Influence of concentration, nanoparticle size, beam energy, and material on dose enhancement in radiation therapy

Abstract

The purpose of this study was to analyse the effects of the type, concentration, and nanoparticle diameter of dose enhancement materials on the dose enhancement of low- and high-energy megavoltage (MV) X-rays acquired from a medical linear accelerator using Monte Carlo simulation. Monte Carlo simulation was performed with the Monte Carlo N-Particle Transport (MCNPX) code, using the energy spectrum of the linear accelerator and a mathematical Snyder head phantom. A 5-cm-diameter virtual tumour was defined in the centre of the phantom. Gold, gadolinium, iodine and iron oxide were used as dose enhancement materials. Varying concentrations (7, 18 and 30 mg/g) of nanoparticles of different diameters (25, 50, 75, 100 and 125 nm) were applied, and the dose enhancement was comparatively evaluated for 4, 6, 10 and 15 MV X-rays, and a ⁶⁰Co source. Higher dose enhancement factors (DEFs) were observed when the incident energy was low. Moreover, the dose enhancement effects were greatest with gold nanoparticles, followed by gadolinium, iodine, and iron oxide nanoparticles; the DEFs were 1.011–1.047 (gold), 1.005–1.030 (gadolinium), 1.002–1.028 (iodine) and 1.002–1.014 (iron oxide). The dose enhancement effects increased with increasing nanoparticle diameter and concentration. However, the concentration of the material had a greater impact than the diameter of the nanoparticles. As the concentration and diameter of nanoparticles increased, the DEF also increased. The 4 and 6 MV X-rays demonstrated higher dose enhancement compared with the 10 and 15 MV X-rays.

INTRODUCTION

In radiotherapy, it is important to increase the therapeutic ratio (TR) through an increase in the tumour control probability (TCP) and through maintenance of sufficiently low normal tissue complication probability (NTCP) [1, 2]. The development of radiotherapy technologies, including intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc radiotherapy (VMAT), has improved the TR [3]. Various strategies, including the application of hyperthermia, concurrent chemoradiation therapy, and radiation dose enhancement, have also been considered to improve the TR [4–6]. In dose enhancement, materials with a high atomic number and electron density are loaded into the tumour volume to increase the cross-section of radiation interactions with these materials, which increases the locally absorbed energy [7–9]. These physical interactions can be explained using the photoelectric effect, Compton scattering, and pair production; increases in secondary electrons generated from these interactions can contribute to dose enhancement [10]. Numerous in vivo and in vitro studies as well as Monte Carlo simulations have been used for several years to investigate the effects of dose enhancement. Previous studies have reported the use of gold (Au), gadolinium (Gd) and iodine (I) in dose enhancement [11–13]. Recently, the use of iron oxide (Fe₂O₃), which shows superior performance as a contrast medium in superparamagnetic magnetic resonance imaging (MRI), has also been used for dose enhancement. In addition, there have been reports on its usage as a drug carrier and radiosensitizer in radiotherapy, because it displays excellent biocompatibility and target directivity [14, 15] With 6-MV X-rays and Au nanoparticles, Hainfeld has reported a 1.17-fold dose enhancement [10]. Bahreyni has reported a dose enhancement of >5% with a brachytherapy source and 30 mg/ml of Gd [16].

In consideration of the absorption within tissues and enhanced permeability and retention (EPR), nanoparticles with diameters of <400 nm have been used for studying dose enhancement [17]. Although the effects of dose enhancement have been shown to vary according to the type of materials, diameter of the nanoparticles, material concentration, and incident energy of the irradiation [18], very few studies have directly compared the impact of dose enhancement with respect to these various factors. Furthermore, most previous studies have reported on dose enhancement of monoenergetic beams and low-energy X-rays. In other words, comparative evaluation of the effects of dose enhancement in clinical radiotherapy has been insufficient.

The present study used Monte Carlo simulation to analyse the effects of various materials, nanoparticle diameters, material concentrations, and incident energies on dose enhancement by applying low- and high-energy megavoltage (MV) X-rays generated by a medical linear accelerator.

MATERIALS AND METHODS

Monte Carlo modelling

Monte Carlo code simulation, which is based on random number sampling, is capable of representing 3D particle transport in various materials and sources [19]. The Monte Carlo N-Particle Transport Code (MCNPX, ver. 2.5.0, USA), developed at Los Alamos National Laboratory (LANL, USA), was used for the simulations in this study. We used the mathematical Snyder head phantom, which was produced by Snyder et al. The mathematical Snyder head phantom is based on three ellipses composed of the brain parenchyma, skull and scalp [20, 21]. The constituent materials follow International Commission on Radiation Units and Measurement (ICRU) Report 46 (Table 1) [22].

Table 1.

The ICRU 46 material specifications for brain parenchyma, skull and scalp

Brain parenchyma			Skull			Scalp
Atom	Mass number	Fraction	Atom	Mass number	Fraction	Atom	Mass number	Fraction
H	1	0.107	H	1	0.050	H	1	0.100
C	NOE	0.145	C	NOE	0.212	C	NOE	0.204
N	14	0.022	N	14	0.040	N	14	0.043
O	16	0.712	O	16	0.435	O	16	0.645
Na	23	0.002	Na	23	0.001	Na	23	0.002
P	31	0.004	Mg	NOE	0.002	P	31	0.001
S	NOE	0.002	P	31	0.081	S	NOE	0.002
Cl	NOE	0.003	S	NOE	0.003	Cl	NOE	0.003
K	NOE	0.003	Ca	NOE	0.176	K	NOE	0.001

NOE = naturally occurring element.

In this study, a virtual tumour with a diameter of 5 cm was defined in the centre of the brain parenchyma of the phantom. Dose variation was obtained at 5 mm intervals from the surface of scalp in the radiation direction. We also obtained dose variation for tumour volume. (Fig. 1).

Fig. 1.

Schematic representation of the geometry through the Snyder head phantom and repeated structure in the Monte Carlo simulations.

To assess various incident beam energies, a ⁶⁰Co source and 4, 6, 10 and 15 MV X-rays were used; for X-ray irradiation, the spectrum of the 2300CD linear accelerator (Varian Medical Systems Co., Ltd, USA) was selected [23, 24]. The distance from the source to the phantom is 100 cm. The radiation was incident vertically toward the scalp surface of phantom. Within the phantom, tracking simulation for photons and electrons was conducted, and 1 keV was designated as the lowest tracking energy. With the use of MCNPX Tally 6, the absorbed energy per unit mass (MeV/g) of the tally cells and the tumour volume was obtained [25]. To achieve a statistical error of ≤1.5%, the number of photons transported was 3 × 10⁷.

Introducing dose enhancement material into the tumour

To describe the dose enhancement materials within the tumour volume, in terms of the concentration and diameter of nanoparticles, we referred to several previous studies; concentrations of 7, 18 and 30 mg/g and nanoparticle diameters of 25, 50, 75, 100 and 125 nm were applied [10, 26–28]. Au, Gd, I and Fe₂O₃ were used as dose enhancement materials, and the number of nanoparticles was calculated by considering each particle's material concentration, density and mass. Appropriate nanoparticles suitable for representing the concentration of each material were portrayed within the tumour volume as repeated structures using the MCNPX lattice, u, and fill card [25] (Fig. 1). To analyse the effects of dose enhancement based on the type and concentration of materials, incident energy, and diameter of nanoparticles, the dose enhancement factor (DEF) in the tumour volume was calculated as [26, 27]:

$$DEF=\frac{Dosedepositedwithenhancementmaterial}{Dosedepositedwithoutenhancementmaterial}$$ (1)

RESULTS

The DEFs were analysed through changes in the absorbed energy with changes in depth within the phantom, and through the DEF in the tumour volume. Figure 2 shows changes in the absorbed energy with depth observed at a concentration of 30 mg/g of 125-nm-diameter nanoparticles. The dose enhancement varied depending on the type of material and incident energy. When the incident energy was lower, the dose enhancement was higher. Further, higher dose enhancement was observed with Au, followed by Gd, I and Fe₂O₃. In addition, due to the effects of dose enhancement within the tumour volume, the influence of the photons was reduced, which subsequently led to decreased dose at the back of the tumour volume. Figure 3 shows changes in the DEF based on the nanoparticle diameter and incident energy at a concentration of 18 mg/g. Larger diameter nanoparticles resulted in a higher DEF as follows: 1.040–1.000 with 125-nm nanoparticles, 1.036–1.000 with 100-nm nanoparticles, 1.035–1.001 with 75-nm nanoparticles, 1.032–1.001 with 50-nm nanoparticles, and 1.028–1.000 with 25-nm nanoparticles. The changes in the DEF with the nanoparticle diameter were more prominent in materials with high dose enhancement effects.

Fig. 2.

Calculated energy deposition for 30 mg of dose enhancement materials with 125-nm-diameter nanoparticles inside the tumour region with (a) 4 MV, (b) 6 MV, (c) 10 MV, (d) 15 MV and (e) ⁶⁰Co sources.

Fig. 3.

Dose enhancement factor of the nanoparticle diameter for 18 mg/g of (a) gold, (b) gadolinium, (c) iodine and (d) iron oxide (Fe₂O₃) dose enhancement materials.

Figure 4 shows changes in the DEF with respect to changes in the concentration of the dose enhancement materials using 100-nm nanoparticles; significant increases in the DEF were observed at higher concentrations of dose enhancement materials. Moreover, at a concentration of 30 mg/g, Au nanoparticles showed the following results: 1.044 (4 MV), 1.040 (6 MV), 1.030 (10 MV), 1.023 (15 MV) and 1.032 (⁶⁰Co). Thus, when the incident energy was lower, higher DEFs were observed. Fe₂O₃ showed the following results: 1.021 (4 MV), 1.017 (6 MV), 1.007 (10 MV), 1.004 (15 MV) and 1.009 (⁶⁰Co). Fe₂O₃ nanoparticles showed dose enhancement that was 2–3% lower than that of Au. Furthermore, changes in dose enhancement were confirmed according to the incident energy of the dose enhancement materials, and the dependence of the dose enhancement on material changes was more pronounced at lower incident energies.

Fig. 4.

Dose enhancement factor of the dose enhancement material for various concentrations (mg/g) of 100-nm-diameter nanoparticles with (a) 4 MV, (b) 6 MV, (c) 10 MV, (d) 15 MV and (e) ⁶⁰Co sources.

Tables 2 and 3 show DEFs of Au, Gd, I and Fe₂O₃ with respect to the incident energy, diameter of nanoparticles and concentration within the tumour volume. In all materials, when the concentration and diameter of the nanoparticles increased, increases in the DEF were observed. However, when the incident energy was lower, higher DEFs were observed. Based on our results, a relatively high dose enhancement was identified for 4 and 6 MV X-rays. The effects of dose enhancement were highest for 4 MV X-rays, followed by 6 MV, ⁶⁰Co, 10 MV and 15 MV. Incident energies of >10 MV showed a DEF of <1%, i.e. a very small dose enhancement.

Table 2.

The average values of the dose enhancement factor inside the tumour for various nanoparticle diameters and concentrations of gold and gadolinium

	Nanoparticle diameter (nm)
	125			100			75			50			25
	Material concentration (mg/g)
	7	18	30	7	18	30	7	18	30	7	18	30	7	18	30
Gold
4 MV	1.033	1.040	1.047	1.029	1.036	1.044	1.026	1.035	1.040	1.023	1.033	1.036	1.021	1.029	1.035
6 MV	1.029	1.035	1.042	1.025	1.032	1.040	1.022	1.029	1.036	1.019	1.028	1.034	1.017	1.025	1.032
10 MV	1.012	1.021	1.031	1.012	1.020	1.030	1.011	1.019	1.028	1.010	1.020	1.026	1.011	1.017	1.024
15 MV	1.010	1.016	1.024	1.008	1.016	1.023	1.007	1.015	1.021	1.007	1.015	1.021	1.007	1.012	1.020
60Co	1.018	1.025	1.034	1.016	1.025	1.032	1.014	1.023	1.031	1.012	1.022	1.028	1.011	1.018	1.025
Gadolinium
4 MV	1.026	1.030	1.030	1.022	1.025	1.027	1.020	1.023	1.023	1.017	1.022	1.021	1.016	1.017	1.019
6 MV	1.023	1.024	1.027	1.018	1.021	1.024	1.016	1.019	1.019	1.014	1.017	1.017	1.012	1.014	1.016
10 MV	1.005	1.010	1.011	1.005	1.010	1.011	1.005	1.009	1.010	1.004	1.009	1.009	1.004	1.006	1.008
15 MV	1.003	1.006	1.007	1.003	1.005	1.007	1.002	1.004	1.006	1.001	1.004	1.006	1.001	1.000	1.004
60Co	1.010	1.013	1.014	1.009	1.012	1.013	1.008	1.012	1.012	1.007	1.012	1.010	1.005	1.007	1.009

Table 3.

The average values of the dose enhancement factor inside the tumour for various nanoparticle diameters and concentrations of iodine and iron oxide

	Nanoparticle diameter (nm)
	125			100			75			50			25
	Material concentration (mg/g)
	7	18	30	7	18	30	7	18	30	7	18	30	7	18	30
Iodine
4 MV	1.021	1.027	1.028	1.018	1.021	1.024	1.018	1.019	1.022	1.014	1.019	1.018	1.012	1.016	1.017
6 MV	1.017	1.023	1.024	1.015	1.019	1.020	1.014	1.016	1.019	1.010	1.015	1.015	1.009	1.012	1.013
10 MV	1.003	1.005	1.010	1.004	1.005	1.010	1.003	1.003	1.009	1.002	1.002	1.007	1.002	1.001	1.006
15 MV	1.001	1.004	1.005	1.000	1.003	1.005	1.000	1.001	1.005	1.000	1.000	1.003	1.000	1.000	1.003
60Co	1.006	1.011	1.013	1.007	1.010	1.012	1.006	1.007	1.010	1.004	1.006	1.009	1.002	1.003	1.007
Iron oxide
4 MV	1.017	1.021	1.024	1.014	1.018	1.021	1.012	1.015	1.018	1.011	1.014	1.016	1.009	1.011	1.014
6 MV	1.012	1.018	1.020	1.012	1.015	1.017	1.009	1.012	1.015	1.006	1.010	1.013	1.005	1.007	1.010
10 MV	1.002	1.002	1.007	1.002	1.003	1.007	1.001	1.002	1.005	1.001	1.002	1.005	1.000	1.002	1.004
15 MV	1.000	1.001	1.005	1.000	1.001	1.004	1.000	1.001	1.002	1.000	1.001	1.001	1.000	1.001	1.000
60Co	1.004	1.006	1.011	1.004	1.005	1.009	1.003	1.004	1.007	1.002	1.003	1.006	1.002	1.002	1.005

DISCUSSION

Due to the high atomic numbers of dose enhancement materials, differences occur between the mass attenuation coefficients and the cross-section within the medium, resulting in dose enhancement [29]. Photons in the kiloelectronvolt (keV) energy spectrum [lower than the megaelectronvolt (MeV) energies considered here] showed a high DEF. This enhancement occurs because the interaction arising from the difference in the atomic numbers of dose enhancement materials increases the cross-section of the photoelectric effects relatively more than that of Compton scattering [17, 30]. However, photons in energy spectrums higher than MeV energies are more likely to respond to Compton scattering than photoelectric effects, because the cross-section of Compton scattering has a lower dependence on the atomic number of materials [31]. Mesbahi et al. reported the following Monte Carlo simulation results: a DEF of 1.01 was observed for 6 MeV photons, and DEFs of ≥3.0 were shown for keV energy X-rays, thus supporting this hypothesis for the effects of the energy spectrum. In particular, when the incident energy is close to the binding energy of the K-shell with a high cross-section of photoelectric effects, high DEFs are observed [32].

When the dose enhancement within the tumour volume was compared with changes in the incident energy, higher DEFs were observed according to the following decreasing order: 4 MV, 6 MV, ⁶⁰Co, 10 MV and 15 MV. The ⁶⁰Co source emits γ-rays with an average energy of 1.25 MeV; thus, the above observed outcomes were due to differences in the average energy between the ⁶⁰Co source and MV X-rays.

Although Fe₂O₃ has received attention as the next-generation contrast medium for MRI because of its excellent biocompatibility, stability inside the body, target directivity, and high enhancement [14], the use of Fe₂O₃ in studies on dose enhancement materials has been limited. In the in vitro study conducted by Khoei et al., using 6-MV X-rays, a dose enhancement of >10% was reported [33]. However, the present study observed a dose enhancement of 1.0–2.4%. This discrepancy seems to be a result of the difference between in vitro methods and the Monte Carlo simulation, and further studies are required on Fe₂O₃.

In external radiation therapy, a high acceleration voltage of >15 MV, rather than a low acceleration voltage, is preferred for better sparing of the healthy tissue surrounding a target volume. It is believed that the higher dose enhancement factors achieved at low energies would create such an effect.

This study showed that higher DEFs were observed with increasing concentration of dose enhancement materials and with increasing nanoparticle diameters. A previous study, using Au nanoparticles, also reported increases in the DEF associated with increases in the concentration and diameter of nanoparticles [31]. However, the concentration and diameter of nanoparticles also have an effect on toxicity [34]. Furthermore, the diameter of the nanoparticles influences the absorption in tissues as well as the EPR; thus, in vivo experimental results are required (at least for the corresponding in vitro experimental results) on dose enhancement that considers the DEF, toxicity, and tissue absorption [17].

CONCLUSIONS

Based on the Monte Carlo simulation, the dose enhancement of MV X-rays generated from a medical linear accelerator resulting from the use of Au, Gd, I and Fe₂O₃ nanoparticles was compared and analysed.

High-energy MV X-rays, which have a polyenergetic energy spectrum, are most commonly used in radiotherapy. This study analysed the dose enhancement for high-energy MV X-rays and the energy spectra generated from a medical linear accelerator in a phantom. Therefore, this study has a significant meaning for clinical radiotherapy applications.

The dose enhancement differed significantly according to the incident energy, material concentration, and the diameter of the nanoparticles. The 4 and 6 MV X-rays showed a relatively high DEF compared with the 10 and 15 MV X-rays. The 10 and 15 MV X-rays improved the dose enhancement only by 1–2%.

Furthermore, as the concentration and diameter of the nanoparticles increased, the DEF in the tumour volume also increased; this result suggests that a higher radiation dose would be delivered to the tumour volume, which would further contribute to improvements in the TR. The results of this study will provide useful data for future in vitro and in vivo studies.

CONFLICT OF INTEREST

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.