Breast cancer is a disease in which cells in the breast grow out of control. After surgery, chemotherapy, and other invasive treatments, hyperthermia is a suitable choice with minimal side effects. This paper investigates the treatment of breast cancer using a combination of laser and ultrasound irradiation in the presence of gold nanoparticles. In the simulations, the breast tissue is represented as a multilayer structure, and the tumor is supposed to consist of two parts: a superficial section and a deeper region. In the initial stage, the superficial parts of the tumor, which also contain gold nanoparticles, are exposed to a continuous laser for 50 seconds, followed by a cooling period of 20 seconds. Then, for deeper sections, ultrasound irradiation is utilized. The results indicated that the application of nanoparticles enhanced the tissue necrosis volume. Furthermore, it was demonstrated that the combinational application of laser and ultrasound irradiation could eradicate both the superficial parts of the tumor and the deep parts.
Article
Breast cancer therapy by both of laser and ultrasound irradiation with the aid of gold nanoparticles injection
https://doi.org/10.21203/rs.3.rs-4890427/v1
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Breast cancer
Laser photothermal therapy
Ultrasound
Gold Nanoparticles
Hyperthermia
Cancer is a cellular-level disease that originates from the uncontrolled growth of abnormal cells and can spread to other areas of the body1. Among all types of cancers, breast cancer is the most common and the most dangerous cancer in women worldwide2. With a global mortality rate of 1 per 5,000 patients, breast cancer has a relatively high mortality rate3. Numerous factors contribute to the development of breast cancer. It is believed to result from the interaction of genetic factors with environmental factors4. There are different methods to treat breast cancer, such as surgery5, radiation therapy6, hormone therapy7, ultrasound irradiation8, and chemotherapy9. Generally, for a malignant tumor that spreads outside the breast and lymph nodes, hormone therapy and chemotherapy are preferable choices3. In addition, there are two common methods of surgery, mastectomy, in which the entire breast is removed, and lumpectomy, in which only some parts of the breast are removed. However, the mentioned methods are invasive and have side effects such as hair loss, weight gain, menopause, osteoporosis, and other complications3. Among all common non-invasive methods, laser therapy and ultrasound radiation, which are both based on hyperthermia, have the fewest side effects and are often recommended10,11. In hyperthermia treatment, the temperature is increased to 40 degrees Celsius, which causes tumor necrosis with minimal damage to healthy tissue12. The main challenge of the hyperthermia method is to create a temperature above 40 degrees Celsius and focus it on the tumor. In recent years, nanoparticles have been proposed for this purpose. As reported in a lot of literature, adding nanoparticles significantly improves the treatment of various cancers. It should be noted that the use of nanoparticles has a considerable effect on destroying tumor cells and reducing the damage to surrounding tissues13,14.
Several studies have been conducted on the treatment of breast cancer with hyperthermia. For instance, X. Ma et al.15 used Fe3O4-Pd Janus nanoparticles for efficient cancer therapy. They showed that Fe3O4-Pd Janus nanoparticles demonstrated significantly high magnetic-photo heating efficiency and enhanced ROS generation, enabling effective tumor regression. They also presented dual-modal MRI/PA imaging signal enhancement, allowing precise imaging-guided therapy with high spatial resolution and accuracy. Furthermore, Burke et al.16 examined the combination of multi-walled carbon nanotubes (MWCNTs) and near-infrared (NIR) laser irradiation. Their research showed rapid tumor regression and long-term survival in a mouse model, providing a promising treatment strategy for breast cancer. In addition, Sharma. D et al.17 investigated the effect of varying hyperthermia and ultrasound-stimulated microbubble (USMB) treatment parameters on tumor cell death and vascular disruption in breast cancer therapy. They demonstrated that combining USMB with hyperthermia enhanced tumor cell death and reduced vascular density in breast tumor xenografts. They also highlighted the role of prolonged ultrasound pulses and increased ultrasound exposure in enhancing particle penetration and tumor response. Hassan et al.18 performed numerical simulations and analytical calculations to compare the interaction of therapeutic ultrasound with a multilayer tissue at different frequencies and stimulation times, by focusing on calculating the temperature in other tissues. According to their research, the highest temperature observed in the tumor was 45.5°C at a frequency of 1.5 MHz, which was favorable in destroying the cancerous cells without causing significant damage to surrounding tissues. Analytical results showed that the highest temperature predicted in the tumor was 47.77°C, and the two solutions were considered to agree.
It has also been reported that integrating different therapeutic methods can produce promising results in treating tumor cells. In 2022, Kabiri and Rezaei19 examined the effectiveness of combining nanoparticle-mediated laser emission and microwave irradiation in treating liver cancer and showed that integrating these two modalities could considerably enhance the efficiency and accuracy of each method. In the present study, the synergistic effect of combining laser photothermal therapy with ultrasound irradiation is investigated through FEM simulation and it is shown that this intelligent integration of methods can help the necrosis of tumors with complex morphology.
2.1 breast cancer model
In this research, the breast is modeled as a multi-layered hemisphere3, including the epidermis, papillary dermis, reticular dermis, fat, and gland containing a tumor. The radius of the breast is assumed to be 65 mm. Moreover, the tumor is considered to have an arbitrary shape including superficial and deep sections. The tumor's width varies from zero to 14.4 mm with a depth of 15 mm. Figure 1 shows a schematic diagram of the tissue and the tumor designed for the simulation. Tables 1 and 2 show the physical properties of tissue, tumor, and blood.
In the present simulation, the finite element method (FEM) solves all of the equations, and due to the luge number of elements in 3 dimensions and the limitations of the solver for calculating this model, the axial symmetry is considered for this geometry. In this paper, an ultrasound beam is produced by an acoustic transducer. Figure 2 shows the geometry of the tissue under the acoustic irradiation. It should be noted that in Fig. 2, both the tissue and the acoustic transducer are immersed in water. The transducer is a bowl-shaped element with a focal length of 62.64 mm, including an aperture with a radius of 35 mm and a hole with a radius of 10 mm in the center. The frequency of the transducer is 1 MHz20.
In this simulation, three lasers with a similar wavelength of 796 nm and various laser powers of 2W/cm2, 0.5W/cm2, and 0.25W/cm2 were utilized19. It should be mentioned here to avoid side effects, we use a more accurate laser with less power, and in real experiments, one laser can be used several times. The laser is continuous with an exposure time of 50 s and a cooling time of 20 s. Table 3 shows the optical properties of the tissue containing the tumor. Moreover, for controlling the produced temperature by ultrasound, it radiates to the tumor for the 60s and then turns off for 10s. This process continues for 10 min.
In addition, gold nanoparticles are added to the medium to increase the heating absorption. The nanoparticles are assumed to be homogeneously distributed in the tissue. In this simulation, nanoparticles' absorption and scattering coefficients are 121/cm and 5/cm, respectively21.
| Layer | Epidermis | Papillary Dermis | Reticular dermis | Fat | Gland | Muscle |
|---|---|---|---|---|---|---|
| h(mm) | 0.1 | 0.7 | 0.8 | 5 | 43.4 | 15 |
| k (W/ (m.K)) | 0.235 | 0.445 | 0.445 | 0.21 | 0.48 | 0.48 |
| ρ (kg/\(\:{\mathbf{m}}^{3}\)) | 1200 | 1200 | 1200 | 930 | 1050 | 1100 |
| c (J/ (kg. K)) | 3589 | 3300 | 3300 | 2770 | 3770 | 3800 |
| \(\:{\varvec{Q}}_{0}(\mathbf{W}/{\mathbf{m}}^{3}\)) | 0 | 368.1 | 368.1 | 400 | 700 | 700 |
| \(\:{\varvec{\omega\:}}_{\mathbf{b}}\) (1/s) | 0 | 0.0002 | 0.0013 | 0.0002 | 0.0006 | 0.0009 |
| property | value |
|---|---|
| \(\:{\varvec{C}}_{\varvec{b}}(\varvec{J}/\:(\varvec{k}\varvec{g}.\:\varvec{K}\left)\right)\) | 4200 |
| ρ (kg/m^3) | 1000 |
| \(\:{\varvec{T}}_{\varvec{b}}\)(K) | 310.15 |
| Layer | Epidermis | Papillary Dermis | Reticular dermis | Fat | Gland | Tumor | |
|---|---|---|---|---|---|---|---|
| \(\:{\varvec{\mu\:}}_{\varvec{a}}\)(1/m) | 19 | 19 | 19 | 6.5 | 6 | 6 | |
| \(\:{\varvec{\mu\:}}_{\varvec{s}}\)(1/m) | 834 | 834 | 834 | 1000 | 1275 | 5 | |
| α(dB/m) | 35 | 35 | 35 | 48 | 75 | 43 | |
| C(m/s) | 1510 | 1510 | 1510 | 1510 | 1510 | 1540 | |
2.2 bioheat transfer
Thermal cancer treatment plays a significant role in the field of clinical applications. This kind of treatment causes an alteration of the tissue temperature to achieve the thermal ablation of tumors. In this procedure, an ultrasound transducer, a laser beam, or a microwave applies mechanical or light energy to tissues, leading to an elevation in temperature and, subsequently, causing the demise of cancerous cells25. The issue with the physical bioheat problems is evaluating the temperature profile and the fluence rate distribution in the tumorous region by knowing the governing initial and boundary conditions, geometry, heat sources, and the tissues' thermophysical and optical properties. Generally, in living tissues, blood perfusion and passage of blood modify the heat transfer. Furthermore, metabolic activity generates heat within the tissue. Therefore, an equation is needed to describe the heat transfer in tissue by considering the effects of both blood perfusion and metabolism.
This relation, widely known as Penne’s equation, was first established by Penne (1948) and Perl (1962)26,27,28 as below:
where, \(\:\rho\:\) is the density of the tissue, \(\:{c}_{P}\) is heat capacity, T is temperature, t is time, \(\:k\) is the thermal conductivity of tissue, \(\:{\rho\:}_{b}\) is blood density, \(\:{\omega\:}_{b}\) is blood perfusion, \(\:{c}_{b}\) is the heat capacity of the blood, \(\:{T}_{b}\) is the temperature of blood, \(\:{Q}_{met}\) indicates the metabolic heat source term, and \(\:{Q}_{s}\) is the external heat source. Here, there are two heat sources, laser and ultrasound, as follows:
$$\:{\mathbf{O}}_{\mathbf{s}}={\mathbf{Q}}_{\mathbf{L}}+{\mathbf{Q}}_{\mathbf{U}\mathbf{S}}$$
2
In the following sections, each of these heat sources will be analyzed and then inserted into Eq. (1)
2.3 Interaction of laser and tissue
In this research, the laser beam is one of the main heat sources for tumor ablation. When an incident laser beam enters the medium in direction Ω, part of its intensity is absorbed, and another part of that is scattered in another direction, \(\:{\varOmega\:}^{{\prime\:}}\). The fraction that is absorbed is shown by \(\:{\sigma\:}_{a}\) I(Ω) and the scattered fraction is indicated by \(\:{\sigma\:}_{s}\) I(Ω), where \(\:{\sigma\:}_{a}\:\)and \(\:{\sigma\:}_{s}\) are absorption and scattering coefficients. One must solve the radiative transfer equation (RTE) to obtain the energy deposited at each point. For quasi-static conditions, which are met in the current study, RTE obeys the following Eq. 29:
$$\:\varvec{\Omega\:}.\nabla\:\mathbf{I}\left(\varvec{\Omega\:}\right)={\varvec{\sigma\:}}_{\mathbf{a}}{\mathbf{I}}_{\mathbf{b}}\left(\mathbf{T}\right)-\:\left({\varvec{\sigma\:}}_{\mathbf{a}}+{\varvec{\sigma\:}}_{\mathbf{s}}\right)\mathbf{I}\left(\varvec{\Omega\:}\right)\:+\:\frac{{\varvec{\sigma\:}}_{\mathbf{s}}}{4\varvec{\pi\:}}{\int\:}_{4\varvec{\pi\:}}\mathbf{I}\left({\varvec{\Omega\:}}^{\mathbf{{\prime\:}}}\right)\varvec{\upvarphi\:}({\varvec{\Omega\:}}^{\mathbf{{\prime\:}}},\:\varvec{\Omega\:})d{\varvec{\Omega\:}}^{\mathbf{{\prime\:}}}$$
3
In the above equation, \(\:{I}_{b}\) denotes the blackbody intensity, which is derived from the Plank function, and ϕ (Ω′, Ω) signifies the probability that the beam will scatter from direction Ω′ toward the direction Ω. The last term of the right-hand side of this equation accounts for the portion of the radiative energy coming from all possible directions scattered toward the considered direction of propagation.
Generally, different methods such as the discrete ordinates method (DOM), P1-approximation, Rosseland approximation, and Beer-Lambert law are employed to solve the RTE. The P1 approximation stands out as one of the best and the most straightforward methods for solving the RTE, utilizing spherical harmonics with the capability of incorporating both isotropic and linear anisotropic scattering within its framework. In the P1-approximation method, incident radiation is defined as30:
$$\:\mathbf{G}={\int\:}_{4\varvec{\pi\:}}\mathbf{I}\left(\varvec{\Omega\:}\right)d\varvec{\Omega\:}$$
4
and radiative heat flux is expressed as30:
$$\:{\mathbf{q}}_{\mathbf{r}}={\int\:}_{4\varvec{\pi\:}}\mathbf{I}\left(\varvec{\Omega\:}\right)\mathbf{d}\varvec{\Omega\:}$$
5
By applying G and \(\:{q}_{r}\) to the RTE, it can be rewritten as below30:
\(\:\mathbf{I}\left(\mathbf{r},\widehat{\varvec{\Omega\:}}\right)=\:\frac{1}{4\varvec{\pi\:}}[\mathbf{G}\left(\mathbf{r}\right)\:+\:3\mathbf{q}\left(\mathbf{r}\right).\:\widehat{\varvec{\Omega\:}}\) ] (6)
When the laser beam irradiates into the medium, I in the equation will consist of the collimated laser beam entering the medium and the diffusion term emerging from scattering within the medium. As described by Modest and Tabanfar in Ref.30, in such scenarios, the impact of the external radiation field can be taken into account by introducing a source term into the diffusion terms. Hence, the simplified version of RTE emphasizes the diffusion of light due to the scattering phenomenon, and the source term directly incorporates the influence of the external collimated beam from the laser as bellow30:
\(\:\nabla\:\cdot\:{(\mathbf{D}}_{\mathbf{P}1}\nabla\:\mathbf{G})\) - \(\:{\varvec{\sigma\:}}_{\mathbf{a}}\)(G-4𝜋\(\:{\mathbf{I}}_{\mathbf{b}}\)) = 0 (7)
here, \(\:{D}_{P1}\)is diffusion coefficient in P1-approximation method and is defined as30:
$$\:{\mathbf{D}}_{\mathbf{P}1}=\:\frac{1}{3{\varvec{\sigma\:}}_{\mathbf{a}}+\:{\varvec{\sigma\:}}_{\mathbf{s}(3-{\mathbf{a}}_{1})}}$$
8
where, \(\:{a}_{1}\) is the linear Legendre coefficient for the scattering phase function. This coefficient is related to anisotropy, so in the case of isotropic scattering, a1 equals zero.
Then, in the Penne equation, \(\:{Q}_{L}\) is the laser heat source based on the divergence of heat flux \(\:{q}_{r}\). That is because the radiative heat flux crossing an element calculated with an area normal to the direction of 𝞨 is a result of intensities incident from all directions, and it is the divergence of heat flux at any point that leads to increasing the temperature at that point. It should be stressed that once G is characterized at each point, ∇ · \(\:{q}_{r}\) can be found.
Moreover, adding gold nanoparticles significantly modifies the tissue's optical features. In this paper, gold nanoparticles' absorption and scattering coefficients are 121/cm and 0.5/cm, respectively21.
2.4 Interaction of ultrasound with tissue
As previously mentioned, ultrasound can be considered as a heat source. Here, the absorbed acoustic energy is calculated and used as the heat source,\(\:{Q}_{US}\), in Penne’s equation.
The propagation of the focused ultrasound waves as a time-independent problem follows the homogenous Helmholtz equation in 2D axisymmetric cylindrical coordinates as below20:
\(\:\frac{\partial\:}{\partial\:\mathbf{r}}\) [- \(\:\frac{\mathbf{r}}{{\varvec{\rho\:}}_{\mathbf{c}}}\left(\frac{\partial\:\mathbf{P}}{\partial\:\mathbf{r}}\right)\) ] + r \(\:\frac{\partial\:}{\partial\:\mathbf{z}}\) [- \(\:\frac{1}{{\varvec{\rho\:}}_{\mathbf{c}}}]-\) [ \(\:{\left(\frac{\varvec{\omega\:}}{{\mathbf{C}}_{\mathbf{C}}}\right)}^{2}]\frac{\mathbf{r}\mathbf{p}}{{\varvec{\rho\:}}_{\mathbf{c}}}\) = 0 (9)
where, r and z are the radial and axial coordinates, p is the acoustic pressure, and 𝜔 is the angular frequency. \(\:{\rho\:}_{c}\) is density and \(\:{C}_{C}\) is the speed of sound, which is also complex-valued to account for the material's damping properties.
The Helmholtz equation assumes that the acoustic wave propagation is linear and that the amplitude of the shear waves in the tissue domain is much smaller than that of the pressure waves. Therefore, nonlinear effects and shear waves are neglected.
The acoustic intensity field can also be derived from the acoustic pressure field. Finally, by knowing the acoustic intensity field, \(\:{Q}_{US\:}\) is calculated as below20:
\(\:{\mathbf{Q}}_{\mathbf{U}\mathbf{S}}\) = 2\(\:{\varvec{\alpha\:}}_{\mathbf{A}\mathbf{B}\mathbf{C}}\)I = 2\(\:{\varvec{\alpha\:}}_{\mathbf{A}\mathbf{B}\mathbf{C}}\left|\mathbf{Re}\left(\frac{1}{2}\mathbf{p}\mathbf{v}\right)\right|\) (10)
here, \(\:{\alpha\:}_{ABC}\), I, p, and v are the attenuation coefficient, acoustic intensity magnitude, acoustic pressure, and acoustic particle velocity vector, respectively. Furthermore, the attenuation coefficient of tissue with and without gold nanoparticles is 70 dB/m and 43 dB/m, respectively24.
2.5 Thermal damage
An important concern in research about bioheat transfer is accurate and appropriate thermal damage of the diseased tissues without destroying the neighboring healthy tissues during tumor treatment. Several investigations have demonstrated that tissue damage depends on the temperature and exposure time. It should be mentioned that as tissue temperature increases, the elapsed time necessary to achieve the threshold of damages decreases. The progression of the thermal injury can be reasonably approximated by the Arrhenius equation. This relation is usually utilized for illustrating the rate of the irreversible heating damage of the biological tissues31,32:
$$\:\varvec{\Omega\:}\left(\mathbf{t}\right)\:=\:{\int\:}_{0}^{\mathbf{t}}{\mathbf{A}}^{\frac{\varvec{\Delta\:}\mathbf{E}}{{\mathbf{e}}^{\mathbf{R}\mathbf{T}}}}d\mathbf{t}$$
11
In the above equation, \(\:\varOmega\:\)(t) indicates the degree of tissue injury, R is the universal gas constant, A is the frequency factor for kinetic expression, and ¬E is the activation energy for irreversible damage reaction. The critical value of \(\:\varOmega\:\) = 1 is the point when thermal necrosis occurs. Generally, two parameters of A and \(\:\varDelta\:\)E depend on the type of tissue. Here, for the breast tissue A and \(\:\varDelta\:E\) are 1.18×\(\:{10}^{44}\) and 3.02×\(\:{10}^{55}\), respectively3.
The ultrasound transducer simulation and nanoparticle-mediated laser therapy model results are compared with previous literature to validate the proposed model's accuracy.
It is essential to mention that the current model's simulation of laser photothermal therapy with nanoparticles is based on the same model utilized in our previous paper19 on liver cancer treatment. In that paper, it was shown that under similar conditions, the results of our simulations agree well with those obtained by Sony et al. 21 [see Fig. 3 of our previous article19].
To validate the results of the FEM simulation of the ultrasonic probe, the present model is compared to the research conducted by Huang et al.33 in 2004. Figure 3 depicts the 2D axisymmetric geometry used by Huang et al. in their paper. For validation, the same model with similar dimensions, boundary conditions, and physical properties is considered to measure the temperature of the tissue phantom at the ultrasound focus. Figure 4 illustrates the heating and cooling curves characteristic of this study, along with the results from the experiments and simulations conducted by Huang et al. As seen in this figure, the data of the present model is in complete agreement with the results of the simulations of the previous literature. Nonetheless, there is a slight difference between the experimental and current simulation data. These differences can be attributed to some approximations assumed in the simulation, while the overall fit of the simulation curve is quite remarkable.
This study utilized numerical analysis to examine the tissue's mechanical and thermal response to ultrasound and laser exposure to determine how adjustable parameters can precisely ablate a tumor while minimizing nociceptive pain and causing no damage to adjacent healthy tissue. Usually, it is difficult to remove the tumor without causing harm to the healthy tissues around it. Therefore, when exposed to diode laser irradiation, gold nanoparticles are introduced into the tumor to reduce the possibility of thermal tissue damage. This raises the tumor's temperature above normal while shielding the surrounding healthy tissues. It should be noted that the lasers used in this instance are pulsed lasers, meaning they heat up for 50 seconds and cool down for 20 seconds. The problem is performed twice, once with and once without the insertion of Au nanoparticles, to determine the impacts of gold nanoparticles on the enhancement of temperature in the tissue. The comparison findings are then displayed.
4.1 The effect of Nanoparticles on heating by laser and ultrasound
To understand the effect of nanoparticles on increasing the temperature of tumor region and the amount of necrosis, the problem is solved once with nanoparticles and again without nanoparticles. The laser used in this study is a continuous laser with an exposure time of 50s and a cooling time of 20s. Also, the exposure time of the US is the 60s, and its cooling time is 10s. Figures 5 shows the temperature of the tissue after laser irradiation, with and without the presence of gold nanoparticles, for 10 min. In the absence of gold nanoparticles, the temperature of the tumor reaches 38°C, and when gold nanoparticles are injected, the temperature increases to 54°C. The Fig. 6 shows the necrosis volume without and again with gold nanoparticle injection into the tumor after 10 min of US irradiation. As shown in picture 6, injection of gold nanoparticles causes cell death in the deep section of the tumor to noticeably increase. The depiction of the acoustic pressure in the water and tissue domain is also given in Fig. 7.
Figure 6. the faction of necrosis after 10 min of ultrasound irradiation (a) without, and (b) with gold nanoparticles injection.
4.2 Combining focused ultrasound and laser photothermal therapy
Figure 6 shows the temperature rise in the tissue after 10 min of receiving laser and ultrasound irradiation simultaneously. As shown in Fig. 6, the minimum temperature is 20°C, i.e., the body temperature and the maximum temperature reach 100°C after 10 minutes of laser and ultrasound irradiation together.
The vital issue in determining the method's success is the fraction of damaged tissue, presented in Fig. 7. Figure 7a shows the fraction of the damage after 10 min of laser illumination, while Fig. 7b presents the damage fraction after 10 min of ultrasound irradiation. Finally, Fig. 7c illustrates the status when the tissue is simultaneously irradiated by laser and ultrasound for 10 min.
To check that this method has not damaged the surrounding healthy tissue, the fraction of the necrotic tissue along four lines, crossing the tissue model, is evaluated at different places. For this purpose, two vertical and two horizontal lines are chosen to help us better judge the damage estimation in both superficial and deep areas. The horizontal lines are positioned at z = 54 and z = 60, while the vertical lines are at r = 6 and r = 10 of Fig. 8. The necrosis fraction along the horizontal and vertical lines are shown in Figs. 9 and 10, respectively.
According to Fig. 8, the border of the safe region is shown by the yellow color (i.e., necrosis fraction equal to 0.7), indicating that there is no serious damage present in the normal sections of tissues and the red area indicates damage within the tumor. Therefore, it is obvious that this method is both safe and effective for treating cancers.
In addition, as seen in Fig. 9, at z = 60 mm and at reduced radial distances, wider areas are more vulnerable to necrosis because they are near to laser and ultrasound radiations. Moreover, the necrosis proportion is minimal at long radial distances in all horizontal lines, demonstrating the lack of adverse effects from this treatment approach.
A similar pattern is seen in Fig. 10 at various radial distances, with a slight increase at r = 6 mm. Furthermore, as this figure makes evident, the necrosis fraction is greater than 0.7 at z > 62 mm, indicating that only the tumor areas are damaged and supporting the usefulness of the suggested method.
In this research, the interaction between laser and breast tissue in the presence of gold nanoparticles combined with ultrasound irradiation is studied. The FEM (finite element method) simulations revealed that this treatment approach could be exceptionally beneficial for treatment of the tumors including both superficial and deep regions. Here, the heat generated by the acoustic transducer was estimated using the acoustic intensity magnitude. Furthermore, the magnitude of energy produced by laser irradiation and absorbed by GNPs was determined by solving the RTE equation. For solving RTE equation, P1-approximation was employed which means isotropic and linear anisotropic scatterings were both considered. Finally, Pennes’ equation was solved to calculate the temperature within the tumor.
In summary, the results showed that: 1) Gold nanoparticle injection greatly enhanced the effectiveness of the photothermal therapy. 2) In the absence of gold nanoparticles, the temperature raised just into 38°C after 10 min laser irradiation. 3) With the injection of gold nanoparticles, the temperature of laser irradiation increased up to 100°C after 10 min of laser irradiation. 4) Moreover, gold nanoparticles caused the temperature rise up to 100°C after ultrasound irradiation. 5) The effect of gold nanoparticles on enhancing the heating effect of laser was more than ultrasound irradiation, and 6) finally, after 10 min irradiation of laser and ultrasound, most parts of the tumor undergo necrosis. Hence, it can be concluded the proposed irradiation of laser and ultrasound with the aid of gold nanoparticles could help in treatment of cancer with no damage to healthy tissue.
Author contributions
Heliya sadat Kazemi Siyanaki performed simulation and wrote paper. Fatemeh Rezaei supervised and reviewed this research and presented discussion. Saeedeh Kabiri checked the correctness of simulation. Moreover, Behnam Ashrafkhani and saeedeh Kabiri helped in writing and reviewing this paper.
Data availability
The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.
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No competing interests reported.