# Quantitative Analysis of Photothermal Therapy of Tumor Tissue Using Various Gold Nanoparticle Injection Schemes

^{*}

## Abstract

**:**

## 1. Introduction

_{3}O

_{4}shell structure on a star-shaped Au core to increase the light conversion efficiency of the light absorption enhancer. Magnetometry and magneto-optical spectroscopy reportedly revealed a pure magnetite shell with excellent saturation magnetization. Furthermore, the plasmonic resistance in the Au@Fe

_{3}O

_{4}system could be converted to 640 nm, showing applicability for photothermal therapy and visible optical imaging. A preliminary experiment was conducted to irradiate a laser on a cancer cell culture suspension into which Au@Fe

_{3}O

_{4}was injected, and its suitability for optical response and photothermal therapy was confirmed. Bi et al. [24] proposed Ag

_{2}O

_{2}nanoparticles, which can control the release of reactive oxygen species, to reduce the toxic side effects of metal peroxide nanoparticles designed to increase oxidative stress. In vitro and in vivo experiments confirmed that Ag

_{2}O

_{2}nanoparticles had a mortality efficiency of 99.9999% or more within 10 min, provided improved antibacterial and antibiotic membrane functions, and accelerated wound suture against Staphylococcus aureus infection with excellent cell and blood compatibility. Through this, a high-efficiency, non-invasive, and safe treatment method for combating bacterial infectious diseases was presented. Wang et al. [25] analyzed the effect of photothermal therapy on tumors containing gold nanoparticles through numerical analysis. The temperature distribution of tumors generated from the skin surface and the surrounding normal tissues was confirmed using the Monte Carlo method, and analysis was performed by varying the treatment conditions for photothermal therapy, such as the tumor size, irradiating laser intensity, and volume fraction of GNPs in the tumor. In addition, the thermal damage to the tissue was confirmed through the Arrhenius thermal damage integral. Yin et al. [26] studied photothermal therapy inside the tissue through numerical analysis. The effects of laser intensity, volume fraction of GNPs, anisotropic scattering characteristics of nanoparticles, and laser incident angle were investigated. Based on this, various treatment strategies, such as single heat source and multiple heat sources, were also identified. In the case of single-dose treatment, it was confirmed that there was almost no difference for the various laser incident angles; in the case of the split treatment, better treatment effects were observed when the laser was irradiated at a constant angle than in the vertical direction. In addition, it was confirmed that multiple heat sources had better therapeutic effects than a single heat source. Guglielmelli et al. [27] developed keratin-coated gold nanoparticles (Ker-AuNPs) as a highly efficient photosensitizing therapeutic agent. The physical, photothermal, chemical, and morphological properties of Ker-AuNPs were investigated by various methods, including dynamic light scattering, ζ-potential, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy. In addition, in vitro experiments were conducted on human glioblastoma cell lines to confirm the efficient cellular absorption, good biocompatibility and local photothermal heating of Ker-AuNPs. Annesi et al. [28] studied an antimicrobial methodology based on gold nanorods (GNRs). The anti-microbial effect of GNRs on Escherichia coli bacteria was confirmed, and it is important to control the concentration of GNRs to exclude toxic effects on cells and to generate the amount of heat required to raise the temperature to 50 degrees in about 5 min in the near-infrared region. In addition, as a result of the experiment, it was confirmed that killing efficiency suitable for reducing Escherichia coli populations to about 2 log colony-forming units was achieved. Candreva et al. [29] synthesized spherical GNPs with a diameter of 50 nm coated with polyethylene glycol and administered into Escherichia coli cultures to activate plasmon in the visible light region. Experiments were performed in the dark and under laser irradiation, with varying concentrations of GNPs. In the dark, 46% of bacterial growth was inhibited, while laser irradiation at the same concentration resulted in 99% growth inhibition. This was attributed to the fact that the bacterial wall promotes the formation of light-induced clusters of nanoparticles, resulting in an increase in temperature and a bactericidal effect. Furthermore, this photothermal effect is achieved with low intensity laser irradiation only when the pathogen is present, proving that this is an innovative response system to bacterial infections.

## 2. Material Properties and Numerical Methods

#### 2.1. Optical Properties of Gold Nanoparticles and Biological Tissues

_{inc,i}represents the initial electric field and k represents the wave number. Equation (4) represents the interaction matrix between dipoles. Here, r

_{ij}represents $\left|{r}_{i}-{r}_{j}\right|$, and A

_{ij}is an interaction matrix under the condition that i ≠ j. If i and j are equal, the interaction matrix can be simplified to ${\alpha}_{i}^{-1}$.

_{eff}and V are the volume and effective radius of the particle, respectively.

_{v}), the effective radius of the particle (r

_{eff}), and the optical efficiency Q, calculated through the DDA method as shown in Equation (10) [37]. After the optical properties of the GNPs are calculated, the optical properties of the entire medium with GNPs injected can be calculated as the sum of the optical properties of the GNPs and the optical properties of the medium, as shown in Equation (11) [38].

#### 2.2. Validation of Numerical Process

_{v}≈ 3 × 10

^{−4}) and 50 ug (f

_{v}≈ 6.5 × 10

^{−4}) of GNPs, respectively. GNPs used in this study are a rod type shape with an effective radius of 10 nm and an aspect ratio of 6.7. They are dispersed at a concentration of 35 ug/mL in H

_{2}O. GNPs were purchased from Sigma Aldrich and the absorption spectrum of the nanoparticles shows a longitudinal peak at 1064 nm and a longitudinal absorbance OD of 1. As shown in the figure, there were blisters (red circles) on the mice’s skin due to burns in the affected area after laser irradiation compared to none before. These were classified as blisters on burns, known to be expressed at about 50–70 °C, as announced by Stoll et al. [40] and Leach et al. [41].

_{v}≈ 6.5 × 10

^{−4}) of GNPs were injected, with an overall temperature increase to above 50 °C in the irradiated part. Through this, it can be judged that the results derived from the in vivo experiment and the numerical analysis are similar. In addition, verification of the numerical model was performed through in vitro experiments using biomimetic phantoms. Comparison between the numerical analysis modeling and the experiment yielded an RMSE of the temperature change over time as an average of 0.1677. It was thus determined that the numerical analysis modeling was valid [33].

#### 2.3. Numerical Investigation

^{−1}–10

^{−8}at intervals of 10

^{−1}in a total of eight steps. It was assumed that GNPs were distributed in the form of spheres with a diameter of 2 mm for all volume fractions based on one-time injection.

_{v}represent the time, density, and specific heat, respectively, while F and P

_{l}represent the fluence rate and laser intensity, respectively [54].

## 3. Results and Discussion

#### 3.1. Temperature Distribution of Biological Tissues

_{v}) for lasers of 40 mW intensity. Figure 6a shows the results for an f

_{v}of 10

^{−6}, while Figure 6b shows the results when GNPs were deposited in six separate injections, according to volume fractions. As shown in Figure 6a, the temperature of the center of the tumor surface varies according to the number of injections. In particular, when the GNPs were injected separately, excessive temperature rise did not occur, compared to the case in which GNPs were injected once in the center. As shown in Figure 6b, the temperature increase at the center of the tumor surface decreases as the f

_{v}decreases. Through this, it was confirmed that the temperature of the entire medium increased differently according to the various number of injected GNPs and f

_{v}. Accordingly, in the results described later, the temperatures of all points in the medium were checked, and the degree of maintenance of the temperature range where apoptosis occurred and the amount of thermal damage to surrounding normal tissues were quantitatively evaluated.

#### 3.2. Apoptosis Occurrence Amount in Tumor Tissue

_{l}according to the various f

_{v}. The tendency of ${\theta}_{A}^{*}$ is similar between various numbers of injections, so only the results of the three and six GNP injection cases are replicated in the graphs below. It was confirmed that there existed a P

_{l}corresponding to the maximum ${\theta}_{A}^{*}$ for each f

_{v}and for each number of injections. In addition, it was confirmed that as f

_{v}decreased, the P

_{l}corresponding to a maximum ${\theta}_{A}^{*}$ increased. This is because a decrease in f

_{v}results in reduced heat absorption capability of the medium for the laser, so a higher P

_{l}is needed to maintain the desired temperature range. As the number of injections increased, the P

_{l}corresponding to a maximum ${\theta}_{A}^{*}$ slightly decreased. This is because, as the number of injections increases, the injected GNPs are distributed more widely and evenly, so the tumor tissue is heated in a larger area even at a relatively low P

_{l}.

_{l}according to various number of injected GNPs for a given f

_{v}. Figure 8a shows the change in ${\theta}_{A}^{*}$ when f

_{v}is 10

^{−3}. In this case, there was a specific P

_{l}corresponding to a maximum ${\theta}_{A}^{*}$ for each number of injections. In addition, it was confirmed that the maximum value of ${\theta}_{A}^{*}$ was higher when GNPs were injected in two or more divided doses compared to one dose. As mentioned above, this is attributed to the increased GNPs diffusion radius which results in a more widespread temperature rise inside the tumor. Figure 8b shows the result when f

_{v}is 10

^{−8}, and it is confirmed that ${\theta}_{A}^{*}$ according to P

_{l}is similar for all numbers of injections. This is because the f

_{v}is very low and the effect of the GNPs’ injection is insignificant—the GNP injections do initiate an increase in the light absorption coefficient of the entire medium. Evaluating the overall treatment conditions, it was concluded that apoptosis occurrence temperature in tumor tissue was best maintained when the number of injections was five times, f

_{v}was 10

^{−5}, and P

_{l}was 58 mW.

#### 3.3. Thermal Damage of Surrounding Normal Tissues

_{l}according to f

_{v}. Figure 9a represents the case of three GNPs injections in the tumor tissue, while Figure 6b represents six injections. In both cases, as f

_{v}decreases, the amount of thermal damage to surrounding normal tissues decreases. This is because as f

_{v}decreases, the temperature increase of the tumor tissue occurs less, as shown in Section 3.2.

_{l}according to the number of GNPs injections when f

_{v}is 10

^{−3}and 10

^{−8}, respectively. As shown in Figure 10a, as the number of injections increases, so does the amount of thermal damage in the surrounding normal tissue. This is because as the number of injections increases, the diffusion radius of GNPs within the tumor increases, resulting in a temperature rise across a wider range of the tumor tissue, and, as a result, more laser heat absorbed from the tumor tissue is transferred to the surrounding normal tissue.

#### 3.4. Quantitative Analysis of Photothermal Therapy Effect

_{l}according to various conditions of photothermal therapy. The trend of the overall graph was derived in the same way as ${\theta}_{A}^{*}$, and it was confirmed that there was a P

_{l}corresponding to an optimal therapeutic effect for each f

_{v}and number of GNPs injections. At P

_{l}values below the optimum point, the temperature of the tumor tissue did not rise sufficiently, resulting in a sub-optimal treatment effect. At values of P

_{l}greater than the optimum point, the temperature of the tumor tissue increased excessively, resulting is significant transfer of laser heat to the surrounding normal tissue, increasing the thermal damage. When summarizing the effects of all treatment conditions, it was confirmed that the optimal treatment effect was achieved when the number of injections was six, f

_{v}was 10

^{−3}, and P

_{l}was 42 mW. The optimal P

_{l}for treatment was lower than that for ${\theta}_{A}^{*}$; this is because a higher P

_{l}results in greater heat transfer from the tumor tissue to the surrounding normal tissue, increasing the amount of thermal damage. Likewise, the higher optimal f

_{v}for treatment vs. ${\theta}_{A}^{*}$ is explained as follows: the effect of f

_{v}on heat absorption (caused by the change in the light absorption coefficient) is greater than the effect of laser penetration depth (caused by higher P

_{l}) on the maximum heat absorption depth. Through this analysis, the treatment conditions that produce optimal treatment effects were identified for the case of photothermal therapy on a skin layer where squamous cell carcinoma has occurred.

## 4. Conclusions

^{−3}, deposited over six direct injections and irradiated at a laser power of 42 mW. It is thus judged that it is possible to present a reference point for optimal treatment in photothermal therapy in which GNPs are directly injected into the tumor. Furthermore, it is believed that the popularization of photothermal therapy can be accelerated by optimizing treatment conditions from a clinical perspective through the process of performing actual treatment trials. In addition, it is necessary to study a more realistic situation, reflecting the phenomenon that GNPs are dissipated by various mechanisms immediately after they are injected.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C | $\mathrm{Cross}-\mathrm{sec}\mathrm{tion}\text{}\mathrm{area}\text{}({\mathrm{m}}^{2}$) |

c_{v} | $\mathrm{Specific}\text{}\mathrm{heat}\text{}(\mathrm{J}/\mathrm{kgK}$) |

E | Electric field ($\mathrm{N}/\mathrm{C}$) |

f_{v} | Volume fraction of GNPs |

F | $\mathrm{Fluence}\text{}\mathrm{rate}\text{}(1/{\mathrm{m}}^{2}\mathrm{s}$) |

g | Anisotropy factor |

k | $\mathrm{wavenumber}\text{}\mathrm{of}\text{}\mathrm{radiation}\text{}(1/\mathrm{m}$) |

k_{m} | $\mathrm{Thermal}\text{}\mathrm{conductivity}\text{}(\mathrm{W}/\mathrm{mK}$) |

P | Polarization vector ($\mathrm{C}/{\mathrm{m}}^{2}$) |

P_{l} | Intensity of laser (W) |

Q | Dimensionless efficiency factor |

r | Position vector |

r_{eff} | Effective radius of nanoparticle (m) |

t | Thickness (m) |

T | Temperature (K) |

Greek symbols | |

$\alpha $ | $\mathrm{Polarizability}\text{}({\mathrm{C}}^{2}{\mathrm{m}}^{2}/\mathrm{J}$) |

${\theta}_{A}^{*}$ | Apoptosis retention ratio |

${\theta}_{eff}^{*}$ | Effective apoptosis retention ratio |

${\theta}_{H}^{*}$ | Thermal hazard retention value |

${\mu}_{abs}$ | Absorption coefficient (1/m) |

${\mu}_{sca}$ | Scattering coefficient (1/m) |

$\rho $ | $\mathrm{Density}\text{}(\mathrm{kg}/{\mathrm{m}}^{3}$) |

$\tau $ | Time (s) |

Subscripts | |

abs | Absorption |

m | Medium |

np | Nanoparticle |

sca | Scattering |

x, y, z | Notation of direction |

Superscripts | |

+ | Next element |

− | Previous element |

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**Figure 2.**Validation experiment results: (

**a**) 25 μg dose, irradiated for 5 min; (

**b**) 50 μg dose, irradiated for 5 min.

**Figure 3.**Validation numerical analysis results: (

**a**) 25 μg dose, irradiated for 5 min; (

**b**) 50 μg dose, irradiated for 5 min.

**Figure 6.**Temperature change of tumor tissue over time for: (

**a**) various numbers of GNPs injections (f

_{v}= 10

^{−6}); (

**b**) various volume fractions of GNPs (over six injections).

**Figure 7.**Apoptosis retention ratio (${\theta}_{A}^{*}$) for various volume fraction of GNPs (f

_{v}) over (

**a**) three injections and (

**b**) six injections.

**Figure 8.**Apoptosis retention ratio (${\theta}_{A}^{*}$) for various number of GNPs injections at (

**a**) f

_{v}= 10

^{−3}and (

**b**) f

_{v}= 10

^{−8}.

**Figure 9.**Thermal hazard retention value (${\theta}_{H}^{*}$) for various volume fractions of GNPs (f

_{v}) over (

**a**) three injections and (

**b**) six injections.

**Figure 10.**Thermal hazard retention value (${\theta}_{H}^{*}$) for various numbers of GNPs injections when (

**a**) f

_{v}= 10

^{−3}and (

**b**) f

_{v}= 10

^{−8}.

**Figure 11.**Effective apoptosis retention ratio (${\theta}_{eff}^{*}$) for (

**a**) various f

_{v}values over three GNPs injections; (

**b**) various numbers of GNPs injections for f

_{v}= 10

^{−6}.

Thermal conductivity k_{m} (W/mK) | 0.34 |

$\mathrm{Density}\text{}\rho $ (kg/m^{3}) | 1000 |

Specific heat c_{v} (J/kgK) | 3000 |

$\mathrm{Absorption}\text{}\mathrm{coefficient}\text{}{\mu}_{abs}$ (1/mm) | 6.1 |

$\mathrm{Scattering}\text{}\mathrm{coefficient}\text{}{\mu}_{sca}$ (1/mm) | 40.65 |

Anisotropy factor g | 0.8 |

$\mathit{t}$ (mm) | k_{m}(W/mK) | $\mathit{\rho}$ (kg/m ^{3})
| c_{v}(J/kgK) | $\mathit{g}$ | ${\mathit{\mu}}_{\mathit{a}\mathit{b}\mathit{s}}$ (1/mm) | ${\mathit{\mu}}_{\mathit{s}\mathit{c}\mathit{a}}$ (1/mm) | |
---|---|---|---|---|---|---|---|

Epidermis | 0.08 | 0.235 | 1200 | 3589 | 0.8 | 0.4 | 45 |

Papillary dermis | 0.5 | 0.445 | 1200 | 3300 | 0.9 | 0.38 | 30 |

Reticular dermis | 0.6 | 0.445 | 1200 | 3300 | 0.8 | 0.48 | 25 |

Subcutaneous fat | 18.82 | 0.19 | 1000 | 2500 | 0.75 | 0.43 | 5 |

Tumor | 2 | 0.495 | 1070 | 3421 | 0.8 | 0.047 | 0.883 |

Parameter | Case | Number | Remarks |
---|---|---|---|

Laser power (P_{l}) | 0 to 100 mW | 51 | Intv: 2 mW |

Volume fraction of GNPs (f_{v}) | 10^{−1} to 10^{−8} | 8 | Intv: 10^{−1} |

Number of injected GNPs | 1 to 6 | 6 | Intv: 1 |

f_{v} | 10^{−1} | 10^{−2} | 10^{−3} | 10^{−4} | 10^{−5} | 10^{−6} | 10^{−7} | 10^{−8} |
---|---|---|---|---|---|---|---|---|

${\mu}_{abs}$ (cm^{−1}) | 5,016,309.16 | 501,631.34 | 50,163.55 | 5016.78 | 502.10 | 50.63 | 5.48 | 0.97 |

${\mu}_{sca}$ (cm^{−1}) | 1,059,239.60 | 105,931.91 | 10,601.14 | 1068.06 | 114.75 | 19.42 | 9.89 | 8.94 |

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## Share and Cite

**MDPI and ACS Style**

Kim, D.; Kim, H.
Quantitative Analysis of Photothermal Therapy of Tumor Tissue Using Various Gold Nanoparticle Injection Schemes. *Pharmaceutics* **2023**, *15*, 911.
https://doi.org/10.3390/pharmaceutics15030911

**AMA Style**

Kim D, Kim H.
Quantitative Analysis of Photothermal Therapy of Tumor Tissue Using Various Gold Nanoparticle Injection Schemes. *Pharmaceutics*. 2023; 15(3):911.
https://doi.org/10.3390/pharmaceutics15030911

**Chicago/Turabian Style**

Kim, Donghyuk, and Hyunjung Kim.
2023. "Quantitative Analysis of Photothermal Therapy of Tumor Tissue Using Various Gold Nanoparticle Injection Schemes" *Pharmaceutics* 15, no. 3: 911.
https://doi.org/10.3390/pharmaceutics15030911