe3O4 particle distributions were present in the
MNP-5 1.2 0.072 0.022 0.30
NC. They also show evidence of particle aggregates
MNP-10 2 0.120 0.037 0.31
(observed as bright lumps) in isolated locations.
MNP-10 6.76 2 0.068 0.004 0.06
Magnetic parameters extracted from SQUID magne- MNP-10 3.98 2 0.004 0 0
tometer measurements are summarized in Table III. The
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233505-6 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
FIG. 4. Temperature as a function
of time for NCs with different amounts
of Fe304 for AMF field strength of
Hmax¼ 11.94 kA m1 at a frequency of
f¼ 298 kHz.
ferromagnetic MNPs when they are exposed to field Fig. 5(c) presents SAR as a function of effective anisot-
strengths within the range examined in our study. ropy, Keff, for MNPs with optimum volume. It is evident
Furthermore, it is important to note here that for ferromag- from the results that the maximum achievable SAR increases
netic nanoparticles, as the field increases the SAR values with a reduction in anisotropy. This is because A / V (vol-
approach a saturation value.23 This tendency to approach ume of MNP) and the optimum volume is inversely propor-
a saturation SAR can be exploited to produce new NC materials tional to Keff [see Eq. (7)].
that have self regulating temperature-controlled characteristics
that are similar to those of metallic alloy thermoseeds.39 2. FEM model validation
Finally, the calculated a values (Table III) show a simi-
The results are presented in Fig. 6. The error bars in the
lar degree of optimization obtained for iron oxide nanopar-
plot represent the error ranges in the experimental measure-
ticles found in the literature.22 This suggests that thermal
ments. These were obtained from standard deviations between
properties of Fe3O4 NCs depend largely on the physical three runs at each individual time point. A maximum uncer-
properties of the nanoparticles.
tainty of 0.3 C was obtained. The predictions from the model
diverge about 5%–10% from the experimental results. This
B. In-vivo predictions
deviation can be attributed to the uncertainty associated with
Having identified the operative sizes of Fe3O4 for opti- the position of the NC sample relative to the thermocouple.
mum heating, the interstitial heating of homogeneous breast The results can also be affected by variations due to the inac-
tissue by the NCs was modeled to assess the temporal and spa- curate material properties that were used in the simulation.
tial in-vivo temperature distributions, and the associated ther-
mal doses (lesions). For the thermal dose, our domain of 3. Temperature profile and thermal dose coverage
interest was restricted to the area in which 100% thermal dose
Fig. 7 shows the cross-sectional temperature distribution
occurred. Unless otherwise stated, AMF field strength and fre-
1 and the corresponding lesion after the homogeneous breastquency were fixed at 5 kA m and 150 kHz, respectively, for
tissue is subjected to 20 min of heating at 46 C (surface tem-
all of the simulations. Consequently, the corresponding opti-
 3 perature) with a cubic MNP (6.85 vol. %.)-PDMS NC with amal radius of 7 nm and anisotropy of 35 kJ m were used.
side length, Lnc¼ 0.25 cm. The result in Fig. 7(a) shows that
the temperature distribution is non-uniform, favoring the
1. Optimum parameters of MNPs
central section of the NC where the maximum temperature
Fig. 5(a) shows the evolution of SAR as a function of occurs. The maximum temperature has no direct effect on
MNP radius, r, ranging from 4 nm to 10 nm, for AMF field the tissue, as it is located within a volume embedded in the
strength, H 1max¼ 5 k Am at a frequency, f¼ 150 kHz. The NC. It can also be observed that the temperature profile is
volume fraction was set to 1%. It can be observed that, for radially symmetric and spreads away from the surface of the
the given AMF parameters, maximum power output occurs NC. Fig. 7(b) shows that, for a cubic NC, the shape of the
at a radius, r 7 nm. According to previous reports,22,24,25 resulting lesion is slightly irregular. However, assuming a
this remains unchanged as the field strength and volume frac- spherical shape, its diameter, D, is about 0.72 cm, and the av-
tion are increased at a constant frequency. erage distance between NC surface and the perimeter of the
In Fig. 5(b), a plot of optimum radius, ropt, is presented lesion, dsd (¼D  Lnc), is about 0.47 cm.
as a function of effective anisotropy, Keff, for AMF field Fig. 7(c) presents the corresponding temperature as
strength, H ¼ 5 k Am1max at a frequency, f¼ 150 kHz. The functions of time. The results show that the temperatures at
results show that the optimum MNP radius decreases with the centers of the NCs and the NC-tissue interface increase
increasing effective anisotropy constant. The condition of and approach plateau x-values with time. The differences in
validity for the LRT is plotted for AMF field strength, the temperatures are consistent with the non-uniformity of
H 1max ¼ 5 kA m , as a horizontal line. According to Ref. 22, the temperature distribution observed previously in the
an appropriate value of effective anisotropy constant is found cross-sectional images. This suggests that for reliable tem-
below the horizontal line. perature monitoring multiple positions should be considered.
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233505-7 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
FIG. 5. (a) SAR as a function of MNP
radius, (b) optimum radius as a func-
tion of anisotropy (the horizontal
dashed line shows the limit above
which the LRT is not valid for different
field strengths), and (c) SAR as a func-
tion of anisotropy for MNPs with opti-
mum volume for AMF field strength,
H 1max¼ 5 kA m at a frequency,
f¼ 150 kHz.
Fig. 7(d) shows that the radial temperature that spreads away homogeneous breast tissue subjected to 20 min of heating at
from the center of the NC decreases with increasing distance a NC surface temperature of 46 C. As expected, increasing
from the center of the NC. the volume of the NC increases the lesion diameter, D. This
is due to the increase in thermal flux that occurs as a result of
the increased surface area. For example, dsd¼ 0.47 cm, for a
4. Effects of nanocomposites properties 0.25 cm size cubic NC, increased to dsd¼ 0.95 cm, for a
The predictions of the effects of cubic NC size on lesion 0.75 cm size cubic NC. The last row of columns 2–4 in
parameters are presented in Table IV (columns 2–4) for the Table IV also shows that the change in lesion size increases
as the size of the NC increases. The maximum temperature
within the NC, Tmax, also remains constant, with decreasing
MNP volume percentage and increasing NC size.
Figs. 7(e) and 7(f) show the cross-sectional temperature
distribution and the corresponding lesion size, respectively,
after the homogeneous breast tissue is subjected to 20 min of
heating at 46 C with a cylindrical MNP (6.5 vol. %.)-PDMS
NC with the same volume (diameter of 0.141 cm and the
length of 0.25 cm) as the cubic NC. It is clear from the
results that compared to the results from the cubic geometry,
the cylindrical NC produced a well-defined thermal dose
profile. However, the diameter of the thermal dose predicted
by the cylindrical NC was smaller. The results, therefore,
suggest that the shapes of the heated regions can be con-
trolled by the geometry of the sample.
5. Effects of treatment parameters
Columns (5–7) in Table IV present the effects of treat-
FIG. 6. Comparison of experiments and models. For the experiments, the fol-
lowing settings were used: time, t¼ 600 s; field strength, H ¼ 11.94 kA m1; ment duration on lesion parameters that were measured aftermax
frequency, f¼ 298 kHz, and medium used was water. homogeneous breast tissue was subjected to heating by a
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233505-8 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
FIG. 7. (a) Temperature distribution,
(b) thermal dose coverage, (c) temper-
ature change as a function of time at
center and surface of NC, (d) tempera-
ture change as a function of distance
from the center, (e) temperature distri-
bution, and (f) thermal dose coverage
after homogeneous breast tissue is sub-
jected to 20 min of heating at 46 C.
Data of (a)–(d) are for a cubic NC, and
(e) and (f) are for a cylindrical NC.
cubic Fe3O4-PDMS NC at a surface temperature of 46
C. from 600 s to 1200 s. We also observed that the maximum
The results show that increasing treatment duration increases temperature within the NC, Tmax, did not change signifi-
lesion diameter, D. This is expected since the main mode of cantly with increasing treatment duration or MNP volume
heat transfer is conduction. percentage.
The last row in Table IV also shows that the change in In the case where the homogeneous breast tissue was
lesion size decreases with increasing treatment duration. For subjected to 20 min of heating by a cubic MNP(Fe3O4)-
example, increasing the treatment duration from 300 s to PDMS NC at a surface temperature of 43 C, it was observed
600 s, resulted in 0.14 cm increase in lesion diameter, D. that compared to the results of heating with the NC surface
This decreases to 0.10 cm when the duration is increased temperature of 46 C, the lesion size decreased from 0.72 cm
to 0.60 cm. The maximum temperature, which occurred
TABLE IV. Predicted lesion parameters for different cubic NC sizes. D is within the NC was 45.8 C, for an MNP volume percent-
the diameter of the lesion and Tmax is the maximum temperature, which age of 3%.
occurs within NC.
Side length (cm) Time (s) 6. Implications
Parameter 0.25 0.50 0.75 300 600 1200 This study has implications for localized and controlla-
 ble cancer treatment. The results suggest that by controllingTmax ( C) 49 49 49 49 49 49
parameters, such as MNP vol. % and AMF strength, Fe O -
MNP (vol. %) 6.85 1.80 0.80 6.90 6.85 6.85 3 4
D (cm) 0.72 1.26 1.70 0.48 0.62 0.72 PDMS NCs can be designed to generate the heat that is
needed for hyperthermia. The NCs can be implanted into
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233505-9 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
cavities created after the surgical removal of tumors.9,40 In other factors, the size of the NC significantly affects the vol-
such cases, they could facilitate post-surgery treatment of ume fraction of Fe3O4 that is required to achieve a given
cancer by localized hyperthermia. treatment temperature.
Also, due to flexibility of the NCs, coupled with the fact
that power output can be controlled by volume fraction of ACKNOWLEDGMENTS
the MNP vol. % and AMF magnetic field, they can be
The authors are thankful for the financial support of the
moulded into different shapes and sizes. This will enable
UG/Carnegie Foundation “Next Generation of Academics in
them to be used in a manner similar to permanent brachy-
Africa” Program, the World Bank STEP B Program, the
therapy.41 Furthermore, the flexibility allows for temperature
World Bank African Centers of Excellence Program, the
sensors to be embedded within the NC to enable surrounding
African Development Bank, the Nelson Mandela Institution,
temperatures to be controlled and monitored. Clearly, further
and the African Capacity Building Foundation. Appreciation
experiments are needed to test these potential enhancements.
is also extended to Dr. Nicolas Cassinelli and Ms. Beatriz
Finally, we have previously reported in-vitro combined
Sanz Sague (thermal experiments), Mr. Andrew Butler
hyperthermia and drug release studies, using paclitaxol
(XRD and FT-IR), and Professor Don Heiman (SQUID).
loaded thermo-responsive hydrogels of PNIPA incorporated
into PDMS.42 The results from our predictions suggest that
the temperatures reached within the polymer matrix are suffi- APPENDIX A: LINEAR RESPONSE THEORY
ciently high to heat up the hydrogel and cause the release of Generally, when constrained superparamagnetic MNPs
the drug from the PNIPA-based gel. It must be noted that are placed in an AMF with a given strength (Hmax), the area
though the lower critical solution temperature (LCST) of the of their hysteresis loop, during one cycle, is equal to A. This
hydrogel will have to be adjusted to match the temperature is defined as
level to ensure that the required amount of drug is released at ð
the appropriate time. The adjustment of the LCST and its þHmax
effects on drug release (in the context of our novel multimo- A ¼ l0 MðHÞdH; (A1)
Hmax
dal implantable NC) has been studied extensively and
reported in prior work by our research group.28,42–44 Further where M(H) is the MNP magnetization. For magnetic hyper-
work is clearly needed to test the drug release characteristics thermia applications, the LRT model has been used by sev-
of such NC system under in-vivo conditions. eral researchers to calculate the hysteresis loop.22,24,25 The
LRT model describes the dynamic response of an assembly
V. SUMMARY AND CONCLUDING REMARKS of constrained MNPs using Neel-Brown relaxation time.
22 It
assumes a linear relationship between the magnetic system
The paper presents a combination of experiments and and magnetic field. This assumption is valid for the condi-
models that show the potential of biocompatible magnetic tion, n< 1. Then, M(H) is given by
NC structures for applications as biomedical implants for
cancer treatment. MðHÞ ¼ ~vHðtÞ; (A2)
Structural, magnetic, and thermal experiments were per-
formed. These provide insights into the dependence of SAR where H(t) is the AMF and ~v is the complex susceptibility,
on the magnetic field, MNP properties and weight fraction, defined as
and cyclic frequency. The magnetic NCs are shown to be v0
nearly optimized for the case where easy axis of MNPs are ~v ¼ þ ; (A3)1 ixs
randomly oriented in the magnetic field. The a values of 0.30
for NCs containing 5 wt. % of Fe3O4, and 0.31 for NCs con- s is defined as
taining 10 wt. % of Fe3O4 were elucidated for a field strength
of 11.94 kA m1. The results suggest that the polymer matrix
s ¼ s expðrÞ; (A4)
does not have a significant effect on the SAR. 0
LRT and 3D FEM models were used to investigate the where s 11 220 (5 10 s) is the frequency factor of s and r is
in-vivo temperature profiles and the thermal dose coverage the reduced anisotropy defined as: KeffVM/kBT. The deriva-
of homogeneous breast tissue and tumors embedded within tion of the static susceptibility, v0, is based on assumed ori-
them. Within the domain of validity of the LRT model, the entations of the MNPs easy axis with respect to the AMF
optimum MNP material properties (r 7 nm and Keff¼ 35 kJ
 and Keff of the MNPs.
22 For randomly oriented MNPs or
m 3) for AMF parameters (Hmax¼ 5 kAm3 at f¼ 150 kHz) aligned MNPs with r 	 1, v0 is given by22
were identified. These were then used to model the heating
of homogeneous breast tissue. The results shows that: (i) the l 2oMSVM
shape of the thermal dose coverage is primarily affected by v0 ¼ : (A5)3kBT
the shape of the NCs for a given set of material properties,
treatment, and AMF parameters; (ii) the size of the thermal To calculate v0 for MNPs with an easy axis aligned along the
dose coverage is affected by both the NC geometry (size and direction of the field, with r 
 1, Eq. (A5) is multiplied by a
shape) and the treatment parameters (time and temperature) factor of 3.25 Assuming that H(t)¼Hmax cos(xt), Eq. (A2),
for a given set of AMF parameters, and (iii) compared to the response of the LRT model, now becomes
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233505-10 Kan-Dapaah, Rahbar, and Soboyejo J. Appl. Phys. 116, 233505 (2014)
MðHÞ ¼ jvjHmax cosðxt þ uÞ; (A6) all FEM analyses, we performed temperature-controlled
(43–46 C) time dependent studies for durations within the
where u is the phase delay between the magnetization range between 5 and 20 min in 10 s steps.
and the magnetic field. From Eq. (A3), it can be shown
that 1R. Katipamula, T. L. Hoskin, J. C. Boughey, A. C. Degnim, C. S. Grant,
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