Investigation of physical properties of Fe3O4/Au-Ag@MoS2 nanoparticles on heat distribution in cancerous liver tissue

Liver cancer has significantly grown in recent years, and thus its mortality rate has also increased since its symptoms appear to be in malignant stages and the treatment path at this stage is extremely challenging. New therapies based on producing heat in cancerous tissues have opened up a new way to treat cancer. This study investigated the treatment of liver cancer by the magnetic hyperthermia approach and nanoparticles (NPs) such as iron oxide ( Fe3O4 ) core with gold (Au), silver (Ag) alloy shell, and molybdenum disulfide ( MoS2 ) coating. The optical properties of these NPs within the tumor, including the extinction coefficient and surface plasmon peak (SPR) as a function of size, structure, different compositions, and thickness, were also examined using the effective medium theory, followed by assessing the impact of temperature distribution through the analytical modeling of an alternating current magnetic field. The results demonstrated that NPs with a compound of Fe3O4−Au0.25Ag0.75@MoS2, a 3 nm thick cover of Au-Ag alloy, and two layers of MoS2 have the best coefficient of extinction and SPR in the biological window. The Au-Ag alloy improved the extinction coefficient and simultaneously prevented the accumulation of magnetic NPs. Considering that the Au-Ag alloy alone cannot function within the range of biological windows, MoS2 was used, which increased the extinction efficiency at higher wavelengths. The examination of the temperature distribution in the tumor for the proposed alloy compound indicated that after a short time from irradiation initiation, the tumor temperature reaches 45 °C. Further, the temperature distribution within the tumor tissue reached its maximum value at the center of the tumor and decreased dramatically while getting away from the center. Finally, the use of magnetic hyperthermia enabled localized delivery of therapeutic doses to malignant tumors, thereby representing superior performance and efficiency over the photothermal method.


Introduction
Since the symptoms of liver cancer appear late in patients, the disease detection/diagnosis is normally achieved in advanced stages, and surgery alone may not be sufficient. Although much progress has been made in treating liver cancer, patients with malignant liver cancer have always had high mortality rates. In this respect, exploring new treatments can significantly affect the efficient management of this cancer. Cancer treatment only encompassed radiotherapy, chemotherapy, and surgery methods in previous decades. Radiation therapy uses high-energy rays to kill cancer cells. Drawbacks of this treatment include damage to healthy tissue, perforation of the colon, infertility, and the possibility of secondary cancer [1,2]. The chemotherapy technique uses targeted substances; however, this method also has disadvantages as these carriers, though targeted, can also damage other healthy cells in the bone marrow, gastrointestinal tract, and hair follicles [2,3]. Finally, there are some limitations associated with the surgery treatment: the entire cancerous tissues cannot be removed depending on the tumors' location [2]. In this regard, hyperthermia is one of the recently employed complementary methods in cancer treatment.
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 insufficient, they could effectively destroy cancerous tissues. Thus, they can be considered a complementary treatment [4,5]. Hyperthermia is one of the minimally invasive therapies based on converting energy sources, 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 [6]. In the hyperthermia technique, the temperature within the tumor commonly ranges from 41 to 45°C. Sharma et al showed that when the temperature exceeds 46°C (i.e., thermal erosion), it can effectively result in cell necrosis [7][8][9]. In the laser interstitial thermal therapy (LITT) technique proposed by Skandalaki et al, surgery is performed by implanting a laser catheter in the tissue that can produce the required local heat after injection of nanoparticles and localization. Therefore, it is an invasive method and may adversely affect healthy tissues [10].
Photodynamic therapy (PDT) is a technique that uses a light-sensitive substance and a laser to stimulate material in the tumor to produce activated oxygen and cure liver cancer. However, Hong Zhu et al showed that it has drawbacks such as severe damage to surrounding tissues. Since light absorbers in this method may accumulate in healthy liver tissue more than cancerous tissue, it may cause damage to healthy tissue. On the other hand, a high wavelength and power laser beam should be used in this method because the liver organ is located deep in the abdomen (in addition to its large volume). Thus, it is likely to cause side effects and damage healthy tissues [11].
When using hyperthermia as a treatment for cancer, it must have very low toxicity and the ability to heat up and kill cancerous tissue topically [12,13]. In magnetic hyperthermia was proposed for deep lesions to address this limitation [14,15]. Magnetic hyperthermia treatment (MHT) is a treatment that has far fewer side effects than chemotherapy and radiotherapy and, unlike other cancer treatments, can activate the immune system [16]. Besides, the abundance of blood vessels in the liver causes rapid heat loss, thereby reducing damage to healthy liver tissue [11]. Inducing local heating can be accomplished using iron-based magnetic nanoparticles, which are extremely biocompatible [17,18]. This technique is minimally invasive and can deliver an adequate heat dose to the targeted region while avoiding injury to the healthy tissue located in the surrounding area. In this technique, heat is generated by applying an alternating magnetic field to the nanoparticles within the target tissue [19]. The choice of nanoparticles depends on the ranges/levels of temperature, heat production efficiency, treatment duration, 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 [20][21][22]. Moreover, the delivery of heat to the target tissue would also be affected by various factors such as size, geometry, environment, and structure of nanoparticles [23,24].
The mass oscillation of electronic charge density in metals causes localized surface plasmon resonance (LSPR), an electromagnetic state [25]. When plasmons are subjected to certain electromagnetic disturbances, the charge density may not be zero in some areas, resulting in the generation of a restoring force that induces an oscillating charge distribution [26,27]. Resonance occurs when the electromagnetic disturbance and plasma oscillation have the same frequency. Four factors affecting the oscillation frequency are electron mass, electron density, charge distribution size, and shape [23]. The surface plasmon resonance (SPR) or LSPR and the extinction coefficient can be adjusted within the desired window by modifying the nanostructure composition. Gold is biologically compatible as it is a noble metal that is thermally and chemically stable [23,28,29]. Despite these good properties of gold for heat treatment, pure gold would result in a poor extinction rate. Silver nanoparticles are the other nanoparticle category that has been widely used in medical trials regarding their antibiotic potential. However, when they are used alone, the Ag + produced through oxidation could hinder the heat production process [30,31]. It is of note that silver alone is not biocompatible. Therefore, bimetallic nanoparticles have favorable optical properties (better heat generation properties) than single metal nanoparticles [32]. 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 [33]. Of the four commonly used TMDCs (namely MoS , 2 WS , 2 MoSe , 2 WSe 2 ), only MoS 2 is biodegradable, and it is eliminated from the body within approximately one month [34,35].
Wang et al used graphene oxide to treat cancer and compared the results with those of MoS . 2 Based on the obtained results, MoS 2 nanomaterials exhibited about 7.8 times more energy absorption, as graphene oxide led to a much higher extinction coefficient than graphene. Moreover, MoS 2 can be heated rapidly under NIR laser radiation. As a result, high-efficiency MoS 2 nanomaterials have gained popularity owing to their effective response to NIR light radiation in cancer treatment [22,34,36]. Recently, magnetic nanoparticles have been considered an essential agent in hyperthermia. Employing these magnetic nanoparticle carriers would increase the penetration/absorption of the drug in the cancer cell membrane. Hence, they can prevent systematic administration and side effects, and increase the therapeutic effects of anti-cancer drugs [37][38][39][40]. When magnetic nanoparticles are exposed to the AC field, the processes of hysteresis, Neel, and Brownian relaxation occur, which may trigger the heating process. 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 [41]. 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 materials [42,43]. Although iron oxide nanoparticles are biocompatible, they are usually coated with biocompatible polymers to prevent oxidation for hyperthermia treatment [44,45]. In addition, we coat iron oxides that are not detected by the immune system and are excreted as an external agent. As a result, the half-life of these substances increases, and there is no need to use high doses [46]. In hyperthermia, iron oxide nanoparticles cause cell apoptosis, necrosis, and cell growth inhibition. Moreover, this superparamagnetic nanoparticle is the most commercial type of nanoparticle for treating hyperthermia because of its biocompatibility, magnetic ability, and functionalization. Fe 3 O 4 , as a combination of divalent and trivalent iron oxides, is the most common form of iron oxide [47].
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 the --Fe O Au Ag MoS @ 3 4 2 structure.

Materials and methods
Compared to their bulk materials, MNPs have demonstrated superior properties such as larger surface-to-volume ratios, excellent reactivity, and unique magnetic responses [48,49]. This is despite their sizes being comparable to biomolecules [50]. For the production of MNPs, it is preferable to use materials that have high saturation magnetizations, such as pure metals (Fe, Co, Ni, etc), alloys (FeCo, alnico, permalloy, etc), and oxides (Fe . Pure metals can produce higher saturation magnetizations; however, this does not make them appropriate for use in clinical settings due to their high toxicity and oxidative properties [47]. Magnetic nanoparticles have been considered for cancer treatment because they can be used as sources of spot heat in the presence of radiofrequency RF magnetic fields. Because there is a limited range of amplitude and magnetic field frequency for biologically induced heating, this treatment method is restricted. To be biologically feasible, the combination of H field strength and frequency f should be in the range´´-  [51]. In this section, we examine the optical, magnetic and, thermal properties of the Fe O , 3 4 -Au Ag @ MoS 2 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 weighted average theory, Bruggeman's theory, and Maxwell Garnet's theory [52][53][54][55].

Effective medium theory for MoS 2 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 a and the dielectric phenomenon [56]. In this regard, it is supposed that several layers of different nanoshells are stacked on top of each other [56]. As shown in figure 1, there is an Au-Ag spherical nanoshell with an inner radius of r core and a thickness of t d surrounded by MoS 2 with a thickness of t , ms while the core of this nanoparticle is of Fe O 3 4 (15,20 and 25 nm). The refractive index of the tumor for liver is 1.349 [57]. e w e w , a n d core shell ( ) ( ) = ¼ i 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 e w x ( ) [58]. According to Maxwell-Garnet's theory, the dielectric effect between the core and the first shell is formulated as follows [58]: Where the volume fraction of the new layer is obtained from: and for other layers, equation (3) could be derived from equations (2) and (3) e e e j e j e j e j = + + - The radius of the new layers is calculated as follows: Here, t , d -r i 1 indicate the radius of the layer and the thickness of the lower shell, respectively. Then, for calculating the efficiency of extinction, scattering, and absorption, equation (5) was used [58]:  Here, e x is the dielectric function for the external medium.

Effective medium theory for MoS 2 coated Au-Ag for different volume fraction
Relying on the weighted average theory, the effective dielectric functions can be calculated for silver-and goldbased alloy nanoparticles using equation (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)  )are the occupied fraction of the nucleus, and e eff denotes the effective dielectric coefficient.

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 [51,61]: are, the permeability of free space, initial susceptibility, amplitude, frequency, effective relaxation time, nanoparticle saturation magnetization, and nanoparticle volume, respectively [61].
In MHT, superparamagnetic nanoparticles in a ferrofluid are put into the tumor, and a noninvasive RF field is used to kill the cancer cells. AC magnetic fields make the magnetization vector relax and give off heat repeatedly. Eddy currents, hysteresis, resonance, and relaxation losses are the heat generation mechanisms for magnetic nanoparticles exposed to an AC magnetic field [51].
The equations of heat generated by magnetic nanoparticles using Neel relaxation and Brownian relaxation are as follows [13,62]: r a n d , , , , , , K are the hydrodynamic volume of the nanoparticle, nanoparticle volume, attempt period, viscosity, ligand layer thickness, the radius of nanoparticle, and nanoparticle anisotropy constant, respectively.
And the effective relaxation time is calculated by: Table 1 lists the values required to calculate heat generation in tumor and healthy tissue. These losses are reduced as the temperature of the ferromagnetic material gets closer to the Curie temperature, T . C Heating can be self-regulating if the composition of a material is tuned so that the temperature coefficient is brought close to the maximum temperature desired [51]. This strategy keeps the tissues from becoming overheated. Eddy currents, hysteresis, resonance, and relaxation losses contribute to the dissipation of applied magnetic energy by magnetic nanoparticles during MHT. When the Curie temperature is low, the magnetic properties are highly temperature-dependent [51]. Saturation magnetism is the first temperature-dependent magnetic property. The saturation magnet is calculated using Bloch's classical law [63] as follows: Here a M and S0 are saturation magnetization at 0 K and Bloch's exponent, respectively, and the value of a equals . 3 2 Temperature also affects metabolic heat production and heat sources from circulation. The following formula can be used to calculate metabolic heat production as a function of tissue temperature [63]: Here Q M0 is basal metabolic rate.
And blood circulation heat source is calculated by [42]: 15 18 Here Q W and C , ,

Blood Blood
Blood are heat sources due to blood circulation, blood perfusion rate and, blood specific heat, respectively.
Magnetic anisotropy is another important property in MNPs since it influences magnetization, remanence, reversibility, and relaxation. As a result, this parameter can also affect the temperature production process [72]. The temperature dependence of magnetic anisotropy is determined using the classical Akulov's theory as follows [62]: For uniaxial and cubic magnets, n equals 3 and 10, respectively. On the other hand, the anisotropy of magnetization at 0 K is represented by the K .

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 [73,74].This model is commonly used for tissues with small blood vessels.
The general form of the bio-heat equations in cartesian coordinates are presented in equation (20) [75]: Here, the subscript t refers to tissue. The boundary conditions due to continuous temperature and heat flux at the tumor boundary are: Wherein,  2 is the Laplace operator, t is time, K is thermal conductivity, and C is the specific heat. Q a n dQ Metabolism r indicate the generators of metabolic heat and the internal heat generated by external sources, respectively. The first part (  k T 2 ) is the heat transfer in the tumor due to the temperature gradient, and the second part of equation (20) is the heat transfer is heat transfer due to blood flow. The third and last parts are related to intra-tissue heat, which results from tissue metabolism and external heat source. The term r ¶ ¶ c T t refers to the changes of temperature flux [73]. T t and T st denote the temperature of the tumor and the surrounding tissues, respectively [62,73].

Arrhenius equation
At all stages of treatment, it is vital to spare healthy tissues from unnecessary thermal therapy. In this regard, we will calculate the temperature distribution in the surrounding tissues. These equations have to include the temperature distribution in these two areas. In this regard, the degree of damage to the tumor tissue should be modeled/estimated as a function of the laser irradiation time t and the distance from the center of the tumor r. Here f initial shows blood flow before starting treatment [76]: W r t , ( )is thermal damage to the tumor tissue according to the Arrhenius equation [76].
Here, A , f E a and R are Arrhenius constant, activation energy, and the global gas constant, respectively.

Effect of number of layers and radius of nanoparticle on the extinction peak and SPR
The intensity of the extinction peaks decreases when the number of layers increases. The shells and core radius are obtained using equation; = --r r t, which depends first on the last shell 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 MoS 2 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 MoS 2 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-Mossotti relationship, A spherical nanotube with an inner radius of r c and a thickness of t b was surrounded by a MoS 2 shell with a thickness of t , M and was modeled as depicted in figure 1. Figure 3 shows that as the thickness of the alloy 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 alloy, 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.
3.3. 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 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 MoS 2 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.

Effect of magnetic field on tissue
The temperature distribution inside the liver tissue is calculated by 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 equation (20). In this regard, using equation (20) and boundary conditions presented in equations (21)-(24), 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 s 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 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 see that at intervals beyond of 2.5 cm, the temperature is in its normal state and will not harm the patient and the healthy tissues.
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 15 s up to 42.5°C. Meanwhile, a temperature increase is also observed in the liver tissue up to 40°C, while for the surrounding tissues, the amount of temperature increase can be ignored. In 30 s, the temperature of the tumor tissue would reach the maximum desired temperature, while the temperature of the liver tissue would stay around 39°C-40°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 liver tissue is about 40°C.

Discussion
The physical properties of -Fe O Au Ag MoS @ 3 4 0.25 0.75 2 nanoparticles for different Au-Ag and MoS 2 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 and liver. 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 [23,28]. Silver, also, is not stable despite its high dispersion efficiency [24,30,31]. 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 [23]. One of the benefits of using Fe O 3 4 over other magnetic materials is that iron oxide can penetrate deep tissues. On the other hand, MoS 2 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 figure 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 liver 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 liver, it can be seen that the best dimensions and number of layers were 25 nm, and 2 layers of MoS 2 coating as shown in figure 7, we have shown which is the most suitable optical response compound by examining other structures. The peaks move toward the first biological window in this structure and are located within the first biological window. Since liver tissue is soft, it is best to place our light response in the first biological window to minimize tissue damage. According to figure 7, the reason for selecting nanoparticles with a radius of 25 nm and 2 layers was to locate the peaks in the biological window range and the appropriate extinction coefficients in the tumor tissue.
Since the laser used in the heating method is a diode laser with a range wavelength of 808 nm, increasing the number of MoS 2 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 25 nm with 2 layers of MoS . 2 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 liver tissue with this structure had the lowest value compared to the other compounds.
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 3 nm 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 1.34. 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 Ag Au compound 0.75 0.25 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 figures 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.

Conclusion
The results of this study showed that the most efficient structure is -Fe O Au Ag MoS @ . 3 4 0.25 0. 75 2 Fe O 3 4 magnetic nanoparticles were used to treat liver cancer using a magnetic field, wherein gold and silver alloy coatings were used to prevent oxidation, since gold alone does not perform well at biological windows, and silver alone is toxic. The combination of Au Ag 0.25 0.75 has the highest coefficient of destruction and SPR in biological windows. MoS 2 was used as the final coating because it increased the body's stability and biological compatibility. The 2-layer coating of MoS 2 would have the best extinction coefficient and SPR coefficient compared to other numbers of layers.