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

Authors: Yvonne Konku; John Kutor; Abu Yaya; Kwabena Kan-Dapaah
Journal: Journal of Nanotechnology
 (2019)

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## Abstract

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.


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## Body

## 1. 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]. The 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. Therefore, 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 [3–5]. The incidence of skin burns after RFA ranges from 0.1–3.2% for second-/third-degree skin burns and up to 33% for first-degree burns [6].The 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] The introduction of these nanomaterials into polymer matrix to form nanocomposites offers opportunities for the development of novel biomedical devices for cancer treatment [10, 11]. The authors have recently reported a novel nanocomposite probe for thermoablation of cancer cells [12, 13]. The 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 (γ−Fe2O3) 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. The FEM model was tested for its validity using an analytical model. The implications of the results are then discussed for the application of the probe for cancer treatment.


## 2. Materials and Methods

### 2.1. Materials

The materials that were used in this study included maghemite (γ−Fe2O3) nanoparticles (high purity, 99.5%, 20 nm, US Research Nanomaterials Inc., Houston, TX, USA) and PDMS (Sylgard 184 silicone elastomer kit, Dow Corning Corp., Auburn, MI, USA). These materials were used as received.


### 2.2. Sample Preparation

Three 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. The 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. Then, 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. The resulting MNP-PDMS nanocomposite mixtures were poured into molds and baked in an oven at 100°C for 43 minutes.


### 2.3. Magnetic Characterization

Magnetic measurements were carried out using the superconducting quantum interface device (SQUID) magnetometer, MPMS XL-5 (Quantum Design, San Diego CA, USA). The 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.


### 2.4. Theory 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(1)A=4ασsμ0H,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. σs (A·m2·kg−1) is the saturation magnetization, μ0 (H·m−1) is the permeability of free space. H (A·m−1) is the amplitude of the AMF.The heat dissipation,P (W·m−3), is determined by the following equation:(2)P=Afρn,where ρn 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 thein vivo performance.


#### 2.5.1. FEM Modeling

Figure1(a) shows a schematic diagram of the probe used in our study. The 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].Figure 1
(a) Schematic of magnetic heating probe. The probe is a cannula with two main parts: a distal active tip made of a nanocomposite (blue) and a proximal insulated shaft (pink). Therapeutic treatment is achieved when the active tip is brought in contact with the target area and exposed to alternating magnetic field. (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) The 3D meshed model of the cylindrical block.
(a)
(b)
(c)The geometric model that was used in our study is shown in Figure1. Hepatic tissue is modeled as a cylindrical block with a diameter and height of 6 cm and 12 cm, respectively. The probe is placed within the cylindrical block such that the active tip is situated at the center of cylindrical block.The temperature distribution within the tissue is determined by the Pennes bioheat equation [15]:(3)ρcp∂T∂t=λ∇2T+ρbcbαbωbTb−T+Qm+Q,where ρkg⋅m−3 is the density, cp (J·kg−1·K−1) is the specific heat capacity at constant pressure, λ (W·m−1·K−1) is the thermal conductivity. ρb, ωb (s−1), cb, and Tb are the density, tissue perfusion rate, specific heat capacity, and temperature of blood, respectively. αb is tissue state coefficient. Qm (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)The boundary conditions for equation (3) were a prescribed temperature, T=37°C, on all outer surfaces; and continuity, n⋅λ1∇⋅T1−λ2∇⋅T2=0, 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 well-established Arrhenius equation was used. It is a first-order thermal-chemical rate equation that enables the determination of damage with temperature history. The damage, which is considered to be due to the transformation of native molecules through an activated state leading to cell death, is quantified using a dimensionless single parameter,Ω, as(4)Ωt=Sf∫​0texp−EaRTtdt,where Ea (J·mol−1) is the activation energy for the injury process, Sf (s−1) is a scaling factor, and R (J·mol−1·K−1) is the gas constant. The values of Ea and A were obtained from [16] as 257.7 kJ·mol−1 and 7.39×1039s−1, respectively. In this study, Ω = 1, which corresponds to a 63% percent probability of cell death, is chosen to indicate that sufficient irreversible damage has been achieved. [17] At this point, it has been reported previously that tissue perfusion ceases [18]. This corresponds to a αb of zero. Therefore, intermediate values of αb were calculated as 1/exp (Ω) [18].The thermal properties of different domains used in the simulation are summarized in Table1. The effective thermal and physical properties of the nanocomposites were estimated using the rule of mixtures. The details of the implementation are summarized in Appendix.Table 1
Thermal properties of the materials used in the FEM models.
Material
ρ (kg m−3)
c
p (J (kg K)−1)
λ (W (m K)−1)
ω (s−1)
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
—
γ
−
Fe
2
O
3 [22]
4,600
746
9.700
—


#### 2.5.2. Parametric Investigations

Generally,0.05−1.2MHz and 0−15kA⋅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 5×109A⋅m−1⋅s−1 [24]. According to [23], the maximum human-safe field amplitude is 15 kA m−1. Ablations were simulated at AMF parameters: H=5−15kA⋅m−1, step size: 5 kA·m−1, f=150−450kHz, and step size of 150 kHz. These 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 ωb− 0%, 50%, and 100% of normal tissue perfusion of 0.0064 s−1 and t= 180 s and 300–900 s (step size: 300).


#### 2.5.3. FEM Model Validation

The FEM model was tested for its validity using an analytical model developed by Andrä et al. [26]. The model, which predicts temperature rise due to a spherical nanocomposite, is given by(5a)ΔT1r,t=PR23λ21+qλ21−r2R2+6πqλ3/2q1/2Rr∫0∞fg1dz,0≤r≤R,(5b)ΔT2r,t=PR33λ2r1+6πqλ∫0∞fg2dzz,r>R,where P is volumetric power (equation (2)), ρ1 is density, c1 is heat capacity, and λ1 is thermal conductivity of the nanocomposite, all approximated by the rule of mixtures. ρ2, c2, and λ2 are the properties of liver tissue. Parameters f, g1, g2, q, and qλ are abbreviations:(6)qλ=λ2λ1,qλ=ρ2c2ρ1c1,sz=qλ−1sinz+zcosz,fz,r,t=z−2exp−λ1tz2ρ1c1R2×zcosz−sinzsz2+qλqsinz2,g1z,r=sinrzR,g2z,r=szsinkz;r+qλq1/2zsinzcoskz,r,kz,r=qλq1/2zrR−1.The nanocomposite was assumed to contain 5 vol. % of MNP and PDMS; its properties were calculated using simple rule of mixtures. The radius of the sphere was taken asR=1.5mm. A volumetric heating power, P, of 33.7 (MW·m−3), was used. The surrounding area was assumed to be liver tissue, thus the corresponding properties in Table 1 were used.


## 2.1. Materials

The materials that were used in this study included maghemite (γ−Fe2O3) nanoparticles (high purity, 99.5%, 20 nm, US Research Nanomaterials Inc., Houston, TX, USA) and PDMS (Sylgard 184 silicone elastomer kit, Dow Corning Corp., Auburn, MI, USA). These materials were used as received.


## 2.2. Sample Preparation

Three 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. The 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. Then, 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. The resulting MNP-PDMS nanocomposite mixtures were poured into molds and baked in an oven at 100°C for 43 minutes.


## 2.3. Magnetic Characterization

Magnetic measurements were carried out using the superconducting quantum interface device (SQUID) magnetometer, MPMS XL-5 (Quantum Design, San Diego CA, USA). The 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.


## 2.4. Theory 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(1)A=4ασsμ0H,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. σs (A·m2·kg−1) is the saturation magnetization, μ0 (H·m−1) is the permeability of free space. H (A·m−1) is the amplitude of the AMF.The heat dissipation,P (W·m−3), is determined by the following equation:(2)P=Afρn,where ρn 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 thein vivo performance.


### 2.5.1. FEM Modeling

Figure1(a) shows a schematic diagram of the probe used in our study. The 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].Figure 1
(a) Schematic of magnetic heating probe. The probe is a cannula with two main parts: a distal active tip made of a nanocomposite (blue) and a proximal insulated shaft (pink). Therapeutic treatment is achieved when the active tip is brought in contact with the target area and exposed to alternating magnetic field. (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) The 3D meshed model of the cylindrical block.
(a)
(b)
(c)The geometric model that was used in our study is shown in Figure1. Hepatic tissue is modeled as a cylindrical block with a diameter and height of 6 cm and 12 cm, respectively. The probe is placed within the cylindrical block such that the active tip is situated at the center of cylindrical block.The temperature distribution within the tissue is determined by the Pennes bioheat equation [15]:(3)ρcp∂T∂t=λ∇2T+ρbcbαbωbTb−T+Qm+Q,where ρkg⋅m−3 is the density, cp (J·kg−1·K−1) is the specific heat capacity at constant pressure, λ (W·m−1·K−1) is the thermal conductivity. ρb, ωb (s−1), cb, and Tb are the density, tissue perfusion rate, specific heat capacity, and temperature of blood, respectively. αb is tissue state coefficient. Qm (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)The boundary conditions for equation (3) were a prescribed temperature, T=37°C, on all outer surfaces; and continuity, n⋅λ1∇⋅T1−λ2∇⋅T2=0, 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 well-established Arrhenius equation was used. It is a first-order thermal-chemical rate equation that enables the determination of damage with temperature history. The damage, which is considered to be due to the transformation of native molecules through an activated state leading to cell death, is quantified using a dimensionless single parameter,Ω, as(4)Ωt=Sf∫​0texp−EaRTtdt,where Ea (J·mol−1) is the activation energy for the injury process, Sf (s−1) is a scaling factor, and R (J·mol−1·K−1) is the gas constant. The values of Ea and A were obtained from [16] as 257.7 kJ·mol−1 and 7.39×1039s−1, respectively. In this study, Ω = 1, which corresponds to a 63% percent probability of cell death, is chosen to indicate that sufficient irreversible damage has been achieved. [17] At this point, it has been reported previously that tissue perfusion ceases [18]. This corresponds to a αb of zero. Therefore, intermediate values of αb were calculated as 1/exp (Ω) [18].The thermal properties of different domains used in the simulation are summarized in Table1. The effective thermal and physical properties of the nanocomposites were estimated using the rule of mixtures. The details of the implementation are summarized in Appendix.Table 1
Thermal properties of the materials used in the FEM models.
Material
ρ (kg m−3)
c
p (J (kg K)−1)
λ (W (m K)−1)
ω (s−1)
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
—
γ
−
Fe
2
O
3 [22]
4,600
746
9.700
—


### 2.5.2. Parametric Investigations

Generally,0.05−1.2MHz and 0−15kA⋅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 5×109A⋅m−1⋅s−1 [24]. According to [23], the maximum human-safe field amplitude is 15 kA m−1. Ablations were simulated at AMF parameters: H=5−15kA⋅m−1, step size: 5 kA·m−1, f=150−450kHz, and step size of 150 kHz. These 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 ωb− 0%, 50%, and 100% of normal tissue perfusion of 0.0064 s−1 and t= 180 s and 300–900 s (step size: 300).


### 2.5.3. FEM Model Validation

The FEM model was tested for its validity using an analytical model developed by Andrä et al. [26]. The model, which predicts temperature rise due to a spherical nanocomposite, is given by(5a)ΔT1r,t=PR23λ21+qλ21−r2R2+6πqλ3/2q1/2Rr∫0∞fg1dz,0≤r≤R,(5b)ΔT2r,t=PR33λ2r1+6πqλ∫0∞fg2dzz,r>R,where P is volumetric power (equation (2)), ρ1 is density, c1 is heat capacity, and λ1 is thermal conductivity of the nanocomposite, all approximated by the rule of mixtures. ρ2, c2, and λ2 are the properties of liver tissue. Parameters f, g1, g2, q, and qλ are abbreviations:(6)qλ=λ2λ1,qλ=ρ2c2ρ1c1,sz=qλ−1sinz+zcosz,fz,r,t=z−2exp−λ1tz2ρ1c1R2×zcosz−sinzsz2+qλqsinz2,g1z,r=sinrzR,g2z,r=szsinkz;r+qλq1/2zsinzcoskz,r,kz,r=qλq1/2zrR−1.The nanocomposite was assumed to contain 5 vol. % of MNP and PDMS; its properties were calculated using simple rule of mixtures. The radius of the sphere was taken asR=1.5mm. A volumetric heating power, P, of 33.7 (MW·m−3), was used. The surrounding area was assumed to be liver tissue, thus the corresponding properties in Table 1 were used.


## 2.5.1. FEM Modeling

Figure1(a) shows a schematic diagram of the probe used in our study. The 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].Figure 1
(a) Schematic of magnetic heating probe. The probe is a cannula with two main parts: a distal active tip made of a nanocomposite (blue) and a proximal insulated shaft (pink). Therapeutic treatment is achieved when the active tip is brought in contact with the target area and exposed to alternating magnetic field. (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) The 3D meshed model of the cylindrical block.
(a)
(b)
(c)The geometric model that was used in our study is shown in Figure1. Hepatic tissue is modeled as a cylindrical block with a diameter and height of 6 cm and 12 cm, respectively. The probe is placed within the cylindrical block such that the active tip is situated at the center of cylindrical block.The temperature distribution within the tissue is determined by the Pennes bioheat equation [15]:(3)ρcp∂T∂t=λ∇2T+ρbcbαbωbTb−T+Qm+Q,where ρkg⋅m−3 is the density, cp (J·kg−1·K−1) is the specific heat capacity at constant pressure, λ (W·m−1·K−1) is the thermal conductivity. ρb, ωb (s−1), cb, and Tb are the density, tissue perfusion rate, specific heat capacity, and temperature of blood, respectively. αb is tissue state coefficient. Qm (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)The boundary conditions for equation (3) were a prescribed temperature, T=37°C, on all outer surfaces; and continuity, n⋅λ1∇⋅T1−λ2∇⋅T2=0, 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 well-established Arrhenius equation was used. It is a first-order thermal-chemical rate equation that enables the determination of damage with temperature history. The damage, which is considered to be due to the transformation of native molecules through an activated state leading to cell death, is quantified using a dimensionless single parameter,Ω, as(4)Ωt=Sf∫​0texp−EaRTtdt,where Ea (J·mol−1) is the activation energy for the injury process, Sf (s−1) is a scaling factor, and R (J·mol−1·K−1) is the gas constant. The values of Ea and A were obtained from [16] as 257.7 kJ·mol−1 and 7.39×1039s−1, respectively. In this study, Ω = 1, which corresponds to a 63% percent probability of cell death, is chosen to indicate that sufficient irreversible damage has been achieved. [17] At this point, it has been reported previously that tissue perfusion ceases [18]. This corresponds to a αb of zero. Therefore, intermediate values of αb were calculated as 1/exp (Ω) [18].The thermal properties of different domains used in the simulation are summarized in Table1. The effective thermal and physical properties of the nanocomposites were estimated using the rule of mixtures. The details of the implementation are summarized in Appendix.Table 1
Thermal properties of the materials used in the FEM models.
Material
ρ (kg m−3)
c
p (J (kg K)−1)
λ (W (m K)−1)
ω (s−1)
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
—
γ
−
Fe
2
O
3 [22]
4,600
746
9.700
—


## 2.5.2. Parametric Investigations

Generally,0.05−1.2MHz and 0−15kA⋅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 5×109A⋅m−1⋅s−1 [24]. According to [23], the maximum human-safe field amplitude is 15 kA m−1. Ablations were simulated at AMF parameters: H=5−15kA⋅m−1, step size: 5 kA·m−1, f=150−450kHz, and step size of 150 kHz. These 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 ωb− 0%, 50%, and 100% of normal tissue perfusion of 0.0064 s−1 and t= 180 s and 300–900 s (step size: 300).


## 2.5.3. FEM Model Validation

The FEM model was tested for its validity using an analytical model developed by Andrä et al. [26]. The model, which predicts temperature rise due to a spherical nanocomposite, is given by(5a)ΔT1r,t=PR23λ21+qλ21−r2R2+6πqλ3/2q1/2Rr∫0∞fg1dz,0≤r≤R,(5b)ΔT2r,t=PR33λ2r1+6πqλ∫0∞fg2dzz,r>R,where P is volumetric power (equation (2)), ρ1 is density, c1 is heat capacity, and λ1 is thermal conductivity of the nanocomposite, all approximated by the rule of mixtures. ρ2, c2, and λ2 are the properties of liver tissue. Parameters f, g1, g2, q, and qλ are abbreviations:(6)qλ=λ2λ1,qλ=ρ2c2ρ1c1,sz=qλ−1sinz+zcosz,fz,r,t=z−2exp−λ1tz2ρ1c1R2×zcosz−sinzsz2+qλqsinz2,g1z,r=sinrzR,g2z,r=szsinkz;r+qλq1/2zsinzcoskz,r,kz,r=qλq1/2zrR−1.The nanocomposite was assumed to contain 5 vol. % of MNP and PDMS; its properties were calculated using simple rule of mixtures. The radius of the sphere was taken asR=1.5mm. A volumetric heating power, P, of 33.7 (MW·m−3), was used. The surrounding area was assumed to be liver tissue, thus the corresponding properties in Table 1 were used.


## 3. Results and Discussion

### 3.1. Materials Characterization

Figure2 shows the magnetization curves of the MNPs and nanocomposites in magnetic fields of 45 kOe. MNPs had a saturation magnetization value, Ms, of 69.33 emu·g−1. The Ms values for samples MNP-1, MNP-2, and MNP-5 were 2.37 emu·g−1, 3.41 emu·g−1, and 6.46 emu·g−1, respectively. These values were about 3.4%, 4.9%, and 9.3%, respectively, of the Ms 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 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].Figure 2
Magnetization curves of (a) maghemite (γ−Fe2O3) nanoparticles and (b) samples MNP-1, MNP-2, and MNP-5 under magnetic fields of 0.4 MA·m−1.
(a)
(b)


### 3.2.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, Tat, 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, Tt, which occurs on the surface of the active tip, is lower. This is consistent with conduction, the main mode of heat transfer in action. Table 2 shows predictions of Tat and Tt for a range of AMF amplitudes (5–15.0 kA·m−1) and frequencies (150–450 kHz) after 15 mins of heating for all three samples. It can be observed that the temperature difference (Tat−Tt) increases with increasing Hf factor and ϕ. For instance, for the nanocomposite containing 2 vol. %, Tat−Tt increases from ≈9.7°C for the Hf factor of 1.5×109A⋅m−1⋅s−1 (H=10kA⋅m−1, f=150kHz) to ≈11.8°C for the Hf factor of 4.5×109A⋅m−1⋅s−1 (H=10kA⋅m−1, f=450kHz). Similarly, for a given Hf factor of 1.5×10−9A⋅m−1⋅s−1 (H=10kA⋅m−1, f=150kHz), Tat−Tt increases from ≈9.7°C (ϕ=2%) to ≈17.6°C (ϕ=5%). Furthermore, different H and f pairs such as H=10kA⋅m−1, f=450kHz and H=15kA⋅m−1, f=300kHz can be used to achieve the same temperature levels (Tat=175.5°C, Tt=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.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=15mins, ϕ=5%, H=10kA⋅m−1, and f=300kHz.
(a)
(b)
(c)
(d)
(e)
(f)Table 2
Temperature predictions for a range of AMF amplitudes (5–15 kA·m−1) and frequencies (150–450 kHz).
Domain
ϕ (vol. %)
σ
s (emu⋅g−1)
H
=
5
kA
⋅
m
−
1
H
=
10
kA
⋅
m
−
1
H
=
15
kA
⋅
m
−
1
f (kHz)
f (kHz)
f (kHz)
150
300
450
150
300
450
150
300
450
Active tip
1
2.37
44.5
52.1
59.6
52.1
67.2
82.3
59.6
82.3
104.9
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
Tissue
1
2.37
41.3
45.5
59.6
45.5
54.0
62.5
49.8
62.5
75.3
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
156.2Table 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.
ϕ (vol. %)
σ
s (emu · g−1)
H
=
5
kA
⋅
m
−
1
H
=
10
kA
⋅
m
−
1
H
=
15
kA
⋅
m
−
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
6.4For our thermal damage analysis, values in the middle range of bothH and f (i.e., 10 kA·m−1 and f=300kHz respectively), resulting in Tt=90°C, were used. A cross-sectional (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 different 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 (ωb=6.4×10−3s−1), it occurs after 3 mins. The time decreases to 2 mins for the case of nonperfusion (ωb=0.0×10−3s−1). This 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. The data show that moving away from the active-tip thermal damage decreases more rapidly than temperature.Table4 summarizes lesion size development as a function of time for nonperfused (ωb=0.0×10−3s−1) and fully perfused (ωb=6.4×10−3s−1). The parameters used to calculate the sizes are shown in Figure 3(c). The results reveal that tissue perfusion greatly affects the development of the lesion. For instance, lesion volume increases from 1.29 cm3 (after 3 minutes) to 11.82 cm3 (after 15 minutes) in a nonperfused (ωb=0.0×10−3s−1) tissue, representing an increase of 916%. This reduced to 293% for fully perfused is considered. At 15 mins, predicted lesion width and depth were in the range of 1.40−2.58cm and 2.58−3.39cm, respectively.Table 4
Comparison of lesion parameters for nonperfused (ω=0.0×10−3s−1) and fully perfused (ω=0.0×10−3s−1) tissue at different times.
Time (s)
ω
=
0.0
×
10
−
3
s
−
1
ω
=
6.4
×
10
−
3
s
−
1
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


### 3.3. Model Validation

In an effort 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 ≈2mm from the center of the nanocomposite (a) and distance from the center of composite (b) after 15 mins of heating. The results reveal that FEM results diverged between ≈0.5−7% from the analytical results. The deviations can be attributed to factors such as mesh sizing and shape of the geometry.Figure 4
Comparison of temperature as function of (a) time at a point≈2mm 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].
(a)
(b)


## 3.1. Materials Characterization

Figure2 shows the magnetization curves of the MNPs and nanocomposites in magnetic fields of 45 kOe. MNPs had a saturation magnetization value, Ms, of 69.33 emu·g−1. The Ms values for samples MNP-1, MNP-2, and MNP-5 were 2.37 emu·g−1, 3.41 emu·g−1, and 6.46 emu·g−1, respectively. These values were about 3.4%, 4.9%, and 9.3%, respectively, of the Ms 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 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].Figure 2
Magnetization curves of (a) maghemite (γ−Fe2O3) nanoparticles and (b) samples MNP-1, MNP-2, and MNP-5 under magnetic fields of 0.4 MA·m−1.
(a)
(b)


## 3.2.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, Tat, 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, Tt, which occurs on the surface of the active tip, is lower. This is consistent with conduction, the main mode of heat transfer in action. Table 2 shows predictions of Tat and Tt for a range of AMF amplitudes (5–15.0 kA·m−1) and frequencies (150–450 kHz) after 15 mins of heating for all three samples. It can be observed that the temperature difference (Tat−Tt) increases with increasing Hf factor and ϕ. For instance, for the nanocomposite containing 2 vol. %, Tat−Tt increases from ≈9.7°C for the Hf factor of 1.5×109A⋅m−1⋅s−1 (H=10kA⋅m−1, f=150kHz) to ≈11.8°C for the Hf factor of 4.5×109A⋅m−1⋅s−1 (H=10kA⋅m−1, f=450kHz). Similarly, for a given Hf factor of 1.5×10−9A⋅m−1⋅s−1 (H=10kA⋅m−1, f=150kHz), Tat−Tt increases from ≈9.7°C (ϕ=2%) to ≈17.6°C (ϕ=5%). Furthermore, different H and f pairs such as H=10kA⋅m−1, f=450kHz and H=15kA⋅m−1, f=300kHz can be used to achieve the same temperature levels (Tat=175.5°C, Tt=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.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=15mins, ϕ=5%, H=10kA⋅m−1, and f=300kHz.
(a)
(b)
(c)
(d)
(e)
(f)Table 2
Temperature predictions for a range of AMF amplitudes (5–15 kA·m−1) and frequencies (150–450 kHz).
Domain
ϕ (vol. %)
σ
s (emu⋅g−1)
H
=
5
kA
⋅
m
−
1
H
=
10
kA
⋅
m
−
1
H
=
15
kA
⋅
m
−
1
f (kHz)
f (kHz)
f (kHz)
150
300
450
150
300
450
150
300
450
Active tip
1
2.37
44.5
52.1
59.6
52.1
67.2
82.3
59.6
82.3
104.9
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
Tissue
1
2.37
41.3
45.5
59.6
45.5
54.0
62.5
49.8
62.5
75.3
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
156.2Table 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.
ϕ (vol. %)
σ
s (emu · g−1)
H
=
5
kA
⋅
m
−
1
H
=
10
kA
⋅
m
−
1
H
=
15
kA
⋅
m
−
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
6.4For our thermal damage analysis, values in the middle range of bothH and f (i.e., 10 kA·m−1 and f=300kHz respectively), resulting in Tt=90°C, were used. A cross-sectional (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 different 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 (ωb=6.4×10−3s−1), it occurs after 3 mins. The time decreases to 2 mins for the case of nonperfusion (ωb=0.0×10−3s−1). This 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. The data show that moving away from the active-tip thermal damage decreases more rapidly than temperature.Table4 summarizes lesion size development as a function of time for nonperfused (ωb=0.0×10−3s−1) and fully perfused (ωb=6.4×10−3s−1). The parameters used to calculate the sizes are shown in Figure 3(c). The results reveal that tissue perfusion greatly affects the development of the lesion. For instance, lesion volume increases from 1.29 cm3 (after 3 minutes) to 11.82 cm3 (after 15 minutes) in a nonperfused (ωb=0.0×10−3s−1) tissue, representing an increase of 916%. This reduced to 293% for fully perfused is considered. At 15 mins, predicted lesion width and depth were in the range of 1.40−2.58cm and 2.58−3.39cm, respectively.Table 4
Comparison of lesion parameters for nonperfused (ω=0.0×10−3s−1) and fully perfused (ω=0.0×10−3s−1) tissue at different times.
Time (s)
ω
=
0.0
×
10
−
3
s
−
1
ω
=
6.4
×
10
−
3
s
−
1
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


## 3.3. Model Validation

In an effort 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 ≈2mm from the center of the nanocomposite (a) and distance from the center of composite (b) after 15 mins of heating. The results reveal that FEM results diverged between ≈0.5−7% from the analytical results. The deviations can be attributed to factors such as mesh sizing and shape of the geometry.Figure 4
Comparison of temperature as function of (a) time at a point≈2mm 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].
(a)
(b)


## 4. 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 andγ−Fe2O3 nanoparticles, was successfully fabricated. Magnetic measurements obtained with a SQUID magnetometer showed that their saturation magnetizations, Ms, increased with increasing nanoparticle concentration to about 9% of the Ms value of pure γ−Fe2O3 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. The results showed that reasonable lesion sizes, which are greatly affected 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 specific times show that the difference 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. These sizes are similar to those obtained by other probe-based thermoablation techniques reported in the literature [18, 28, 29].The results demonstrate the potential of our magnetic nanocomposite probes to treat small (≤1−3cm) 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. Further studies, including in vitro and in vivo experiments, are needed for a realistic assessment of the probe.



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*Source: 6802125-2019-03-03.xml*