# Xerogels Morphology Details by Multifractal Analysis and Scanning Electron Microscopy Images Evaluations of 5-Fluorouracil Release from Chitosan-Based Matrix

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}solutions) and drying methods (supercritical drying, freeze drying, and oven drying) to obtain particles with a broad range of physicochemical and textural properties. Xerogels and cryogels are obtained after the atmospheric drying and freeze drying of gels, respectively.

^{2}/g. It has many important properties such as a large amount of controlled pore size distribution, high conductivity, transparency, low density, flexibility, low dielectric constant, and high mechanical strength.

## 2. Results and Discussion

#### 2.1. Theoretical Part: Delivery Kinetics Mathematical Modeling

^{l}is one of the multifractal 3D coordinates, and ${V}_{D}^{l}$ is the “multifractal fluid” speed of differentiable scale resolution (the polymer–medicament binary system is assumed to be a “multifractal flowing substance”) [23,24]. In continuation, ρ is the “multifractal fluid” state density, λ is the configurational constant associated with the deliverance procedure related to the fractal–multifractal specific passage, dt is the scale resolution factor and f(α) is the α order singular spectrum contingent based on the calculated fractal dimension.

_{0}is the initial velocity of the polymer–medicament binary structure:

^{2}= 1 fixed value (where the calibration is indicated) is shown.

^{2}= 1 fixed value (where the calibration is indicated) is shown.

_{0}, this permits the normalized delivered medicament mass definition as having the expression

_{D}= V

_{0}) and ξ = η, we have the case in which Equation (12) (because of the fact that μ

_{0}≡ 1 has a fixed value) becomes

_{1}), the other two (P

_{2}and P

_{3}) tend towards infinity for large time values, while curve P

_{4}seems to decrease for long periods of time. The solid curves are the theoretical ones, according to the model used, and the experimental points are close to them, denoting a good agreement between them.

#### 2.2. Box-Counting Method

#### 2.3. Lacunarity

^{2}is the number of possible box positions; and Q(P, ε) is the probability calculated by Equation (1). At the same time, P•Q(P, ε) and P

^{2}•Q(P, ε) are the first and second moments, while Z

^{(1}) and Z

^{(2)}are the sum of the first and second moments, calculated by Equations (3) and (4), respectively. Equation (2) is the lacunarity $\mathsf{\Lambda}\left(\epsilon \right)$ of the dataset for box size ε.

#### 2.4. Assessment of Scanning Electron Microscope Images Using Fractal Analysis

_{1}, P

_{2}, P

_{3}, and P

_{4}. The number associated with each letter/compound is appropriate to the molar proportion of the amino/aldehyde class, i.e., 1:1, 2:1, 3:1, and 4:1, respectively.

_{1}, P

_{2}), while for the hydrogel compounds with lower reticulated density (P

_{4}), a birefringent, granular structure was observed, characteristic of crystal submicrometric dimensions distributed below the apparatus detection tolerance [30].

_{1}, P

_{2,}and P

_{4}. The scale bar for the POM photographic images is 20 microns. Figure 5a shows POM-P

_{1}, Figure 5b shows POM-P

_{2}, and Figure 5c shows POM-P

_{4}.

_{1}, P

_{2,}and P

_{3}). The scale bar for the SEM photographic images is 400 microns. Figure 6a shows SEM-P

_{1}, Figure 6b shows SEM-P

_{2}, and Figure 6c shows SEM-P

_{3}.

_{1}, P

_{2,}and P

_{3}—was investigated by scanning electron microscopy, and was then evaluated. Strictly speaking, in this paper, a new way of interpreting the SEM images of the samples is presented (fractal analysis), which is the main novelty of this paper compared to [8].

_{1}of the entire portion, Figure 7b is the grayscale version of the original image, Figure 7c is the grayscale version of the image without luminance, and Figure 7d is the binarized version image without luminance.

_{1}image in order to apply the fractal analysis procedure and calculate the fractal dimension and lacunarity. For image binarization, a threshold of 30 units was utilized.

_{1}) with fractal analysis software [35], it was found that the fractal dimension value D = 1.8621 had a standard deviation of $\mathrm{s}=\pm \sqrt{{\sigma}^{2}}=\pm 0.0733$ and a lacunarity value of Λ = 0.0385, as shown in Table 1.

_{1}picture zone (fractal dimension computation) with the Harmonic and Fractal Image Analyzer Demo computer program (Prague, Czech Republic), version 5.5.30 [36]. The fractal dimensions of the different ruler scales are equal to r.

_{1}image and a 3D graphic representation. The gray level is shown on the oZ axis, while the corresponding numbers of pixels are on the other two axes (oX and oY) [37].

_{2}SEM image are presented. In Figure 11a, the original image of the entire portion is depicted, the grayscale version of the original image is shown in Figure 11b, the grayscale version of the image without luminance is shown in Figure 11c, and Figure 11d is the binarized version of the image without luminance.

_{2}image in order to apply the fractal analysis procedure and calculate the fractal dimension and lacunarity. For image binarization, a threshold of 25 units was utilized.

_{2}) with fractal analysis software [35], it was found that the fractal dimension value D = 1.8837 had a standard deviation of $\mathrm{s}=\pm \sqrt{{\sigma}^{2}}=\pm 0.0894$ and a lacunarity value of $\mathsf{\Lambda}=0.0498$, as shown in Table 2.

_{2}picture zone (fractal dimension computation) with the Harmonic and Fractal Image Analyzer Demo program, version 5.5.30 [36]. The fractal dimensions of the different ruler scales are equal to r.

_{2}image and a 3D graphical representation. The gray level is shown on the oZ axis, while the corresponding numbers of pixels are on the other two axes (oX and oY) [37].

_{3}SEM image are presented. In Figure 15a, the original image of the entire portion is shown, the grayscale version of the original image is shown in Figure 15b, the grayscale version of the image without luminance is shown in Figure 15c, and Figure 15d is the binarized version of the image without luminance.

_{3}image are shown in order to apply the fractal analysis procedure and calculate the fractal dimension and lacunarity. For image binarization, a threshold of 10 units was utilized.

_{3}) with fractal analysis software [35], it was found that the fractal dimension value D = 1.8561 had a standard deviation of $\mathrm{s}=\pm \sqrt{{\sigma}^{2}}=\pm 0.0702$ and a lacunarity value of $\mathsf{\Lambda}=0.0324$, as shown in Table 3.

_{3}picture zone (fractal dimension computation) with the Harmonic and Fractal Image Analyzer Demo program, version 5.5.30 [36]. The fractal dimensions of the different ruler scales are equal to r.

_{3}image and a 3D graphical representation. The gray level is shown on the oZ axis, while the corresponding numbers of pixels are on the other two axes (oX and oY) [37].

_{1}, P

_{2}, and P

_{3}from the amended zone. The three coordinate axes are assigned as follows: the pixel number is on the ox axis, the pixel number is on the oy axis, and the gray intensity level for the respective pixel is on the oz axis. In line with the generated computer graphics, the so-called voxel shows the numerical amount/value directly connected to the regular grid in a 3D spatial configuration.

## 3. Conclusions

_{1}, P

_{2,}and P

_{3}SEM images of the three formulations were found to conform with the fractal analysis procedures, and the fractal dimension and lacunarity values were calculated. Thereby, the P

_{1}image had the fractal dimension value of D = 1.8621 ± 0.0733 and the lacunarity value of Λ = 0.0385. The P

_{2}image had the fractal dimension value of D = 1.8837 ± 0.0894 and the lacunarity value of Λ = 0.0498. Finally, image P

_{3}had the fractal dimension value of D = 1.8561 ± 0.0702 and the lacunarity value of Λ = 0.0324.

## 4. Materials and Methods

#### 4.1. Materials

#### 4.2. Formulation Preparation

#### 4.3. Methods

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Three-dimensional graphical representations of 𝑉 (ξ, η) velocity multifractal theoretical function.

**Figure 2.**Three-dimensional graphical representation of the ϕ = ϕ (ξ, η) mass state density theoretical function.

**Figure 5.**Typical POM pictures of the compounds/formulations: (

**a**) POM-P

_{1}; (

**b**) POM-P

_{2}; (

**c**) POM-P

_{4}.

**Figure 6.**Typical SEM pictures of the compounds/formulations: (

**a**) SEM-P

_{1}; (

**b**) SEM-P

_{2}; (

**c**) SEM-P

_{3}.

**Figure 7.**Processing stages of P

_{1}image. (

**a**) Original image (the entire portion); (

**b**) grayscale version; (

**c**) grayscale version without luminance; (

**d**) binarized version.

**Figure 11.**Processing stages of the P

_{2}image. (

**a**) Original image (the entire portion); (

**b**) grayscale version; (

**c**) grayscale version without luminance; (

**d**) binarized version.

**Figure 15.**Processing stages of the image P

_{3}. (

**a**) Original image (the entire portion); (

**b**) grayscale version; (

**c**) grayscale version without luminance; (

**d**) binarized version.

Name | Fractal Dimension | Standard Deviation | Lacunarity |
---|---|---|---|

Image P_{1} | 1.8621 | 0.0733 | 0.0385 |

Name | Fractal Dimension | Standard Deviation | Lacunarity |
---|---|---|---|

Image P_{2} | 1.8837 | 0.0894 | 0.0498 |

Name | Fractal Dimension | Standard Deviation | Lacunarity |
---|---|---|---|

Image P_{3} | 1.8561 | 0.0702 | 0.0324 |

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**MDPI and ACS Style**

Paun, M.-A.; Nichita, M.-V.; Paun, V.-A.; Paun, V.-P.
Xerogels Morphology Details by Multifractal Analysis and Scanning Electron Microscopy Images Evaluations of 5-Fluorouracil Release from Chitosan-Based Matrix. *Gels* **2022**, *8*, 820.
https://doi.org/10.3390/gels8120820

**AMA Style**

Paun M-A, Nichita M-V, Paun V-A, Paun V-P.
Xerogels Morphology Details by Multifractal Analysis and Scanning Electron Microscopy Images Evaluations of 5-Fluorouracil Release from Chitosan-Based Matrix. *Gels*. 2022; 8(12):820.
https://doi.org/10.3390/gels8120820

**Chicago/Turabian Style**

Paun, Maria-Alexandra, Mihai-Virgil Nichita, Vladimir-Alexandru Paun, and Viorel-Puiu Paun.
2022. "Xerogels Morphology Details by Multifractal Analysis and Scanning Electron Microscopy Images Evaluations of 5-Fluorouracil Release from Chitosan-Based Matrix" *Gels* 8, no. 12: 820.
https://doi.org/10.3390/gels8120820