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Ablation of Hepatic Tumors through the Use of a Novel Magnetic
Nanocomposite Probe: Magnetic Characterization and Finite Element Method
Analysis
Article  in  Journal of Nanotechnology · March 2019
DOI: 10.1155/2019/6802125
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Journal of Nanotechnology
Volume 2019, Article ID 6802125, 9 pages
https://doi.org/10.1155/2019/6802125
Research Article
Ablation of Hepatic Tumors through the Use of a Novel Magnetic
Nanocomposite Probe: Magnetic Characterization and Finite
Element Method Analysis
Yvonne Konku,1 John Kutor,1 Abu Yaya ,2 and Kwabena Kan-Dapaah 1
1Department of Biomedical Engineering, University of Ghana, P. O. Box LG 25, Legon, Ghana
2Department of Materials Science and Engineering, University of Ghana, P. O. Box LG 25, Legon, Ghana
Correspondence should be addressed to Kwabena Kan-Dapaah; kkan-dapaah@ug.edu.gh
Received 8 July 2018; Revised 25 December 2018; Accepted 10 January 2019; Published 3 March 2019
Academic Editor: Paresh Chandra Ray
Copyright © 2019YvonneKonku et al.+is is an open access article distributed under the Creative CommonsAttribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
+e authors recently proposed a novel system for thermoablation—based on nanoheating—that can potentially overcome
limitations associated with previously reported techniques. +e aim of this study was to evaluate the therapeutic performance of
the system in the ablation of hepatic tissue, the most frequently ablated. Amodel nanocomposite system, maghemite nanoparticle-
filled polydimethylsiloxane, was prepared, and its magnetic properties were studied as a function of nanoparticle concentration.
On the basis of measured magnetic properties, a 3D finite element method (FEM) model was used to explore the development of
temperature and thermal damage in nonperfused and fully perfused tissue using alternating magnetic field (AMF) parameters that
are acceptable for human use. +e FEM model was tested for its validity using an analytical model. +e saturation magnetization
increased to about 9% of the value of pure maghemite nanoparticles over the range of volume fraction (vol. %) between 1 and 5%.
Lesion sizes were shown to be greatly affected by tissue perfusion and time. FEM predictions showed good agreement with results
obtained with an analytical model to within 7%. Probes fabricated withmagnetic nanocomposite can potentially be used to achieve
reasonable lesion sizes in hepatic tissues using human-safe AMF parameters.
1. Introduction Common locoregional therapies include percutanous
ethanol injection, cryoablation, laser ablation, microwave
Hepatocellular carcinomas (HCC), which is the most ablation, high-focused ultrasound, and radiofrequency ab-
common type of liver cancer, originate from hepatocytes, the lation (RFA). RFA is the most widely used technique due to
main liver cells. It is the third major cause of cancer death its general availability and recent technical advances;
worldwide with the highest incidence rates in less developed however, issues such as the need for high-current radio-
countries [1]. +e main curative treatment options include frequency to increase lesion sizes lead to an increased risk of
resection, transplantation, or ablation. Resection is limited skin burns that in turn limits lesion sizes [3–5]. +e in-
to patients with small localized tumors and well-preserved cidence of skin burns after RFA ranges from 0.1–3.2% for
liver function [2]. Unavailability of donors limits the ap- second-/third-degree skin burns and up to 33% for first-
plicability of transplantation [2]. Minimally invasive degree burns [6].
locoregional ablation is the most frequently used treatment, +e unique heat generating capabilities of nano-
due to their potential to localize treatment and reduce in- materials have been exploited to develop smart and efficient
juries to surrounding healthy tissue. +erefore, there is a systems for cancer therapy. Promising inorganic nano-
need for minimally invasive nonsurgical techniques that can materials—metallic [7] and magnetic [8]—have been
overcome challenges associated with conventional methods demonstrated to enable localized and/or multimodal
to enhance treatment. treatment that can potentially enhance treatment efficacy.
2 Journal of Nanotechnology
[9] +e introduction of these nanomaterials into polymer MNPs were mounted in capsules, whereas solid nano-
matrix to form nanocomposites offers opportunities for the composites were mounted in drinking straws. Due to the
development of novel biomedical devices for cancer varying masses of the samples, specific magnetization values
treatment [10, 11]. +e authors have recently reported a were used for our analysis.
novel nanocomposite probe for thermoablation of cancer
cells [12, 13]. +e probe is essentially a cannula with a distal
heat generating magnetic nanocomposite tip and a prox- 2.4. +eory of Magnetic Heating. When a constrained MNP
imal insulated shaft. In vivo predictions demonstrated the is exposed to an AMF, the specific losses, A (J·g−1), during
feasibility of the probe to achieve hyperthermic or ablative one cycle of the AMF are defined as the area of the hys-
levels in postoperative breast tissue. teresis loop. According to Carrey et al. [14], an experi-
In this paper, we present an evaluation of the therapeutic mentally measured hysteresis loop area, A, can be
performance of our novel probe during the ablation of represented by
hepatic tumor, which has been demonstrated to be the most A � 4ασ μ H, (1)
frequently ablated [2]. First, we prepared samples of a model s 0
nanocomposite, maghemite (c− Fe2O3) nanoparticle where α is a dimensionless parameter that depends on the
(MNP) filled polydimethylsiloxane (PDMS), containing orientation of MNP’s easy axes with respect to the AMF. An
varying concentrations of nanoparticles and measured their α value of 0.30, previously reported in [12], was used in all
saturation magnetization. A 3D finite element method our analysis. σs (A·m
2·kg−1) is the saturation magnetization,
(FEM) model was used to perform a parametric study to μ (H·m−10 ) is the permeability of free space.H (A·m
−1) is the
investigate the development of temperature and thermal amplitude of the AMF.
damage in nonperfused and fully perfused tissue using al- +e heat dissipation, P (W·m−3), is determined by the
ternating magnetic field (AMF) parameters that are ac- following equation:
ceptable for human use. +e FEM model was tested for its
validity using an analytical model. +e implications of the P � Afρn, (2)
results are then discussed for the application of the probe for where ρ is density of nanocomposite.
cancer treatment. n
2. Materials and Methods 2.5. In Vivo Predictions. Finite element method (FEM)
model, implemented with Comsol Multiphysics 4.3a soft-
2.1. Materials. +e materials that were used in this study ware package (Comsol, Burlington MA, USA), was used to
included maghemite (c− Fe2O3) nanoparticles (high purity, characterize the in vivo performance.
99.5%, 20 nm, US Research Nanomaterials Inc., Houston,
TX, USA) and PDMS (Sylgard 184 silicone elastomer kit,
Dow Corning Corp., Auburn, MI, USA). +ese materials 2.5.1. FEM Modeling. Figure 1(a) shows a schematic dia-
were used as received. gram of the probe used in our study. +e probe is a 6 cm
cannula with a distal 2 cm active nanocomposite (MNP-
2.2. Sample Preparation. +ree types of nanocomposites, PDMS nanocomposite) tip and a proximal 4 cm insulated
designated as MNP-1, MNP-2, and MNP-5—with volume shaft (PDMS only). Its concept and mode of operation has
fractions, ϕ, of 1, 2, and 5 vol. % of MNP respectively—were been previously reported. [12].
prepared. +e sample were prepared by, first, adding the +e geometric model that was used in our study is shown
nanoparticles to the PDMS elastomer base and stirring the in Figure 1. Hepatic tissue is modeled as a cylindrical block
mixtures thoroughly with a spatula for 15mins to ensure with a diameter and height of 6 cm and 12 cm, respectively.
uniform nanoparticle distribution and also minimize clus- +e probe is placed within the cylindrical block such that the
tering. +en, the curing agent of the PDMS base was added active tip is situated at the center of cylindrical block.
at a weight ratio of 10 :1 and, again, stirred with the spatula +e temperature distribution within the tissue is de-
to produce a uniform mixture with adequate cross-linking. termined by the Pennes bioheat equation [15]:
To ensure that air bubbles were completely removed, the zT 2 (3)
resulting mixtures were placed in a glass beaker connected to ρcp � λ∇ T + ρbcbαbωb( Tb −T􏼁 + Qm + Q,zt
a vacuum pump for about 30minutes. +e resulting MNP- −3 −1
PDMS nanocomposite mixtures were poured into molds where ρ(kg ·m ) is the density, cp (J·kg ·K
−1) is the specific
and baked in an oven at 100°C for 43minutes. heat capacity at constant pressure, λ (W·m
−1·K−1) is the
thermal conductivity. ρ , ω (s−1b b ), cb, and Tb are the density,
tissue perfusion rate, specific heat capacity, and temperature
2.3. Magnetic Characterization. Magnetic measurements of blood, respectively. αb is tissue state coefficient. Qm
were carried out using the superconducting quantum in- (W·m−3), the metabolic heat, was ignored. Q is the heat
terface device (SQUID) magnetometer, MPMS XL-5 generation term, which is defined differently for each do-
(Quantum Design, San Diego CA, USA). +e magnetiza- main. For the tissue and the insulated shaft domains, it was
tion curves were obtained by varying magnetic fields be- set to zero. For the active tip (nanocomposite), it was cal-
tween 0MA·m−1 and 0.4MA·m−1 at a temperature of 298K. culated as volumetric power as defined by equation (2)
Journal of Nanotechnology 3
2 mm
Active tip Insulated shaft
20 mm 40 mm
(a)
Insulated
sha 40 mm 5
Active
tip 20 mm
0
Hepatic
tissue –5
5
5
z 0
y 0x
60 mm –5 –5
(b) (c)
Figure 1: (a) Schematic of magnetic heating probe. e probe is a cannula with two main parts: a distal active tip made of a nanocomposite
(blue) and a proximal insulated shaft (pink). erapeutic treatment is achieved when the active tip is brought in contact with the target area
and exposed to alternating magnetic ­eld. (b) Schematic of the geometry model (cylindrical block: diameter, 6 cm; height, 12 cm), showing
the cross section of the probe inserted in the tissue. (c) e 3D meshed model of the cylindrical block.
e boundary conditions for equation (3) were a pre- damage has been achieved. [17] At this point, it has been
scribed temperature, T  37°C, on all outer surfaces; and reported previously that tissue perfusion ceases [18]. is
continuity, n · (λ1∇ · T1 − λ2∇ · T2)  0, on all of interior corresponds to a αb of zero.erefore, intermediate values of
boundaries. A temperature of 37°C (for the normal body) αb were calculated as 1/exp (Ω) [18].
was used as the initial temperatures in all domains of the e thermal properties of di•erent domains used in the
model. simulation are summarized in Table 1. e e•ective thermal
To predict thermal damage of the tissue, the well- and physical properties of the nanocomposites were esti-
established Arrhenius equation was used. It is a ­rst- mated using the rule of mixtures. e details of the
order thermal-chemical rate equation that enables the de- implementation are summarized in Appendix.
termination of damage with temperature history. e
damage, which is considered to be due to the transformation
of native molecules through an activated state leading to cell 2.5.2. Parametric Investigations. Generally, 0.05− 1.2 MHz
death, is quanti­ed using a dimensionless single parameter, and 0− 15 kA ·m−1 are considered the usable ranges for f and
Ω, as H of the AMF for thermotherapy. [23] However, taking
​t −Ea patient safety and health into consideration, it is essential toΩ(t)  Sf∫ exp( )dt, (4)
0 RT(t) ensure that the factor,Hf, does not exceed the limit that has
been experimentally estimated to be 5 × 109 A ·m−1 ·s−1 [24].
where Ea (J·mol
−1) is the activation energy for the injury According to [23], the maximum human-safe ­eld ampli-
process, S (s−1f ) is a scaling factor, and R (J·mol
−1·K−1) is the tude is 15 kAm−1. Ablations were simulated at AMF pa-
gas constant.e values of Ea andAwere obtained from [16] rameters: H  5− 15 kA ·m−1, step size: 5 kA·m
−1,
as 257.7 kJ·mol−1 and 7.39 × 1039 s−1, respectively. In this f  150− 450 kHz, and step size of 150 kHz. ese ranges
study,Ω 1, which corresponds to a 63% percent probability were selected to maintain the Hf factor below the limit.
of cell death, is chosen to indicate that su‘cient irreversible Furthermore, thermal damage was studied as a function of
120 mm
4 Journal of Nanotechnology
Table 1: +ermal properties of the materials used in the FEM R � 1.5 mm. A volumetric heating power, P, of 33.7
models. (MW·m−3), was used. +e surrounding area was assumed to
Material ρ cp λ ω
be liver tissue, thus the corresponding properties in Table 1
(kg m−3) (J (kg K)−1) (W (m K)−1) (s−1) were used.
Liver [19] 1,060 3,600 0.502 —
Blood [20] 1,000 4,180 0.543 0.0064 3. Results and Discussion
PDMS [21] 1,190 1,460 0.190 —
c− Fe2O3 [22] 4,600 746 9.700 — 3.1. Materials Characterization. Figure 2 shows the mag-
netization curves of the MNPs and nanocomposites in
magnetic fields of 45 kOe. MNPs had a saturation magne-
tissue perfusion and time to determinate the maximum tization value, Ms, of 69.33 emu·g
−1. +e Ms values for
−1
variation in lesion size during a typical ablation where this samples MNP-1, MNP-2, and MNP-5 were 2.37 emu·g ,
−1 −1
parameter can be varied [25]. Simulations were made at ω − 3.41 emu·g , and 6.46 emu·g , respectively. +ese valuesb
0%, 50%, and 100% of normal tissue perfusion of 0.0064 s−1 were about 3.4%, 4.9%, and 9.3%, respectively, of the Ms
and t � 180 s and 300–900 s (step size: 300). value obtained for pure MNP. Although Ms values of the
nanocomposites increased with increasing concentration of
nanoparticles, it is important to note that, at higher con-
2.5.3. FEM Model Validation. +e FEM model was tested centrations (about above 10% volume fraction), particle
for its validity using an analytical model developed by Andrä agglomeration due to factors suchmagnetic attraction or van
et al. [26].+emodel, which predicts temperature rise due to der Waals forces can affect the magnetic properties and,
a spherical nanocomposite, is given by consequently, the specific loss power [27].
PR2 q r2
ΔT λ1(r, t) � 􏼢1 + 􏼠1−3λ 2 R2
􏼡
2 3.2. In Vivo Predictions. On the basis of the magnetic
(5a) measurements, we assessed the performance of the device
6 ∞3/2 1/2R 0≤ ≤ during the heating of hepatic tissue using a parametric+ qλ q 􏽚 fg1 dz􏼣, r R,π r 0 study.
A cross-sectional (x-z plane) view of the temperature
PR3 6 ∞ dz distribution within the fully perfused tissue (Figure 3(a))
ΔT2(r, t) � 􏼢1 + qλ 􏽚 fg2 􏼣, r>R, (5b)3λ r π z after heating for 15mins reveals that the temperature is2 0 nonuniformly distributed with a maximum temperature,
where P is volumetric power (equation (2)), ρ1 is density, c1 Tat, occurring at the center of the active tip. It can be
is heat capacity, and λ1 is thermal conductivity of the observed that the generated heat spreads out to the sur-
nanocomposite, all approximated by the rule of mixtures. ρ2, rounding tissue; therefore, the maximum tissue tempera-
c2, and λ2 are the properties of liver tissue. Parameters f, g1, ture, Tt, which occurs on the surface of the active tip, is
g2, q, and qλ are abbreviations: lower.+is is consistent with conduction, the main mode of
λ heat transfer in action. Table 2 shows predictions of T2 at
and
qλ � ,λ Tt for a range of AMF amplitudes (5–15.0 kA·m
−1) and
1 frequencies (150–450 kHz) after 15mins of heating for all
ρ2c2 three samples. It can be observed that the temperatureqλ � ,ρ c difference (Tat −Tt) increases with increasing Hf factor1 1 and ϕ. For instance, for the nanocomposite containing
°
s(z) � ( qλ − 1􏼁sin z + z cos z, 2 vol. %, Tat −Tt increases from ≈ 9.7 C for the Hf factorof 1.5 × 109 A ·m−1·s−1 (H � 10 kA ·m−1, f � 150 kHz)
λ tz2 z cos z− sin z to ≈ 11.8°C for the Hf factor of 4.5 × 10
9 A ·m−1 ·s−1
−2
f(z, r, t) � z exp􏼠− 1 2􏼡 ×ρ 2 2
, (H � 10 kA ·m−1, f � 450 kHz). Similarly, for a given Hf
1c1R [s(z)] + qλq(sin z) factor of 1.5 × 10−9 A ·m−1 ·s−1 (H � 10 kA ·m−1,
rz f � 150 kHz), Tat −Tt increases from ≈ 9.7°C (ϕ � 2%) to
g1(z, r) � sin􏼒 􏼓, ≈ 17.6°C (ϕ � 5%). Furthermore, different H and f pairsR such as H � 10 kA ·m−1, f � 450 kHz and H � 15 kA ·m−1,
1/2
g (z, r) � s(z) sin[k(z; r)] +( q q􏼁 z sin z cos[k(z, r)], f � 300 kHz can be used to achieve the same temperature2 λ levels (Tat � 175.5°C, Tt � 116.4) for a given MNP con-
1/2 r centration. Taking patient safety and health into consid-
k(z, r) � ( qλq􏼁 z􏼒 − 1􏼓.R eration, it is prudent to use lower AMF values. Table 3
(6) summarizes the heating power density (W·m
−3) and total
heating power (W) values of the active tip of the probe that
+e nanocomposite was assumed to contain 5 vol. % of were used to obtain the temperature values in Table 2.
MNP and PDMS; its properties were calculated using simple For our thermal damage analysis, values in the middle
rule of mixtures. +e radius of the sphere was taken as range of both H and f (i.e., 10 kA·m−1 and f � 300 kHz
Journal of Nanotechnology 5
70 7
35 3.5
0 0
0 0.1 0.2 0.4 0 0.1 0.2 0.4
H (MA/m) H (MA/m)
[MNP] vol. % [MNP] vol. %
100 1
2
5
(a) (b)
Figure 2: Magnetization curves of (a) maghemite (c− Fe2O3) nanoparticles and (b) samples MNP-1, MNP-2, and MNP-5 under magnetic
­elds of 0.4MA·m−1.
respectively), resulting in T °t  90 C, were used. A cross- 15mins, predicted lesion width and depth were in the range of
sectional (x-z plane) view of the lesion, region where tissue 1.40− 2.58 cm and 2.58− 3.39 cm, respectively.
damage occurs, reveals its ellipsoidal shape (Figure 3(b)),
which is distributed symmetrically about the active tip of the
probe. Figure 3(d) shows a plot of tissue temperature and 3.3. Model Validation. In an e•ort to validate the com-
thermal damage calculated at a point 0.3 cm away from the putational model, the numerical results were compared
center of the active-tip after 15mins of heating at di•erent with results obtained with the analytical model developed
rates of tissue perfusion. It can be observed that 100% by Andrä and co-workers [26]. Figure 4 shows the com-
thermal damage is reached a few minutes after the AMF is parison of the temperature as a function of (a) time at a
applied. For the case of fully perfused tissue point ≈ 2 mm from the center of the nanocomposite (a)
(ω  6.4 × 10−3 s−1b ), it occurs after 3mins. e time de- and distance from the center of composite (b) after 15mins
creases to 2mins for the case of nonperfusion of heating. e results reveal that FEM results diverged
(ω  0.0 × 10−3 s−1b ). is relatively fast attainment of between ≈0.5− 7% from the analytical results. e de-
thermal damage can be attributed to the initial heating rates, viations can be attributed to factors such as mesh sizing and
resulting in exposure of the tissue to ablative temperatures shape of the geometry.
almost the entire duration of treatment. Although at dis-
tances farther away from the active tip overall temperature 4. Conclusion
levels decrease, adequate thermal damage is possible due to
long durations of exposure at those temperatures In this work, a combination of experiments and models was
(Figure 3(e)). Figure 3(f ) shows a plot of tissue temperature used to investigate the thermoablation of hepatic tumors
and thermal damage as function of radial distance after through the use of a magnetic nanocomposite probe.
15minutes for varying rates of tissue perfusion. e data A model, polymer-based nanocomposites consisting of
show that moving away from the active-tip thermal damage PDMS and c− Fe2O3 nanoparticles, was successfully fab-
decreases more rapidly than temperature. ricated. Magnetic measurements obtained with a SQUID
Table 4 summarizes lesion size development as a function magnetometer showed that their saturation magnetizations,
of time for nonperfused (ω  0.0 × 10−3 s−1b ) and fully per- Ms, increased with increasing nanoparticle concentration to
fused (ω  6.4 × 10−3 s−1b ). e parameters used to calculate about 9% of the Ms value of pure c− Fe2O3 nanoparticles
the sizes are shown in Figure 3(c).e results reveal that tissue over the range of volume percentages between 1 and 5%. On
perfusion greatly a•ects the development of the lesion. For the basis of the magnetic measurement, the in vivo per-
instance, lesion volume increases from 1.29 cm3 (after formance of the probe, using human-safe AMF parameters,
3minutes) to 11.82 cm3 (after 15minutes) in a nonperfused was investigated. e results showed that reasonable lesion
(ω  0.0 × 10−3 s−1b ) tissue, representing an increase of 916%. sizes, which are greatly a•ected by time and tissue perfusion,
is reduced to 293% for fully perfused is considered. At are achievable. Lesion volumes increased by 916% and 293%,
M (emu/g)
M (emu/g)
6 Journal of Nanotechnology
6 6
T (°C) Thermal Tissue
4 4 dose (%) Insulated100 100 shaft Active
90 Probe tip
2 90 2 80
70 Lesion80
0 0 6070 50
60 40
W
–2 –2 30
50 20
–4 1040 –4 H
0
–6 –6
–6 –4 –2 0 2 4 6 –6 –4 –2 0 2 4 6
x (cm) x (cm)
(a) (b) (c)
100 100 100 100 100 100
80 80 80 80 80 80
60 60 60 60 60 60
40 40 40 40 40 40
20 20 20 20 20 20
0 0 0 0 0 0
0 5 10 15 0 5 10 15 0 1 2 3 4
Time (min) Time (min) Radial distance (cm)
ω  (s–1) ω  (s–1b b ) ωb (s
–1)
0.0000 0.0000 0.0000
0.0032 0.0032 0.0032
0.0064 0.0064 0.0064
(d) (e) (f )
Figure 3: Cross-sectional (x-z plane) (a) temperature distribution and (b) thermal damage on the central slice. (c) A schematic of the lesion
and the measured parameters. Tissue temperature (solid lines) and thermal damage (broken lines) at a distance of (d) 0.3 cm and (e) 1 cm
from the outer surface of the active tip as a function of time. (f ) Tissue temperature (solid lines) and thermal damage (broken lines)
measured from the surface of the active tip. Study settings: t  15 mins, ϕ  5%, H  10 kA ·m−1, and f  300 kHz.
Table 2: Temperature predictions for a range of AMF amplitudes (5–15 kA·m−1) and frequencies (150–450 kHz).
H  5 kA ·m−1 H  10 kA ·m−1 H  15 kA ·m−1
Domain ϕ (vol. %) σs (emu·g
−1) f (kHz) f (kHz) f (kHz)
150 300 450 150 300 450 150 300 450
1 2.37 44.5 52.1 59.6 52.1 67.2 82.3 59.6 82.3 104.9
Active tip 2 3.41 48.2 59.5 70.8 59.5 82.0 104.6 70.8 104.6 138.4
5 6.46 60.1 83.1 106.2 83.1 129.3 175.4 106.2 175.4 244.6
1 2.37 41.3 45.5 59.6 45.5 54.0 62.5 49.8 62.5 75.3
Tissue 2 3.41 43.4 49.8 56.2 49.8 62.6 75.3 56.2 75.3 94.5
5 6.46 50.2 63.5 76.7 63.5 90.0 116.4 76.7 116.4 156.2
for nonperfused and fully perfused tissue, respectively, be- similar to those obtained by other probe-based thermoa-
tween 3 and 15mins of heating. A comparison of lesion blation techniques reported in the literature [18, 28, 29].
volumes for nonperfused and fully perfused tissue at speci­c e results demonstrate the potential of our magnetic
times show that the di•erence increased with time. For nanocomposite probes to treat small ( ≤ 1− 3 cm) solid
instance, at 3mins, the predicted volume for a nonperfused hepatic tumors. Furthermore, a potential advantage of our
tissue was about 2 times bigger than volume obtained for probe over other probe-based techniques is the possibility
fully perfused tissue. At 15mins, it doubled. ese sizes are of incorporating multimodal (heat and drugs) features.
ermal dose (%) z (cm)
Temperature (°C)
ermal dose (%) z (cm)
Temperature (°C)
ermal dose (%)
Temperature (°C)
Journal of Nanotechnology 7
Table 3: Power density, P (W m−3), and total power, PT (W), values of the active tip of the probe that was used to obtain the temperature
predictions in Table 2.
H  5 kA ·m−1 H  10 kA ·m−1 H  15 kA ·m−1
ϕ (vol. %) σs (emu · g
−1) f (kHz) f (kHz) f (kHz)
150 300 450 150 300 450 150 300 450
Power density, PT (MW m
−3)
1 2.37 2.8 5.6 8.5 5.6 11.3 17.0 8.5 17.0 25.4
2 3.41 4.4 8.9 13.3 8.9 17.8 26.7 13.3 26.7 40.0
5 6.46 11.7 23.4 35.1 23.4 46.8 70.2 35.1 70.2 105.3
Total Power, P (W)
1 2.37 0.2 0.3 0.5 0.3 0.7 1.0 0.5 1.0 1.5
2 3.41 0.3 0.5 0.8 0.5 1.1 1.6 0.8 1.6 2.4
5 6.46 0.7 1.4 2.1 1.4 2.8 4.3 2.1 4.3 6.4
Table 4: Comparison of lesion parameters for nonperfused (ω  0.0 × 10−3 s−1) and fully perfused (ω  0.0 × 10−3 s−1) tissue at di•erent
times.
ω  0.0 × 10−3 s−1 ω  6.4 × 10−3 s−1
Time (s)
Width (cm) Depth (cm) V (cm−3) Width (cm) Depth (cm) V (cm−3)
180 1.04 2.28 1.29 0.80 2.19 0.73
300 1.42 2.50 2.64 0.98 2.30 1.16
600 2.04 2.96 6.45 1.26 2.46 2.04
900 2.58 3.39 11.82 1.40 2.58 2.65
70 120
110
60 100
90
50
80 Breast
tissue
40 70
60
30 50
0 5 10 15 0 0.5 1 1.5 2
t (min) r (min)
FEM FEM
Analytical Analytical
(a) (b)
Figure 4: Comparison of temperature as function of (a) time at a point ≈ 2 mm mm from the center of the nanocomposite and (b) the
distance from the center of composite after 15mins of heating between FEM model and the analytical model by Andrä et al. [26].
Further studies, including in vitro and in vivo experi- global de­nition or variable under the model node. A 3D
ments, are needed for a realistic assessment of the probe. geometric model was used for the analysis.
e temperature distribution was achieved with the
Appendix bioheat heat transfer application mode. 37°C was taken as
the initial temperature of the model, and all boundary
Implementation of FEM Model conditions were speci­ed as those outlined in Section 2 E1.
e heat source was added to the bioheat transfer appli-
e numerical analyses were performed with the FEMmodel cation mode as a user-de­ned heat source.
COMSOL Multiphysics 4.3a software package (Comsol, e geometric model was meshed with varying sizes of
Burlington MA, USA). All physical, magnetic, and thermal 3D triangular mesh elements. e mesh size for all calcu-
properties were added explicitly to the FEM model as a lations was de­ned as a physics-controlled mesh with the
T (°C)
T (°C)
Magnetic
nanocomposite
8 Journal of Nanotechnology
element size specified as “extra fine” and “extremely fine” for biocompatibility, pharmaceutical and biomedical applica-
tissue and probe domain, respectively. +e numerical so- tions,” Chemical Reviews, vol. 112, no. 11, pp. 5818–5878,
lutions were obtained using the “PARADISO” method. +e 2012.
simulations were run on a midrange workstation with [9] A. C. Anselmo and S. Mitragotri, “A review of clinical
Intel(R) Xeon(R) E5-1620 CPU and 8GB RAM. translation of inorganic nanoparticles,” AAPS Journal, vol. 17,
+e numerical solution was broken down into 3 steps: (i) no. 5, pp. 1041–1054, 2015.
the volumetric power output, P, was obtained from equation [10] K. Kan-Dapaah, N. Rahbar, and W. Soboyejo, “Implantablemagnetic nanocomposites for the localized treatment of breast
(2); (ii) the temperature distribution was determined as a cancer,” Journal of Applied Physics, vol. 116, no. 23, article
function of time, using the volumetric power output from 233505, 2014.
step (i) as heat generation term in equation (3); and (iii) the [11] K. Kan-Dapaah, N. Rahbar, A. Tahlil, D. Crosson, N. Yao, and
thermal dose was calculated as a function of time, using the W. Soboyejo, “Mechanical and hyperthermic properties of
temperature history, and was used as the input to equation magnetic nanocomposites for biomedical applications,”
(4). For all FEM analyses, time-dependent studies for Journal of the Mechanical Behavior of Biomedical Materials,
15mins in 10 s steps. vol. 49, pp. 118–128, 2015.
[12] K. Kan-Dapaah, N. Rahbar, and W. Soboyejo, “Novel mag-
Data Availability netic heating probe for multimodal cancer treatment,”Medical Physics, vol. 42, no. 5, pp. 2203–2211, 2015.
+e data used to support the findings of this study are in- [13] K. Kan-Dapaah, O. A. Asimeng, S. K. Kwofie, and A. Yaya, “A
cluded within the article. plasmonic photo-thermal probe for thermoablation of post-
operative breast cancer cells,” Cogent Engineering, vol. 4, no. 1,
article 1331966, 2017.
Conflicts of Interest [14] J. Carrey, B. Mehdaoui, and M. Respaud, “Simple models for
dynamic hysteresis loop calculations of magnetic single-
+e authors declare that they have no conflicts of interest. domain nanoparticles: application to magnetic hyperther-
mia optimization,” Journal of Applied Physics, vol. 109, no. 8,
Acknowledgments article 083921, pp. 1–17, 2011.
[15] H. H. Pennes, “Analysis of tissue and arterial blood tem-
+is work was made possible with financial support from the peratures in the resting human forearm,” Journal of Applied
Building a New Generation of Academics in Africa Physiology, vol. 1, no. 2, pp. 93–122, 1948.
(BANGA-Africa) project which is funded by the Carnegie [16] S. Jacques, S. Rastegar, S. +omsen, and M. Motamedi, “+e
Corporation of New York. role of dynamic changes in blood perfusion and optical
properties in laser coagulation of tissue,” IEEE Journal of
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