Numerical simulation of magnetic fluid hyperthermia based on multiphysics coupling and recommendation on preferable treatment conditions

Current Applied Physics 19 (2019) 1031–1039

Contents lists available at ScienceDirect

Current Applied Physics journal homepage: www.elsevier.com/locate/cap

Numerical simulation of magnetic fluid hyperthermia based on multiphysics coupling and recommendation on preferable treatment conditions

T

Jing Lia, Huan Yaoa, Yan Leib, Weihua Huangc,∗, Zhe Wanga a

South China University of Technology, 381 Wu Shan Rd, Tianhe District, Guangzhou, 510641, China Southern Medical University Hospital of Traditional Chinese and Western Medicine, 13 Shiliu Gang Rd, Haizhu District, Guangzhou, 510315, China c Fuda Cancer Hospital, Jinan University, 2 West Tangde Rd, Tianhe District, Guangzhou, 510665, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Numerical simulation Multiphysics coupling Magnetic fluid hyperthermia Recommended treatment conditions Deep tumors

In this study, we established a multiphysics coupling model of magnetic fluid hyperthermia (MFH), using complex magnetic permeability to solve the magnetic losses of magnetic nanoparticles (MNPs). The experiments were performed to verify the validity of numerical coupling method. The optimal treatment time (OTT) was regarded as the time required for the lowest temperature point of the tumor to attain the damage criteria. The OTT increased by about 42 s as the tumor radius increased by 1 cm, and decreased by 10 s for the increase in MNP dose per gram of tumor by 1 mg. To achieve cost-effective therapies under moderate treatment conditions, the preferable ranges of external magnetic field intensity H0 and frequency f, MNP radius R and volume fraction ϕ are 3–11 kA/m, 200–500 kHz, 8–10 nm, and 5%–10%, respectively. It is greatly encouraged to adopt the combination of higher H0 (8–11 kA/m) and lower f (200–300 kHz), and the conjunction of higher R and ϕ . There was a slight thermal damage to normal tissues due to eddy current loss. In conclusion, MFH can provide an excellent therapeutic effect for deep tumors.

1. Introduction In 1993, Jordan et al. [1] explored the potential application of magnetic fluid in tumor therapy and proposed a new technique, magnetic fluid hyperthermia (MFH). During MFH, magnetic fluid is delivered to cancerous tissues, and generates tremendous heat dissipation due to the magnetic moment reversal of magnetic nanoparticles (MNPs) when exposed to an external alternating magnetic field (AMF). Subsequently, the tumor tissues are heated to above the critical damage temperature (42.5–43 °C) [2] through the absorption of thermal energy from magnetic fluid, whereas the normal tissues remain at a safe temperature owing to the scant magnetic losses. More recently, MFH has received increasing interests and was expected to be used in combination with chemotherapy and radiotherapy due to fewer side effects and significant heating effects [3,4]. Petryk et al. [5] stated that MFH with cisplatin chemotherapy can effectively improve the safety and efficacy of chemotherapy, and the growth inhibition ratio in mouse breast tumor was 1.4 times that of cisplatin alone. Maier-Hauff et al. [6] performed the clinical tolerability trial of MFH combined with radiotherapy in fourteen patients suffering from recurrent glioblastoma multiforme, and the results showed that all patients were well tolerated with minimal side effects. MFH in conjunction with lower radiation

∗

dose produced a significant increase in the survival rate of patients [7,8]. In addition, research into magnetic hyperthermia devices has yielded breakthroughs. Gneveckow et al. [9] designed an AMF applicator MFH 300F, which was suitable for deep regions of the human body, and a magnetic field strength of 12–18 kA/m at 100 kHz was attained within a cylindrical treatment area of 20 cm diameter and 30 cm height. Lv et al. [10] conducted a numerical investigation of the electromagnetic field distribution and transient tissue temperature response induced by two planar electrodes, and found that MNPs provide sufficiently focused heating of tumor tissues without overheating the healthy tissues. Ho et al. [11] presented a highly targeted magnetic thermotherapy system consisting of 12 coils disposed symmetrically in the space around the patient, and the high frequency AMF was generated merely in the tumor area by selectively supplying alternating current for several coils according to the tumor site. Barba et al. [12] designed an novel air-cored solenoid inductor for MFH, and the magnetic field intensity reached up to 15 kA/m in the treatment space. Extensive study was conducted to explore the influence of magnetic field parameters and magnetic fluid properties on the heating power of MNPs. Benjamin et al. [13] found that the nonmonotonicity in the influence of volume concentration on the thermal energy dissipation of nanoparticles with optimal concentrations of appropriately 1%, and the

Corresponding author. Fuda Cancer Hospital, Jinan University, Guangzhou, 510665, China. E-mail address: [email protected] (W. Huang).

https://doi.org/10.1016/j.cap.2019.06.003 Received 31 January 2019; Received in revised form 1 April 2019; Accepted 7 June 2019 Available online 08 June 2019 1567-1739/ © 2019 Korean Physical Society. Published by Elsevier B.V. All rights reserved.

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

Fig. 1. Schematics of MFH model and the distribution of temperature, MNP volume fraction, magnetic field strength and flux density in section A after 600 s of treatment with H0 = 5 kA/m, f = 100 kHz, R = 10 nm, ϕ = 5%, and w = 5 mg/g, and the separate element is the zoomed image of the tumor region. (A) is a wireframe rendering of the MFH model; (B) is the slice of MFH model along section A; (C) is the distribution of temperature; (D) is the distribution of MNPs volume fraction; (E & F) are the distribution of magnetic field strength and flux density, respectively.

optimization of treatment parameters, and some useful conclusions were drawn by solving magnetic field distribution and nanoparticle heating separately [17,19,26–29]. However, there does not exist a model that neatly incorporates the magnetic and thermal fields into a single calculation. In the present study, we aimed to solve these problems using FEM in COMSOL. Using complex magnetic permeability to solve the magnetic losses of MNPs during magnetization reversals, a multiphysics coupling model of MFH was established, and verified by comparing the numerical and experimental results for the heating curves of magnetic fluid. The optimal treatment time (OTT) was obtained through the integral analysis of damaged tissue, and the impact of several factors, including external magnetic field intensity H0 and frequency f, the radius R and volume concentration ϕ of nanoparticles, and the MNP dose w, on the OTT was investigated. Furthermore, the preferable treatment conditions were deduced from the ingenious union of univariate and multivariate analysis. Moreover, we quantitatively researched the highest thermal dose delivered to normal tissues due to eddy current loss when the therapeutic purpose in tumor tissues was achieved.

optimal concentration varied slightly with the applied frequency. Lahiri et al. [14] reported that the heating power increased initially with the concentration of magnetic fluid and reached a maximum at a mass concentration of roughly 2%, and then decreased with increasing particles loading. Shadie et al. [15] declared that the lowest concentration presents the maximum amount of heat dissipation for the same magnetic field, and increasing the temperature of MNPs before hyperthermia can greatly improve the heating effects on tumor tissues. Phong et al. [16] concluded that the heat generation reached a peak at the superparamagnetic critical diameter, and the critical diameter monotonically decreases with increasing magnetic anisotropy. Beković et al. [4] presented a measurement system for determining the heating power of magnetic fluid at a constant magnetic field and arbitrary temperature, and found that the heating power decreased non-negligibly with increasing sample temperature. Many researchers have investigated the factors affecting the temperature rise of target tissues during MFH by using the finite element method (FEM). Candeo et al. [17] developed a numerical MFH model of abdomen district using anatomical CT images, and declared that the radius and volume concentration of MNPs, as well as the frequency and magnitude of the applied magnetic field, may critically influence the heating effects on target tissues. Wu et al. [18] substituted the power density obtained from electromagnetic field simulation as a heat source into Penne's bio-heat transfer equation, and the results indicated that the magnetic field generated by the Helmholtz coil can effectively heat target tissues without collateral tissue damage. Tang et al. [19] proposed an optimal critical power dissipation of MNPs (Pc = 7 × 106 W m−3) for the purpose of guaranteeing the highest tumor temperature within the reasonable limit of 46 °C while controlling the thermal damage to surrounding tissues, and the uniformity of the temperature field can be greatly enhanced adopting the lower-curietemperature nanoparticles. MFH has exhibited the advantages of low toxicity, high heating power and excellent transparency in the human torso, and it has shown substantial promise as an alternative therapy for deep and inaccessible tumors [20–24]. However, the difficulties in the accurate determination of temperature distribution, and the precise control of thermal dose within treated tissues greatly constrained the clinical applications of MFH [25]. Numerous studies focused on the numerical methods for the

2. Numerical method 2.1. Establishment of MFH model In this paper, the human abdomen was adopted as the study object, and the vital organs, vascular tissues, and skeletal tissues surrounding the tumor regions were assumed as muscle tissues. The simplified threedimensional MFH model was established, and the wireframe rendering diagram is shown in Fig. 1A. Referring to the characteristics of human abdomen contours, the outer contours of skin tissue were considered to be elliptical, and the dimensions of the major and minor axes were set to 32 cm and 24 cm, respectively. Importantly, the characteristic parameters of MFH model were adopted by averaging, and a model height of 20 cm and skin thickness of 2 mm were applied. Direct intratumoral injection is more conducive to the aggregation of nanoparticles in treated tissues [21], and multisite injection can be exploited to ameliorate the MNP distribution in target volumes [30]; so, we initially set two injection domains at the half radius of the tumor mass along the x, y, and z axes, respectively. To clearly show the distribution of tumor 1032

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

Table 1 Physical parameters. Tissue

Density ρ [kg m−3]

Specific heat Cp [J kg−1 K−1]

Thermal conductivity k [W m−1 K−1]

Conductivity σ [S m−1]

Relative permittivity εr [1]

Blood perfusion rate wb [s−1]

Basal metabolic heat rate Qmet [W m−3]

Tumor Muscle Skin Blood Magnetic fluid Air Water

1050 1090 1109 1050 1100 1.2 994

3500 3421 3391 3617 3750 1004 4178

0.50 0.49 0.37 0.52 0.50 0.03 0.6

0.35–0.52 0.35–0.52 2.7E-4–1.8E-2 0.70–0.85 1.5 0 5.7E-10–3.3E-77

1.5E3–1.0E4 1.5E3–1.0E4 0.96E3–1.1E3 2.6E3–5.2E3 1 1 84.64

8.33E-4 6.72E-4 1.96E-3 – – – –

5790 992 1830 – – – –

and magnetic fluid domains, the slice graph along the xz plane at y = 0 (defined as section A) is shown in Fig. 1B. Additionally, the tumor radius was set to 1–5 cm, and the radius of magnetic fluid regions was determined by ϕ , w, and tumor radius. In general, a reasonable MNP injection dose w is 5–10 mg nanoparticles per gram of tumor [31], and the volume fraction ϕ of MNPs in magnetic fluid is 1%–10%.

χ′ =

χ0 1 + (ωτ )2

The thermal and electromagnetic parameters of biological tissues and magnetic fluid are presented in Table 1 [32]. Importantly, the relative permittivity and electrical conductivity of various tissues are given with a range as they are dependent with frequency in 0.05–1.2 MHz, according to Ref. [33]. In particular, the complex permeability of magnetic fluid was defined to solve the magnetic losses of nanoparticles, and the detailed derivation is illustrated in Equations (4)–(9).

Considering the metabolic heat production and blood perfusion of biological tissues during hyperthermia, the temperature distribution of tumors and the surrounding normal tissues was calculated using Pennes bio-heat transfer equation [34]: (1)

μ″ = χ ″

3⎛ 1⎞ ⎜coth ξ − ⎟ ξ⎝ ξ⎠

(8)

μ0 ϕMd2 Vm 3kB T

ξ=

μ0 Md Hm Vm kB T

(9) −2

Here, μ0 is the permeability of vacuum (4π × 10 N A ), Md is the domain magnetization of magnetite nanoparticles, set to 446 kA/m [35], Hm is the magnetic field strength of magnetic fluid regions [A/m], and ϕ is the volume fraction of nanoparticles [%]. For the macroscopically static magnetic fluids, the molecular diffusion of nanoparticles within biological tissues may be independent of the pressure gradient, and the concentration distribution of MNPs in biological tissues was calculated using:

∂C = D∇2 C ∂t

(10)

Here, D is the diffusion coefficient of MNPs, which can be estimated using Stokes–Einstein formula:

D=

kB T 6πηR

(11)

The magnetic field module was applied in the whole computational domain, and the AMF in the z direction was set on the outer surface of the skin:

⎧ Hx = 0 Hy = 0 ⎨ ⎩ Hz = H0

where μ′ and μ″ are the real and imaginary parts of the complex magnetic permeability, respectively. These can be derived from the complex susceptibility:

μ′ = χ ′ + 1

(7)

−7

where ρ is the tissue density [kg m−3], Cp is the tissue specific heat [J kg−1 K−1], t is the treatment time [s], T is the tissue temperature [K], k is the tissue thermal conductivity [W m−1 K−1)], wb is the tissue blood perfusion rate [s−1], Cb is the specific heat of the blood [J kg−1 K−1], Tb is the blood temperature [K], Qmet is the tissue metabolic heat production rate [W m−3], and Qml is the magnetic loss of unit volume magnetic fluid or tissue [W m−3]. In particular, Qml is the amount of magnetic field energy converted into heat, which is caused by the magnetization reversal processes of hysteresis and relaxation. For superparamagnetic nanoparticles, it is generally known that the heat dissipation is mainly due to the Néelian and Brownian relaxation [16,35,36]. Even though the MNPs with large diameters (10–100 nm) have increased magnetic losses caused by hysteresis [37], it is difficult to define a universal simulation model combined the two mechanisms. Therefore, the current study investigated the dominant part of magnetic losses generated by Néel–Brown relaxation, and Qml can be represented by the following:

(3)

3ηVh kB T

where the initial susceptibility χi and the Langevin parameter ξ are expressed as follows:

χi =

⇀ ⇀ B = μ0 (μ′ − iμ″) H

τB =

where Γ = KVm/ kB T , K is the magnetic anisotropy parameter, set to 10 kJ m−3 [38,39], and Vm = 4/3πR3 is the volume of a single nanoparticle [m3], R is the particle radius, ranging from 1 to 10 nm as the single domain critical radius of Fe3O4 nanoparticles is about 10 nm [40]. τ0 is the attempt period, which has a typical value of 10−9 s, Vh is the hydrodynamic particle volume [m3], η is the viscosity of magnetic fluid (1 × 10−3 Pa s), and kB is Boltzmann constant (1.38 × 10−23 J K−1). The static susceptibility χ0 is represented as:

χ0 = χi

(2)

(6)

π exp(Γ ) τ0 2 Γ

2.3. Governing equations and boundary conditions

1 ⇀⇀ Re(iωB ⋅H ) 2

(5)

1 1 1 = + τ τN τB τN =

Qml =

χ0 ωτ 1 + (ωτ )2

Here, τ is the effective relaxation time of the fluid [s], which can be determined by Néelian and Brownian relaxation times τN and τB :

2.2. Physical parameters

∂T = ∇ (k∇T ) + ρ b Cb w b (Tb − T ) + Qmet + Qml ρC p ∂t

χ″ =

(12)

where H0 is the external magnetic field intensity [A/m]. The applicable ranges of H0 and f for magnetic hyperthermia are 0.05–1.2 MHz and 0–15 kA/m [31], respectively, and the product of H0 and f cannot exceed 4.85 × 108 A m−1 s−1 [41]. Other boundaries were set to be

(4) 1033

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

magnetically insulated:

⎯⇀ ⇀ n × A =0

(13)

The bio-heat transfer module was employed in all domains, the initial temperature of tumor and muscular tissues was set to 37 °C, and that of skin tissue and magnetic fluid was adopted as 33 °C and 25 °C, respectively. The convective heat flux was set on the outer surface of the skin:

∂T − k ⎛ ⎞ = h (Ts − Ta ) ⎝ ∂n ⎠s

(14)

where h is the convective heat transfer coefficient, valued as 6 W m−2 K−1 [42], and Ta is the ambient temperature, taken as 25 °C. Other boundaries were assumed to maintain a constant temperature of 37 °C. The chemical species diffusion module was also employed in all domains, and the initial concentration of magnetic fluid regions is determined:

C0 = ϕ

ρm M

(15)

where M is the molar mass of Fe3O4 (232 g/mol), and ρm is the density of magnetite nanoparticles (5180 kg/m3).

Fig. 2. The experimental scheme for the determination of the magnetic fluid heating curves.

2.4. Selection of damage threshold

on the measurements. The axial-length and outer diameter of supply coil were 95 mm and 78 mm, respectively, and the number of turns was 9. To verify the validity of multiphysics coupling, a two-dimensional axisymmetric calculation model was established based on the above measurement system, and we measured and simulated the heating effects of magnetic fluid under four cases of heating conditions. Fig. 3B presents the numerical and experimental results of the temperature rise curves in the magnetic fluid center for different nanoparticle doses mp, inductive current I, volume concentration ϕ , at a frequency of f = 58.4 kHz and nanoparticle radius R = 10 nm. From the figure, even though the simulation results increased slightly faster than the experimental results versus time, the numerical results was in agreement with experimental results, and the relative error did not exceed 5%. The figure also indicated that the temperature-rise rate of the magnetic fluid decreased considerably with time, and the magnetic fluid temperature reached a steady state at 2000 s. One potential explanation for the divergence may be that neither the magnetic parameters of nanoparticles nor the ambient thermal conditions may be exactly the same as the experimental situations. Alternatively, the measuring error of thermometer and stochastic error in the position temperature measuring point may need to be considered in model validation. As a consequence, it is possible that discrepancies in magnetic parameters and ambient thermal conditions, system measuring error, and random measurement error caused inevitable deviations between the simulation and experimental results. Therefore, the numerical method of multiphysics coupling applied in the current study can yield credible results when used to calculate the temperature distribution during MFH.

To achieve a comprehensive evaluation of the thermal damage resulting from different heating temperatures and durations, Sapareto and Dewey [43] converted the heating time at an arbitrary temperature to equivalent treatment minutes at 43 °C. The cumulative equivalent minutes integrated over the time domain is also known as the equivalent thermal dose:

CEM 43(t) =

∫t

t final

φ(316 − T(t)) dt

0

(16)

T < 312 K ⎧ 0 φ = 0. 25 312 K ≤ T < 316 K ⎨ 316 K ≤ T ⎩ 0. 5

(17)

where t0 and tfinal represent the times at which heating begins and ends, respectively, T(t) is a function of temperature over time, and φ is a temperature-dependent constant (see Equation (17)) [23]. Rempp [44] and Hoopes [45] found that an equivalent thermal dose greater than 41 min may result in severe damage to muscle tissues. Rhoon [46] and Yarmolenko [47] reported that the thermal dose thresholds for reversible and irreversible damage to muscle tissues were 40 min and 80 min, respectively. In this study, an equivalent thermal dose of 80 min was chosen as the damage threshold, and the OTT was regarded as the time required for the lowest temperature point of the tumor to attain the damage criteria. Ultimately, the OTT for deep tumors of arbitrary radius under various treatment conditions was obtained through the integral analysis of damaged tissue. 3. Results and discussion

3.2. Analysis of magnetic, temperature, and diffusion fields

3.1. Model verification

Fig. 1D shows the volume concentration distribution of MNPs in section A 60 min after magnetic fluid injection with ϕ = 5%, w = 5 mg/g, R = 10 nm. As can be seen, most of the nanoparticles were still concentrated in the initial injection domains owing to the slow diffusion rate, though a small amount of MNPs spread to adjacent tumor tissues. For nearly static magnetic fluids, the diffusion mechanism was dominated by the molecular microscopic movement of nanoparticles, which was driven by the temperature gradient and concentration gradient. Moreover, the volume fraction of MNPs in normal tissues integrally approached zero, indicating that the cytotoxicity of MNPs to healthy tissues and the resulting heating effects may be negligible during MFH.

The LH-15A high frequency induction heating equipment was provided by Dongguan Lihua Machinery Equipment Co., Ltd., and the water-based Fe3O4 nano-magnetic fluid was supplied by Shanghai Hao Biological Technology Co., Ltd. The mean diameter of the nanoparticles is 20 nm, and the magnetic fluid was supplied in concentrations of 3% and 5%. The heating space of the device consisted of the copper-tubewound solenoid coil; the measurement system was built as shown in Fig. 2. The magnetic fluid was held by a wooden base and placed in the center of the supply coil which was cooled with a steady flow of cooling water at 20 °C, to avoid the disturbance of joule losses from supply coil 1034

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

Fig. 3. The axial temperature profile and the model validation results for the temperature of magnetic fluid center. (A) is the axial temperature profile along the long axis of the ellipse in section A after 600 s of treatment with H0 = 5 kA/m, f = 100 kHz, R = 10 nm, ϕ = 5%, and w = 5 mg/g; (B) is a comparison of time evolution of magnetic fluid center temperature between simulation and experimental results under four cases of heating conditions at f = 58.4 kHz with R = 10 nm.

Fig. 1E and F shows the distribution of the magnitude and flux density of the magnetic field, respectively, with H0 = 5 kA/m, f = 100 kHz, R = 10 nm, ϕ = 5%, and w = 5 mg/g. From Fig. 1E, it is clear that the magnetic field intensity of normal tissues and most tumor was in close proximity to 5 kA/m, and that of magnetic fluid regions was less than 3 kA/m, whereas that of tumor regions near the edge of magnetic fluid was up to 8.2 kA/m. According to the Ampere circuital theorem (B = μ0 μr H ), the lower the relative permeability of the magnetic medium, the higher the strength of the magnetic field. As shown in Fig. 1F, the magnetic flux density in magnetic fluid domains and adjacent tumor tissues reached up to 10–13 mT, while that of other tissues was less than 6.5 mT. Possible explanations for this are the considerable differences in magnetic properties between magnetic fluid and biological tissues, or perhaps a small amount of MNPs diffused to adjacent tumor tissues. Fig. 1C shows the temperature distribution of section A after 600 s of treatment with H0 = 5 kA/m, f = 100 kHz, R = 10 nm, ϕ = 5%, and w = 5 mg/g. As seen in the figure, the maximum temperature of magnetic fluid regions reached up to 83.7 °C owing to the significant relaxation loss of MNPs, and the tumor tissue was heated to above 43 °C by absorbing thermal energy from the magnetic fluid in the form of heat conduction; that is, the farther away from magnetic fluid regions, the lower the tumor temperature. To clearly present the temperature difference between cancerous and healthy tissues, the axial temperature curve along the long axis of the ellipse in section A is shown in Fig. 3A. The figure clearly shows that the highest and lowest temperature points of the tumor tissue were located at the magnetic fluid center and the outer boundary of the tumor, respectively. The temperature of the superficial muscle tissue was increased locally due to eddy current loss, resulting in a small heat peak. Moreover, the important thermal difference between the tumor and normal tissues can be seen in Fig. 3A, and the temperature in tumor edge exceeded the peak temperature of the superficial muscle tissue by 4.7 °C. It may be preliminarily inferred that the excellent targeted heating for deep tumors may be achieved with slight heating effects on normal tissues, except of the inevitable overheating of normal cells on the border of the tumor.

remained at approximately zero in the initial stage of therapies before increasing exponentially with treatment time, and the higher the magnetic field intensity and frequency, the faster the increase in thermal dose with time. In addition, an accelerating increase in the OTT with a reduction in H0 or f can be seen in the graph, and the OTT decreased by 125 s and 33 s respectively, as f increased from 200 kHz to 400 kHz and from 400 kHz to 600 kHz with H0 = 10 kA/m. Analogously, we quantitatively researched the highest thermal dose delivered to normal tissues due to eddy current loss, as shown in Fig. 4B. As shown in the figure, the resulting thermal dose in healthy tissues from eddy current increased slowly with treatment time, and it varied in 0.05–2.5 min under various magnetic field conditions when the therapeutic purpose in tumor tissues was achieved. Accordingly, there was a slight thermal damage to normal tissues, except of the inevitable overheating of normal cells on the border of the tumor. In the light of the inherent difference of heat sensitivity between cancerous and healthy tissues, there is good potential for limiting thermal damage to normal cells during MFH. Previous studies [23,38,39] have reported that several factors, including H0, f, R, and ϕ , significantly influence the power dissipation of MNPs, and this paper will further study the impact of the above factors on the OTT. Fig. 5 shows the changes in the OTT as a function of the magnetic field intensity H0 and frequency f with R = 10 nm, ϕ = 5%, w = 5 mg/g and a tumor radius of 2 cm. An accelerating growth in the OTT can be seen in Fig. 4 with increasing magnetic field intensity H0 and frequency f, and an excessive increment in treatment time may be caused when H0 and f were lower than 3 kA/m and 200 kHz, respectively. Moreover, the decrement of OTT varied in 6–12 s with f increased by 100 kHz, and did not exceed 7 s as H0 increased by 1 kA/m when H0 and f were higher than 11 kA/m and 500 kHz, respectively. Supposing that the magnetic field intensity and frequency is enhanced simultaneously in the therapeutic space required for exposure of a human body, the technical challenges increase dramatically, and it may cause unwanted thermal damage to healthy tissues due to eddy current loss. In order to achieve cost-effective therapies under moderate treatment conditions, the preferable magnetic field condition was considered to be 3–11 kA/m and 200–500 kHz. Furthermore, we investigated the influence of magnetic fluid properties, MNP dose and tumor radius on the OTT under a moderate magnetic field condition. Fig. 6 shows the dependence of the OTT on the nanoparticles radius R, MNP volume fraction ϕ , injection dose w, and tumor radius with H0 = 10 kA/m and f = 400 kHz. Fig. 6A depicts the change curves of the OTT vs. R and ϕ with w = 5 mg/g, and it can be seen that the OTT substantially decreased with any increase in R. The OTT was reduced from 2059 s to 1700 s as R increased from 1 nm to 5 nm, and it was decreased by 400–600 s as R increased by 1 nm in the range of 6–8 nm; however, the decrement was less than 250 s for the

3.3. Preferable treatment conditions As the lowest temperature point of the tumor was located at the outer boundary, the OTT was regarded as the time required for monitoring point L (see Fig. 1A) to reach the damage threshold of 80 min, to minimize the additional damage to normal tissues. Based on Equations (16) and (17), the time evolution of the equivalent thermal dose at point L was obtained under multiple magnetic field conditions with R = 10 nm, ϕ = 5%, w = 5 mg/g and a tumor radius of 2 cm, as shown in Fig. 4A. From the figure, the thermal dose delivered to point L 1035

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

Fig. 4. Time evolution of the equivalent thermal dose at point L and the highest thermal dose delivered to normal tissues with R = 10 nm, ϕ = 5%, w = 5 mg/g (A & B) show the changes in the equivalent thermal dose at monitoring point L and the highest thermal dose of normal tissues due to eddy current loss as a function of time under various magnetic conditions, respectively.

concentration increased, the magnetic permeability of magnetic fluid increased, and the injection volume decreased; subsequently, increasing magnetic permeability resulted in the enhanced heat dissipation, whereas the decreasing injection volume resulted in reduced heat production due to increasing reluctance; the overall heating power was determined comprehensively by the two sides, so there may exist optimal concentrations with the highest heating power. Furthermore, possible interpretations for the monotonicity in the influence of ϕ on OTT are as follows: in the range of 1%–3%, while the heating power was enhanced with increasing ϕ , the decreasing injection volume resulted in a significant increase in the thermally conductive gap between magnetic fluid and the tumor edge. It is highly likely that the reduced heat conduction flux outweighed the enhanced heat production, which leads to increasing OTT; with respect to ϕ higher than 3%, both the heating power and heat conduction flux was decreased with increasing ϕ , so the OTT was increased. Fig. 6B presents the scatter plot of the OTT under different tumor radii and MNP dose with H0 = 10 kA/m, f = 400 kHz, R = 10 nm, ϕ = 5%, and the linear relationships between the OTT and tumor radius, MNP dose w were fitted. As shown in the figure, the OTT decreased by about 10 s as the MNP dose increased by 1 mg/g, and it decreased from 138 s to 85 s as the MNP dose increased from 5 mg/g to 10 mg/g. Clearly, increasing the nanoparticle dose produced only a slight decrease in the OTT, so a lower nanoparticle dose may be preferred to

increase in R by 1 nm in the range of 8–10 nm. Therefore, the appropriate magnetite nanoparticles radius is in the range of 8–10 nm for the purpose of shortening the treatment time. In contrast, the OTT was positively correlated with the volume fraction, and it was increased by 3–15 s for the increase in ϕ by 1%. Since the volume fraction did not have a considerable impact on the OTT, the volume fraction in the range of 5%–10% may be preferred considering the limitations in injection capacity for deep tumors, and the OTT decreased by 3–8 s as ϕ decreased by 1% within the recommended range. According to Equations (4)–(9), it can be deduced that the heating power of magnetic fluid increases monotonously with particle concentration, and the OTT should have decreased with increasing concentration. In this case, we further researched the effect of ϕ on the heating power. Fig. 7A shows the temperature rise curves of the magnetic fluid center for different volume fractions with H0 = 10 kA/m, f = 400 kHz, w = 5 mg, R = 9 nm. The temperature rise rate initially increased with ϕ , and attained a maximum at the optimal concentration and then decreased. The figure also shows that the magnetic fluid temperature reached a steady state after 1500 s. Furthermore, the steady temperature of magnetic fluid was adopted as an assessment for heating power, and the variation of the steady temperature vs. ϕ for different particle sizes was depicted in Fig. 7B. It can be seen that the heating power is nonmonotonic with volume fraction with an optimal concentration of 3%. In my view, possible explanations are as follows: as the particle

Fig. 5. Changes in the OTT as a function of the magnetic field intensity H0 and frequency f with R = 10 nm, ϕ = 5%, w = 5 mg/g and a tumor radius of 2 cm. (A) is the OTT vs. H0 in the range of 1–15 kA/m at f = 400 kHz, and the magnified view in the range of 4–15 kA/m is shown separately for highlighting detailed changes; (B) is the OTT vs. f in the range of 50–900 kHz with H0 = 10 kA/m. 1036

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

Fig. 6. The dependence of OTT on the nanoparticles radius R, volume fraction of MNPs ϕ , injection dose w and tumor radius with H0 = 10 kA/m, f = 400 kHz. (A) is the OTT vs. R in the range 1–10 nm, and vs. ϕ in the range of 1–10%; (B) is the OTT vs. w in the range of 5–10 mg/g, and vs. tumor radius in the range 1–5 cm.

Fig. 7. The temperature rise curves of the magnetic fluid center and the relationships between the steady temperature and the particle concentration with H0 = 10 kA/m, f = 400 kHz, w = 5 mg/g (A) is the temperature rise curves of the magnetic fluid center for different volume fractions with R = 9 nm; (B) is the relationships between the steady temperature of magnetic fluid and the volume fraction for different particle sizes.

separately. It can be seen from Fig. 8A that increasing the H0 has a more prominent effect on the reduction of OTT, instead of f. Although the OTT decreased monotonically with advancing magnetic parameters, it is impracticable to simultaneously improve H0 and f due to the technical problems of the magnetic hyperthermia device. Consequently, a combination of higher H0 (8–11 kA/m) and lower f (200–300 kHz) is preferred to reduce the time and equipment costs. The combined effect of R and ϕ on the OTT is shown in Fig. 8B, and the effect of particle size was much greater than volume concentration. Taking the time cost and

minimize the possible toxicity of nanoparticles to normal cells. Additionally, the OTT increased by 42 s as the tumor radius increased by 1 cm, and it was increased from 81 s to 250 s as tumor radius increased from 1 cm to 5 cm. While the preferable treatment parameters have been proposed through the univariate analysis, the comprehensive impact of multidimensional parameters on the OTT were yet to be determined. To aid understanding, Fig. 8 was plotted, in which magnetic field parameters (H0 and f) and magnetic fluid properties (R and ϕ ) were analyzed

Fig. 8. The multivariate analysis on the OTT. (A) is the combined effect of the magnetic field parameters on the OTT with ϕ = 5%, R = 10 nm, w = 5 mg/g; (B) is the combined effect of the magnetic fluid properties on the OTT with H0 = 10 kA/m, f = 400 kHz, w = 5 mg/g. 1037

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

injection difficulty into account, it is greatly encouraged to adopt the conjunction of higher R and ϕ . In the present simulation, the simplified MFH model neglected the organs, bones, vascular tissues surrounding the tumor, and the complex outer contour of the abdomen, which may affect the accuracy of the numerical results. Additionally, we did not investigate various magnetic fluid injection regimens, tumor shape and location, which may considerably affect the generalizability of the research results. Consequently, there are some limitations to the simulation results. Our group will further study the effects of above factors on the optimal treatment conditions based on a more accurate numerical model, to provide a more sufficient theoretical basis for clinical MFH trials.

11.034. [5] A.A. Petryk, A.J. Giustini, R.E. Gottesman, P.A. Kaufman, P.J. Hoopes, Magnetic nanoparticle hyperthermia enhancement of cisplatin chemotherapy cancer treatment, Int. J. Hyperth. Off. J. Eur. Soc. Hyperthermic Oncol. North Am. Hyperth. Gr. 29 (2013) 845–851, https://doi.org/10.3109/02656736.2013.825014. [6] M.H. Klaus, R. Ronny, S. Regina, G. Uwe, W. Peter, T. Burghard, F. Annelie, V.D. Andreas, W. Norbert, F. Roland, Intracranial thermotherapy using magnetic nanoparticles combined with external beam radiotherapy: results of a feasibility study on patients with glioblastoma multiforme, J. Neuro Oncol. 81 (2007) 53–60, https://doi.org/10.1007/s11060-006-9195-0. [7] S. Roger, W.P. Mason, M.J. Bent Van Den, W. Michael, F. Barbara, M.J.B. Taphoorn, B. Karl, A.A. Brandes, M. Christine, B. Ulrich, Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma, Clin. Med. Insights Oncol. 9 (2005) 196–197, https://doi.org/10.1016/j.canrad.2005.05.001. [8] R. Stupp, M. Hegi Wp, M. Van-Den-Bent, M. Taphoorn, R. Janzer, S. Ludwin, A. Allgeier, B. Fisher, K. Belanger, P. Hau, Effects of radiotherapy with concomitant and adjuvant temozolomide versus radiotherapy alone on survival in glioblastoma in a randomised phase III study: 5-year analysis of the EORTC-NCIC trial, Lancet Oncol. 10 (2009) 434–435, https://doi.org/10.1016/S1470-2045(09)70025-7. [9] U. Gneveckow, A. Jordan, R. Scholz, V. Brüß, N. Waldöfner, J. Ricke, A. Feussner, B. Hildebrandt, B. Rau, P. Wust, Description and characterization of the novel hyperthermia- and thermoablation-system MFH 300F for clinical magnetic fluid hyperthermia, Med. Phys. 31 (2004) 1444–1451, https://doi.org/10.1118/1. 1748629. [10] Y.G. Lv, Z.S. Deng, J. Liu, 3-D numerical study on the induced heating effects of embedded micro/nanoparticles on human body subject to external medical electromagnetic field, IEEE Trans. NanoBioscience 4 (2005) 284–294, https://doi.org/ 10.1109/TNB.2005.859549. [11] S.L. Ho, L. Jian, W. Gong, W.N. Fu, Design and analysis of a novel targeted magnetic fluid hyperthermia system for tumor treatment, IEEE Trans. Magn. 48 (2012) 3262–3265, https://doi.org/10.1109/tmag.2012.2195161. [12] P. Di Barba, F. Dughiero, E. Sieni, Magnetic field synthesis in the design of inductors for magnetic fluid hyperthermia, IEEE Trans. Magn. 46 (2010) 2931–2934, https:// doi.org/10.1109/tmag.2010.2044769. [13] B.A. Evans, M.D. Bausch, K.D. Sienerth, M.J. Davern, Non-monotonicity in the influence of nanoparticle concentration on SAR in magnetic nanoparticle hyperthermia, J. Magn. Magn. Mater. 465 (2018) 559–565, https://doi.org/10.1016/ j.jmmm.2018.06.051. [14] B.B. Lahiri, T. Muthukumaran, J. Philip, Magnetic hyperthermia in phosphate coated iron oxide nanofluids, J. Magn. Magn. Mater. 407 (2016), https://doi.org/ 10.1016/j.jmmm.2016.01.044 S0304885316300440. [15] S. Hatamie, B. Parseh, M.M. Ahadian, F. Naghdabadi, R. Saber, M. Soleimani, Heat transfer of PEGylated cobalt ferrite nanofluids for magnetic fluid hyperthermia therapy: in vitro cellular study, J. Magn. Magn. Mater. 462 (2018), https://doi.org/ 10.1016/j.jmmm.2018.05.020 S0304885317331050. [16] P.T. Phong, L.H. Nguyen, D.H. Manh, I.J. Lee, N.X. Phuc, Computer simulations of contributions of Néel and Brown relaxation to specific loss power of magnetic fluids in hyperthermia, J. Electron. Mater. 46 (2017) 2393–2405, https://doi.org/10. 1007/s11664-017-5302-6. [17] A. Candeo, F. Dughiero, Numerical FEM models for the planning of magnetic induction hyperthermia treatments with nanoparticles, IEEE Trans. Magn. 45 (2009) 1658–1661, https://doi.org/10.1109/tmag.2009.2012769. [18] L. Wu, J. Cheng, W. Liu, X. Chen, Numerical analysis of electromagnetically induced heating and bioheat transfer for magnetic fluid hyperthermia, Magn. IEEE Trans. 51 (2015) 1–4, https://doi.org/10.1109/tmag.2014.2358268. [19] Y. Tang, R.C.C. Flesch, T. Jin, Numerical analysis of temperature field improvement with nanoparticles designed to achieve critical power dissipation in magnetic hyperthermia, J. Appl. Phys. 122 (2017) 1172–1653, https://doi.org/10.1063/1. 4994309. [20] A.H. Lu, E.L. Salabas, F. Schüth, Magnetic nanoparticles: synthesis, protection, functionalization, and application, Angew. Chem. Int. Ed. 46 (2010) 1222–1244, https://doi.org/10.1002/anie.200602866. [21] G. Bellizzi, O.M. Bucci, Magnetic nanoparticle hyperthermia, in: L. Crocco, I. Karanasiou, M. James, R. Conceição (Eds.), Emerg. Electromagn. Technol. Brain Dis. Diagnostics, Monit. Ther. Springer, Cham, 2018, pp. 129–191 https://doi.org/ 10.1007/978-3-319-75007-1_6. [22] Ö. Çelik, T. Fırat, Synthesis of FeCo magnetic nanoalloys and investigation of heating properties for magnetic fluid hyperthermia, J. Magn. Magn. Mater. 456 (2018) 11–16, https://doi.org/10.1016/j.jmmm.2018.01.090. [23] J. Beik, Z. Abed, F.S. Ghoreishi, S. Hosseini-Nami, S. Mehrzadi, A. Shakeri-Zadeh, S.K. Kamrava, Nanotechnology in hyperthermia cancer therapy: from fundamental principles to advanced applications, J. Control. Release 235 (2016) 205–221, https://doi.org/10.1016/j.jconrel.2016.05.062. [24] S. Laurent, S. Dutz, U.O. Häfeli, M. Mahmoudi, Magnetic fluid hyperthermia: focus on superparamagnetic iron oxide nanoparticles, Adv. Colloid Interface Sci. 166 (2011) 8–23, https://doi.org/10.1016/j.cis.2011.04.003. [25] K. Yue, C. Yu, Q. Lei, Y. Luo, X. Zhang, Numerical simulation of effect of vessel bifurcation on heat transfer in the magnetic fluid hyperthermia, Appl. Therm. Eng. 69 (2014) 11–18, https://doi.org/10.1016/j.applthermaleng.2014.04.035. [26] M. Pavel, A. Stancu, Ferromagnetic nanoparticles dose based on tumor size in magnetic fluid hyperthermia cancer therapy, IEEE Trans. Magn. 45 (2009) 5251–5254, https://doi.org/10.1109/TMAG.2009.2031076. [27] H.G. Bagaria, D.T. Johnson, Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment, Int. J. Hyperth. 21 (2005) 57–75, https://doi.org/10.1080/02656730410001726956. [28] M. Lahonian, A.A. Golneshan, Numerical study of temperature distribution in a

4. Conclusions In this study, a multiphysics coupling model of MFH was established and verified by comparing the numerical and experimental results for the heating curves of magnetic fluid. The OTT was obtained through the integral analysis of damaged tissue, and the preferable treatment conditions were deduced from the ingenious union of univariate and multivariate analysis. To achieve cost-effective therapies under moderate treatment conditions, the preferable ranges of external magnetic field intensity and frequency, MNP radius and volume fraction are 3–11 kA/m, 200–500 kHz, 8–10 nm, and 5%–10%, respectively. The multivariate analysis encourages adoption of the combination of higher H0 (8–11 kA/m) and lower f (200–300 kHz), the conjunction of higher R and ϕ . In addition, our results presented the nonmonotonicity in the influence of ϕ on the heating power of MNPs with an optimal concentration of 3%. Moreover, the OTT increased by about 42 s as the tumor radius increased by 1 cm and decreased by 10 s for the increase in MNP dose per gram of tumor by 1 mg. Since increasing the MNP dose produced a slight decrease in the OTT, a lower MNP dose may be preferred to minimize the possible toxicity of the nanoparticles to normal cells. Even more importantly, there was a slight thermal damage to normal tissues, except of the inevitable overheating of normal cells on the border of the tumor. In conclusion, MFH can provide an excellent therapeutic effect for deep tumors, based on the main advantages of high transparency and superior heating capability. Declarations of interest None. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgment We would like to thank Elsevier (webshop.elsevier.com) for providing linguistic assistance during the preparation of this manuscript. References [1] A. Jordan, P. Wust, H. Fähling, W. John, A. Hinz, R. Felix, Inductive heating of ferrimagnetic particles and magnetic fluids: physical evaluation of their potential for hyperthermia, Int. J. Hyperth. 9 (1993) 51–68, https://doi.org/10.3109/ 02656739309061478. [2] M.W. Dewhirst, B.L. Viglianti, M. Lora-Michiels, M. Hanson, P.J. Hoopes, Basic principles of thermal dosimetry and thermal thresholds for tissue damage from hyperthermia, Int. J. Hyperth. 19 (2003) 267–294, https://doi.org/10.1080/ 0265673031000119006. [3] O.O. Ahsen, U. Yilmaz, M.D. Aksoy, Heating of magnetic fluid systems driven by circularly polarized magnetic field, J. Magn. Magn. Mater. 322 (2010) 3053–3059, https://doi.org/10.1016/j.jmmm.2010.05.028. [4] M. Beković, M. Trlep, M. Jesenik, V. Goričan, A. Hamler, An experimental study of magnetic-field and temperature dependence on magnetic fluid's heating power, J. Magn. Magn. Mater. 331 (2013) 264–268, https://doi.org/10.1016/j.jmmm.2012.

1038

Current Applied Physics 19 (2019) 1031–1039

J. Li, et al.

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36] [37]

[38]

spherical tissue in magnetic fluid hyperthermia using lattice Boltzmann method, IEEE Trans. NanoBioscience 10 (2011) 262–268, https://doi.org/10.1109/TNB. 2011.2177100. M. Salloum, R. Ma, L. Zhu, Enhancement in treatment planning for magnetic nanoparticle hyperthermia: optimization of the heat absorption pattern, Int. J. Hyperth. Off. J. Eur. Soc. Hyperthermic Oncol. North Am. Hyperth. Gr. 25 (2009) 309, https://doi.org/10.1080/02656730902803118. M. Salloum, R. Ma D, L. Zhu, Controlling nanoparticle delivery in magnetic nanoparticle hyperthermia for cancer treatment: experimental study in agarose gel, Int. J. Hyperth. Off. J. Eur. Soc. Hyperthermic Oncol. North Am. Hyperth. Gr. 24 (2008) 337, https://doi.org/10.1080/02656730801907937. Q.A. Pankhurst, J. Connolly, S.K. Jones, J. Dobson, Applications of magnetic nanoparticles in biomedicine, J.Phys.d Appl.Phys. 36 (15) (2003) R167–R181, https://doi.org/10.1088/0022-3727/36/13/201. P.A. Hasgall, F. Gennaro, C. Baumgartner, E. Neufeld, M.C. Gosselin, D. Payne, A. Klingenböck, N. Kuster, ITIS Database for thermal and electromagnetic parameters of biological tissues, Version 2.5, 2014. http://www.itis.ethz.ch/database. C. Gabriel, S. Gabriel, E. Corthout, The dielectric properties of biological tissues: I. Literature survey, Phys. Med. Biol. 41 (1996) 2231, https://doi.org/10.1088/00319155/41/11/001. H.H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm. 1948, J. Appl. Physiol. 85 (1998) 5–34, https://doi.org/10.1152/ jappl.1998.85.1.5. R.E. Rosensweig, Heating magnetic fluid with alternating magnetic field, J. Magn. Magn. Mater. 252 (2002) 370–374, https://doi.org/10.1016/s0304-8853(02) 00706-0. G. Nedelcu, Magnetic nanoparticles impact on tumoral cells in the treatment by magnetic fluid hyperthermia, Dig, J. Nanomater. Biostructures. 3 (2008) 103–107. R. Hergt, S. Dutz, M. Röder, Effects of size distribution on hysteresis losses of magnetic nanoparticles for hyperthermia, J. Phys. Condens. Matter 20 (2008) 385214, https://doi.org/10.1088/0953-8984/20/38/385214. S. Maenosono, S. Saita, Theoretical assessment of FePt nanoparticles as heating

[39]

[40] [41]

[42]

[43]

[44]

[45]

[46]

[47]

1039

elements for magnetic hyperthermia, IEEE Trans. Magn. 42 (2006) 1638–1642, https://doi.org/10.1109/tmag.2006.872198. R. Hergt, S. Dutz, M. Zeisberger, Validity limits of the Néel relaxation model of magnetic nanoparticles for hyperthermia, Nanotechnology 21 (2010) 15706, https://doi.org/10.1088/0957-4484/21/1/015706. G.F.G. Grazu V, M.R. Ibarra, Magnetic nanoparticles for cancer therapy, Curr. Nanosci. 4 (2008) 1–16, https://doi.org/10.2174/157341308783591861. R. Hergt, S. Dutz, Magnetic particle hyperthermia—biophysical limitations of a visionary tumour therapy, J. Magn. Magn. Mater. 311 (2007) 187–192, https://doi. org/10.1016/j.jmmm.2006.10.1156. M. Ning, M. Song, D. Pan, S. Deng, Computational fluid dynamics analysis of convective heat transfer coefficients for a sleeping human body, Appl. Therm. Eng. 117 (2017) 385–396, https://doi.org/10.1016/j.applthermaleng.2017.02.012. S.A. Sapareto, W.C. Dewey, Thermal dose determination in cancer therapy, Int. J. Radiat. Oncol. Biol. Phys. 10 (1984) 787–800, https://doi.org/10.1016/03603016(84)90379-1. H. Rempp, J. Roland, A. Buck, A. Kickhefel, C.D. Claussen, P.L. Pereira, F. Schick, S. Clasen, Threshold-based prediction of the coagulation zone in sequential temperature mapping in MR-guided radiofrequency ablation of liver tumours, Eur. Radiol. 22 (2012) 1091–1100, https://doi.org/10.1007/s00330-011-2335-8. P.J. Hoopes, K.A. Wishnow, L.R. Bartholomew, E. Jonsson, J.C. Williams, K.L. Moodie, T.Z. Wong, R.D. Harris, T.P. Ryan, B. Trembly, B.T. Stuart, Evaluation and comparison of five experimental BPH/prostate cancer treatment modalities, Crit. Rev. Collect. (2017) 102970K, https://doi.org/10.1117/12.375221. G.C. Van Rhoon, T. Samaras, P.S. Yarmolenko, M.W. Dewhirst, E. Neufeld, N. Kuster, CEM43°C thermal dose thresholds: a potential guide for magnetic resonance radiofrequency exposure levels? Eur. Radiol. 23 (2013) 2215–2227, https://doi.org/10.1007/s00330-013-2825-y. P.S. Yarmolenko, E.J. Moon, C. Landon, A. Manzoor, D.W. Hochman, B.L. Viglianti, M.W. Dewhirst, Thresholds for thermal damage to normal tissues: an update, Int. J. Hyperth. Off. J. Eur. Soc. Hyperthermic Oncol. North Am. Hyperth. Gr. 27 (2011) 320–343, https://doi.org/10.3109/02656736.2010.534527.