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 Table of Contents  
Year : 2015  |  Volume : 11  |  Issue : 4  |  Page : 752-759

Tumor dose enhancement by nanoparticles during high dose rate 192 Ir brachytherapy

1 Department of Medical Physics, School of Medicine; Department of Radiotherapy and Radiation Oncology, Golestan Hospital, Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran
2 Department of Medical Physics, School of Medicine, Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran

Date of Web Publication15-Feb-2016

Correspondence Address:
Mansour Zabihzadeh
Department of Medical Physics, School of Medicine, Ahvaz Jundishapur University of Medical Sciences, Golestan Blvd, Ahvaz-61357-33118
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0973-1482.153668

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 > Abstract 

Aims and Objectives: The present study aims to evaluate and compare the dose enhancement factor (DEF) of tumor injected with different nanoparticles (NPs) around high dose rate (HDR) 192 Ir brachytherapy source.
Materials and Methods: Monte Carlo calculations were performed with MCNPX code to determine the DEF caused by in tumor injected with 79 Au, 64 Gd, 26 Fe, and 22 Ti NPs during HDR 192 Ir brachytherapy. The uniform and non-uniform distribution of NPs within tumor was modeled with simple NPs-water mixture, and realistic nano-scale-lattice model. Furthermore, a margin of 79 Au and 64 Gd NPs was implemented around the tumor volume.
Results: The increased dose caused by uniformly distributed 79 Au and 64 Gd NPs with 7, 18, and 30 mgr/gr concentrations was 4.7%, 11.8%, 19.4%, and 3.3%, 8.3%, and 18.6%, respectively. For non-uniform distribution, it was 0.4%, 1.2%, 1.9%, and 0.2%, 0.7%, and 1.2%, respectively. Increased tumor dose due to 26 Fe and 22 Ti was not significant. The peripheral-healthy tissue dose as margin with 2, 5, and 8.5 mgr/gr of 79 Au and 64 Gd increased by 1.3%, 3.6%, 6.5%, and 1.1%, 2.5%, and 4.2%, respectively. Increase the radial depth of tumor (from 1.5 to 5 cm) increase DEF (up to 22.3%). The nano-lattice model underestimated the DEF up to 4% and 3.6% for 79Au and 64 Gd NPs, respectively.
Conclusion: Injecting of high-Z gold NPs into tumor increases the absorbed dose of tumor irradiated with 192 Ir HDR brachytherapy source. Size, geometry, concentration, and distribution model of NPs and tumor depth are crucial factors to accurately estimate the DEF.

Keywords: Brachytherapy, dose enhancement factor, Monte Carlo simulation, nanoparticles, photoelectric interaction

How to cite this article:
Zabihzadeh M, Arefian S. Tumor dose enhancement by nanoparticles during high dose rate 192 Ir brachytherapy . J Can Res Ther 2015;11:752-9

How to cite this URL:
Zabihzadeh M, Arefian S. Tumor dose enhancement by nanoparticles during high dose rate 192 Ir brachytherapy . J Can Res Ther [serial online] 2015 [cited 2022 Aug 18];11:752-9. Available from: https://www.cancerjournal.net/text.asp?2015/11/4/752/153668

 > Introduction Top

The most challenging issue in a radiotherapy is to deliver a lethal dose precisely to tumor cells while minimizing the delivered dose to healthy surrounding tissue. [1],[2] In theory, photoelectric cross-section is approximately proportional to (Z/E 3 ) where Z is atomic number of mass and E is the energy of emitted photon. In this regard, the idea of using high-Z absorbent materials with low energy photon beams to enhance dose in tumor has gain a research interest during last years. [3],[4],[5],[6],[7],[8] The application of nanotechnology in various scientific fields has been studied by several authors in recent years. [9] Nanoparticles (NPs) as their nano-scale size can easily traverse blood vessels into tumor making them efficient agents to improve different medical treatments. [10] For instance, NPs are currently used in infrared activated thermal therapy, [11],[12],[13] diagnostic imaging, [13],[14] targeted drug and gene delivery, and molecular labeling. [15],[16],[17],[18],[19] In recent years, various NPs-based studies have been conducted to enhance tumor dose. Hainfeld et al., successfully detected a small size tumor in a mouse using gold NPs as a contrast enhancing agent in a 250-kVp X-ray beam. [20] Cho [9] and Zhang et al., [21] calculated dose enhancement factors for various radiation sources and gold NPs concentrations. In addition, other studies [10],[19],[22],[23],[24],[25],[26],[27],[28],[29] demonstrated the efficiency of NPs in increasing absorbed dose. Brachytherapy sources contain relatively low energy (<500 Kev) with the most efficient output in interaction with high-Z target substances. In addition, these sources can be implanted near or inside the target because of their small volumes. These properties increase the potential of local dose delivery to tumor as the dose intensity fall off with increasing radial distance. [30]

However, few qualitative and quantitative studies with controversial findings are available on the application and efficiency of NPs to enhance tumor dose during brachytherapy to enhance existed with controversial findings. Therefore, the present study aims to evaluate and compare the dose enhancement factor (DEF) of tumor injected with different NPs in Nucletron MicroSelectron high dose rate (HDR) 192 Ir brachytherapy source. Different concentrations of NPs are evaluated in the study.

Direct injecting NPs into a tumor, as the target volume, is not practically possible as it increases the effective Z in the surrounding healthy tissue. Compared with the normal surrounding tissue, center and periphery regions of a tumor, respectively, have lower and higher blood flow resulting in a heterogeneous distribution of NPs in the field of radiotherapy. Therefore, the non-uniform distribution of NPs was modeled separately as well as the uniform distribution. Finally, the effects of these two NPs distribution models within tumor (water-NPs mixture and real geometry NPs models) on DEF were investigated.

 > Materials and methods Top

Monte Carlo calculations were performed with MCNPX (2.6.0) code to determine the dose enhancement factor (DEF), defined as the ratio of dose with and without gold NPs in the tumor region. [9]

192 Ir source

The HDR 192 Ir source was produced using a MicroSelectron-HDR remote after loading system. The structure and dimensions of the source are presented in [Figure 1]. The active source was radioactive material uniformly distributed inside a pure iridium metal (22.42 gr/cm 3 ) cylinder, 0.60 mm diameter, 3.5 mm height. It was encapsulated in stainless steel and welded to a steel cable. The capsule was 5 mm long and 1.1 mm in overall diameter. Its distal end was a steel cap with a 0.55 mm radius. The American Iron and Steel Institute (AISI) 316L steel of 8.02 gr/cm 3 density with elemental composition by weight: 2% Mn, 1% Si, 17% Cr, 12% Ni, and 68% Fe. [31],[32] The source was positioned in the center of water phantom (30 cm 3 ) with 4π-isotropic beam geometry irradiation. Its gamma spectrum ranging 0 to 885 Kev was extracted from evaluated nuclear structure data file (ENSDF) decay data reported by Medical Internal Radiation Dose (MIRD). [33],[34] Beta irradiation from 192 Ir decay and characteristic X-ray irradiation produced in its capsule were mostly absorbed in the source capsulation or delivered some extra dose only in short distance from the source (<1 mm). [35] This issue was not implemented in the simulation to considerably shorten running time.
Figure 1: Internal construction and dimensions of 192Ir microSelectron HDR source and a water phantom (30 × 30 × 30 cm3) with tumor (1 × 1 × 1 cm3) located 1.5 cm from the source

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TG-43 Dose parameter calculations

Dose-rate constant (L), radial dose function (g(r)), and two-dimensional (2D) anisotropy function, F(r, θ) were calculated as defined by the American Association of Physicist in Medicine (AAPM) in the TG-43 Report. [34] Our data were compared with the published data by Karaiskos et al., [32] and others for the same source to validate our simulated source. The water phantom (30 cm 3 ) is voxelized to cell with size 2 mm 3 by lattice geometry to calculate AAPM TG-43 parameters. Because of the symmetry of phantom relative to the longitudinal axis of source, its voxelization was limited only in the upper part to save the running time of the programs. Dose in each 11250 voxels was calculated using the total energy deposition tally (i. e., *F8). Energy cut-off threshold to terminate photon and electron transports were 5 and 10 keV, respectively. No other variance reduction methods were used in the simulations.

Dose enhancement factor

NPs-water model

A cube water phantom (30 cm 3 ) was simulated [Figure 1]. The 192 Ir source was centered in the phantom and tumor was defined as a cube (1 cm 3 ) located 1.5 cm above the source along the Z-axis. In separate MC simulations, DEF of tumor injected with four different NPs (79Au, 64Gd, 25Fe, 22Ti) was calculated. The four NPs were implemented in three concentrations (7, 18, 30 mgr/gr) in the simulations. Three levels of NP concentrations 7, 18, and 30 mgr/gr, were previously reported suitable for clinical applications. [9],[20],[27],[31],[36] In the first simulation round, tumor volume was divided into 11 sections with the thickness of 2 mm. Dose was calculated with no NPs injection into tumor volume [Figure 1]. In the second round, the NPs-water mixture model was used to simulate the NPs within the tumor. NPs were uniformly distributed within the tumor. Most of solid tumors have non-uniform vascularity distribution with higher vascularity in their outer layers compared with the inner layers. As a result, NPs distribution would not be uniform throughout the tumor. Therefore, in the third round of calculation, DEFs were estimated by substituting the NP-containing region with the same total concentrations of NPs but with non-uniform distribution.

C = Aexp(r) (1)

Where C (mgr/gr) is the concentration of GNPs in each section; A the constant dependent on the total concentration, and r (cm) is distance from the tumor center. In this case, dividing tumor volume into 11 slices, the concentration of the central slice was set to 0% and gradually increased toward the outer slices with the same total NP capacities, as considered for uniform distribution.

To investigate the effect of NPs surrounding the tumor, a 0.27 cm thickness margin around the tumor with concentrations of 2, 5, 8.5 mgrAu/gr of water was considered for the three concentrations 7, 18, and 30 mgr/gr, [9],[27] respectively. For more evaluations, the effect of radial distance of tumor from source (1.5, 2, 2.5, 3, 5 cm) and energy (mono-energy or energy spectrum emission of 192 Ir source) on DEFs were studied. Irradiation of beta and the characteristic X-ray from beta absorption in stainless steel capsule of 192 Ir source were not implemented in simulations since these irradiations, if penetrate the encapsulation, do not increase dose significantly except in small distances (<2 mm). In this study, the tumor volume was centered 1.5 cm above the source.

NPs lattice geometry model

Zhang et al., (2009) reported that the mixture model overestimates DEF compared with nanometer geometry model up to 16%. Therefore, implementing a real model to estimate dose in the presence of NPs is crucial. Reconstructing nano-scale geometry of NPs is a time consuming process challenging computer capabilities. In the case of uniform distribution, nano-scale geometry model was considered for all the NPs to investigate more details of DEFs. Each NP was considered spherical with radius of 100 nm centered in the grid. Using lattice geometric, the tumor volume (1 cm 3 ) was divided into 125000 parts and used to calculate tally. Each part (0.2 mm 3 ) was voxelized by grids including nanospheres. The grid size differs for each material and concentration. In this regard, grid size for 7 mgr 79 Au/gr concentration was 1.13 × 10 -4 cm resulting in 6.92 × 10 11 NPs for the tumor volume, while for 7 mgr 22 Ti/gr concentration it was 6.96 × 10 -5 cm with total 2.97 × 10 12 NPs. Similar to the NPs-water model, the tumor volume was divided into 11 segments and DEFs were reported for them. DEFs were calculated in five points at before and after depths of the tumor volume. For the non-uniform distribution model, only gold GNPs were implemented and the tumor volume was divided into 5 segments with concentration defined by Eq. 1. Each equal segment (thickness 2 mm) was filled with related grid and concentration of GNPs. In each segment, DEF was reported for two parts along the axis perpendicular to the central axis of the source whereas the averaged DEF of tumor was calculated as the average on the total grids in all parts of segments. The same geometry was simulated for the uniform NPs distribution.

 > Results Top

The statistical uncertainty (1σ) to calculate TG-43 dosimetry parameters was less than 2.7% at all radial distances with transporting 10 8 photon histories in phantom with lattice geometry. The maximum statistical uncertainty (1σ) to calculate tumor dose was 0.44% at all radial distances with transporting 10 9 histories.

TG-43 Parameters

The statistical uncertainties of the calculated air kerma rates at all distances were less than 0.01%. Air kerma strengths (Sk) for all the calculated radial distances were constant with 0.2% fluctuation. Therefore, the average values of air kerma strengths were used to calculate dose rate constant. The calculated dose rate constant, 1.127 (±0.84%) cGyh -1 U -1, was in good agreement with previous studies with acceptable errors [Table 1]. The maximum difference of 1.45% was calculated compared with the Kirov et al., study. [39]

The calculated radial dose function, g (r), in water phantom for the 192 Ir MicroSelectron HDR source [Table 2] were compared with the data reported by Karaiskos et al., [32] Maximum difference of 2.75% was calculated for the largest radial distance of 14 cm which is insignificant compared to the related error.
Table 3: 2D anisotropy function, F(r, è), as function of polar angles (è) in water phantom for the 192Ir MicroSelectron high dose rate (HDR) source

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Table 1: Dose rate constant, Ë (cGy h-1 U-1), for the 192Ir MicroSelectron high dose rate (HDR) source

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2D anisotropy functions, F(r, θ), are listed in [Table 3]. Because of the cubic lattice geometry of upper part of water phantom, there are few voxels with the same radial distance from the center of the source. To validate our results, the data for r = 10 and 50 mm were compared with those reported by Karaiskos et al., [33] For example, discrepancies of <5% were obtained for r = 50 mm in θ =143.13°.
Table 2: Radial dose function, g (r), in water phantom for the 192Ir MicroSelectron high dose rate (HDR) source. The uncertainty of radial dose was calculated as

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Dose enhancement factor

Maximum uncertainties to calculate dose enhancement factor for NPs-water mixture and NPs geometry models with transport of 10 8 histories were 0.44% and 4.5%, respectively.

Dose enhancement from NPs-water mixture model

The average calculated DEFs by NPs-water mixture model for uniformly and non-uniformly distributed NPs within the tumor volume and non-uniform NPs distribution with NPs surrounding the tumor volume are presented in [Table 4]. In the all cases, the maximum average DEF was calculated for the gold NPs and for the highest concentration. Whereas, the calculated DEFs for 64 Gd were lower compared to 79 Au.
Table 4: Average dose enhancement factor (DEF) in total tumor volume in nanoparticles (NPs) - water mixture model. The value in parentheses are in the case of mono-energy irradiation (360 Kv) of 192Ir source

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The differences between the DEFs inside and surrounding the tumor volume depend on the radial distances from the center of the 192 Ir source [Figure 2]. The dose did not change in the depths before the tumor location, whereas it gradually increased (for 79 Au and 64 Gd) with depth inside the tumor volume to reach its maximum at the bottom of the tumor. From [Table 4] and [Figure 2], this increase was not considerable for 26 Fe and insignificant for 22 Ti.
Figure 2: Calculated dose enhancement factor (DEF) for uniform NPs distributions as function of radial distance from the 192Ir source; for (a) 79Au, (b) 64Gd, (c) 26Fe, and (d) 22Ti. The amount of NPs shown in the legend is per gram of tumor

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Similar to uniform distribution, maximum DEFs for non-uniform distribution for 79 Au increased with increasing concentration [Figure 3]. In whole, uniform distribution overestimates dose enhancement compared to non-uniform distribution (averaged on all concentrations, 11.10% and 7.65% for 79 Au and 64 Gd, respectively).
Figure 3: Calculated dose enhancement factor (DEF) for non-uniformly NPs distributions as function of radial distance from the 192Ir source; (a) for 79Au and (b) for 64Gd. The amount of NPs shown in the legend is per gram of tumor

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The DEFs due to considering of gold or gadolinium NPs margins in the surrounding tissue of the tumor were estimated [Figure 4] while within the tumor remained almost the same of without margin.
Figure 4: Calculated DEFs for non-uniformly distribution of NPs in tumor with presence of NPs in surrounding normal tissue with 0.27 mm thickness as function of radial distance along transverse axis of the 192Ir source; (a) for 79Au (b) for 64Gd. The amount of NPs shown in the figure legend is per gram of tissue

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Mono-energetic versus energy-spectrum emission

As could be seen from [Table 4], while DEFs for mono-energy are slightly greater compared to real spectrum 192 -Ir source, these differences were not significant.

Effect of radial distance

Calculations showed that DEFs for 18 mgr Au/gr concentration increases as tumor depth increases [Table 5]. This increase could be due to decrease of average energy of photon with penetrating and resulted increased photoelectric interaction. However, dose decrease with increase of distance but DEF as a ratio would be increased.
Table 5: Average dose enhancement factor (DEF) in the tumor volume for different distances of tumor from 192Ir source

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Dose enhancement from NPs geometry model

From [Table 6], the NPs geometry model underestimates DEF compared to the water-NPs mixture model (in average 1.13% and 1.61% overall concentrations for 74 Au and 69 Ga, respectively). The averaged DEFs for non-uniform distribution of gold NPs-water mixture and gold NPs geometry model did not show significant differences.
Table 6: Calculated dose enhancement factors (DEFs) in nanoparticles (NPs) geometry model with 100 nm diameter for uniform and non - uniform distribution

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 > Discussion Top

Comparisons of our data with previous studies for dose rate constant [Table 1], radial dose function [Table 2], and 2D anisotropy functions [Table 3] showed a good reliability of our model to estimate dose distribution for 192 Ir source as recommended by the update AAPM TG-43 protocol. [35]

Our results show that injecting tumor with high-Z NPs increases the absorbed dose of the tumor irradiated by low energy photons of 192 Ir HDR brachytherapy source due to increased photoelectric interactions. As shown in [Table 4] and [Figure 2], the tumor injected with high-Z 79 Au and 64 Gd that increase photoelectric interactions (13.6% and 20.1% for 79 Au and 64 Gd, respectively; 30 mgr/gr concentration). These increases were not significant for 26 Fe and 22 Ti (7% and ≈ 0%, respectively). These results were expected as photoelectric interaction is proportional with Z 3 . The increased effective atomic number of tumor volume due to the presence of low atomic number NPs such as 26 Fe and 22 Ti could not shift considerable amount of interactions (most of them are Compton interactions in the range of emitted energy from 192 Ir) to the photoelectric interactions. It can be concluded that applying only high-Z NPs (i.e., gold NPs) will have therapeutic gain in radiation therapy. In addition, as shown in [Figure 2], if NPs accumulations are limited only inside the tumor volume, dose enhancement occurs only in the tumor depths which are ideal in targeting radiation therapy. Our data for uniform distribution were compared with the findings of other studies [Table 7]. Cho et al., (2005) reported an increased dose up to 26% for 30 mg Au/gr concentration in the tumor volume that is comparable to our results as 20%. However, for the lower energy 140 kVp and for the higher energies of 4 and 6 MV, the increase was 100%, 5% and 7%, respectively. Robar et al., (2007) reported that the absorbed dose of tumor volume irradiated by unfiltered-linac photon energies of 2, 4, 6, and 18 MV increased by 8.4%, 10.8%, 13.7%, and 23.1%, respectively. However, they reported the increase for filtered photons (with higher average energy was not greater than 5%. Cho et al., (2009) showed an increased dose of 116%, 108%, and 92% for low energy sources of 125 I, 169 Yb, and 50 kVp with 18 mgr Au/gr concentration in tumor at radial distance of 1 cm. It indicated decreasing energy increases DEFs of the injected tumor with high-Z NPs due to higher photoelectric interactions. However, for the higher energies, increasing energies, i. e, 18 MV, results in higher DEFs because of shift of interactions toward pair production. [40]
Table 7: Calculated dose enhancement factor (DEF) in injected tumor with gold nanoparticles (NPs) for 192Ir source compared to the previous reported data. Positive and negative numbers in parentheses are referred to % difference of our data with others

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Our data are in relatively good agreement with previous studies [Table 7]. However, there are some little discrepancies that can be attributed to the differences in the components of the used materials (tumor, tissue, and phantom), the source models, the tumor sizes and the radial distance from the source, and the initial energy spectra of photon sources. Among the compared data, the maximum difference, under estimation of 7.6%, was with the Cho (2005) study that was because of different models of 192 Ir sources and different distances of the source from the tumor volume ( 192 Ir source centered in the tumor volume, whereas in our study it is located 1.5 cm from the source). Considering the emitted photon beam from 192 Ir in simulations as mono-energy (360 Kv in average) or its real spectrum did not change DEFs. Therefore, this parameter is not crucial to estimate DEF for the 192 Ir source. Increasing distance of tumor from the source from 1.5 to 5 cm increased average DEFs. This increase for 18 mgr/gr was 22.3%, 2.4%, and 7.1% for uniform, non-uniform distribution and margin with non-uniform distribution, respectively [Table 5]. Therefore, depth of tumor is an effective factor that must be considered to estimate DEF in tumors injected with NPs.

Increased NP concentrations inside the tumor volume increased DEF (from 4.9% to 20.1% and from 3.3% to 13.6% for 79 Au and 64 Gd, respectively). Obviously, possibility of photoelectric interaction increases with increasing NP concentration due to increase in effective total cross-section. Direct injection of gold NPs into the mammary tumors induced in mice legs followed by irradiation by 250-kVp X-ray resulted in the survival of 86%. However, it was 20% in irradiation only and the survival fraction of 0% was reported for the control group. [11] The number of cells with apoptosis following injection of gold NPs and 6 Mev electron beam irradiation (25 Gy) was 2 times higher compared to irradiation without NPs. [25] In a study by Zheng et al.,(2009), 2 to 10 kR of gamma irradiation did not induce any obvious instability and size variations in gold NPs. Among NPs, gold are chemically inert with extra capability to penetrate cell membranes that can accumulate inside the tumor region. The concentration levels of gold NPs (up to 30 mgr Au/gr), used in this study, were reportedly used in animal trials as reported by Hainfeld et al., (2008). However, for clinical trials, using high concentrations of some NPs such as carbon nano-tubes has been limited for the unexpected short- and long-term toxicity effects.

Increasing depth inside the tumor increases DEF from the front to the end of the tumor [Figure 2]. Locating maximum DEF at the bottom of tumor following beam attenuation is because of decrease in the average energy of photons by scattering or secondary photons and electrons from upper layers increasing photoelectric interactions. In theory, minimizing surrounding healthy tissue while delivering administrated lethal dose to the tumor cells makes the dose heterogeneities within the tumor volume no serious obstacle in radiation treatment. It is expected that injecting tumor with high-Z number elements decreases DEF beyond depths of the tumor because of increased attenuation of photon by photoelectric interactions within the tumor. This decrease has not been clearly reported for energy range of 192 Ir source. However, as reported by Cho et al., (2009) for lower energy sources such as 125 I and 169 Yb, the amount of this decrease has clinical advantage to save the healthy tissues in deeper depths beyond the tumor site.

Most of the previous studies assumed a uniform distribution for NPs within the tumor volume. However, in real situation, the most of NPs diffuse in outer layers of tumor with higher vascularity. Therefore, DEF decreased with depth as most fraction of energy deposited in the outer layer with higher concentration compared to the inner layers toward the tumor center. Uniform NPs distribution within the tumor volume overestimated the average DEF on the total volume (11.10% and 7.65% for 79 Au and 64 Gd, respectively). Therefore, to accurately predict DEF in NPs application, non-uniform NPs distribution within the target volume should be considered to represent the real condition.

In agreement with an animal study by Hailnfeld et al., (2004), presence of NPs in the outside of the tumor volume is potentially associated with extra irradiation to surrounding healthy tissue. This is a limitation for NPs application in brachytherapy. Diffusion of NPs into the surrounding healthy tissue increases the absorbed dose. This unwanted extra dose increases as NP concentration increases. However, magnitude of DEF in tumor volume showed no significant decrease. This limiting factor can be reduced by improving NP labeling methods to deliver NPs only over the tumor volume.

Nano-lattice model as the more realistic model to simulate the nano-scale of NPs, underestimates DEF up to 4% and 3.6% for gold and gadolinium NPs (30 mgr/gr concentration), respectively [Table 6]. Zhang et al., (2009) reported that simple-mixture model overestimates DEF up to 16%, compared to the nano-lattice model. Implementing a realistic NP model considering geometry, concentration, NPs distribution, and radiation energy during Monte Carlo simulation is crucial that can guarantee an accurate estimation of dose distribution.

 > Conclusion Top

Increasing atomic number and concentration of NPs, and radial distance between tumor and the source increased DEF. Non-uniformly distribution and the nano-lattice model of NPs underestimated dose compared to the uniform distribution and the simple mixture model. Delivering a higher local dose to the target volume injected with high-Z NPs during low energy brachytherapy has a significant potential to increase therapeutic efficacy due to increased photoelectric interactions. The present study successfully provided an accurate model to estimate DEF by tumor injected by NPs.

 > Acknowledgement Top

This study was supported financially by the research deputy of Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran (Grant No. U-90244).

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  [Figure 1], [Figure 2], [Figure 3], [Figure 4]

  [Table 2], [Table 3], [Table 1], [Table 4], [Table 5], [Table 6], [Table 7]

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