Investigation of the effects of cell model and subcellular location of gold nanoparticles on nuclear dose enhancement factors using Monte Carlo simulation Zhongli Cai, Jean-Philippe Pignol, Niladri Chattopadhyay, Yongkyu Luke Kwon, Eli Lechtman, and Raymond M. Reilly Citation: Medical Physics 40, 114101 (2013); doi: 10.1118/1.4823787 View online: http://dx.doi.org/10.1118/1.4823787 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/40/11?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Influence of photon beam energy on the dose enhancement factor caused by gold and silver nanoparticles: An experimental approach Med. Phys. 41, 032101 (2014); 10.1118/1.4865809 Monte Carlo investigation of the increased radiation deposition due to gold nanoparticles using kilovoltage and megavoltage photons in a 3D randomized cell model Med. Phys. 40, 071710 (2013); 10.1118/1.4808150 Changes in dose with segmentation of breast tissues in Monte Carlo calculations for low-energy brachytherapy Med. Phys. 38, 4858 (2011); 10.1118/1.3613167 Enhanced relative biological effectiveness of proton radiotherapy in tumor cells with internalized gold nanoparticles Appl. Phys. Lett. 98, 193702 (2011); 10.1063/1.3589914 The difference of scoring dose to water or tissues in Monte Carlo dose calculations for low energy brachytherapy photon sources Med. Phys. 38, 1526 (2011); 10.1118/1.3549760

Investigation of the effects of cell model and subcellular location of gold nanoparticles on nuclear dose enhancement factors using Monte Carlo simulation Zhongli Cai Department of Pharmaceutical Sciences, University of Toronto, Toronto, Ontario M5S 3M2, Canada

Jean-Philippe Pignol Department of Radiation Oncology, University of Toronto, Toronto, Ontario M4N 3M5, Canada and Department of Medical Biophysics, University of Toronto, Toronto, Ontario M4N 3M5, Canada

Niladri Chattopadhyay and Yongkyu Luke Kwon Department of Pharmaceutical Sciences, University of Toronto, Toronto, Ontario M5S 3M2, Canada

Eli Lechtman Department of Medical Biophysics, University of Toronto, Toronto, Ontario M4N 3M5, Canada

Raymond M. Reillya) Department of Pharmaceutical Sciences, University of Toronto, Toronto, Ontario M5S 3M2, Canada; Department of Medical Imaging, University of Toronto, Toronto, Ontario M5S 3E2, Canada; and Toronto General Research Institute, University Health Network, Toronto, Ontario M5G 2C4, Canada

(Received 3 January 2013; revised 24 August 2013; accepted for publication 14 September 2013; published 16 October 2013) Purpose: The authors’ aims were to model how various factors influence radiation dose enhancement by gold nanoparticles (AuNPs) and to propose a new modeling approach to the dose enhancement factor (DEF). Methods: The authors used Monte Carlo N-particle (MCNP 5) computer code to simulate photon and electron transport in cells. The authors modeled human breast cancer cells as a single cell, a monolayer, or a cluster of cells. Different numbers of 5, 30, or 50 nm AuNPs were placed in the extracellular space, on the cell surface, in the cytoplasm, or in the nucleus. Photon sources examined in the simulation included nine monoenergetic x-rays (10–100 keV), an x-ray beam (100 kVp), and 125 I and 103 Pd brachytherapy seeds. Both nuclear and cellular dose enhancement factors (NDEFs, CDEFs) were calculated. The ability of these metrics to predict the experimental DEF based on the clonogenic survival of MDA-MB-361 human breast cancer cells exposed to AuNPs and x-rays were compared. Results: NDEFs show a strong dependence on photon energies with peaks at 15, 30/40, and 90 keV. Cell model and subcellular location of AuNPs influence the peak position and value of NDEF. NDEFs decrease in the order of AuNPs in the nucleus, cytoplasm, cell membrane, and extracellular space. NDEFs also decrease in the order of AuNPs in a cell cluster, monolayer, and single cell if the photon energy is larger than 20 keV. NDEFs depend linearly on the number of AuNPs per cell. Similar trends were observed for CDEFs. NDEFs using the monolayer cell model were more predictive than either single cell or cluster cell models of the DEFs experimentally derived from the clonogenic survival of cells cultured as a monolayer. The amount of AuNPs required to double the prescribed dose in terms of mg Au/g tissue decreases as the size of AuNPs increases, especially when AuNPs are in the nucleus and the cytoplasm. For 40 keV x-rays and a cluster of cells, to double the prescribed x-ray dose (NDEF = 2) using 30 nm AuNPs, would require 5.1 ± 0.2, 9 ± 1, 10 ± 1, 10 ± 1 mg Au/g tissue in the nucleus, in the cytoplasm, on the cell surface, or in the extracellular space, respectively. Using 50 nm AuNPs, the required amount decreases to 3.1 ± 0.3, 8 ± 1, 9 ± 1, 9 ± 1 mg Au/g tissue, respectively. Conclusions: NDEF is a new metric that can predict the radiation enhancement of AuNPs for various experimental conditions. Cell model, the subcellular location and size of AuNPs, and the number of AuNPs per cell, as well as the x-ray photon energy all have effects on NDEFs. Larger AuNPs in the nucleus of cluster cells exposed to x-rays of 15 or 40 keV maximize NDEFs. © 2013 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4823787] Key words: x-rays, gold nanoparticles, Monte Carlo simulation, dose enhancement, cell nucleus, radiosensitization

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© 2013 Am. Assoc. Phys. Med.

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1. INTRODUCTION

and 100 keV), a 100 kVp x-ray beam (peak energy: 33 keV; mean energy: 49 keV) (Ref. 20), or 125 I (average energy 27.4 keV) (Ref. 14) and 103 Pd (average energy 20.6 keV) (Ref. 21) brachytherapy seeds. The cell and cell nucleus were modeled as concentric spheres with radii of 9.3 and 6.3 μm, respectively, based on the experimentally determined sizes of breast cancer cells.22 We used geometries consisting of a single cell, a monolayer of cells, or a cluster of cells, to represent a single cancerous cell, a monolayer of cells grown on a culture dish simulating an experimental condition often used to evaluate radiosensitization in vitro or a cluster of cells potentially simulating a small tumor xenograft in an in vivo radiosensitization experiment.22 The calculation of the NDEFs and CDEFs was performed in the following four steps. 2.A.1. Secondary electron/photon yield

To calculate the yields of secondary electrons and photons per x-ray photon, resulting from the interaction of x-rays with the AuNPs (YAuNP e and YAuNP p ), we modeled a single cell as four concentric spheres, with radii of 11.0, 9.4, 9.3, or 6.3 μm, respectively. These represented the EC (9.4–11.0 μm), the CS to which AuNPs were bound (9.3–9.4 μm), the Cy (6.3–9.3 μm), and N (0–6.3 μm) [Figs. 1(a)–1(d)].22 In order to distribute AuNPs evenly inside these compartments, either EC, CS, Cy, or N, each was filled with 2.01 × 104 , 2.01 × 105 , 4.05 × 105 , or 8.10 × 105 closely packed hexagons, respectively, and a single 5, 30, or 50 nm diameter gold sphere was positioned at the center of those hexagons. As shown in Figs. 1(e)–1(h), the size of the hexagonal prism lattice was varied to accommodate the chosen number of AuNPs in each cell compartment. The remainder of the cell was defined as vacuum. To calculate the yields of secondary electrons and photons (YC e and YC p ) resulting from the interaction of x-rays with the cell material, in the absence of AuNPs, we modeled a single cell as a sphere with a radius of 11.0 μm. The 11.0 μm spherical volume is equivalent to the extracellular space, cell surface, cell, and nucleus. (a)

(b)

(c)

(d)

6.3 µm 9.3 µm

Nanoparticles of high Z-materials such as gold,1–4 platinum,5 gadolinium oxide,6 and hafnium oxide7 have been reported to be effective radiosensitizers of x-ray irradiation. Currently, gold nanoparticles (AuNPs) are widely explored as a radiosensitizer, since gold has a 10–171 times higher absorption coefficient than tissue for 3–200 keV x-rays, with the largest difference at 40 keV.8 The radiation dose enhancement of AuNPs has been demonstrated experimentally both in vitro1, 2, 9, 10 and in vivo studies.2, 11–13 This also has been modeled at macroscopic,14 microscopic,15 and even down to nanometer levels.16 In addition, various radiobiological models have been proposed to account for increased relative biological effectiveness (RBE) of low energy electrons emitted after photoelectric events.4, 17 However, the reported dose enhancement factors (DEFs) of AuNPs vary widely from one study to another, due to differences in experimental conditions, the definition of DEFs, and computational models. It has been widely documented that AuNPs are nonhomogenously distributed within tumors and in cells.1, 2, 9, 10, 13 Subcellular location of AuNPs (e.g., cell membrane vs cytoplasm) was found to affect the DEF of AuNPs.9 On the other hand, DNA in the cell nucleus is believed to be the biologically relevant target of radiation.18 In this work, we propose the nuclear dose enhancement factor (NDEF) as the ratio of absorbed doses to the cell nucleus in the presence and absence of AuNPs in various cellular compartments. For comparison, we also calculated the cellular dose enhancement factor (CDEF) as the ratio of absorbed doses to the cell with and without AuNPs in various cellular compartments. In the absence of AuNPs, according to this definition, NDEF and CDEF are always 1. Experimentally, AuNPs are more likely to locate in different compartments including the extracellular space (EC), the cell surface (CS), the cytoplasm (Cy), and the nucleus (N). This reality makes the experimental assessment of how subcellular location of AuNPs affects DEFs technically challenging, if not impossible. Monte Carlo simulation allows creating experimental conditions in which AuNPs could be localized in individual compartments and therefore permits an assessment of the impact on NDEFs or CDEFs. Our overarching goal is to develop a model that could predict in which compartment the AuNPs should be located, what size of the AuNPs, and what energy of x-ray sources should be used to maximize the NDEF. This would inform on the design of AuNPs and identification of the optimal irradiation conditions for an enhancement effect.

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33X

(e)

33X

33X

(f)

(g)

33X

(h)

2. MATERIALS AND METHODS 2.A. Calculation of NDEF and CDEF

MCNP (Version 5, Los Alamos National Laboratory, Los Alamos, NM) was used to simulate photon and electron transport in cells.19 Four concentrations of 5, 30, or 50 nm AuNPs (2.01 × 104 , 2.01 × 105 , 4.05 × 105 , 8.10 × 105 AuNPs per cell) were hypothetically homogeneously placed in the EC, on the CS, in the Cy or N, respectively. The cells were exposed to monoenergetic x-rays (10, 15, 20, 30, 40, 50, 65, 80, 90, Medical Physics, Vol. 40, No. 11, November 2013

F IG . 1. Schematic geometry of a cell used in MCNP simulation. The cell contains 2.01 × 105 AuNPs in the extracellular space (a) and (e), on the cell surface (b) and (f), in the cytoplasm (c) and (g), or in the nucleus (d) and (h), respectively, and is exposed to x-rays. (e)–(h) are 33 times magnification of (a)–(d), respectively, to highlight the arrangement of gold nanospheres (circles in the center of hexagonals).

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An x-ray beam with a radius of 11.0 μm was directed toward the cell [Figs. 1(a)–1(d)]. 5 × 107 photon histories were simulated to calculate electron, bremsstrahlung, first and second fluorescence events per source particle. 2.A.2. Secondary electron/photon emission spectra

To simulate the spectra of secondary electron/photon emission from the AuNP or hypothetical water nanoparticle (WNP) exposed to x-rays, a nanosphere (diameter: 5, 30, or 50 nm) composed of gold or water was placed at the center of a 0.05 cm diameter sphere of water. An x-ray beam with the same diameter as the AuNP or WNP was directed toward the nanosphere. The electron and photon flux over the nanosphere surface were tallied. Secondary photon spectra were obtained by the subtraction of the primary photon spectrum from the overall photon spectrum over the nanosphere surface. We launched 5 × 109 –2 × 1010 photons to ensure that the relative error of the calculated flux was lower than 5% for the important secondary electrons or photons. The secondary electrons or photons were regarded as important if their abundance was larger than 1%.

(a)

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AuNPs in a single cell

(b)

in a monolayer of cells

(c)

in a cluster of cells

(f)

in a cluster of cells

Nucleus Cytoplasm Surface Extracellular

(d)

AuNPs in a single cell

(e)

in a monolayer of cells

Nucleus Cytoplasm Surface Extracellular

(g)

AuNPs on cell surface

(h)

in cell cytoplasm

(i)

in cell nucleus

Cluster Monolayer Single

10 30 50 70 90 X-ray energy (keV)

10 30 50 70 90 X-ray energy (keV)

10 30 50 70 90 X-ray energy (keV)

F IG . 3. Plots of NDEF (a)–(c), (g)–(i) and CDEF (d)–(f) vs x-ray photon energy for 2.01 × 105 AuNPs (30 nm) per cell deposited in a single cell (a) and (d), a monolayer of cells (b) and (e), or a cluster of cells (c) and (f). (a)–(f) show the effects of AuNP location (in the EC, on the CS, in the Cy, or in the N). (g)–(i) demonstrate the influence of cell model (cluster, monolayer, or single cell). Error bars indicate the standard deviation.

2.A.3. Absorbed dose to each cell compartment by secondary electrons or photons

To simulate a single cell or cluster of cells, the studied volume was defined as a cube of 0.24 × 0.24 × 0.24 cm3 of breast tissue equivalent phantom [ICRU-44, density: 1.02 g cm−3 ; element composition (fraction by weight): H: 0.106; C: 0.332; N: 0.03; O: 0.527; Na: 0.001; P: 0.001; S: 0.002; Cl: 0.001] [Figs. 2(a) and 2(c)].23 These dimensions (0.24 cm) were 20 times the penetration depth of the most energetic photoelectrons examined in this study. To model a monolayer of cells cultured in wells of a 24-well tissue culture plate, the studied volume was defined as a cylinder with a diameter of 0.77 cm that held 0.2 cm depth of water and had a 0.1 cm thick polystyrene bottom [Fig. 2(b)]. One monolayer of cells was attached to the polystyrene surface. The single cell was placed at the center of the study volume [Fig. 2(a)]. In the case of a monolayer and a cluster of cells, the cells were fitted tightly in closely packed hexagonal lattices [Figs. 3(e)–3(g)]. Four concentrations of 5, 30, or 50 nm AuNPs (2.01 × 104 , 2.01 × 105 , 4.05 × 105 , 8.10 × 105 (a) (d)

(b) (e)

(c) (f)

(g) CS

EC

RN RC N Cy

F IG . 2. Schematic model of a single cell (a) and (d) at the center of a 0.24 × 0.24 × 0.24 cm3 cube of tissue, a monolayer of cells in one well of a 24-well plate (b) and (e), and a cluster of cells [(c) and (f); 0.24 × 0.24 × 0.24 cm3 cube)]. (d), (e), and (f) showed the xz slices of (a), (b), and (c), respectively, while (g) illustrates the xy slice of (b) and (c) through the monolayer of cells. Medical Physics, Vol. 40, No. 11, November 2013

AuNPs per cell) were homogeneously placed in the EC, on the CS, in the Cy or N, respectively. Secondary electron/photon emission spectra were included in the MCNP input file as point sources. The point sources were distributed homogeneously in the EC, on the CS, in the Cy or N, respectively. The energy deposition per starting particle in each cell compartment was tallied. The absorbed dose to a cell compartment per starting particle (D) was calculated by dividing the deposited energy by the mass of the cell compartment. For each simulation, 1 × 106 –1 × 107 particles were launched to reach a standard deviation less than 5% for all energy deposition results.

2.A.4. Calculation of NDEFs and CDEFs

In the absence of AuNPs, the energy deposited in the cells comes solely from the secondary electrons and photons emitted by the interaction of x-rays with tissue. In the presence of AuNPs, x-rays interact not only with the tissue but also with AuNPs. Both interactions produce secondary electrons and photons, and deposit energy in the cells. The yields of secondary electrons (Ye ) and photons (Yp ) per x-ray photon were calculated in Sec. 2.A.1. The absorbed doses to each cell compartment per secondary electron (De ) or photon (Dp ) were calculated in Sec. 2.A.3. Thus, the total absorbed dose to a cell compartment per x-ray photon was Ye × De + Yp × Dp . Since NDEF is the ratio of the absorbed dose to the cell nucleus with and without AuNPs in the cell, the NDEF for AuNPs present in an individual hypothetical cell compartment i (i was EC, CS, Cy, or N) was calculated using

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Eq. (1) NDEFi =

p p (Dei→NAuNP × Yei AuNP + Di→NAuNP × Yi AuNP ) p p (DeNCell × YeCell + DNCell × YCell )

+ 1.

(1)

Similarly, CDEF for AuNPs present in a single hypothetical cell compartment i (i was EC, CS, Cy, or N) was calculated using Eq. (2) p

CDEFi =

p

(Dei→CAuNP × Yei AuNP + Di→CAuNP × Yi AuNP ) p p (DeCell × YeCell + DCell × YCell ) + 1.

(2)

From a biological perspective, AuNPs would distribute in all cell compartments, and most likely nonhomogenously, with most on the CS and the least in the N. The NDEF or CDEF from AuNPs in all cell compartments could be calculated using Eqs. (3) and (4), respectively,  (NDEFi − 1) + 1, (3) NDEF = i

CDEF =



(CDEFi − 1) + 1.

(4)

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(TEM) study revealed internalization of Au-Ps and Au-Ts into the cell cytoplasm, but apparently not in the cell nucleus.2 However, the amount of Au-Ps and Au-Ts in each cell compartment was not measured. To calculate NDEFs or CDEFs, it is necessary to know the amount of Au-Ps and Au-Ts in each cell compartment. Therefore, we prepared 111 In-labeled Au-Ps and Au-Ts following a protocol previously published by our group.24 After MDA-MB-361 cells in 24-well tissue culture plate were incubated with 2.4 mg/ml 111 In-labeled AuPs or Au-Ts in medium overnight, we measured the amount of 111 In present on the CS and in the Cy by cell fractionation. Briefly, the surface bound 111 In-Au-Ps or 111 In-Au-Ts were displaced by applying an acidic wash to the cells using a solution of 200 mM of sodium acetate and 500 mM of sodium chloride (pH 2.5). Then the cells were lyzed using 0.1 M NaOH to obtain the internalized 111 In-Au-Ps or 111 In-AuTs. The radioactivity associated with the 111 In-Au-Ps or 111 InAu-Ts was measured using a γ -counter (Wallac 1480, Perkin Elmer). The number of cells was counted using a ScepterTM automatic cell counter (Millipore). The use of 111 In-labeled AuNPs to measure the concentration of AuNPs in tissues was previously validated by our group.24

i

2.B. AuNP per cell required to double the prescribed x-ray dose

We calculated NDEF or CDEF vs AuNP number in the EC, on the CS, in the Cy or N, for a single cell, monolayer, and cluster of cells for all studied x-ray sources. We performed one parameter linear regression with the y-intercept fixed at 1.0 using Prism Version 4.03 (GraphPad Software, Inc., La Jolla, CA) and Eqs. (5) and (6) NDEF = 1 + a × AuNP/cell,

(5)

CDEF = 1 + b × AuNP/cell.

(6)

Therefore, 1/a or 1/b represents the AuNP/cell required to double the prescribed x-ray dose (i.e., NDEF or CDEF = 2). Noting that a single 5, 30, or 50 nm AuNP (the density of gold is 19.32 g/cm3 ) and one hexagon (density assumed as 1.02 g/cm3 ) used in the simulation weigh 1.26 × 10−18 , 2.73 × 10−16 , 1.26 × 10−15 , and 5.68 × 10−9 g, respectively, the conversion factor from AuNP concentration (i.e., number of AuNP/cell) to mg Au/g tissue was 2.22 × 10−7 , 4.81 × 10−5 , 2.22 × 10−4 for 5, 30, or 50 nm AuNPs, respectively. 2.C. Measurement of the subcellular distribution of AuNPs in MDA-MB-361 cells

Previously, we experimentally determined the DEFs for PEGylated 30 nm AuNPs (Au-Ps) and trastuzumab conjugated PEGylated 30 nm AuNPs (Au-Ts) as 1.3 and 1.6, respectively, by clonogenic assay.2 Prior to the clonogenic assay, subconfluent MDA-MB-361 breast cancer cells in a 24-well tissue culture plate were incubated with 2.4 mg/ml Au-Ps or Au-Ts in fresh medium overnight, and then exposed to 100 kVp x-rays. A transmission electron microscopy Medical Physics, Vol. 40, No. 11, November 2013

3. RESULTS 3.A. Influence of photon energy on NDEF and CDEF

Figures 3(a)–3(c) show the dependence of NDEF on x-ray energy when 2.01 × 105 AuNPs (30 nm) per cell were deposited in a single cell, a monolayer of cells, or a cluster of cells, respectively. If AuNPs were in the N, regardless of cell model, NDEF had one peak at 15 keV (NDEF = 3.4 ± 0.2) and the other at 90 keV (NDEF = 1.6 ± 0.1, 1.7 ± 0.1, and 2.1 ± 0.1, respectively, for a single cell, a monolayer, and a cluster of cells). If AuNPs were in the EC, on the CS, or in the Cy, NDEF reached a peak around 30–40 keV and showed a shoulder at 90 keV. The peak was at 30 keV for a single cell, but moved to 40 keV for a cluster of cells. For comparison, Figs. 3(d)–3(f) show the dependence of CDEF on x-ray energy. When AuNPs were in the N, like NDEF, CDEF had one peak at 90 keV regardless of the cell model. But in contrast to NDEF, CDEF had another peak at 15 keV only for a single cell model. This peak moved to 30 keV for a monolayer of cells, then to 40 keV for a cluster of cells. For AuNPs in the EC, on the CS, or in the Cy, the dependence of CDEF on x-ray energy was similar to NDEF, except that CDEF had a shoulder at 15 keV. 3.B. Influence of subcellular location of AuNPs on NDEF and CDEF

Regardless of the cell model (single cell, monolayer, or cluster of cells), NDEF was highest when AuNPs were in the N, followed by the Cy, on the CS, and in the EC when photon energy and the number of AuNPs per cell were kept constant [Figs. 3(a)–3(c)]. Similar trends were observed for CDEF [Figs. 3(d)–3(f)]. But localization of AuNPs in the N had a greater effect on NDEF than on CDEF.

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stant. As an example, Fig. 4 shows the linear dependence of NDEF on the number of AuNPs (30 nm) per cell for 40, 90, and 100 kVp x-rays when AuNPs were located in the Cy of a cluster of cells. 3.E. Amount of AuNPs required to double the prescribed x-ray dose to the cell nucleus

F IG . 4. Linear dependence of the NDEF on the number of AuNPs per cell for 40 keV, 90 keV, and 100 kVp x-rays. AuNPs (30 nm) are present in the cytoplasm of a cluster of cells. Error bars represent the standard deviation.

3.C. Influence of cell model on NDEF and CDEF

As shown in Figs. 3(g)–3(i), for photon energy of 10–20 keV, no significant difference in NDEF was observed among a single cell, monolayer, and a cluster of cells. For photon energy ranging from 30 to 100 keV, regardless of the subcellular location of AuNPs, NDEF increased in the order of a single cell, a monolayer, and then a cluster of cells. Similar effects of the cell model on CDEF were also noted. 3.D. Influence of number of AuNPs per cell on NDEF and CDEF

Both NDEF and CDEF increased linearly as the number of AuNPs per cell increased when the x-ray source, cell model, and subcellular location and size of AuNPs were kept con-

Table I lists the amount of 30 nm AuNPs required to double the prescribed x-ray dose to the cell nucleus (NDEF = 2) for different x-ray sources, subcellular locations, and cell models. The concentration of AuNPs (mg Au/g tissue) required to double the prescribed x-ray dose was the least when AuNPs were located in the N, followed by the Cy, then the CS and the EC. It was also the least for a cluster of cells, followed by a monolayer of cells, then a single cell. Photon energies between 30 and 50 keV, a 100 kVp x-ray beam (peak at 33 keV), or 125 I (mean energy: 27.4 keV) seeds are good choices to double the prescribed x-ray dose with the least amount of Au/g tissue. 3.F. Influence of AuNP size on NDEFs

To test the influence of AuNP size on NDEF, we chose 40 keV x-rays and three sizes of AuNP (5, 30, and 50 nm) for the simulation. The effects of subcellular location and cell model on NDEF for 5 and 50 nm AuNPs were similar to those for 30 nm AuNPs. Table II lists the concentration of AuNPs required to double the prescribed x-ray (40 keV) dose to the N as a function of AuNP size. Using the same cell model and subcellular location, the amount of AuNPs (in terms of mg Au per g tissue) needed to reach NDEF = 2 was lowest for 50 nm AuNPs, and highest for 5 nm AuNPs.

TABLE I. The concentration of AuNPs (mg Au/g tissue) required to double the prescribed x-ray dose to the cell nucleus.a Cell nucleus

Cell cytoplasm

Cell surface

Extracellular space

X ray (keV)

3Db

2Dc

1Dd

3D

2D

1D

3D

2D

1D

3D

2D

1D

10 15 20 30 40 50 65 80 90 100 100 kVp 125 I 103 Pd

12 4 5 5 5 6 10 17 8 16 6 5 4

12 4 5 6 7 9 22 44 13 25 8 5 5

12 4 5 6 10 16 42 88 16 27 9 5 5

180 22 19 11 9 10 14 23 19 39 14 13 16

180 26 21 13 13 17 36 75 63 100 20 15 19

180 26 22 20 30 49 150 320 160 160 32 19 23

...e 94 35 14 10 10 14 23 21 46 17 17 25

... 170 44 17 16 20 41 86 95 190 28 22 31

... 170 44 25 36 61 210 490 530 430 46 27 36

... 100 35 13 10 10 14 23 21 47 17 16 23

... 280 47 17 16 19 40 82 89 190 27 21 30

... 470 72 35 48 77 260 610 660 760 66 39 55

a

AuNPs are 30 nm in diameter. The standard deviation ranges between 0.06% and 3.7% of the mean mg Au/g tissue. 3D: cluster of cells. c 2D: monolayer of cells. d 1D: single cell. e The slope of NDEF vs AuNP number on CS or EC was too small to derive a statistically valid value of AuNP concentration required to double the prescribed x-ray dose to the cell nucleus. b

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TABLE II. The concentration of AuNPs (mg Au/g tissue) required to double the prescribed x-ray (40 keV) dose to the cell nucleus.a Diameter of AuNPs (nm) 5 30 50

3Db

Cell nucleus 2Dc

1Dd

3D

Cell cytoplasm 2D

1D

3D

Cell surface 2D

1D

3D

6 5 3

8 7 4

12 10 5

9 9 8

13 13 12

32 30 22

10 10 9

17 16 14

42 36 26

10 10 9

Extracellular space 2D 1D 17 16 15

53 48 38

a

The standard deviation ranges between 0.2% and 12% of the mean mg Au/g tissue. 3D: cluster of cells. c 2D: monolayer of cells. d 1D: single cell. b

3.G. Comparison of calculated NDEFs and CDEFs with experimentally derived DEFs

To validate whether NDEF or CDEF was the most suitable predictor of the experimentally derived DEF, we compared the calculated NDEFs and CDEFs with the DEFs experimentally derived from clonogenic assays of MDA-MB-361 cells accumulating human epidermal growth factor receptor-2 (HER2)-targeted AuNPs (Au-Ts) or nontargeted AuNPs (AuPs) and exposed to 100 kVp x-rays. In our recent publication, we reported DEFs of 1.6 and 1.3 for 30 nm Au-Ts and AuPs, respectively.2 Under the same experimental conditions as used for these clonogenic assays, we measured the amount of Au-Ts and Au-Ps in each cell compartment of MDA-MB-361 cells (Table III). Based on the cell fractionation data and the “a” and “b” derived from the linear least-squares fits of NDEF and CDEF vs the number of AuNPs per cell (Fig. 4), we calculated NDEFs and CDEFs for 100 kVp x-ray and three cell models. The results are compared with the experimentally derived DEFs in Table IV. Both calculated NDEFs and CDEFs using the monolayer cell model were not significantly different from the experimentally derived DEFs. However, some calculated NDEFs and CDEFs using models of either single cell or cluster cells were significantly different from the experimentally derived DEFs.

4. DISCUSSION In this study, we defined the NDEF of AuNPs and studied by MCNP modeling the effects of cell model, subcellular location and size of AuNPs, as well as photon energies on TABLE III. The number of 30 nm AuNPs in each cell compartment determined by cell fractionation.a AuNP type location Au-Tsc Au-Psd

Cell cytoplasm

Cell surface

Extracellular spaceb

(7.7 ± 0.9) × 103 (1.0 ± 0.3) × 103

(2. 8 ± 1.4) × 105 (1.6 ± 0.2) × 105

(1.9 ± 0.2) × 104 (1.9 ± 0.2) × 104

a

Performed under the same experimental conditions as used for the clonogenic assay (Ref. 2). b Calculated based on 2.4 mg/ml Au-Ts or Au-Ps in culture medium. c Au-Ts: HER2-targeted AuNPs. d Au-Ps: nontargeted AuNPs.

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NDEF using 2.01 × 104 –8.1 × 105 AuNPs uniformly distributed in defined compartments (EC, CS, Cy, and N). To our knowledge, this report is the first to describe energy deposition as a combined function of subcellular location of AuNPs and cell model (i.e., single cell, monolayer, or cluster of cells). To take full advantage of the NDEF, we introduced a higher degree of complexity in regards to the geometry of the Monte Carlo simulation. First, we were able to clearly differentiate between NDEF and CDEF for AuNPs (Fig. 3). Second, while most authors derived radiation enhancement metrics from simulation of the photoelectric effects caused by photon interaction with a single nanoparticle,3, 16, 17 we modeled 2.01 × 104 –8.1 × 105 AuNPs per cell uniformly distributed in defined cell compartments. This approach incorporates further interactions of secondary electrons and photons with other AuNPs. Third, we incorporated in our modeling measured cell and cell nucleus diameters from a well-known tumor cell type (human breast cancer cells), and have also introduced different cell arrangements that are experimentally relevant such as a single cell, monolayer, or a cluster of cells.22 This allows an assessment of the influence of crossfiring electrons originating from neighboring cells. Therefore, we could directly calculate the amount of AuNPs per cell required to reach any predefined NDEF for various experimental conditions. By varying these experimental conditions, we found large differences in the radiosensitization effect, and conversely in the number of AuNPs required to double the radiation dose (Tables I and II). This general approach could be further extended to model the NDEF of nanoparticles composed of other high Z materials or located in other cell types. Comparing NDEF to CDEF, we found that calculating the dose to the N instead of the cell led to a more conceptually sensible prediction of the influence of subcellular location of AuNPs on the dose enhancement. The difference between NDEF and CDEF was most significant when AuNPs were located in the N and for photon energy close to the L and K edge of gold. To further validate NDEF as a dose enhancement predictor, we compared the calculated NDEFs and CDEFs with the results from a clonogenic assay of MDA-MB-361 cells exposed to AuNPs and x-rays.2 We found that the calculated NDEFs and CDEFs based on the monolayer cell model both accurately predicted the experimentally derived DEFs (Ref. 2) (Table IV). In our previous study,2 AuNPs did not localize in the cell nucleus. This could be the reason that the

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TABLE IV. Comparison of calculated NDEFs and CDEFs with experimentally derived DEFs.a

AuNP

Cell model

NDEF

CDEF

Au-Ts

Single cell Monolayer Cluster

1.3 ± 0.1 1.5 ± 0.2 1.9 ± 0.4

1.5 ± 0.2 1.7 ± 0.3 2.1 ± 0.5

Single cell Monolayer Cluster

1.19 ± 0.02 1.32 ± 0.04 1.52 ± 0.07

1.24 ± 0.04 1.40 ± 0.05 1.64 ± 0.08

Au-Ps

a b

p value (NDEF vs DEF)

p value (CDEF vs DEF)

1.6 ± 0.2

0.046b 0.542 0.293

0.542 0.642 0.169

1.3 ± 0.1

0.078 0.725 0.018b

0.315 0.138 0.004b

DEFa

Experimentally derived DEFs were reported in our recent publication (Ref. 2). Calculated NDEFs or CDEFs were significantly different from the experimental derived DEFs (p < 0.05).

calculated NDEFs and CDEFs were not significantly different, and both were consistent with the experimentally derived DEFs.2 A simplified spherical shape of cancer cells was used in this study to facilitate the MCNP simulation. Since cancer cells often have nonspherical shapes, it is likely that additional geometrical effects would be manifested such that our results cannot be considered as “absolute” values. On the other hand, this simplified cell shape enabled us to better understand the effects of subcellular location of AuNPs and cell models on NDEF (Fig. 3), and enabled us to differentiate more efficiently the impact of AuNP compartmental localization and cellular arrangement. Indeed, there is no experimental scenario that permits exclusive location of nanoparticles in cellular compartments such as the CS, Cy, or N. But this enabled us to model precisely the contribution of secondary particles originating in these compartments to the energy absorbed in the N. The NDEF of AuNPs in the EC, on the CS, in the Cy and N could be calculated using Eq. (3) if their distribution in each cell compartment was experimentally determined. When AuNPs were placed in the EC, on the CS, or in the Cy, NDEF reached a peak at 30 keV for single cell and monolayer models. For a cluster of cells, the peak shifted to 40 keV [Figs. 3(g) and 3(h)]. This may reflect the additional contribution of photoelectron crossdoses to neighboring cells (i.e., crossfire effect), as higher energy primary photons increase the average range of photoelectrons. NDEF peaked at 15 keV when AuNPs were located in the N regardless of the cell model. These results suggest that besides the ratio of mass absorption coefficients of gold vs soft tissue as suggested by McMahon,25 the range and types of secondary electrons, as well as the sizes of the cell and nucleus are important factors influencing NDEF. We found that placing AuNPs in the nucleus maximized NDEF for photon energies ranging from 10 to 100 keV. AuNPs located in the Cy also led to slightly higher NDEF than AuNPs on the CS when photon energies were lower than 65 keV. We also found that NDEF depended on the cell model [Figs. 3(g)–3(i)]. NDEF was the highest for a cluster of cells, followed by a monolayer, and then a single cell regardless of the subcellular location of AuNPs, if the photon energy was greater than 20 keV. Crossfire effects by secondary electrons and photons emitted from AuNPs are likely responsible for these effects. Medical Physics, Vol. 40, No. 11, November 2013

Lechtman et al.3 provided a detailed study on the range of electrons escaping a single AuNP exposed to 103 Pd (20.6 keV), 125 I (27.0 keV), 169 Yb (100.7 keV), 192 Ir (324.3 keV) brachytherapy sources, or 300 kVp (127.1 keV) and 6 MV (1861 keV) x-ray beams. This report suggested that targeting AuNPs to tumor cells and the nucleus in particular were important to allow these secondary electrons to reach the DNA and yield radiosensitizing effects for x-ray sources with mean photon energy lower than the K-edge of gold. Leung et al.16 calculated the radial dose in water as a function of the distance away from the center of a single AuNP for 50 kVp, 250 kVp, 60 Co, and 6 MV beams. Their results suggested that dose enhancement was most sensitive to the subcellular location of AuNPs for 50 kVp x-rays. It should be recognized that while Lechtman3 used PENELOPE, a code that has the ability to follow individual electron tracks, we used MCNP 5 that employs condensed history for electron energy deposition. However, the cutoff for our study was set by default to 1 keV which correspond to an electron range below 50 nm in biological materials.19 Since our simulation of energy deposition was modeled for a 12.6 μm diameter cell nucleus within a 18.6 μm diameter cell, these dimensions were well above the MCNP 5 cutoff, making our analysis valid. Indeed, these two previously reported studies were in good agreement with our results. Our predicted CDEFs and NDEFs using monolayer cell model were also in good agreement with the experimentally derived DEFs (Table IV). We chose 30 nm AuNPs for most calculations in this study, because this gold particle size was previously used by our group for studies of HER2-targeted AuNPs as an x-ray radiosensitizer.1, 2 We also estimated NDEF for 5 and 50 nm AuNPs for 40 keV x-rays (Table II). The effects of subcellular location and cell models on NDEF of 5 and 50 nm AuNPs were similar to those for 30 nm AuNPs. The number of 30 and 50 nm AuNPs per cell needed for NDEF = 2 was 10 and 100 times lower than that for 5 nm AuNPs, but the mass of AuNPs per g tissue required for NDEF = 2 only slightly decreased as the particle size increased (Table II). NDEF increased linearly as the number of AuNPs per cell increased if the x-ray source, cell model, subcellular location and size of the AuNPs were maintained constant (Fig. 4). This agreed well with similar observations for in vitro dose enhancement experimental studies10 and theoretical calculations of DEF.15, 16 Tumor cells often have overexpressed

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receptors such as the human epidermal growth factor receptor-2 (HER-2), which is found on 15%–25% of breast cancers. HER-2 overexpressing breast cancer cells have receptor density ranging from 1 × 105 to 2 × 106 receptors per cell.26 Therefore, for HER2-targeted AuNPs, it appears feasible to specifically deliver sufficient 30–50 nm AuNPs, but not 5 nm AuNPs to double the prescribed x-ray dose.

5. CONCLUSIONS We calculated the NDEF for 5, 30, and 50 nm AuNPs arranged in different subcellular locations (EC, CS, Cy, or N), three cell models (single cell, monolayer, and a cluster of cells), and for multiple photon energies. NDEF is a good predictor of the radiosensitizing effect of AuNPs combined with x-rays under experimental conditions. NDEF is highly sensitive to subcellular location of AuNPs, cell model, and the x-ray source energy. Delivery of 50 nm AuNPs to a cluster of cells, especially with localization in the cell nuclei, and exposure to x-rays of 15 or 40 keV would maximize NDEF and the radiosensitizing effects of AuNPs.

ACKNOWLEDGMENTS This research was supported by a grant (# 019374) from the Canadian Breast Cancer Research Alliance) and a grant by the Canadian Institute for Health Research (CIHR) Terry Fox Program—Ultrasound for Cancer Therapy from the Terry Fox Foundation. N.C. is supported by a Vanier Canada Graduate Scholarship from the Canadian Institute of Health Research, a predoctoral fellowship from the U.S. Department of Defense Breast Cancer Research Program (W81XWH-08-10519, P00002), and a predoctoral fellowship from the Connaught Fund, University of Toronto. Part of this work was presented at seventh International Symposium on Physical, Molecular, Cellular, and Medical Aspects of Auger Processes, Jülich, Germany, 24–26 August, 2011. a) Author

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Investigation of the effects of cell model and subcellular location of gold nanoparticles on nuclear dose enhancement factors using Monte Carlo simulation.

The authors' aims were to model how various factors influence radiation dose enhancement by gold nanoparticles (AuNPs) and to propose a new modeling a...
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