Gold nanoparticles-based brachytherapy ...

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radiotherapy enhancement by GNPs in the choroidal melanoma, the cases referred to above have .... Plaque brachytherapy can be used for the treatment of.
Gold nanoparticles-based brachytherapy enhancement in choroidal melanoma using a full Monte Carlo modelling of human eye Somayeh Asadi1*, Mehdi Vaez-zade1, S. Farhad Masoudi,1 Faezeh Rahmani2 1

Department of Physics, K.N. Toosi University of Technology, Tehran, Iran

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Department of Radiation Application, Shahid Beheshti University, Tehran, Iran

Abstract Materials of high atomic number such as gold, can provide a high probability for photon interaction by photoelectric effects during radiation therapy. In cancer therapy, the object of brachytherapy as a kind of radiotherapy is to deliver adequate radiation dose to tumor while sparing surrounding healthy tissue. Several studies demonstrated that the preferential accumulation of gold nanoparticles within the tumor can enhance the absorbed dose by the tumor without increasing the radiation dose delivered externally. Accordingly, the required time for tumor irradiation decreases as the estimated adequate radiation dose for tumor is provided following this method. The dose delivered to healthy tissue is reduced when the time of irradiation is decreased. Hear, GNPs effects on choroidal Melanoma dosimetry is discussed by Monte Carlo study. Monte Carlo Ophthalmic brachytherapy dosimetry usually, is studied by simulation of water phantom. Considering the composition and density of eye material instead of water in these simulations may make a difference in calculations especially when the tumor loaded with GNPs. Hear, the Monte Carlo simulation using MCNP code has been implemented to investigate the application of gold nanoparticles in dose enhancement in brachytherapy of Choroidal melanoma in both water phantom and eye globe.

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corresponding authors: Somayeh Asadi, E-mail address: [email protected]

PACS numbers: 87.53.Jw, 87.85.Rs, 87.10.Rt Keywords: Choroidal Melanoma, Brachytherapy, MCNP, Gold nanoparticles, Dose enhancement

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Introduction Ocular Melanoma or more specifically Uveal Melanoma is a malignant tumor which can arise from the melanin-producing cells or Melanocytes residing within the Uvea. This kind of ocular tumor has the highest rate of Metastasis compared with the other intraocular cancers. The method of treatment is determined according to the type of the cancer and the rate of its progress.1-3 Enucleation, local resection and Brachytherapy are the most common methods of treatment for Ocular Melanoma4. In radiation therapy, penetrating radiation like X-ray, Alpha, Beta and Gamma are used. These rays could be radiated either from the radiation apparatus or medicines containing the labeled substance. Local radiotherapy or Brachytherapy is a form of radiation therapy which involves placing small radioactive seeds inside the body.5-6 Studies have shown that for most eye Melanomas, the method of using removable ophthalmic plaque is as effective as surgery (Enucleation).7-9 125

I, 131Cs, 103Pd, 192Ir, 60Co, 90Sr, 198Au and 106Ru are different artificial radioactive elements with

different shapes and structures which are used in the brachytherapy of choroidal Melanoma.10-12 Obviously, every treatment brings about damage to some extent; therefore, with regard to the known effects made by the use of penetrating radiation on the tissue, transferring proper and almost lethal dose to the tumor on the one hand and decreasing the dose to the healthy tissue on the other hand is one of the biggest challenges in radiotherapy. On this basis, clinical standard design of radionuclides and ophthalmic plaques used for intraocular cancers have been the primary goal of the clinical study aimed at delivering a high dose of radiation to the tumor cells while sparing surrounding healthy tissue.13-15 Several Monte Carlo and practical investigations have been done in the choroidal Melanoma dosimetry using different ophthalmic plaques containing different brachytherapy sources7-11, 14. Today, much attention is paid to the potential use of gold nanoparticles (GNPs) as radio sensitizers in dealing with the mentioned challenge in treating cancer through ionization radiation.16-17 In the context of such a treatment method, GNPs are considered to have noticeable characteristics. Biocompatibility, inertness and lack of any report based on the obvious toxicity are the distinguished characteristics of GNPs.18-19 High scattering cross section of GNPs resulting from its high atomic number and electron density increases the possibility of phenomena such as Compton scattering, Rayleigh scattering, Photoelectric and Florescent. The probability of the 2

occurrence of each of these phenomena strongly depends on the energy of the radiated beam. 20-21 Because of the strong photoelectric absorption and second electron caused by gamma or X-ray irradiation, GNPs can accelerate DNA strand breaks. As a result of these phenomena, there will be an increase in the locally absorbed dose in the tumor area and transformation of irradiation into heat and, finally, an increase in Dose Enhancement Factor (DEF).21-22 Because of the mentioned factors, GNPs have been found to be very useful in photo thermal therapy of cancers. Hainfeld et al.23 have done an in-vivo study on GNPs. Their research has shown that the presence of GNPs within the tumor which is exposed to radiation will cause more dose absorption by the cancerous tissue than the healthy tissue. Besides, it has been reported that by intravenous injection of GNPs into the body of mice bearing EMT-6 mammary subcutaneous tumors, the radiation therapy results in a long-term treatment up to 86% while only 20% treatment could be realized by solely making use of radiotherapy. Irradiation stability and cytotoxicity of GNPs in human K562 cells have been investigated by XiaoDong Zhang et al17 and the result indicated that GNPs had been stable under high energy ray irradiation and showed concentration-dependent cytotoxicity. Numerous other studies and researches have been carried out through examining the effects of GNPs in the treatment of the tumor along with irradiation.24-25 There are also some reports on the examination of the toxicity of these nanoparticles via the study of the cell viability.17,26 Some of the cases referred to above have been investigated using theoretical or Monte Carlo studies.13, 27-33 In Monte Carlo study by Lechman et al30. it is reported that the energy deposited by photoelectrons in the tumor area is more important than the size and concentration of GNPs while in some other works31 MC study shows that GNPs with larger diameter and concentration increase the /DEF in the tumor area. This means that for having access to more precise results and knowing the parameters that are effective in cancer treatment by GNPs, more studies and examinations should be carried out. Although considerable advance has been made in the application of nanotechnology- based cancer therapy and numerous studies have been carried out in this field through Monte Carlo simulation and practical study, limited studies have been reported on the use of this technology in curing eye tumors.

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Sheng Zhang et al34 have studied the particles accumulation in the Uveal tissue and have reported that nanoparticles can escape through the Uveal into the Melanoma tissue with much higher accumulation than micro-particles and optimal size of 100 to 300 nm. In another study, Shin J. kang et al35 have evaluated the efficacy of subconjunctival nanoparticles carboplatin in the murine Retinoblastoma treatment. With respect to intraocular cancer, if GNPs with proper dimension and concentration could be injected inside the eye tumor, then the irradiation effects of GNPs on the absorbed dose by tumor could be examined. To this end, it is necessary to culture the sample of Melanoma tumor (in-vivo or in-vitro model). Then, the GNPs with proper dimensions and concentration should be injected into the tumor. The cytotoxicity test for GNPs is necessary for radiotherapy and also drug delivery. The irradiation effects of GNPs on cancerous cells and healthy tissues can be assessed, using related cell viability assay. It is obvious that basic laboratory investigation and numerous tests are required to be done in order to carry out this study. So far, there has not been any report concerning a similar study conducted by other researchers. However, as a first step and for examining the radiotherapy enhancement by GNPs in the choroidal melanoma, the cases referred to above have been examined in this work by Monte Carlo study on the water phantom and human eye globe. In Refs [36-37], it was shown that using the eye model instead of water phantom in ophthalmic brachytherapy would significantly change the dosimetry results. Additionally, it is already known that the use of the GNPs enhances brachytherapy21-26. Nevertheless, in the present study for the first time we have investigated the application of the GNPs in brachytherapy of the eye tumors using the eye model36. We have also performed a similar study in the water phantom and discussed the significance of the eye model. In the majority of some reported work based on the investigation of human eye dosimetry, the melanoma tumor is modeled at the center of a cubic or spherical water phantom with a certain distance from the irradiation source. Also, Nanoparticles are usually simulated inside the tumor homogeneously and sometimes in the shape of a sphere with specific dimensions and concentrations. However, in this study we consider a realistic model in which DEF has been calculated in the water phantom and the eye globe by defining 50nm GNPs having four concentrations of 7, 10, 18 and 30mg/gr tumor inside the melanoma tumor. The effects of the presence of GNPs in choroidal melanoma dosimetry calculation have been investigated. DEF calculation in both water and eye phantoms has been done through calculating the ratio of the 4

absorbed dose by the tumor containing GNPs to the dose received by the tumor without these nanoparticles. Also, the effects of considering eye composition instead of water in choroidal melanoma dosimetry calculation have been investigated during the study of the irradiation effects of GNPs on tumor dose enhancement. This study has been done by simulating full loaded COMS standard eye plaque with a diameter of 16 mm, using the GE Healthcare/Oncura model 6711 for 125I as radionuclide source. Central axis depth dose curves for this source and dose distribution in some parts of the eye have been determined in both water phantom and simulated human eye, with and without GNPs and a comparison has been made between them.

2-Material and Method 2-1 Monte Carlo Simulation Regarding the accidental nature of radiation emission or transport process, there has been an increase in the use of Monte Carlo techniques in the area of the medical radiation physics applications. This method simulates the tracks of particles using statistical sampling process. For Monte Carlo simulation of the particles transport, there is a need to a great deal of information such as interaction of particles and probability of each interaction. Each of the random selected particles from the source has been followed and the outcome has been determined at the end of related individual physical processes considering the probability of distributions. For each particle, the tracking process ends when the particles deposit their energy completely or leave the geometry. Some of the general purpose Monte Carlo-based codes are designed for transport the particles in a wide range of energy using the modern cross section libraries and a best available transport algorithm. These codes have been developed for radiation transport calculation. In the study of brachytherapy dosimetry, the calculation of dose distributions at small distances and also validation of experimental measurement can be done by one of the powerful codes such as MCNP, BEAM, EGSnrc, PENELOPE, GEANT4, and ETRAN/ITS.38-40 This work aims to evaluate the radiotherapy dosimetry of human eye for COMS eye plaque containing brachytherapy source in the presence and absence of the GNPs. We employed the MCNP code to do this study. This code uses a three-dimensional heterogeneous geometry and transports photons and electrons in the energy range from 1 KeV to 100 MeV.

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In this code, According to the Monte Carlo method, the type of interaction is randomly sample based on the probabilities of each individual interaction type. Also, the energy deposited in material, the production of progeny particle and the angel of scatter are randomly sampled from differential cross section. By repeating these steps for the large histories, the expectation value of the absorbed dose can be tallied.41 This study has been conducted with two phantom test cases (water phantom and complete simulated human eye) in which, the brachytherapy treatment of a choroidal melanoma tumor has been calculated, using the COMS standard eye plaque loaded with I125 sources. We simulated the water phantom and the human eye globe in a manner similar to the one indicated in our previous work.36 A full human eye globe has been simulated by this code precisely by considering different parts of the eye and their components. The geometric characteristic of this phantom is in accordance with the eye of an adult. The dimensions of the adult human eye are relatively constant and differ by only one or two millimeter. It has an anterior to posterior diameter of 24 millimeters, but the vertical diameter is generally less than that of the horizontal of that and are 23mm and 23.5 mm respectively so the spherical shell of 24.6 mm has been considered as an eye globe. In this work, in order to define a complete eye globe, its components have been simulated using interface among different shapes with specific geometry and characteristic.  The common volume between Four concentric spheres with radii of 0.93, 1.03, 1.13 and 1.23 cm (centered at the origin of the coordinate) are the introducer of Retina, Choroid and Sclera, (three primary layers of the eye), respectively.  The common volume between two ellipsoids centered on (0, 0, 0.73) cm with the coordinates of (0.80, 0.79, 0.78) and (0.88, 0.85, 0.81) cm and the outer surface of the Sclera are descriptive geometries of the Cornea and Anterior Chamber in this Monte Carlo simulation.  The lens is defined as an ellipsoid centered on (0, 0, 0.77) cm with an equatorial diameter of 0.8 and 0.9cm and a polar diameter of 0.25 cm.  The optic nerve has been defined as the common volume between two concentric cylinder with the diameters of 7 and 8 mm and the outer layer of the Sclera.  The skull bone has been simulated by considering the common volume between two concentric sphere with radii of 1.505 and 2.05 cm and a plane defined at Y = 1.23 cm. The longitudinal section of the simulated human eye phantom at origin and the voxels which are the introducer of the critical points of interest have been showed in figure 1. 6

Figure 1: The longitudinal section of simulated human eye. The voxels (numbered 1 to 6) indicate the points of interest for center of Lens, sclera, Tumor apex, opposite side, Macula and optic nerve, respectively.

The coordinates of these pointes are as follows: 1: Center of lens (0, 0, 0.77) cm 2: Sclera (0, 1.13, 0) cm 3: Apex (0, 0.63, 0) cm 4: opposite side of the eye (0, -1.13, 0) cm 5: Macula (0, 0, -1.13) cm 6: Optic disk (0, -0.4, -1.06) cm The complete information about the simulated eye geometry and the composition of some of its parts can be accessible in the previous report and some medical references36, 42-49. However, the composition and density of a certain eye tissue used in this simulation are given in table1. As has been emphasized in the previous report, the geometry and characteristic of this simulated eye globe have been determined in a manner that the dimension and specification of main parts of the human eye could be in conformity with the medical data.

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2-2 Choroidal Melanoma Choroidal Melanoma as one of the three kinds of the Uvea melanoma (choroidal, ciliary body and iris melanoma) is the malignant primary intraocular tumor which arises from the pigmented cells of the blood-vessel layer of the eye (Choroid) beneath the Retina. The treatment of the intraocular tumor depends on its size and apical height. Plaque brachytherapy can be used for the treatment of tumors with the apical height of 2.5 to 10 mm and the basal diameter of 16 mm or less. In this work, a choroidal melanoma tumor with the apical height of 0.5 cm (6mm from the exterior surface of the Sclera according to COMS definition for the point of dose prescription) has been simulated in both phantoms. This tumor has been assumed to be on the equator temporal to the eyeball.

2-3 Ophthalmic Plaque and brachytherapy source In our previous investigation, we have reported the absorbed dose to some points of interest in the water phantom and the simulated human eye globe, using 16 mm COMS standard eye plaque loaded by one 125I seed in the central slot of the plaque. In the current investigation, the fully-loaded 16 mm COMS eye plaque containing 13 125I (model 6711, GE Healthcare/Oncura) seeds as brachytherapy sources has been modeled. These sources are sandwiched between a gold outer plaque constructed of a gold alloy modulay with a density of 15.8 g/cm3 and an inner plastic seed career constructed of silastic with a density of 1.12 g/cm3. The geometric information and composition of the simulated plaque obtained from some references50-55 and, also, the coordinate of 13 seeds for this plaque are in accordance with the standard position for COMS-plaque56. Detailed geometry and characteristic for I125 seed model 6711 have been taken from the publicly accessible website of Carleton Laboratory for Radiotherapy physics seeds database57. The photon spectra quoted in TG-4358 has been used to sample the initial photon energies and probabilities for this brachytherapy source. The full loaded eye plaque has been modeled at the center of the 30×30×30 cm3 simulated water phantom and also has been simulated next to the tumor in the eye globe. This radioactive plaque has been positioned on the sclera to cover the simulated tumor base which has been centered on (x y z) = (0 1.23 0) cm.

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2-4 Gold nanoparticles Recent studies found that GNPs increase the radiation sensitivity of cancer cells and can potentially be used for targeted cancer treatment26,

59-62

. In these studies, after intravenous injection,

transmission electron microscopy (TEM) demonstrated that GNPs are accumulated in clusters within the membrane bound vesicles and lysosomes. The tumor vasculature is leakier than the normal blood vessels and there is no lymphatic drainage in the tumor. So, regarding the poorly formed tumor vasculature, the accumulation of unlabeled nanoparticles within the tumor can occur under passive targeting by increasing the permeability and the retention effect (EPR) 63-64. Regarding the report by Sheng Zhang et al34 about the eye tumor, the conjunction of nanoparticles in a suitable size with the ligands specified for the uveal melanoma cells has been found to be a good way for transferring these particles to the tumor area which would help them to stay in the melanoma tissue for a long time. Due to the difference of the pressure of the cancerous tumor between the center and surface of that, it is predictable the permeation of nanoparticle inside the tumor can occur only in the specific parts of that. In some studies it has been shown that intravitreous (for eye tumors) or intravenous injection of nanoparticles resulted in accumulation of these particles in the Melanoma tissue near the capillary34, 65. The primary goal of this work as a first step -due to the limited number of studies in this field-, has been just to study of the effect of GNPs inside the eye melanoma tumor on dosimetry calculation. In our simulation, the tumor filled by a 0.1 cm3 quadrilateral lattice and the spherical GNPs of 50nm has been simulated inside the tumor. The DEF has been calculated in both water phantom and eye globe for different concentrations of GNPs.

3-Result Calculation of Tg-43 parameter The seed model used in this study has been benchmarked via calculations of the TG-43 dosimetry parameters (Air Kerma Strength, dose rate constant and radial dose function) and has been compared with the results reported by Taylor et al57 and M. J. Rivard et al58.

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The radial dose function has been calculated through simulation of the source at the center of the water phantom with dimensions of 30×30×30 cm3. To calculate the dose fall-off on the transverse plane, the toroid cells (torus-shaped cells) at radial distances ranging from 0.05 to 10 cm, have been simulated. This calculation has been done using *F8 tally. The thickness of the toroid cells has been chosen in the following way: 0.008 cm for the distance between 0.05 < r ≤ 0.1, 0.01 cm for 0.1 < r ≤ 1 cm, 0.05 cm for 1 < r ≤ 5 and 0.1 cm for 5 < r ≤ 10. Calculated Radial Dose Function (DEF) reported in TG-4358, which was measured by Taylor et al57 and calculated in this work, has been shown in table2 and figure 2.

Figure 2: Radial dose function for I125 source. Voxel sizes are: 0.008 cm for distance between 0.05 < r ≤ 0.1, 0.01 cm for 0.1 < r ≤ 1 cm, 0.05 cm for 1 < r ≤ 5 and 0.1 cm for 5 < r ≤ 10. Symbol of Circle and Triangle are values calculated by Taylor et al57 and J. Rivard et al58.

Under the same condition, the dose rate Ḋ (r0, 𝜃0) has been calculated as the dose to water per history at the reference point (r0 = 1 cm, 𝜃0 = Π/2) in a torus with 0.01cm thickness. It should be noted that R0 and 𝜃0 are the transverse distance and the axis from the source center, respectively.

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The dose rate constant, Ʌ, has been obtained as the ratio of the calculated dose rate to the air kerma strength (Sk) with the unit of cGy.h-1U-1, where U is the unit of air-kerma strength of the source and is defined as 1U=1 µGym2/h-1. The air kerma strength is defined as the product of the air kerma rate in vacuo multiplied by the square of the transverse distance from the source center according to the TG-43U1 report. The Sk should be independent from the distance so in the Monte Carlo calculation, the cells used to score collision kerma should be positioned at distances that are large enough versus the radioactive distribution length. Here, the air kerma rate has been scored in the toroid cells filled with the dry air and located at distances ranging from 0.05 cm to 20 cm. In this calculation, the source and toroid cells have been positioned in vacuum and F6 tally was used to score collision kerma. The air kerma strength has been calculated for all the considered distances and has been found to be constant from 1cm to 10 cm with uncertainties less than 0.1%, so the average value in this region has been taken as the air kerma strength per history. The result gained from this study and those reported by TG-4358 and Taylor et al57 are listed in table3. Figure 3 displays the isodose contours in the x, y plane at z=0 for the 13 I125 seeds contained in 16 mm Modulay/ Silastic plaque. This plaque has been simulated at the center of the water phantom and the dose has been scored in (0.1 cm)3 voxels. In this plot, 100% depth dose is equal to the dose found at the tumor apex. The more the distance from this point increases, the more the dose increases.

Figure 3: Z-plane, 16 mm plaque (in water) isodose lines from MCNP, 100% at tumor apex.

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Dosimetry calculations In both water phantom and human eye globe, the array of 0.5×0.5×0.5 mm3 voxels have been simulated for scoring the average energy deposition to compare the central axis depth dose between two phantoms. The first and the end voxels are positioned at 0.5 mm distance from the posterior surface of the sclera in the vicinity of the plaque and opposite side of the eye. Figure 4 shows the depth dose curve for 125I sources in the fully-loaded 16 mm COMS eye plaque in both the water and the eye phantoms where the dose is quoted relative to the dose at the tumor apex. The calculated depth dose in water phantom has been compared with those calculated by Thomson et al43. An acceptable agreement can be observed between them.

Figure 4: The Plaque central axis depth-dose curves for I125 in water and eye phantom. The vertical axis represents the ratio of dose to the dose at the tumor apex.

As it is clear in this figure, the dose in the first and the end voxel which are in the sclera are about 30 % higher than that of the voxels which contain water. Based on the similarity between the elemental composition of the vitreous body and water, it is clear that the dose in the vitreous is approximately similar to that of the water. The depth dose shows only the dose in the plaque central axis direction, so to study the effect of considering eye composition instead of water in the Monte Carlo eye Melanoma dosimetry, (0.05 cm3) voxels have been simulated at the critical points of interest and the tumor apex whose coordinates have been specified before. Following 2×109 histories, the dose rate at points of interest and tumor apex have been calculated using *F8 tally in 12

both water and eye phantoms. Also, to make a comparison between the effects of GNPs concentration on the dose enhancement factor (DEF) calculation, the spheroid 50 nm gold particles with four different concentrations have been simulated inside the tumor in these phantoms. Considering the treatment time of 100 hours to achieve the dose of 85 Gy at the tumor apex (TG129) and by utilizing the approach of Thomson et al43, the total dose at points of interest has been calculated and reported in table 4. The relative statistical uncertainty is lower than about 1% with the highest percent in the opposite side of the eye and the lowest percent in the sclera among the prescription points represented in this table. The calculated dose at points of interest for seeds in water and plaque in water has been compared with that reported by Thomson et al43. The air kerma strength per seed has been calculated for

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I model 6711 following the way of the air kerma

strength per seed chosen in this report43. Figure 5 presents a comparison between 4 concentrations of GNPs in the calculation of dose enhancement factor (DEF) in both phantoms. The dose enhancement factor has been plotted in the figure as a function of radial distances from the center of the plaque while the plaque is placed next to the tumor in the simulated human eye and the water phantom.

Figure 5: The calculated dose enhancement factors for 50nm GNPs within the tumor with concentrations of (7, 10, 18 and 30mg)/ (gr of tumor) in the water phantom and the eye model. The first voxel has been positioned in the sclera and the second to eleventh voxels have been placed inside the tumor. The other voxels have been placed outside of the tumor. DEF calculations have been done in the simulated human eye using the data of table 1 and the water phantom too. Full loaded 16 mm COMS eye plaque has been positioned next to the tumor on the equator temporal to the eyeball. (eye) referred to a full simulated human eye globe filled with eye material and (water) referred to the water phantom. 13

Figure 6 shows the ratio of the central axis depth dose to the dose at the tumor apex for 16mm COMS eye plaque in water phantom, eye globe and simulated human eye with nanoparticlesinduced tumor.

Figure 6: The ratio of the full loaded 16mm COMS eye plaque’s depth doses to the dose at the tumor apex in the water phantom, simulated human eye, and simulated eye in which 4 concentrations of GNPs are defined inside the tumor.

4-Discussion In the cancer radiotherapy, an adequate radiation dose for tumor treatment is estimated, considering the type of the tumor and the rate of its progress. Determination of the required dose for tumor treatment or control of the tumor growth specifies the treatment time. Regarding the defined prescription dose to the tumor apex, when the dose to the tumor is increased, the time that is required to irradiation decreases which results in a dose reduction in other parts of the eye. During the process of tumor irradiation, the healthy tissue nearby and the tumor follow the same pattern in absorbing the energy from ionizing radiation. The results of table 4 show that defining the nanoparticles in the tumor area lead to the dose increase inside the tumor with no significant changes in the absorbed dose by other parts of the eye in both phantoms. Upon calculating the dose to the tumor apex in the presence of GNPs inside 14

the tumor with the concentrations of 7, 10, 18 and 30 mg/ (gr of tumor), the amount of the dose to apex is found to be increased by about 1.9, 2.2, 3.2 and 4.6 orders of magnitude, respectively, in the eye model and about 1.9, 2.3, 3.3 and 4.8 orders of magnitude, respectively, in the water phantom. Although the difference between the amounts of the increased dose in the apex of the tumor seems to be not very much in both phantoms, the results of the table 4 show that considering the composition of the eye materials has an influence on the dose calculation in the Choroidal Melanoma dosimetry, particularly, when the GNPs present inside the tumor. For instance, in the absence of the GNPs, the dose to all points of interest in the eye phantom differs from that of water phantom. The dose to the center of lens and optic disk in the eye is lower than the dose calculated in these points in water. On the contrary, the dose to the sclera, apex and the opposite side in the eye are more than that of the water phantom. The dose increase in the sclera is about 28% and the dose reduction in the lens is about 11.6%. The difference between the results of dosimetry in the eye model and water phantom observed more prominently when the GNPs are defined in the tumor in both phantoms. For example, in the presence of 18mg/g GNPs there is an increase of 20% in the eye model and 4% in the water phantom in the dose absorbed by sclera relative to that of the eye and water phantom with no nanoparticles present. This can be a result of the fact that the back scattering in the eye model is lower than the water phantom. Also, in the presence of the same concentration of GNPs the dose absorbed by the Lens in the water phantom is increased about 10% whereas in the eye model, no significant change is observable. Furthermore, in the opposite side from the plaque, there is an increase of about 10% in the water phantom while a decrease of about 7% is observable in the eye phantom in compare with that of these phantoms with no nanoparticles present. In table 4, a comparison of the effect of the plaque for multiple seed simulation has been shown too. The data shows that the presence of the plaque around the seeds causes a decrease in the dose to all points of interest. In the water phantom at the point at the sclera from the plaque and at the tumor apex, the dose reduction is about 14 % in the presence of the plaque relative to the same configuration of seeds with no plaque present in the water. This amount is increased as the distance from the plaque is increased. The dose reduction is a consequence of the elemental composition of the plaque backing gold alloy and the silastic seeds career. The high atomic number of the gold causes enhanced photoelectric absorption and results in a dose reduction. When the plaque is 15

placed in the eye phantom the dose absorbed by the sclera is increased by about 28% as compared to that of water phantom and is increased by about 9% as compared to that of the seeds in water. The aforementioned increase and decrease can be due to the eye material and the plaque presence, respectively. Considering the elemental composition and density, the difference between the eye material and water causes a difference in such a dose calculation. Regarding the results of Table 4 and considering the relative statistical uncertainty lower than about 1% in all calculations, the discrepancies between water and eye phantom are considerable in all parts of the eye. However, considering systematic uncertainties in eye plaque therapy, the discrepancies in some parts such as center of eye and Macula may be in the range of uncertainties, and therefore they may not be reliable. As can be noticed from the figure 5, the tumor dose enhancement in the higher concentration of GNPs is larger than that in the lower concentration in both the water and the eye phantoms. However, the notable result is that in the certain concentrations of GNPs, the DEF value in the water phantom is more than that in the eye phantom. Such a difference is more prominent at higher concentrations. In this figure, the results show that the difference between the eye and the water phantom increases by increasing the nanoparticles concentration. For a certain concentration, the calculated DEF is not the same for all parts of the tumor and the DEF distribution is heterogeneous. Since the photoelectric cross-section depends on the atomic number of the material and photon beam energy, using the I125 as a low energy photon source and GNP as a high Z material, can increase the number of photoelectric interaction inside the tumor. Heterogeneous DEF distribution within the tumor can be a consequence of the high scattering when the low energy photon beam interacts with GNP. Non-uniformity in DEF distribution is more observable in higher GNP concentrations. The results of figure 6 show that the presence of the GNPs inside the tumor increases the dose to apex, so the ratio of the depth dose to the dose at the tumor apex is decreased by increasing the GNP concentration. As it is evident from the figure, the reduction of this ratio inside the tumor is the same for all concentrations of GNP and also in both water phantom and eye globe without GNP. This shows that the percentage of the dose reduction or dose increase inside the tumor is the same for all points on the plaque central axis.

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6-Conclusion In this study, we built a Monte Carlo simulation model of human eye considering its composition closer to reality and the water phantom to investigate the effects of the GNPs on radiation dose enhancement in ophthalmic brachytherapy dosimetry. The results show that a significant tumor dose enhancement could be achieved, using GNPs inside the tumor during the irradiation by low energy source. In a certain diameter of GNPs, the results of the dose calculation show a higher dose enhancement for the higher concentration of GNPs. Certainly, a different size of GNPs with considering the cytotoxicity effects of GNPs will make a difference in similar calculations. The presence of GNPs inside the tumor made no significant changes in the dose to other parts of the eye. This can be a reliable approach to irradiate the eye tumor with making no dose increase to healthy tissue. Furthermore, comparing the dosimetry calculations in the presence of GNPs between the water phantom and the eye model, lays emphasis on the significant of the more accurate definition of the eye material in ophthalmic brachytherapy. Although the results of the Monte Carlo study in this investigation show that the presence of GNPs inside the tumor could play an important role in dose enhancement the availability of the experimental study (in-vitro or in-vivo) in Melanoma could result in a better understanding of the effect of GNP in the melanoma dosimetry. A full experimental investigation of the effects of the GNPs inside the choroidal melanoma on brachytherapy dosimetry is left to a future study which requires a real experimental melanoma tumor.

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22

Table 1: Composition and density of certain eye tissues used in this simulation.39-46 Density (gr/ cm3)

Material Elemental Composition (% by Mass) Material

H

O

C

N

Na

Mg

P

S

Ar

Cl

K

Ca

Water

11.11901

88.8099

---

---

---

---

---

---

---

---

---

---

0.9980

Dry air

---

23.17812

0.012425

75.52673

---

---

---

---

1.282725

---

---

---

0.0012

Lens

9.60

64.60

19.50

5.70

0.10

---

0.10

0.30

---

0.10

---

---

1.07

Sclera

9.60

74.40

9.90

2.20

---

0.50

2.20

0.90

---

0.30

---

---

1.09

Vitreous

11.0867

88.052

0.068

---

0.2647

0.0025

0.002

---

---

0.502

0.0171

0.005

1.00

Aqoues humor

11.085

88.06

0.056

0.00001

0.348

0.0025

0.0018

0.00001

---

0.432

0.00798

0.0067

1.01

Optic nerve

10.70

76.70

9.50

1.80

0.20

---

0.30

0.20

---

0.30

0.30

---

1.039

Skull bone

5.00

21.20

4.00

0.10

0.20

8.10

0.30

---

---

---

17.60

1.61

Tumor

10.8

4.10

1.10

---

0.30

---

0.10

---

0.40

---

---

1.03

43.50

83.2

23

Table 2:Radial dose function data for the oncoseed 6711 source Distance from source(cm) 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

This work

Taylor et al56

TG-4355

1.115 1.050 1.068 1.069 1.071 1.050 1.064 1.066 1.062 1.059 1.050 1.075 1.060 1.040 1.040 1.030 1.012 0.995 0.900 0.800 0.710 0.615 0.550 0.472 0.406 0.361 0.310 0.267 0.230 0.199 0.172 0.143 0.123 0.104 0.092 0.0762

1.139 1.094 1.08 1.077 1.078 1.08 1.089 1.096 1.096 1.093 1.086 1.075 1.062 1.048 1.042 1.035 1.018 0.998 0.909 0.813 0.721 0.633 0.557 0.484 0.419 0.361 0.313 0.269 0.231 0.198 0.171 0.146 0.125 0.107 0.0914 0.0775

---------------1.055 1.078 ---1.082 ------1.071 ------1.042 ------1 0.908 0.814 ---0.632 ---0.496 ---0.364 ---0.270 ---0.199 ---0.148 ---0.109 ---0.0803

24

Table 3: Calculated dose rate constant, Ʌ, of I125 brachytherapy source in water. dose rate constant

R. Taylor, D. Rogers55 0.942

M. J. Rivard et al56 0.965

25

This work 0.923±0.011

Table 4: Comparison of the dose at point of interest in (Gy) for a 16 mm eye plaque located next to the tumor on the equator temporal to the eyeball. Columns labeled “S.W” compare the dose for 13 125I seeds in water phantom no plaque present and columns labeled “P.W” compare the dose for 13 125I seeds with plaque present in water phantom. (Eye) refers to simulated human eye using the data of table 1 and (water) refers to the simulated human eye in which all parts of the eye filled with water. “Plaque in eye” refers to the 13 125I seeds with plaque present in eye phantom. “7, 10, 18 and 30 mg/gr” refer to the concentration of GNPs define inside the tumor in both phantom. The relative statistical uncertainty is lower than 1%.

S.W

S.W

P.W

P.W

Thamson

This

Thamson

This

et al43

work

et al43

work

Sclera

262.1

261.53

222.7

223.54 285.93 267.73 298.92 267.73 298.92

270.33 298.92 270.33 298.92

Apex

85.00

85.00

74.40

73.66

76.50

141.38

142.8

168.58 170.29

244.80 245.08

355.0

354.16

27.92

27.63

23.68

22.66

22.49

23.80

23.74

23.82

23.77

23.82

23.77

23.80

23.80

6.83

6.80

5.453

5.16

6.53

5.72

6.09

5.72

6.01

5.72

6.01

5.75

6.01

11.35

10.39

8.947

8.11

7.80

8.26

8.11

8.24

8.08

8.24

8.08

8.26

8.05

Lens

21.75

21.45

17.53

17.30

15.30

18.98

15.49

19.09

15.32

19.06

15.32

19.01

15.28

Macula

16.45

15.75

12.80

11.46

11.62

12.55

12.40

12.53

12.40

12.53

12.40

12.63

12.40

location

Center of eye

Opposite side

Optic disk

Plque in

7mg/gr

7mg/gr

10mg/gr

10mg/gr

18mg/gr

18mg/gr

30mg/gr

30mg/gr

eye

(water)

(eye)

(water)

(eye)

(water)

(eye)

(water)

(eye)

26