Characterization of for brain treatment using magneto plasmonic approach Tina Seyedjamali1† , Mohamadreza Kazem Farahzadi2, and Hossein Arabi3

1Department of Physics, Iran University of Science and Technology, Narmak, Tehran 16846, Iran 2Department of Radiation Medical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 3Division of Nuclear Medicine and Molecular Imaging, Department of Medical Imaging, Geneva University Hospital, CH-1211 Geneva 4, Switzerland

ABSTRACT This study investigates the treatment of brain cancer by the magnetic approach and nanoparticles including 퐹푒푂 core with gold, silver alloy shell, and 푀표푆 coating. Optical properties of these nanoparticles within the tumor, including the extinction coefficient and surface plasmon peak (SPR) as a function of size, structure, different compositions, and thickness are also investigated using the effective medium theory. Moreover, the impact of temperature distribution was assessed through the analytical modeling of alternating current (AC) magnetic field. The results of this study indicated that nanoparticles with a compound of 퐹푒푂 −

퐴푢.퐴푔.@푀표푆 and a thickness of 3 nm of gold-silver alloy and 3 layers of 푀표푆 have the best coefficient of extinction and SPR in the biological window. The gold-silver alloy improved the extinction coefficient and, at the same time, prevented the accumulation of . Since the gold-silver alloy alone cannot function within the range of biological windows, 푀표푆 was used, which increased the extinction efficiency at higher wavelengths. Examination of the temperature distribution in the tumor for the proposed alloy compound indicated that after a short time from the start of irradiation, the tumor temperature reaches 45 ° C. Also, the temperature distribution within the tumor tissue reached its maximum value at the center of the tumor and decreased dramatically as getting away from the center. The use of magnetic hyperthermia enabled localized delivery of therapeutic dose to malignant brain tumors; hence, exhibiting superior performance/efficiency over the photothermal method.

KEYWORDS: Magnetic Hyperthermia Treatment (MHT), Brain cancer, Magnetic Nanoparticles, Surface Plasmon Resonance (SPR), Extinction coefficient

1. INTRODUCTION

Since cancer cells are more sensitive to temperature, recent therapeutic initiatives have mostly relied on the heating characteristics of the tumor cells. Although the heating techniques alone are not sufficient, they could effectively destroy cancerous tissues, and hence can be considered as a complementary treatment [1, 2]. Hyperthermia is known as one of the minimally invasive based on the conversion of energy sorces including microwaves, radio waves and ultrasound into heat. In this method, nanoparticles with high energy absorption and high light-to-heat conversion efficiency are used in the near-infrared (NIR) region [3]. In the hyperthermia technique, the temperature within the tumor commonly ranges from 41 to 45 ° C. S.K. Sharma et al. showed that when the temperature rises above 46 ° C, which is known as thermal erosion, it can effectively result in cell necrosis [4-6] . In the laser interstitial thermal (LITT) technique, proposed by Skandalaki et al., surgery is required to create a field to place the cavity in the tissue, wherein the creation of cavities or invasive operations may adversely affect healthy tissues [7]. On the other hand, Yue He et al. have shown that photothermal therapy cannot treat deep tumors such as brain lesions, since the skull does not allow the emitted wavelength to pass through; and thus, the heat delivery cannot be effectively controlled [8].

To address this limitation, magnetic hyperthermia was proposed for deep lesions [9, 10]. In this technique, heat is generated by applying an alternating magnetic field to the nanoparticles within the target tissue [11]. The choice of nanoparticles depends on the ranges/levels of temperature, the efficiency of heat production, duration of treatment, toxicity, solubility in biofuels fluids, damage to the healthy tissue, and efficiency in destroying the cancerous tissue. The favorable nanoparticles should have high coefficients of extinction and adsorption in the range of biological windows (680- 1400 nm) in the target tissue [12-14]. Moreover, the delivery of heat to the target tissue would also be affected by the environment, size, geometry, and structure of nanoparticles [15, 16].

Heat generation properties of different types of nanoparticles have been studied for having efficient hyperthermia treatment. In this regard, bimetallic nanoparticles have favorable optical properties (better heat generation properties) than single metal nanoparticles [17]. Through modifying the nanostructure composition, the surface plasmon resonance (SPR) and the extinction coefficient can be adjusted within the desired window. Gold is biologically compatible as it is a noble metal, which is thermally and chemically stable [15, 18, 19]. Despite these good properties of gold for heat treatment, pure gold would result in a poor extinction rate. Silver nanoparticles are the other category which have been widely used in medical trials due to their antibiotic potential, but when they are utilized alone, the Ag + produced through oxidation could hinder the process of heat production [20, 21]. It should also be noted that silver alone is not biocompatible. Therefore, in recent years, the use of two-dimensional (very thin) materials, especially graphene and Transition Metal Dichalcogenides (TMDC) for heat treatment has received much attention [22]. Of the four commonly used TMDC (namely 푀표푆, 푊푆, 푀표푆푒,

푊푆푒), only 푀표푆 is biodegradable, and it is eliminated from the body within approximately one month [23, 24].

Wang et al. utilized graphene oxide to treat brain cancer in comparison with 푀표푆, wherein 푀표푆 nanomaterials exhibited about 7.8 times more energy absorption (i.e., graphene oxide led to a much higher coefficient of extinction than graphene). Moreover, 푀표푆 can be heated rapidly under NIR laser radiation. As a result, high-efficiency 푀표푆 nanomaterials have gained popularity owing to their effective response to NIR light radiation in cancer treatment [14, 23, 25]. Recently, magnetic nanoparticles have been considered as an important agent in hyperthermia. Employing these magnetic nanoparticles carriers would increase the penetration/absorption of drug in the cancer cell membrane. Hence, they can prevent systematic administration and side effects, and increase the therapeutic effect of anti-cancer drugs [26-29]. Iron oxide has been extensively studied because of its fascinating properties such as easy synthesizing process, low cost, biocompatibility, depth of penetration and most importantly, superparamagnetism, compared to other materia [30, 31]. Although iron oxide nanoparticles are biocompatible, they are usually coated with biocompatible polymers to prevent oxidation for hyperthermia treatment [32, 33]. The most common form of iron oxide is 퐹푒푂 (combination of divalent and trivalent iron oxides) [34].

In this paper, relying on effective medium theory, bio-heat and magnetic equations were employed to investigate the extinction coefficients and SPR as a function of core radius, the number of layers, environment effect, and the percentage of alloy compounds for 퐹푒푂 − 퐴푢 − 퐴푔@푀표푆 structure.

2. MATERIALS AND METHODS

In this section, we examine the optical and thermal properties of the 퐹푒푂,퐴푢 −

퐴푔@푀표푆 structure Figure 1. First, we relied on the dedicated equations to model the effect of the number of layers on the optical properties of the nanoparticle, then we examined the different percentages of the alloy components and calculated the extinction efficiency and SPR. In the third section, regarding the magnetic nanoparticles, we examined the governing equations of magnetism; and finally, we investigated the bio-heat equations and temperature distribution. This study relied on the effective medium theory, which is based on the wighted average theory, Bruggeman's theory, and Maxwell Garnet's theory [35-38].

Figure 1: Schematic of nanoparticle with 퐹푒푂 core and 퐴푢 − 퐴푔@푀표푆 shell.

2.1 Effective medium theory for 푴풐푺ퟐ coated with Au-Ag In this section, we employed the governing equations for the number of layers using effective medium theory. Maxwell-Garnet's theory is based on the Clausius-Mossotti relation, which considers the correlation between polarization 훼 and the dielectric phenomenon [39]. In this regard, it is supposed that several layers of different nanoshells are stacked on top of each other

[39]. As shown in Figure 1, there is an Au-Ag spherical nanoshell with an inner radius of 푟 and a thickness of 푡 surrounded by 푀표푆 with a thickness of 푡, while the core of this nanoparticle is of 퐹푒푂 (15,20 and 25 nm). The refractive indices of the healthy tissue and the tumor are 1.82 and 2.12, respectively. 휀(휔), 휀(휔) and 푖 = 1,2,…, denote the dielectric function of the core and the shell, respectively. The dielectric performance of the target external environment is frequency- dependent, which is equal to 휀(휔) [40]. According to Maxwell-Garnet’s theory, the dielectric effect between the core and the first shell is formulated as follows [40]:

휀(1 + 2푓) + 휀(2 − 2푓) (1) 휀, = 휀 휀(2 + 푓) + 휀(1 − 푓) Where the volume fraction of the new layer is obtained from: 푓 = (푟⁄푟) (2) and for other layers, Eq. (3) could be derived from Eqs. (2) and (3)

휀,(1 + 2푓) + 휀(2 − 2푓) (3) 휀, = 휀 휀(2 + 푓) + 휀,(1 − 푓)

The radius of the new layers is calculated as follows:

푟 = 푟 + 푡 (4)

Here, 푡, 푟 indicate the radius of the layer and the thickness of the lower shell, respectively. Then, for calculating the efficiency of extinction, scattering, and absorption, Eq. (5) was used [41]: 휌 휌 (5) 푄 = 4휌퐼푚 훼 + 훽 + 휀 − 1 12 30

8 휌 휌 푄 = 휌 |훼| + |훽| + 휀 −1 3 240 900

푄 = 푄 − 푄

Wherein 휌 = 푘푟 , 푘 =( )휀 corresponds to the wavenumber of the incoming light (α and β). The coefficients related to dielectric calculations are obtained through the following equations. [40]:

휀푒푓푓,푛 − 휀푚 α = (6) 휀푒푓푓,푛 + 2휀푚

휀푒푓푓,푛 − 휀푚 훽 = (7) 3 휀푒푓푓,푛 + 2 휀푚

Here, 휀 is the dielectric function for the external medium.

2.2 Effective medium theory for 푴풐푺ퟐ coated Au-Ag for different volume fraction Relying on the weighted average theory, the effective dielectric functions can be calculated for silver- and gold-based alloy nanoparticles using Eq. (8). 푎 shows the volume fraction of gold that

,occupies the environment. 휀, 휀 = 3.7، 휀 = 9.8 indicate the dielectric coefficients of alloy gold, and silver, respectively [42]: 휀(휔) = (1 − 푎)휀(휔) + 푎휀(휔) (8)

In Bruggeman's theory, several different materials can be used to create a heterogeneous environment. In this case, materials have the same contribution and the effective dielectric performance in Equation (9) :

휀 − 휀 휀 − 휀 (9) 푓 + (1 − 푓) = 0 휀 + 2휀 휀 + 2휀

Wherein, the dielectric function of the shell and the core are 휀 and 휀, respectively. 푓 is the occupied fraction of the nucleus, and 휀 denotes the effective dielectric coefficient.

2.3 Magnetic equations When an alternating magnetic field is used, the magnetic nanoparticles injected into the tumor generate heat in the radial direction. The partial differential equations of heat generation/transmission within the interface material between the tumor and the surrounding tissue are [43]: " 푃 = 휋 + 휇푋 퐻 푓 (10)

휙 푋" = 푋 (11) 1 + (휙)

휇푀 푣 푋 = 휙 = 푓휏 (12) 푘푇

The predominant heat generation mechanisms for magnetic nanoparticles which are exposed to an AC magnetic field are Neel and Brown relaxation [44]. Neel relaxation occurs due to the rotation of magnetic moments inside the nanoparticle while the particle is stationary. Brown relaxation results from the general rotation of particles. These mechanisms lead to the production of volumetric heat induced by the electromagnetic field.

Table 1. Physical parameters of tumor and brain tissue [44-46]. Parameter Value Unit 푔 휌 1.0355 푚. 푙 푔 휌 1.05 푚. 푙 퐶 3680 푘푗 푘푔. 퐾 퐶 3636 푘푗 푘푔. 퐾 푤 푘 0.56 푚. 퐾 푤 푘 0.051 푚. 퐾

푟 2 푐푚

푟 7.4 푐푚

푇 310.15 퐾 푇 318 퐾 푤 0.0005 푚푙 푚푙. 푠 푤 0.013289 푚푙 푚푙. 푠

푟 20 푛푚

2.4 Laser

When the nanoparticles inside the tissue are exposed to laser radiation, the absorbed energy would excite the surface electrons, subsequently, stimulate the surface plasmons, and generate heat. Here, to estimate the temperature distribution within the tissue, at first, the absorption coefficient was calculated using Eq. (13):

퐾 = 휋푟 푄푁 (13)

푁 is the density of nanoparticles inside the tumor, and the amount of uptake inside the tissue is calculated using Eq. (14).

푑퐼 (14) 푄 = − = (푘 + 푘 )퐼 푒() 푑푟 퐼is the intensity of the laser, 푘 and 푘 are the absorption coefficients of the nanoparticles and the cancerous tissue, respectively.

2.5 Bioheat As cancer cells die, the proteins and biological structures decay, and the blood pressure in the tumors may drop, while at the same time, the healthy tissue would not change dramatically. Penne's bio-heat equation is thus used to model the process of heat dissipation within a tumor. Nanoparticles are considered a source of point heat. In 1948, Penne developed the equation for heat transfer in biological tissues, which includes a term for heat transfer due to blood perfusion [47, 48].This model is commonly used for tissues with small blood vessels.

The general form of the bio-heat equations are presented in Eq. (15):

(15) 휕푇 푘∇푇 + 휌 푐 휔 (푇 − 푇) + 푄 + 푄 = 휌푐 푥 ∈ Ω 휕푡

The boundary conditions due to continuous temperature and heat flux at the tumor boundary are:

푇(푅, 푡) = 푇(푅, 푡) (16) 휕푇 (푅, 푡) 휕푇 (푟 , 푡) (17) 휎 = 휎 휕푟 휕푟

푇(0, 푡) = 푓푖푛푖푡푒 (18)

푇(푟, 0) = 푇(푟, 0) = 푇 (19) Wherein, ∇ is the Laplace operator, 푡 is time, 퐾 is thermal conductivity, and 퐶 is the specific heat.

푄푎푛푑 푄 indicate the generators of metabolic heat and the internal heat generated by external sources, respectively. The first part (푘∇푇) is the heat transfer in the tumor due to the temperature gradient, and the second part of Eq. (15) is the heat transfer between the tissue and the bloodstream. The third and last parts are related to intra-tissue heat, which results from tissue metabolism and external heat source. The term 휌푐 refers to the changes of temperature flux [47]. 푇 and 푇 denote the temperature of the tumor and the surrounding tissues, respectively [44, 47].

Arrhenius Equation: At all stages of treatment, it is vital to spare healthy tissues from unnecessary toxicity. In this regard, we will calculate the temperature distribution in the surrounding tissues. To model this, the equations have to include the temperature distribution in these two areas. To obtain the treatment effect, the degree of damage to the tumor tissue should be calculated as a function of the laser irradiation time t and the distance from the center of the tumor 푟 (Eq. (20)):

푃 = 1 − exp (−Ω(푟, 푡)) (20)

Ω(푟, 푡) is thermal damage to the tumor tissue according to the Arrhenius Equation [49].

푡 −퐸푎 (21) Ω(r, t) = 퐴푓 exp ( )푑휏 0 푅푇(푟, 휏)

Here, 퐴, 퐸 and 푅 are Arrhenius constant, activation energy, and the global gas constant, respectively.

3. RESULTS

Effect of number of layers and core radius on the extinction peak and SPR

Figure 2. Effect of the number of layers and different core radius on extinction coefficient and SPR, N = 0 to model the absence of 푀표푆 layer. The intensity of the extinction peaks decreases when the number of layers increases. The shells radius are obtained using Equation 푟 , = 푟 + 푡 , which depends first on the core radius and then on the radius of the underlying layers and their thickness. On the other hand, the plasmonic peak will have the effect of redshift wavelength. If N = 0 (no layer), the peak of extinction will be at its maximum value, representing the peak of surface plasmon intensification. The cause of this phenomenon is the excitation of free electrons on the alloy surface . As the number of 푀표푆 layers increases, the SPR peak will move towards the redshift wavelengths; hence, the intensity of the extinction peak will decrease. This is because as the number of layers increases, fewer electrons participate in the surface plasmon resonance reaction, resulting in fewer oscillating electrons and ultimately, reducing the extinction coefficient. As the number of shell layers increases, the effect of the phase delay will increase as well, but the hybridization power will decrease so that the peaks will move to the redshift wavelength. In this light, as the number of 푀표푆 layers increases, the temperature will increase significantly. Moreover, by changing the nanoparticle radius, the number of participating electrons will change, which in turn causes the displacement of the extinction, plasmonic peaks, and the creation of the dominant phase delay effect.

Effect of gold and silver alloy thickness on plasmonic peaks for hyperthermia application The relationship between polarization and dielectric performance was investigated using the

Clausius-Mossoti relationship,. A spherical nanotube with an inner radius of 푟 and a thickness of

푡 was surrounded by a 푀표푆 shell with a thickness of 푡 , and was modeled as depicted in Figure 1. Figure 3 shows that as the thickness of the gold shell decreases, the power of composition will decrease, while the effect of the phase delay will prevail and lead to the shift of the peak towards the redshift. In addition, as the thickness of our shell decreases, the free electrons participating in the SPR oscillations decrease, which reduces the height of our annihilation peak. This observation is due to the decrease in plasmon hybridization power and an increase in the optical phase delay effect. Figure 3 illustrates the different thicknesses of gold and silver alloy nanoshells. Although the intensity of the SPR peak is stronger for the nanospheres with the larger thickness of gold, it resides in the blue shift wavelength range and outside the biological window range. As a result, by adjusting the thickness of the alloy nanoshell, the desired peak can be easily placed in the biological windows.

Figure 3. Investigation of the effect of 퐴푢 − 퐴푔 alloy thickness on the coefficient of extinction and SPR

Effect of gold and silver alloy percentage on plasmonic peaks for hyperthermia application

The effect of alloy percentage on plasmonic peaks can be investigated using Equation (8), Since it is possible to change the percentage of gold and silver during the experimental stages, it is necessary to check. According to Figure 4.a, as the percentage of gold increases, the extinction cross-section decreases, and the peak of the surface plasmon moves toward the red transition. In contrast, as the percentage of silver increases, this trend will be reversed. On the other hand, it should be noted that with an increase in the percentage of silver, the biocompatibility and stability of nanoparticles decrease. Silver alone can produce Ag + ions with a greater ionic radius than iron, and it can form a three-layer structure, reducing the extinction efficiency. Figure 4.b shows the effect of gold and silver alloy composition on SPR and extinction coefficient.

Figure 4. (a) Effect of gold and silver percentage on SPR peak and extinction coefficient, (b) Effect of alloy composition on extinction coefficient and SPR.

Effect of nanoparticle thickness and radius

Figure 5 illustrates the effect of internal radius and shell thickness on SPR locations Figure 5.a and the extinction efficiency for a specific wavelength related to the laser. According to Figure 5, as the nanoparticle thickness increases, the plasmon peak will move towards the blue shift wavelengths. This is because as the 푀표푆 shell thickness increases, the hybridization power decreases, and the phase delay effect prevails. Moreover, as the radius of the nanoparticles increases, the number of conductive electrons available to participate in the group oscillation reaction increases, leading to the production of plasmonic peaks in the redshift range.

Figure 5. (a) Effects of different thicknesses and radius on SPR, (b) effects of different thicknesses and radius on

extinction coefficient at 808 nm for the 퐹푒푂 − 퐴푢.퐴푔.@푀표푆 structure

Effect of magnetic field on tissue

The temperature distribution inside the brain tissue is calculated by the Penne's biothermal equation. This equation is used to predict heat loss within the tumor during heat generation through laser radiation and using mechanisms such as conductivity, convection, radiation, and metabolism. The bioheat transfer equation of Penne's in spherical coordinates for a tumor of radius R can be represented as Eq. (15). In this regard, using Eq. (15) and boundary conditions presented in Eqs. (16-19), we conclude that the temperature at the r = R boundary will be high due to tissue homeostasis. The thermal penetration of magnetic hyperthermia into the tumor is primarily modeled through the partial differential equation (PDE) by a heat source in spherical coordinates. The heat source depends on the power density, which in turn depends on the type and amount of nanoparticles used for the patient. Although the specific heat and density of the target tissue can be measured experimentally, it is more challenging to determine the heat conductivity. In this model, we observe that the produced heat inside the tumor would be transmitted to the surrounding healthy tissues. Since low toxicity to healthy tissues is a priority within treatment, the temperature of the surrounding healthy tissue will increase to an acceptable level in a short period of time. Figure 6.a shows a temperature increase for 15 seconds in the tumor tissue. Over time, the temperature will increase up to 45 ° C. By moving away from the tumor, the temperature will reach its normal state. Since in the magnetic hyperthermia treatment (MHT) technique, we can control the temperature in the required range, the temperature does not exceed the range limit. According to Figure 6.a, it can be seen that at the intervals of 2 cm and beyond, related to tissues, brain, CSF, Skull, and Scalp, the temperature is in its normal state and will not harm the patient and the healthy tissues.

Figure 6. (a) Temperature distribution in tumor and brain tissue as a function of time, distance, and temperature when using a magnetic field. (b) Investigation of temperature changes in terms of time and radial distance from tumor tissue.

In Figure 6.b, the induced temperature is investigated as a function of radius. As can be seen in this Figure, the tumor temperature rises rapidly within 0-15 seconds up to 42.5 ° C. Meanwhile, a temperature increase is also observed in the brain tissue up to 40 ° C, while for the CSF, Skull, and Scalp tissues, the amount of temperature increase can be ignored. In 30 seconds, the temperature of the tumor tissue would reach the maximum desired temperature, while the temperature of the brain tissue would stay around 41 ° C. Since the temperature of the target tissue does not exceed the desired range in the self-controlling magnetic hyperthermia, the maximum tolerable temperature for the brain tissue is about is 41 ° C. 4. DISCUSSION

The physical properties of 퐹푒푂 − 퐴푢.퐴푔.@푀표푆 nanoparticles for different Au-Ag and

푀표푆 shell thicknesses, different alloy compositions, and different refractive indices were theoretically investigated using effective medium theory with Penne's and Magnetic biothermal equations. In the LITT technique, a cavity must be created inside a part of the tissue, and the photothermal technique cannot be used for deep tissues such as the brain. Moreover, the temperature should not exceed 45 ° C; therefore, the MHT method was investigated. The motivation to concentrate on this compound is that pure gold nanoparticles have low thermal stability, and non-coated gold nanoparticles would have some limitations such as functionalization [15, 18]. Silver, also, is not stable despite its high dispersion efficiency [16, 20, 21]. Therefore, the composition of nanoparticles of noble metals has better optical properties and higher stability than the monometallic state, especially because coated nanoparticles induce less toxicity [15]. One of the benefits of using 퐹푒푂 over other magnetic materials is that iron oxide can penetrate deep tissues. On the other hand, 푀표푆 coating is more biocompatible than other two-dimensional materials such as graphene, and has a higher refractive index and subsequently higher heat generation efficiency. According to Figures 2, it can be observed that the dimensions, number of layers, and the surrounding environment have a significant effect on the extinction coefficient and SPR peak. It should be noted that the nanoparticles used in the treatment of tumors residing in the brain must have proper optical coefficients and size. Since high extinction coefficients will cause damage to healthy tissues, the nanoparticles must have optimal dimensions to be able to move through thin arterial vessels. According to Figure 2 and the structure of the brain, it can be seen that the best dimensions and number of layers were 20nm, and 3 layers of 푀표푆 coating. As shown in Figure 7, the refractive index of the environment can have a significant effect on the extinction coefficients and plasmonic peak. As the refractive index increases, the peaks will move toward the redshift because the optical response of different materials depends on the environment. According to Figure 7, the reason for selecting nanoparticles with a radius of 20 nm and 3 layers was to locate the peaks in the biological window range and the appropriate extinction coefficients in the tumor tissue.

Figure 7. Effect of refractive index on SPR peak and extinction coefficient for brain tissue and tumor. Since the laser used in the heating method is a diode laser with a range wavelength of 808nm, increasing the number of 푀표푆 layers would result in the production of peaks at higher wavelengths and better spectral overlap with the laser wavelength. This would ultimately lead to efficient heat production and an increase in temperature. In Figure 8, we investigated the coefficients of extinction, absorption, and scattering in tumor tissue with nanoparticles with a radius of 20 nm with 3 layers of 푀표푆. It was observed that the scattering in this condition was minimal while the maximum amount of absorption and extinction occurred. Moreover, the extinction rate in brain tissue with this structure had the lowest value compared to the other compounds.

Figure 8. Extinction, absorption, and scattering coefficients for a nanoparticle with a radius of 20 nm and 3 layers of 푀표푆. The maximum peak occurred in the second biological window (pink area) in the range of 1000-1400 nm. According to Figure 5, we found that by using a suitable structure, we can make nanoparticles with high absorption efficiency in biological windows while exhibiting less side effects, which will eventually lead to the application of low-power lasers with less unwanted damage to the healthy tissues. The investigation of the alloy coating thickness on the tumor tissue revealed that the best thickness for the alloy is 3nm since it leads to a favorable extinction coefficient and the peak in the redshift wavelength range for the tumor tissue. Figure 8 shows that the maximum value for extinction and absorption coefficients occurred with a refractive index of 2.12. On the other hand, the scattering coefficient can be ignored.

Since using only silver nanoparticles can be very toxic and pure gold nanoparticles would result in a low extinction rate and stability, different compounds for the nanoparticle should be examined.

The graph presented in Figure 4.b shows that 퐴푔0.75퐴푢0.25 compound would have relatively more significant plasmonic peaks in the biological windows.

According to Figure 5.a, the spectral regions located in the biological window have a suitable radius and thickness for being used in hyperthermia, because their peaks would occur in the range of biological windows. In Figure 5.b, a constant wavelength of 808 nm was set to determine the maximum extinction efficiency. In this case, more transparent areas indicate more efficient size and thickness, and subsequently higher extinction efficiency. Finally in Figure 6, through applying a magnetic field, the amount of possible damage to the tumor and healthy tissue was examined, which reached the desired temperature quickly, but according to the MHT technique, the temperature will not exceed the desired level. The results suggest that the strength of the magnetic field and the duration of treatment can be so severe that healthy tissue would also be damaged.

5. CONCLUSION

The results of this study showed that the most efficient structure is 퐹푒푂 − 퐴푢.퐴푔.@푀표푆.

퐹푒푂 magnetic nanoparticles were used to treat brain cancer using a magnetic field, wherein gold and silver alloy coatings were used to prevent oxidation, since gold alone does not have good stability, and silver alone is toxic. The combination of 퐴푢.퐴푔. has the highest coefficient of destruction and SPR in biological windows. 푀표푆was used as the final coating because it increased the body's stability and biological compatibility. The 3-layer coating of 푀표푆 would have the best extinction coefficient and SPR coefficient compared to other numbers of layers.

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