Ablation of Hepatic Tumors through the Use of a Novel Magnetic Nanocomposite Probe : Magnetic Characterization and Finite Element Method Analysis

The authors recently proposed a novel system for thermoablation—based on nanoheating—that can potentially overcome limitations associated with previously reported techniques. The aim of this study was to evaluate the therapeutic performance of the system in the ablation of hepatic tissue, the most frequently ablated. A model 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. The FEM model was tested for its validity using an analytical model. The 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 with magnetic nanocomposite can potentially be used to achieve reasonable lesion sizes in hepatic tissues using human-safe AMF parameters.


Introduction
Hepatocellular carcinomas (HCC), which is the most common type of liver cancer, originate from hepatocytes, the main liver cells.It is the third major cause of cancer death worldwide with the highest incidence rates in less developed countries [1].e main curative treatment options include resection, transplantation, or ablation.Resection is limited to patients with small localized tumors and well-preserved liver function [2].Unavailability of donors limits the applicability of transplantation [2].Minimally invasive locoregional ablation is the most frequently used treatment, due to their potential to localize treatment and reduce injuries to surrounding healthy tissue.erefore, there is a need for minimally invasive nonsurgical techniques that can overcome challenges associated with conventional methods to enhance treatment.
Common locoregional therapies include percutanous ethanol injection, cryoablation, laser ablation, microwave ablation, high-focused ultrasound, and radiofrequency ablation (RFA).RFA is the most widely used technique due to its general availability and recent technical advances; however, issues such as the need for high-current radiofrequency to increase lesion sizes lead to an increased risk of skin burns that in turn limits lesion sizes [3][4][5].
e incidence of skin burns after RFA ranges from 0.1-3.2% for second-/third-degree skin burns and up to 33% for firstdegree burns [6].
e unique heat generating capabilities of nanomaterials have been exploited to develop smart and efficient systems for cancer therapy.Promising inorganic nanomaterials-metallic [7] and magnetic [8]-have been demonstrated to enable localized and/or multimodal treatment that can potentially enhance treatment efficacy.[9] e introduction of these nanomaterials into polymer matrix to form nanocomposites offers opportunities for the development of novel biomedical devices for cancer treatment [10,11].e authors have recently reported a 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 proximal insulated shaft.In vivo predictions demonstrated the feasibility of the probe to achieve hyperthermic or ablative levels in postoperative breast tissue.
In this paper, we present an evaluation of the therapeutic performance of our novel probe during the ablation of hepatic tumor, which has been demonstrated to be the most frequently ablated [2].First, we prepared samples of a model nanocomposite, maghemite (c − Fe 2 O 3 ) nanoparticle (MNP) filled polydimethylsiloxane (PDMS), containing varying concentrations of nanoparticles and measured their saturation magnetization.A 3D finite element method (FEM) model was used to perform a parametric study to investigate 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 implications of the results are then discussed for the application of the probe for cancer treatment.

Sample Preparation.
ree types of nanocomposites, designated as MNP-1, MNP-2, and MNP-5-with volume fractions, ϕ, of 1, 2, and 5 vol.% of MNP respectively-were prepared.e sample were prepared by, first, adding the nanoparticles to the PDMS elastomer base and stirring the mixtures thoroughly with a spatula for 15 mins to ensure uniform nanoparticle distribution and also minimize clustering.en, the curing agent of the PDMS base was added at a weight ratio of 10 : 1 and, again, stirred with the spatula to produce a uniform mixture with adequate cross-linking.To ensure that air bubbles were completely removed, the resulting mixtures were placed in a glass beaker connected to a vacuum pump for about 30 minutes.e resulting MNP-PDMS nanocomposite mixtures were poured into molds and baked in an oven at 100 °C for 43 minutes.

Magnetic Characterization.
Magnetic measurements were carried out using the superconducting quantum interface device (SQUID) magnetometer, MPMS XL-5 (Quantum Design, San Diego CA, USA).e magnetization curves were obtained by varying magnetic fields between 0 MA•m −1 and 0.4 MA•m −1 at a temperature of 298 K.
MNPs were mounted in capsules, whereas solid nanocomposites were mounted in drinking straws.Due to the varying masses of the samples, specific magnetization values were used for our analysis.

eory of Magnetic
Heating.When a constrained MNP is exposed to an AMF, the specific losses, A (J•g −1 ), during one cycle of the AMF are defined as the area of the hysteresis loop.According to Carrey et al. [14], an experimentally measured hysteresis loop area, A, can be represented by where α is a dimensionless parameter that depends on the orientation of MNP's easy axes with respect to the AMF.An α value of 0.30, previously reported in [12], was used in all our analysis.σ s (A•m 2 •kg −1 ) is the saturation magnetization, μ 0 (H•m −1 ) is the permeability of free space.H (A•m −1 ) is the amplitude of the AMF.e heat dissipation, P (W•m −3 ), is determined by the following equation: where ρ n is density of nanocomposite.
2.5.In Vivo Predictions.Finite element method (FEM) model, implemented with Comsol Multiphysics 4.3a software package (Comsol, Burlington MA, USA), was used to characterize the in vivo performance.
2.5.1.FEM Modeling.Figure 1(a) shows a schematic diagram of the probe used in our study.e probe is a 6 cm cannula with a distal 2 cm active nanocomposite (MNP-PDMS nanocomposite) tip and a proximal 4 cm insulated shaft (PDMS only).Its concept and mode of operation has been previously reported.[12].e geometric model that was used in our study is shown in Figure 1.Hepatic tissue is modeled as a cylindrical block with a diameter and height of 6 cm and 12 cm, respectively.e probe is placed within the cylindrical block such that the active tip is situated at the center of cylindrical block.
e temperature distribution within the tissue is determined by the Pennes bioheat equation [15]: , c b , and T b are the density, tissue perfusion rate, specific heat capacity, and temperature of blood, respectively.α b is tissue state coefficient.Q m (W•m −3 ), the metabolic heat, was ignored.Q is the heat generation term, which is defined differently for each domain.For the tissue and the insulated shaft domains, it was set to zero.For the active tip (nanocomposite), it was calculated as volumetric power as defined by equation ( 2) e boundary conditions for equation (3) were a prescribed temperature, T 37 °C, on all outer surfaces; and continuity, n on all of interior boundaries.A temperature of 37 °C (for the normal body) was used as the initial temperatures in all domains of the model.
To predict thermal damage of the tissue, the wellestablished Arrhenius equation was used.It is a rstorder thermal-chemical rate equation that enables the determination 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 death, is quanti ed using a dimensionless single parameter, Ω, as where E a (J•mol −1 ) is the activation energy for the injury process, S f (s −1 ) is a scaling factor, and R (J•mol −1 •K −1 ) is the gas constant.e values of E a and A were obtained from [16] as 257.7 kJ•mol −1 and 7.39 × 10 39 s −1 , respectively.In this study, Ω 1, which corresponds to a 63% percent probability of cell death, is chosen to indicate that su cient irreversible damage has been achieved.[17] At this point, it has been reported previously that tissue perfusion ceases [18]. is corresponds to a α b of zero.erefore, intermediate values of α b were calculated as 1/exp (Ω) [18].e thermal properties of di erent domains used in the simulation are summarized in Table 1.e e ective thermal and physical properties of the nanocomposites were estimated using the rule of mixtures.
e details of the implementation are summarized in Appendix.

Parametric
Investigations.Generally, 0.05 − 1.2 MHz and 0 − 15 kA•m −1 are considered the usable ranges for f and H of the AMF for thermotherapy.[23] However, taking patient safety and health into consideration, it is essential to ensure that the factor, Hf, does not exceed the limit that has been experimentally estimated to be 5 × 10 9 A•m −1 •s −1 [24].According to [23], the maximum human-safe eld amplitude is 15 kA m −1 .Ablations were simulated at AMF parameters: H 5 − 15 kA•m −1 , step size: 5 kA•m −1 , f 150 − 450 kHz, and step size of 150 kHz.ese ranges were selected to maintain the Hf factor below the limit.Furthermore, thermal damage was studied as a function of tissue perfusion and time to determinate the maximum variation in lesion size during a typical ablation where this parameter can be varied [25].Simulations were made at ω b − 0%, 50%, and 100% of normal tissue perfusion of 0.0064 s −1 and t � 180 s and 300-900 s (step size: 300).

FEM Model Validation.
e FEM model was tested for its validity using an analytical model developed by Andrä et al. [26].e model, which predicts temperature rise due to a spherical nanocomposite, is given by where P is volumetric power (equation ( 2)), ρ 1 is density, c 1 is heat capacity, and λ 1 is thermal conductivity of the nanocomposite, all approximated by the rule of mixtures.ρ 2 , c 2 , and λ 2 are the properties of liver tissue.Parameters f, g 1 , g 2 , q, and q λ are abbreviations: e nanocomposite was assumed to contain 5 vol.% of MNP and PDMS; its properties were calculated using simple rule of mixtures.
e radius of the sphere was taken as R � 1.5 mm.A volumetric heating power, P, of 33.7 (MW•m −3 ), was used.e surrounding area was assumed to be liver tissue, thus the corresponding properties in Table 1 were used.

Results and Discussion
3.1.Materials Characterization. Figure 2 shows the magnetization curves of the MNPs and nanocomposites in magnetic fields of 45 kOe.MNPs had a saturation magnetization value, M s , of 69.33 emu•g −1 .
ese values were about 3.4%, 4.9%, and 9.3%, respectively, of the M s value obtained for pure MNP.Although M s values of the nanocomposites increased with increasing concentration of nanoparticles, it is important to note that, at higher concentrations (about above 10% volume fraction), particle agglomeration due to factors such magnetic attraction or van der Waals forces can affect the magnetic properties and, consequently, the specific loss power [27].

In Vivo Predictions.
On the basis of the magnetic measurements, we assessed the performance of the device during the heating of hepatic tissue using a parametric study.
A cross-sectional (x-z plane) view of the temperature distribution within the fully perfused tissue (Figure 3(a)) after heating for 15 mins reveals that the temperature is nonuniformly distributed with a maximum temperature, T at , occurring at the center of the active tip.It can be observed that the generated heat spreads out to the surrounding tissue; therefore, the maximum tissue temperature, T t , which occurs on the surface of the active tip, is lower.is is consistent with conduction, the main mode of heat transfer in action.Table 2 shows predictions of T at and T t for a range of AMF amplitudes (5-15.0kA•m −1 ) and frequencies (150-450 kHz) after 15 mins of heating for all three samples.It can be observed that the temperature difference (T at − T t ) increases with increasing Hf factor and ϕ.For instance, for the nanocomposite containing 2 vol.%, T at − T t increases from ≈ 9.7 °C for the Hf factor of 1.5 kHz), T at − T t increases from ≈ 9.7 °C (ϕ � 2%) to ≈ 17.6 °C (ϕ � 5%).Furthermore, different H and f pairs such as H � 10 kA•m −1 , f � 450 kHz and H � 15 kA•m −1 , f � 300 kHz can be used to achieve the same temperature levels (T at � 175.5 °C, T t � 116.4) for a given MNP concentration.Taking patient safety and health into consideration, it is prudent to use lower AMF values.Table 3 summarizes the heating power density (W•m −3 ) and total heating power (W) values of the active tip of the probe that were used to obtain the temperature values in Table 2.
For our thermal damage analysis, values in the middle range of both H and f (i.e., 10 kA•m −1 and f � 300 kHz Liver [19] 1,060 3,600 0.502 -Blood [20] 1,000 4,180 0.543 0.0064 PDMS [21] 1,190 1,460 0.190 c − Fe 2 O 3 [22] 4,600 746 9.700 -4 Journal of Nanotechnology respectively), resulting in T t 90 °C, were used.A crosssectional (x-z plane) view of the lesion, region where tissue 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 thermal damage calculated at a point 0.3 cm away from the center of the active-tip after 15 mins of heating at di erent rates of tissue perfusion.It can be observed that 100% thermal damage is reached a few minutes after the AMF is applied.For the case of fully perfused tissue (ω b 6.4 × 10 −3 s −1 ), it occurs after 3 mins.e time decreases to 2 mins for the case of nonperfusion (ω b 0.0 × 10 −3 s −1 ). is relatively fast attainment of thermal damage can be attributed to the initial heating rates, resulting in exposure of the tissue to ablative temperatures almost the entire duration of treatment.Although at distances farther away from the active tip overall temperature levels decrease, adequate thermal damage is possible due to long durations of exposure at those temperatures (Figure 3(e)).Figure 3(f ) shows a plot of tissue temperature and thermal damage as function of radial distance after 15 minutes for varying rates of tissue perfusion.e data show that moving away from the active-tip thermal damage decreases more rapidly than temperature.
Table 4 summarizes lesion size development as a function of time for nonperfused (ω b 0.0 × 10 −3 s −1 ) and fully perfused (ω b 6.4 × 10 −3 s −1 ).e parameters used to calculate the sizes are shown in Figure 3(c).e results reveal that tissue perfusion greatly a ects the development of the lesion.For instance, lesion volume increases from 1.29 cm 3 (after 3 minutes) to 11.82 cm 3 (after 15 minutes) in a nonperfused (ω b 0.0 × 10 −3 s −1 ) tissue, representing an increase of 916%.
is reduced to 293% for fully perfused is considered.At 15 mins, predicted lesion width and depth were in the range of 1.40 − 2.58 cm and 2.58 − 3.39 cm, respectively.

Model Validation.
In an e ort to validate the computational model, the numerical results were compared with results obtained with the analytical model developed by Andrä and co-workers [26].Figure 4 shows the comparison of the temperature as a function of (a) time at a point ≈ 2 mm from the center of the nanocomposite (a) and distance from the center of composite (b) after 15 mins of heating.e results reveal that FEM results diverged between ≈0.5 − 7% from the analytical results.e deviations can be attributed to factors such as mesh sizing and shape of the geometry.

Conclusion
In this work, a combination of experiments and models was used to investigate the thermoablation of hepatic tumors through the use of a magnetic nanocomposite probe.
A model, polymer-based nanocomposites consisting of PDMS and c − Fe 2 O 3 nanoparticles, was successfully fabricated.Magnetic measurements obtained with a SQUID magnetometer showed that their saturation magnetizations, M s , increased with increasing nanoparticle concentration to about 9% of the M s value of pure c − Fe 2 O 3 nanoparticles over the range of volume percentages between 1 and 5%.On the basis of the magnetic measurement, the in vivo performance of the probe, using human-safe AMF parameters, was investigated.e results showed that reasonable lesion sizes, which are greatly a ected by time and tissue perfusion, are achievable.Lesion volumes increased by 916% and 293%, for nonperfused and fully perfused tissue, respectively, between 3 and 15 mins of heating.A comparison of lesion volumes for nonperfused and fully perfused tissue at speci c times show that the di erence increased with time.For instance, at 3 mins, the predicted volume for a nonperfused tissue was about 2 times bigger than volume obtained for fully perfused tissue.At 15 mins, it doubled.ese sizes are similar to those obtained by other probe-based thermoablation techniques reported in the literature [18,28,29].e results demonstrate the potential of our magnetic nanocomposite probes to treat small ( ≤ 1 − 3 cm) solid hepatic tumors.Furthermore, a potential advantage of our probe over other probe-based techniques is the possibility of incorporating multimodal (heat and drugs) features.

Appendix
Implementation of FEM Model e numerical analyses were performed with the FEM model COMSOL Multiphysics 4.3a software package (Comsol, Burlington MA, USA).All physical, magnetic, and thermal properties were added explicitly to the FEM model as a global de nition or variable under the model node.A 3D geometric model was used for the analysis.
e temperature distribution was achieved with the bioheat heat transfer application mode.37 °C was taken as the initial temperature of the model, and all boundary conditions were speci ed as those outlined in Section 2 E1.
e heat source was added to the bioheat transfer application mode as a user-de ned heat source.
e geometric model was meshed with varying sizes of 3D triangular mesh elements.e mesh size for all calculations was de ned as a physics-controlled mesh with the  element size specified as "extra fine" and "extremely fine" for tissue and probe domain, respectively.e numerical solutions were obtained using the "PARADISO" method.e simulations were run on a midrange workstation with Intel(R) Xeon(R) E5-1620 CPU and 8 GB RAM. e numerical solution was broken down into 3 steps: (i) the volumetric power output, P, was obtained from equation ( 2); (ii) the temperature distribution was determined as a function of time, using the volumetric power output from step (i) as heat generation term in equation (3); and (iii) the thermal dose was calculated as a function of time, using the temperature history, and was used as the input to equation (4).For all FEM analyses, time-dependent studies for 15 mins in 10 s steps.

Figure 1 :
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.

Figure 3 :
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.

Figure 4 :
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 15 mins of heating between FEM model and the analytical model by Andrä et al. [26].

Table 1 :
ermal properties of the materials used in the FEM models.

Table 3 :
Power density, P (W m −3 ), and total power, P T (W), values of the active tip of the probe that was used to obtain the temperature predictions in Table2.