# Microdosimetric Investigation and a Novel Model of Radiosensitization in the Presence of Metallic Nanoparticles

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## Abstract

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^{TM}), and 220 kVp X-ray irradiation with the presence of 50 nm gold NPs (AuNPs), respectively, and compared with existing experimental data. Geant4-based Monte Carlo (MC) simulations were used to (1) generate the electron spectrum and the phase space data of photons entering the NPs and (2) calculate the proximity functions and other related parameters for the TDRA and the Bomb model. The Auger cascade electrons had a greater proximity function than photoelectric and Compton electrons in water by up to 30%, but the resulting increases in α were smaller than those derived from experimental data. The calculated RBEs cannot explain the experimental findings. The relative increase in α predicted by TDRA was lower than the experimental result by a factor of at least 45 for SQ20B cells with AGuIX under 250 kVp X-ray irradiation, and at least four for Hela cells with AuNPs under 220 kVp X-ray irradiation. The application of the Bomb model to Hela cells with AuNPs under 220 kVp X-ray irradiation indicated that a single ionization event for NPs caused by higher energy photons has a higher probability of killing a cell. NPs that are closer to the cell nucleus are more effective for radiosensitization. Microdosimetric calculations of the RBE for cell death of the Auger electron cascade cannot explain the experimentally observed radiosensitization by AGuIX or AuNP, while the proposed Bomb model is a potential candidate for describing NP-related radiosensitization at low NP concentrations.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Generalized Formulation of the Theory of Dual Radiation Action (TDRA)

_{D}(x), the proximity function (or called differential proximity function in some literature), which describes the geometry of the pattern of energy deposition. Specifically, t

_{D}(x)dx is defined as the expected sum of energy deposited to a shell of radius x and thickness dx centered at a transfer point.

^{2}is the expected fraction of the shell that belongs to the sensitive matrix. The expected number of sublesions in the spherical shell is equal to ct

_{D}(x) s(x)/4πx

^{2}, where c is a constant that relates the energy transfer to the yield of sublesions. t

_{D}(x) can be separated into a term t(x) that is independent of D, and a second term that is proportional to the absorbed dose. The dose independent term t(x) stands for the intra-track contribution from the same primary particle, which is affected by radiation quality. The second term represents energy transfers by other, uncorrelated charged particles, i.e.,

_{i}is energy deposited in a single energy transfer, i runs over all energy transfer points of a track and j runs over all transfer points of the track with a distance in the range [x, x + dx] from the transfer point i. A similar method has developed for the analysis of track structures of electrons and protons at the microscopic level through construction of an interface between Geant4-DNA MC and molecular dynamics of DNA and its environment [28].

#### 2.2. The Application of TDRA to NP Radiosensitization

_{1}(D)), exclusively due to water (N

_{2}(D)) and from sublesions by secondary electrons due to NPs and water (N

_{3}(D)). For clinically relevant concentrations we considered, the combination of sublesions caused by secondary electrons from different NPs could be neglected. As the number of photons entering an NP is proportional to the dose to the surrounding water without the NPs, let λ be the proportionality coefficient, then the number of photons entering an NP equals λD. Consequently, the probability of an ionization event in an NP is μλD, where μ is the probability of an ionization event in the NP when only one photon enters the NP. If there are n NPs in a cell, then the expected number of photon ionization events in the cell due to the NPs is nμλD. Suppose the energy deposited in the nucleus by all secondary electrons from an ionization event in an NP is E (which is essentially the product of nucleus mass and the specific energy (z) to the nucleus, i.e., E = m

_{nucleus}· z), then

_{NP}(x, E) is calculated from all energy transfer points inside the nucleus, no matter whether the NP is inside or outside—the total energy deposit in the nucleus is E and t(x) is the proximity function of the electrons from water molecules. p(E)dE is the probability of energy deposit in the nucleus within the range [E, E + dE] due to a photon ionizing event in an NP, which depends on the track structure of the secondary electrons and the distribution of NPs in the cell and the nucleus size.

^{2}is regarded constant in the nucleus and equals the ratio of effective DNA volume and the nucleus volume, which varies among cell lines and is denoted as η in the following derivations. Using Equation (7) and assuming C is 1, we have

_{2}(D) takes the form of Equation (4), i.e.,

_{NP}denote the doses absorbed by the water without and with NPs that cause equal biological effects. It follows that

#### 2.3. A Novel Phenomenological Model—Bomb Model

_{1}and the number inside is N

_{2}, and the corresponding probabilities of cell killing are p

_{1}and p

_{2}, respectively; and ignore the additional physical dose due to the NPs. The expected number of lethal events in a cell added by irradiated NPs would be

_{ioni1}and N

_{ioni2}denote the numbers of ionizations in all NPs in the cytoplasm and in the nucleus, respectively; and ${p}_{1\mathrm{Gy}}$ is the probability of one ionizing event in one NP when the dose to the surrounding water is 1 Gy, which equals the product of μ and λ. Here the probability of two or more ionizations in one NP is neglected, because it is generally much less than ${p}_{1\mathrm{Gy}}$. According to Equation (20), the radiosensitizing effect of NPs can be quantitatively described by an increase in α (the linear term) of the LQ model of the survival curve. As the model is intended to describe the local effect of NPs to the cell, it should be noted that it is applicable only when the physical dose added by the NPs is small compared with the X-ray dose to the surrounding water. Otherwise, the enhanced dose should also be considered. This model assumes a higher biological effect of the NP + radiation + ionization-within-NP combination than the physical dose enhancement alone. It is aimed to address the experimentally observed radiation damage enhancement at relatively low NP concentration, which cannot be explained by the physical dose enhancement alone. The relatively low NP concentration (e.g., on the order of 0.1 mM in Gd for AGuIX) is in the clinically feasible range for human applications, similar to that used clinically for diagnostic imaging. Many simulation studies assumed much higher NP concentrations that are not easily achievable in clinic.

_{1}and p

_{2}theoretically, the model provides testable predictions on the upper limit of change in α if the concentration of NP in a cell can be measured, because both p

_{1}and p

_{2}are less than 1, and ${p}_{1\mathrm{Gy}}$ can be determined using a Monte Carlo (MC) simulation. In this study, based on the measured α values, we calculated the p

_{1}for the four sets of irradiation conditions of Hela cells described in Chithrani et al. [30], one set of irradiation condition of SQ20B cells described in Miladi et al. [31] and one set of irradiation condition with two incubation concentrations of A549 cells described by Liu et al. [32].

#### 2.4. The Nanoparticles and the Cell Models

^{®}[33,34], (~3 nm diameter) and an AuNP [30] 50 nm in diameter were investigated. There are on average 10 Gadolinium atoms on each AGuIX NP. The atomic mass of an AGuIX is approximately 9 kDa. The size of 50 nm was chosen for AuNP because Chithrani et al. [35] found the maximum uptake of AuNPs by Hela cells occurred at an NP size of 50 nm. For simplicity, in the MC calculations both NPs were modeled as a uniform sphere, with a diameter of 3.0 nm and density of 1.2 g/cm

^{3}for AGuIX, and 50 nm and 19.32 g/cm

^{3}for the AuNP.

^{3}and 466 μm

^{3}, respectively [39]. Therefore, a nucleus radius of 4.8 μm and a cell radius of 7.4 μm were used for the A549 cell. To quantify NP radiosensitization, three scenarios of NP distribution in the cell were considered (Figure 1) (a) uniformly distributed throughout the entire cell, (b) uniformly distributed in the cytoplasm only, and (c) uniformly distributed around the nuclear membrane. The third scenario was simulated because some researchers found that NPs were located around the nuclei [30,40]. As we only focused on the local radiation effects of NPs, the effect of NPs outside the cell was not considered.

#### 2.5. MC Simulation of Irradiation on NP and Secondary Electrons Transport

^{137}Cs (660 kev) and 6 MV. All photon beams were directed uniformly from the top of the water cylinders, and the height and diameter of which were 1.0 mm, 2.0 mm, 2.0 mm, 20 mm, and 30 mm, respectively for the five energies (105 kVp, 220 kVp, 250 kVp,

^{137}Cs (660 keV) and 6 MV), to allow electron build-up at the depths of the cells.

#### 2.6. Postprocessing of the Results from the MC Simulations

_{NP}(x, E)) of electrons from individual ionizations in the NPs and the corresponding E’s from the output of Step 4, Equation (18) was used to calculate the change in ξ based on the number of NPs per cell (n), and the results of λ and μ from Step 1 and Step 3, respectively. The increases in α and RBE were calculated afterwards.

## 3. Results

#### 3.1. Parameters λ and μ

#### 3.2. The Spectrum of Energy Deposited in the Nucleus and the Proximity Function

^{−4}, 6.4 × 10

^{−4}and 9.1 × 10

^{−4}Gy for the three scenarios, respectively. The corresponding results for AuNP in Hela cells with the irradiation of the 220 kVp beam were 2.0 × 10

^{−3}, 1.7 × 10

^{−3}and 2.6 × 10

^{−3}Gy for the three scenarios, respectively. Figure 4 shows the energy weighted proximity functions of the secondary electrons produced from water at 1.0 mm depth and the proximity functions of the electrons in the nucleus due to NPs for the three scenarios. The proximity function of 10 keV electrons is also presented for comparison.

#### 3.3. Parameter a of the Distance Model, and the Changes in α and RBE

^{8}NPs of AGuIX in a typical SQ20B cell. The number of 50 nm AuNPs per Hela cell was taken to be 6000 according to the measurement by Chithrani et al. [35]. For comparison, the dose enhancement ratio (DER), defined as the ratio of total nucleus dose (dose to the surrounding water + average specific energy to the nucleus by the NPs) to the dose to the surrounding water, was also calculated.

#### 3.4. Predictions by the Bomb Model for the Radiosensitization

_{2}= 0 in Equation (20) and are left with one parameter, p

_{1}, the probability of cell killing due to an ionization by NPs outside the nucleus. The results of p

_{1}together with other parameters of Equation (20), are shown in Table 3 for Hela, SQ20B and A549 cells irradiated with photon beams. Although the p

_{1}calculated from the experiments might be subject to uncertainties other than those that were considered in the experiment and in our MC simulations—for example, the influence of NPs on the cell membrane—the results do show a trend that NPs ionized by photons of higher energy have higher killing potential. One estimate of p

_{1}is slightly more than 1. This could be caused by the inaccuracy of the experimental data or spectral data, or by the inconsistency of irradiation settings between the MC simulation and experiment.

## 4. Discussion

#### 4.1. Study Limitations and Implications of the Microdosimetric Investigation

#### 4.2. Implications of the Bomb Model

_{1}(probability of cell killing per ionization in NP) between AuNPs and AGuIXs, we can see that the ionization of AGuIXs provides a greater killing potential than that of AuNP at approximately the same photon energy. This is because at the same mass of NPs per cell, the larger NPs tend to absorb more secondary electrons within them, especially for low energy electrons; thus, less are left to damage the cells. Chithrani et al. [35] compared the intracellular uptake of different sized and shaped colloidal AuNPs and found the maximum uptake of AuNPs by Hela cells occurred at an NP size of 50 nm. Studies on AGuIX [40,54], TiO

_{2}[49] and AuNPs [50] did not detect NPs in cell nuclei. However, Huo et al. [59] found gold NPs smaller than 6 nm may enter the nucleus.

_{1}) in accordance with Equation (20), which results in a more significantly increased α, indicating enhanced radiosensitivity.

_{1}can be estimated using Equation (20) based on the increase in α, which is fitted from experimental observations, and the intra-cellular NP concentration can be determined via imaging or other means, the model can be used to guide treatment planning, as the RBE can be calculated directly from the increase in α based on the α and β in the LQ survival model, similarly to the calculation of Equation (19). For example, for Hela cells with 50 nm AuNPs irradiated by 220 kVp beams, the increase in α is 0.202 Gy

^{−1}when there are on average 6000 AuNPs per cell; the corresponding RBE would be 1.56 at 2 Gy. According to the Bomb model, the RBE at 2 Gy increases to 2.02 if the number of AuNPs per cell doubles. In addition, the comparison of p

_{1}among different cell lines, NP types or irradiating photon energies can provide us an insight into the nature of NP radiosensitization. For instance, Table 3 shows that p

_{1}increases monotonously for Hela cell with AuNPs when the energy of irradiating photons increases, which implies that NPs ionized by photons of higher energies have higher killing power, and because for an MV beam, the Compton scattering in NP dominates over the photoelectric effect, it can have a stronger effect than the photoelectric effect, even though the latter can result in the Auger cascade.

_{1}would need to be determined for each individual tumor and for each type of NPs if the model were to be applied in clinical treatment, accumulating knowledge of the approximate range of the p

_{1}values in various conditions should be achieved with more experimental data.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Technical details of the MC simulations (the checklist item number is in line with TG 268 [64]).

Checklist Item # | Item Name | Description | References |
---|---|---|---|

2, 3 | Code, version/release date | Geant4, v.10.07.p02/released on 14 June 2021 | Ref. [41] http://geant4.web.cern.ch/ accessed on (10 December 2021) |

4, 17 | Validation | The general Geant4 framework has been validated extensively. | https://geant-val.cern.ch/ accessed on (10 December 2021) |

5 | Timing | All simulations were performed on an Intel^{®} Xeon(R) CPU E5-2690 v2, with a 64GB memory. In Step 1, each simulation took about 7500 s for 2 × 10^{9} histories.In Step 2, each took about 1800 s for 2 × 10 ^{4} histories. In Step 3, each took about 1800 s for 5 × 10^{5} histories. In Step 4, each took about 2700 s for 2 × 10^{6} histories. | |

8 | Source description | The spectra of the parallel beams of 105 kVp, 220 kVp, 250 kVp were generated using SpekCalc. Elekta 6 MV spectrum presented by Sheikh-Bagheri et al. was used for the 6MV source. | Refs. [65,66] |

9 | Cross-sections | Steps 1 and 3, Livermore package incorporated in Geant4; Step 2: Geant4-DNA option 2. Step 4: Livermore package incorporated in Geant4 was used for photon and electron transport in the NPs, and Geant4-DNA option 2 was used for electron transport in water. | Refs. [42,43,44,45,67] |

10 | Transport parameters | Steps 1 and 3, the minimum threshold of secondary particle production was used (250 eV); Step 2: tracking cut was set to 7.4 eV; Step 4: tracking cut was set to 7.4 eV for the transport of electrons in water; the minimum threshold of secondary particle production (250 eV) and lowest electron energy of 7.4 eV were used for the transport of electrons in the NPs. | |

11 | VRT and/or AEIT | Step 1: Geometrical importance sampling was used for the region near the water cylinder center; Step 2: Neither VRT nor AEIT was used; Step 3: physics-based biasing was used to amplify the Compton scattering and photo-electric interaction cross-sections, secondary electrons and photons were killed upon generation; Step 4: the same physics-based biasing as in Step 3 was used for the transport of photons in the NPs. | Ref. [68] |

12 | Scored quantities | Step 1: number and phase-space data of photons entering the NP-representing sphere, electrons spectrum in the sphere and dose near the sphere; Step 2: the energy deposition of electrons in water; Step 3: the number of ionizations in an NP and the number of photons entering the NP; Step 4: the number of ionizations and the energy deposition of secondary electrons in the nucleus. | Ref. [69] |

13, 18 | # of histories/statistical uncertainty | To achieve <2% relative uncertainty for the quantities to calculate, 2 × 10^{9}, 2 × 10^{4}, 5 × 10^{6}, and 2 × 10^{6} histories were used for the simulations in Steps 1, 2, 3, and 4, respectively. | |

14 | Statistical methods | The history-by-history method was used. | Ref. [70] |

15, 16 | Postprocessing | See Section 2.6 for details. |

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**Figure 2.**Scoring of the energy deposits in the nucleus. The right dashed circle is a magnified view of the small dotted circle on the left with an NP at the center. It represents an ionized NP in the cytoplasm. To score the energy deposits by the electrons from the NPs, each ionized NP is fixed to the origin in the simulation, and the volume of the nucleus, i.e., the volume that has energy deposits scored, is translated accordingly such that the position of the NP relative to the nucleus is kept the same. In the plot, the blue circle represents the boundary of the nucleus.

**Figure 3.**The distribution of energy deposited in the nucleus from one photon ionizing event for AGuIXs (

**a**) and AuNPs (

**b**), irradiated with 250 kVp and 220 kVp beams, respectively.

**Figure 4.**Energy weighted proximity functions of the secondary electrons produced from water at 1 mm depth, and the proximity functions of the electrons in the nucleus due to AGuIXs (

**a**) and AuNPs (

**b**) for the three scenarios.

NP | Photon Beam | λ (Photons per Gy per NP) | μ (Ionizations per Photon) | ${\mathit{p}}_{1\mathbf{G}\mathbf{y}}$ (Ionizations per Gy per NP) |
---|---|---|---|---|

AGuIX | 250 kVp | 0.168 ± 0.003 | (3.00 ± 0.06) × 10^{−7} | (5.04 ± 0.14) × 10^{−8} |

50 nm AuNP | 105 kVp | 46.1 ± 0.9 | (6.41 ± 0.13) × 10^{−4} | (2.96 ± 0.08) × 10^{−2} |

220 kVp | 47.7 ± 1.0 | (4.09 ± 0.08) × 10^{−4} | (1.95 ± 0.05) × 10^{−2} | |

^{137}Cs (660 keV) | 5.97 ± 0.12 | (8.96 ± 0.18) × 10^{−6} | (5.35 ± 0.15) × 10^{−5} | |

6 MV | 2.63 ± 0.05 | (4.63 ± 0.09) × 10^{−6} | (1.22 ± 0.03) × 10^{−5} |

**Table 2.**Relative theoretical and measured increases in α, RBEs and DERs due to NPs for different scenarios of NP distribution in the cells at reported and hypothetical NP concentrations.

NP | Scenarios of NP Distribution | Concentration (# per Cell) | Δξ (Gy) | Δα_{cal}/α ^{a} | Δα_{exp}/α | RBE at 2 Gy | DER ^{b} |
---|---|---|---|---|---|---|---|

AGuIX (3 nm) | 1 | 6.06 × 10^{8} | 0.027–0.078 | 0.034 | 1.7–11 | 1.016–1.020 | 1.025 |

6.06 × 10^{9} | 0.27–0.78 | 0.34 | 1.15–1.19 | 1.25 | |||

2 | 6.06 × 10^{8} | 0.020–0.059 | 0.025 | 1.012–1.015 | 1.019 | ||

6.06 × 10^{9} | 0.20–0.59 | 0.25 | 1.12–1.15 | 1.19 | |||

3 | 6.06 × 10^{8} | 0.031–0.089 | 0.038 | 1.017–1.022 | 1.027 | ||

6.06 × 10^{9} | 0.31–0.89 | 0.38 | 1.16–1.21 | 1.27 | |||

50 nm AuNP | 1 | 6000 | 0.93 | 0.25 | 1.35 | 1.31 | 1.24 |

18,000 | 2.8 | 0.76 | 1.76 | 1.71 | |||

2 | 6000 | 0.75 | 0.21 | 1.25 | 1.20 | ||

18,000 | 2.3 | 0.62 | 1.64 | 1.59 | |||

3 | 6000 | 1.20 | 0.33 | 1.38 | 1.30 | ||

18,000 | 3.6 | 0.98 | 1.93 | 1.91 |

^{a}The relative increases in α were calculated from Δξ and ξ;

^{b}Dose enhancement ratio $DER\equiv \frac{{D}_{\mathrm{NP}}}{{D}_{W}}=\frac{{D}_{W}+\Delta D}{{D}_{W}}$, where ΔD is the dose deposited in the nucleus by all ionized NPs in the cell, and D

_{W}is the dose given to the surrounding water.

Cell and NP | Irradiation Photons | # of NPs per Cell | α without NPs (Gy^{−1}) | α with NPs (Gy^{−1}) | p_{1} | Survival Fraction (SF) at 2Gy without NPs | Survival Fraction (SF) at 2Gy with NPs | RBE at 2Gy |
---|---|---|---|---|---|---|---|---|

SQ20B, AGuIX | 250 kVp | 6.06 × 10^{8} | 0.04 | 0.5 | 0.015 ^{a} | 0.76 | 0.33 | 2.17 |

A549, AGuIX | 1.66 × 10^{7} | 0.332 ± 0.045 [51] | 0.349 ± 0.054 ^{b} | 0–5.6 × 10^{−2} | 0.48 | 0.46 | 1.04 | |

1.32 × 10^{9} | 0.488 ± 0.063 ^{b} | (2.34 ± 0.67) × 10^{−3} | 0.35 | 1.37 | ||||

Hela, AuNP | 105 kVp | 6000 | 0.237 ± 0.005 | 0.528 ± 0.007 | (1.64 ± 0.04) × 10^{−3} | 0.53 | 0.28 | 1.69 |

220 kVp | 6000 | 0.150 ± 0.004 | 0.352 ± 0.005 | (1.73 ± 0.05) × 10^{−3} | 0.63 | 0.42 | 1.56 | |

^{137}Cs (660 keV) | 6000 | 0.119 ± 0.013 | 0.259 ± 0.011 | 0.436 ± 0.055 | 0.67 | 0.53 | 1.39 | |

6 MV | 6000 | 0.110 ± 0.008 | 0.191 ± 0.002 | 1.11 ± 0.12 | 0.71 | 0.60 | 1.35 |

^{a}The experimental data from Miladi et al. [31] did not have uncertainty info; therefore, the corresponding uncertainty in p

_{1}is not given.

^{b}The survival data from Liu et al. [32] were not complete, and the change in α was calculated by assuming no change in β (β = 0.018 Gy

^{−2}according to Wera et al. [51]).

References | NP Type and Concentration | Radiation (Photons) | Cell Type | Change in α (Gy^{−1}) | Change in β (Gy^{−2}) |
---|---|---|---|---|---|

Chithrani et al. [30] | 50 nm Gold NP, 6000 NPs per cell, | 105 kVp | HeLa | 0.237 to 0.528 | 0.041 to 0.054 |

220 kVp | 0.150 to 0.352 | 0.041 to 0.041 | |||

^{137}Cs (660 keV) | 0.119 to 0.259 | 0.040 to 0.030 | |||

6 MVp | 0.110 to 0.191 | 0.029 to 0.031 | |||

Jain et al. [60] | 1.9 nm Gold NP, 12 μM | 160 kVp | MDA-MB-231 | 0.019 to 0.091 | 0.052 to 0.093 |

6 MV | 0.002 to 0.104 | 0.079 to 0.098 | |||

15 MV | 0.083 to 0.061 | 0.059 to 0.121 | |||

Butterworth et al. [61] | 1.9 nm Gold NP, 10 μg/mL^{−1} | 160 kVp | AGO-1552B | 0.25 to 0.30 | 0.04 to 0.05 |

Astro | 0.37 to 0.40 | 0.08 to 0.09 | |||

DU-145 | 0.03 to 0.05 | 0.04 to 0.04 | |||

L132 | 0.12 to 0.11 | 0.03 to 0.03 | |||

MCF-7 | 0.46 to 0.28 | 0.02 to 0.07 | |||

MDA-231-MB | 0.09 to 0.15 | 0.03 to 0.03 | |||

PC-3 | 0.12 to 0.29 | 0.06 to 0.03 | |||

T98G | 0.04 to 0.14 | 0.03 to 0.02 | |||

1.9 nm Gold NP, 100 μg/ml | AGO-1552B | 0.25 to 0.68 | 0.04 to <0.04 | ||

Astro | 0.37 to 0.23 | 0.08 to 0.16 | |||

DU-145 | 0.03 to 0.04 | 0.04 to 0.04 | |||

L132 | 0.12 to 0.05 | 0.03 to 0.04 | |||

MCF-7 | 0.46 to 0.24 | 0.02 to 0.08 | |||

MDA-231-MB | 0.09 to 0.27 | 0.03 to 0.02 | |||

PC-3 | 0.12 to 0.21 | 0.06 to 0.03 | |||

T98G | 0.04 to 0.06 | 0.03 to 0.02 | |||

Stefancikova et al. [40] | AGuIX, 0.5 mM | 1.25 MV | U87 | 0.4 to 0.71 | 0.03 to 0 |

Miladi et al. [31] | AGuIX, 0.6 mM AGuIX | 250 kVp | SQ20B | 0.04 to 0.5 | 0.05 to 0.03 |

FaDu | 0.01 to 0.2 | 0.08 to 0.07 | |||

Cal33 | −0.05 to 0.07 | 0.08 to 0.11 | |||

AGuIX, 0.4 mM AGuIX | SQ20B | 0.04 to 0.15 | 0.05 to 0.05 | ||

Kotb et al. [62] | AGuIX, 0.6 mg/L AGuIX | 220 kVp | B16F10 | 0.056 to 0.275 | 0.025 to 0.022 |

Stewart et al. [63] | Bi_{2}O_{3} NP, 50 μg/mL | 125 kVp | 9 L gliosarcoma cell | 0.075 to 0.355 | 0.017 to 0 |

10 MV | 0.150 to 0.256 | 0.013 to 0.009 | |||

Wozny et al. [47] | AGuIX, 0.8 mg/mL AGuIX | 250 kVp | SQ20B | 0.07 to 0.19 | 0.03 to 0.04 |

Simonet et al. [54] | AGuIX, 0.8 mM Gd | 250 kVp | SQ20B J.L. | 0.1593 to 0.2357 | 0.0079 to 0.0088 |

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Yan, H.; Carlson, D.J.; Abolfath, R.; Liu, W.
Microdosimetric Investigation and a Novel Model of Radiosensitization in the Presence of Metallic Nanoparticles. *Pharmaceutics* **2021**, *13*, 2191.
https://doi.org/10.3390/pharmaceutics13122191

**AMA Style**

Yan H, Carlson DJ, Abolfath R, Liu W.
Microdosimetric Investigation and a Novel Model of Radiosensitization in the Presence of Metallic Nanoparticles. *Pharmaceutics*. 2021; 13(12):2191.
https://doi.org/10.3390/pharmaceutics13122191

**Chicago/Turabian Style**

Yan, Huagang, David J. Carlson, Ramin Abolfath, and Wu Liu.
2021. "Microdosimetric Investigation and a Novel Model of Radiosensitization in the Presence of Metallic Nanoparticles" *Pharmaceutics* 13, no. 12: 2191.
https://doi.org/10.3390/pharmaceutics13122191