Fractal Dimension Image Processing for Feature Extraction and Morphological Analysis: Gd<sup>3+</sup>/13X/DOX/FA MRI Nanocomposite

Ghaderi, Sadegh

doi:https://doi.org/10.1155/2023/8564161

Journal of Nanomaterials

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Abstract Introduction Methods Results Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 8564161 | https://doi.org/10.1155/2023/8564161

Fractal Dimension Image Processing for Feature Extraction and Morphological Analysis: Gd³⁺/13X/DOX/FA MRI Nanocomposite

Sadegh Ghaderi¹

Academic Editor: Mazeyar Parvinzadeh Gashti

Received13 Feb 2023

Revised10 Mar 2023

Accepted16 Mar 2023

Published21 Apr 2023

Abstract

One of the most fundamental subjects in nanoscience and nanotechnology is structural analysis. We employed a scanning electron microscope (SEM) image of the manufactured Gd³⁺/13X/DOX/FA nanocomposite in this study. The size, dimensions, and morphology of nanocomposite materials were studied to ensure the uniformity and homogeneity of SEM images. This is the first study to look at segmented SEM images for fractal dimension (FD) and other statistical criteria, including average, maximum, minimum, skewness, and range for magnetic resonance imaging (MRI) nanocomposite. The average of FD (FD_avg), the standard deviation of FD (FD_sd), and the lacunarity of FD (FD_lac) fractal data analysis criteria were also employed. The findings show that particle sizes and shapes vary because the minimum-to-maximum range is not zero, and our data provide a reasonable range. This interpretation is further supported by an analysis of the nanocomposite’s SEM image. At first glance, the image seemed to be uniform. However, when the calculations were performed, it was discovered that the generated particles were not particularly uniform. The particles were uniformly dispersed throughout all surfaces, although their sizes, dimensions, and morphologies varied. In conclusion, the study was supported by fractal data analysis, emphasizing the importance of structural analysis for future research, particularly for medical applications like MRI.

1. Introduction

The powers of structural, directional, and functional control are the most essential issues in nanoscience and emerging nanotechnology. Many attempts have been made to regulate the spatial distribution of nanoparticles (NPs) as well as their physical and functional features [1–3].

Magnetic resonance imaging (MRI) is a noninvasive and novel imaging modality [4–6]. The use of contrast agents (CAs) in MRI is offered to enhance image contrast as well as the identification of diseased cells [7]. Magnetic NPs are one of the primary types of nanoscale materials that have the potential to fundamentally alter current diagnostic and treatment approaches [8, 9].

The scanning electron microscope (SEM) is a technique that is used to scan and analyze microscopic characteristics on solid surfaces, as in MRI CAs. SEM images are often used to qualitatively analyze the surface features of morphological variables like size, surface composition, and shape of samples. They are also used to find sample characteristics like compositional changes, topography (shape, inclination, edges, etc.), and physical differences (crystalline structure, magnetic fields, electrical fields, etc.) [1, 6, 10].

Image processing of nanostructures involves a variety of preparations, subdivisions, and data preprocessing processes that end in quantitative data extraction. Recently, computer-based image-processing techniques have advanced significantly, allowing for the quantitative representation of complex hues, patterns, texture properties, and sizes. According to research done in the past, computer-aided diagnostics and image analysis may be some of the best screening methods because they make it easier to process large amounts of information [10–13].

Fractal geometry is a mathematical method that is used to analyze irregular geometric shapes. The fractal dimension (FD) may show some of the properties of natural imagery [11–14].

Calculating the predictable edge of the length acquired along the border and the number of ladders characterizes the FD parameter [14–21]. Because lower step sizes represent the existence of more features on the particle output, the boundary length rises as the step size is reduced [11, 22–24]. Furthermore, incorporating other metal cations (such as gadolinium (Gd³⁺)) into the nanosized zeolites may alter their behavior, raising interest in zeolite NP as an imaging tool [26]. It is possible that this is a strong argument for the fractal analysis of images [25].

Gd³⁺-based MRI CAs have the best structure for producing a positive signal, or T1 CA. Because of its low toxicity, good solubility, great physicochemical qualities, and high relaxation, it is also commonly employed in clinical diagnostics to promote the relaxation of water protons. Also, using Gd³⁺ nanocomposite, which is paramagnetic, may slow down the rate of relaxation and improve contrast [26–28].

Doxorubicin (DOX) is an anticancer medication that has the potential to be used against a variety of cancers. The folic acid receptor is utilized to target materials in MRI CAs because of folic acid’s high absorption and toxicity promote binding to its receptor on the surface of cancer cells. The CA structure, which we presented in the prior work, was targeted with doxorubicin and folic acid [29–31].

Zeolite has a microporous structure made up of crystalline aluminosilicate and specific chemical forms and is widely employed for three major properties: adsorption, ion exchange, and catalytic properties. Zeolite, particularly zeolite 13X, has a crystalline structure and a hydrated aluminum main framework with a hole filled with water particles and ions. Previous research has focused on two forms of zeolites, X and A [32–35]. Tatlier and Erdem-Çenatalar [33] estimated the value of the FD of the 13X zeolite in the following earlier reports: 2.08. Finally, in this study, we will use the SEM image of the Gd³⁺/13X/DOX/FA nanocomposite [6].

According to our findings, no FD research has been conducted on MRI-Gd-based CAs. Furthermore, there are substantial differences across related research regarding the type and structure of the contrast material used and the SEM image processing technique employed. Also, the FD method on a manufactured MRI nanocomposite with anticancer and targeting properties, Gd³⁺/13X/DOX/FA nanocomposite, will be performed for the first time [6].

Our work is valuable because we perform preprocessing operations to improve image quality, automatic image segmentation to remove human error interference, and statistical data calculations using a more user-friendly application. The purpose of this work is to investigate the size, dimensions, and morphology of synthesized Gd³⁺/13X/DOX/FA nanocomposite at the molecular level to confirm or reject the uniformity and homogeneity of SEM images of nanocomposites based on the range of particles. Consequently, it is important to examine the support for FD analysis, underlining the significance of structural analysis on nanocomposites for future study, especially for medical applications.

2. Methods

2.1. Nanocomposite and Summary of Methods

Ghaderi et al. [6] developed the Gd³⁺/13X/DOX/FA. X-ray diffraction (XRD) patterns and SEM images were applied to determine the physicochemical parameters of the Gd³⁺/13X/DOX/FA nanocomposite. Lashgari et al. [14] assessed the FDs of 30 randomly selected SEM images (manganese–chromium bimetallic nanocomposite) using MATLAB software. Lastly, the SPSS software was used to acquire the image’s histogram and normalize the image’s histogram, mean, median, maximum and minimum values, range, skewness, and harmonic mean. In this study, however, based on prior research, 30 random images are needed after applying the pre-processing SEM image in Gd³⁺/13X/DOX/FA nanocomposite using the automated segmentation approach through the toolbox and MATLAB program. Then, using Excel, we will determine the average of FD (FD_avg), standard deviation of FD (FD_sd), and lacunarity of FD (FD_lac) for all images, as well as the average, maximum, minimum, skewness, and range of the chosen images. Lacunarity has been developed to distinguish between distinct texture appearances that may have the same FD value. Lacunarity quantifies the distribution of gap sizes: geometric objects with low lacunarity are homogenous since all gap sizes are the same, while objects with high lacunarity are heterogeneous [36, 37]. For the first time, our image processing research relies on a synthetic MRI nanocomposite with anticancer and targeting characteristics.

2.2. Calculation of FD and Image Analysis

Dimension is one of the most important concepts in fractal geometry [38]. Currently, numerous FD analysis and computation methods have been followed by comparable bases, which are briefly summarized in three steps:(i)Object quantification using various step sizes and stages.(ii)Values were measured against the size of the steps, and the minimum squares of the regression line across data points were determined.(iii)Estimating FDs as a regression line slope.

We will employ the box-counting approach in our research since the box-counting dimension [14] is a mathematical design, and an estimate of the box-counting dimension is simple. This value has become one of the most commonly used generic dimensions [39, 40]. We used MATLAB version r2022b to do the FD assessments and analyses. The SEM image of the Gd³⁺/13X/DOX/FA nanocomposite is shown in Figure 1. This image will be used in the image processing section [6].

2.3. FD Methodical Concepts

Fractals may be defined numerically as a geometrical set with a Hausdorff–Besicovitch measurement that carefully exceeds the topological measurement. Mandelbrot [41] used the word “fractal” to describe non-Euclidean structures that exhibit self-similarity at different sizes. Because most organic and common highlights include discontinuities and fractures, they will have an FD. In the same way, most of these regular structures are complicated and sometimes have a precise Euclidean (smooth) form so that they can be approximated accurately.

In Euclidean n-space, a restricted set S is manifestly self-comparable if it is the union of Nr no overlapping subsets as for a scaling factor r, each of which has the structure r(Sn), where the Nr and Sn sets are consistent in circulation to S. As a result, the Hausdorff–Besicovitch—the fractal measurement—of a finite set S in Rn is a legitimate number used to depict the geometric multidimensional character of S in the same way that length is employed as an estimating tool in Euclidean (discrete) space. Nr is simply the number of comparable (invariant) shapes, and r is the scaling factor for comparison [42, 43]. The FD may now be calculated in Equation (1) as follows:

In reality, most regular and some numerical self-comparable fractals are arbitrary, meaning that they scale accurately. The similarity between shapes seen at different scales in conventional fractals is often inexact and seen as irregular rather than self-comparable. In general, the FD of an investigated structure should have self-comparable split and sporadic forms that do not change as the size of the estimate goes up or down, all the way up to infinity.

Depending on the goals and profundity of the acquired image, this must be true for a limited number of scales. So, for each studied typical fractal, there is a small scaling range below or above which the structure is either smooth (i.e., Euclidean) or completely rough and not self-comparable (i.e., arbitrary) [44].

To differentiate between two surfaces if their FD worth is indistinguishable despite the fact that the two surfaces are unlikely to be comparable, we must calculate the lacunarity of the FD surface. Lacunarity quantifies the “knottiness” of fractal information, providing meta-data on the figured FD values in the image. The greater the lacunarity, the more inhomogeneous the investigated fractal region, and vice versa [45].

It is defined in terms of the fraction of the difference over the mean capacity estimate, as in, where M and N are the sizes of the FD-produced images [46–48] (Equation (2)):

2.4. General Schema of the Proposed Algorithm

As can be seen from Figure 2, the algorithm consists of four general stages. The first step is to read and preprocess the SEM image. The second step is to perform nonlinear filtering on a pixel block of varying sizes (box counting). The third step is to compute the slope using linear regression, and finally, in the last step, selecting a ROI and finding the corresponding average FD and lacunarity are applied.

2.5. Image Preparation

The image evaluation process is separated into many parts. The first stage is the handling step, in which all arrangements of SEM image groups are generated for each instance in computerized imaging and correspondence in version design (DICOM image) and then translated to FD values for each pixel. The FD shift produced images with much higher contrast than the originals, as well as easier SEM image segmentation.

At this point, the fractal analysis is performed to find the most severe normalized FD (FD_avg)—a normalized FD value is obtained for each image in time sequence, and the biggest is chosen—along with its comparative lacunarity (i.e., level of inhomogeneity). Finally, an apparent structure is used to study the influence of SEM logistical factors on FD_avg and lacunarity. All of the steps are generally divided into four categories:(1)Image preprocessing.(2)FD transformation.(3)Region of interest (ROI) and feature extraction.(4)FD_avg and lacunarity calculations.

2.6. Image Preprocessing

The proposed design was performed through image reading. The process of preprocessing is described below.

2.6.1. Grayscale Conversion

After interpreting the SEM image, the image is grayed out in this stage.

2.6.2. Histogram Equalization

The histogram equalization function improves image quality. Histogram equalization is a method for enhancing contrast by altering image intensities. Figures 3 and 4 show the histograms of the original and enhanced images, respectively.

2.6.3. Segmentation

Segmentation is the process of labeling each pixel. In other terms, segmentation divides a digital image into several segments called “pixels.” The purpose of segmentation is to reduce an image’s representation into something more relevant and simpler to examine. Image segmentation produces a collection of segments that encompass the full image or a set of contours taken from the image. The threshold approach is the most basic method of image segmentation. The choice of a thresholding method depends on the specific characteristics of the image being analyzed, such as the type of image, the distribution of pixel intensities, and the presence of noise or artifacts. There are many thresholding methods available, including global thresholding, adaptive thresholding, and Otsu’s thresholding, among others. Global thresholding is the most basic method and involves selecting a fixed threshold value that separates the foreground and background pixels based on the pixel intensity values. To calculate the FD of an image using the box-counting method, first convert a grayscale image to a binary image. This approach uses a threshold value [49–51].

Otsu’s thresholding method is a popular choice for this step, as it can automatically determine an optimal threshold value based on the pixel intensity distribution of the image. Once the image is binarized, it is divided into a grid of equal-sized boxes. The size of the boxes is varied over a range of scales, and for each scale, the number of boxes that contain at least one foreground (i.e., object) pixel is counted. The box counts are then plotted against the box size on a log–log scale. The slope of the resulting plot represents the FD of the image. To obtain a more accurate estimate of the FD, the box-counting procedure is typically repeated with multiple grid sizes, and the slope is calculated for each size range. The average of these slopes is then used as the final estimate of the FD. Finally, every pixel in an image is designated an object pixel if its value is more than the threshold value and a background pixel if its value is less than the threshold value. A “1” value is assigned to an object pixel, whereas a “0” value is assigned to a background pixel. Following that, a binary image containing all of the object and background pixels is produced (see Table 1) [49–53].

2.7. Performing Nonlinear Filtering on a Varying Size Pixel Block

Nonlinear image filtering is based on the idea that instead of utilizing the spatial mask in a convolution process, the mask is used to acquire nearby pixel values, and then ordering processes generate the output pixel. In other words, when the mask is moved around the image, the order of the pixels in the windowed area of the image is rearranged, and the output pixel is formed from the rearranged input pixels [54].

2.8. FD Transformation

The resulting SEM images are converted to FD images using the differential box-counting (DBC) technique at various scales, after which they are shown for ROI proof, followed by surface analysis. The DBC technique is often used when dealing with a large number of information values per test (the images below are all 512 × 512 pixels in size). In this study, both the DBC and fragmented Brownian movement computations were first attached to the images; nevertheless, the DBC method was chosen for the subsequent analysis since it performed faster on the FD counts of the 512 × 512 SEM images. The initial DICOM image I(x, y) of size M × N is converted to an FD image by applying a varying-size nonlinear bit w(s, t) of size m × n in Equation (3), which works by square preparation on the nearby pixels and determines the distinction between the most substantial (p_max) and least significant (p_min) force pixels. The two components and b are nonnegative whole values that are used to concentrate the bit w(s, t) on the first picture’s pixel p_xy. The component is determined in Equation (3) and connected in Equation (4) as follows:where d = 1, 2, 3,…, j – 1 represents the number of boxes required to overlay the image on the grid N_{d(x, y, d)}. The scaling factor r was chosen experimentally to be between 2 and 9. In theory, r should indicate how much a certain pixel structure is self-like in its entirety.

2.9. Selecting a ROI and the Finding Corresponding Average FD and Lacunarity

After applying the previous steps and also using the output of the image segmentation stage (obtaining 30 sample images), each of the FD-average and lacunarity were calculated (Table 1).

3. Results and Discussions

Following the preprocessing and segmentation, 30 images from the SEM image were extracted (as described in the Methods section) to execute the fractal calculation procedure using MATLAB and Excel software. Table 1 shows the FD calculation (FD_avg, FD_sd, and FD_lac) results for 30 chosen SEM images. Table 2 shows the results of calculating the average, maximum, minimum, skewness, and range from the data in Table 1.

The variations within the pattern dimensions of the particles may be clearly seen, which reveals the nonhomogeneity of the created particles. Based on the obtained SEM image information in Tables 1 and 2, Figure 5 shows a chart in which there are 30 particles, which range from 1.7623 to 1.9209, 0.510 to 0.6855, and 0.0720 to 0.1331 for FD_avg, FD_sd, and FD_lac, respectively.

The SD is a term that describes the scattering of data in a collection, and it is, therefore, one of the most significant statistical scales in the area of descriptive statistics. We can say that the SD represents the amount of data dispersion from the average point if the average estimations of the data distribution’s center point are a set. Figures 6–8 show the FD_avg, FD_sd, and FD_lac for each of the 30 images.

Skewness is another statistical criterion for symmetry distribution probability. Skewness is the degree of distortion in the probability distribution’s symmetric bell curve. To varying degrees, the distributions may be found on the right (positive) or left (negative). The derived statistical FD_avg, skewness = –0.13904, is therefore based on the selection criteria in Table 2. Distributions may also be skewed to the left (negatively) or pulled to lower values.

To evaluate for errors in the normal distribution, normal probability plots were created. If the plot points were in a straight line, normally distributed errors are assumed. In Figure 9, a typical quantile–quantile (Q–Q) plot is used to compare the forms of distributions, where the vertical axis quantiles the deviation from normal and the horizontal axis quantiles the observed values. Linearly linked points in the normal distribution mode suggest that the data are normally distributed.

As shown in Figure 9, the FD distribution of the nanocomposite particles is a regularly distributed error. Further, a residuals curve is a helpful tool for illuminating the data’s fit to the model. To visualize the most prevalent forms of imbalance, a scatter plot of residuals vs. their matching fitted values may be constructed. The points and curve should be evenly spaced and symmetrical if the fitted model is correct. If the fitted model is acceptable, the curve in a detrended normal Q–Q plot of average should be symmetrical, and the points should be equally distributed. Figure 10 shows that the points are not evenly distributed, accepting and revealing an asymmetric curve with a skewness of −0.13904.

Therefore, the comparison of results based on FD_avg shows that the mean and median of our synthesized NPs were larger. The range of synthesized NPs is closer to zero, indicating that the morphology and fabrication of NPs were more homogenized. The particle range (range = 0.1586) is smaller. Finally, the quantity distribution of the skewness (skewness = –0.13904) is skewed to the left (negative).

Lashgari et al. [14] and this study both found that the size and distribution of the particles were mostly the same but that the sizes and shapes of the particles varied within an appropriate range in our study. However, we found that the particles were not very uniform in terms of size, dimensions, and morphology, which is a crucial factor to consider for future research. To sum up, our results seem to be in line with what Lashgari et al. [14] found about how important it is to look at the uniformity and homogeneity of nanocomposite structures, especially for medical imaging studies like MRI [14].

Also, Tadic et al. [55] look at how hematite nanoparticles are made, their structure and morphology, their magnetic properties, and how they might be used in biomedicine. The study synthesized two different shapes of hematite nanoparticles, rhombohedron and plate-like, and compared their structural, morphological, and magnetic properties. The authors characterized the nanoparticles using various techniques such as XRD, SEM, and magnetic measurements. In comparison to this study, both studies focus on the morphological analysis of nanoparticles using SEM. However, the materials and applications are different. The hematite nanoparticles synthesized in the study have potential biomedical applications for MRI, whereas our work focuses on the fabrication of a nanocomposite for MRI. In terms of methodology, our study segmented the SEM image and used FD analysis to determine the uniformity and homogeneity of the nanoparticles. The study on hematite nanoparticles, on the other hand, used SEM to observe the morphology and size of the nanoparticles. The results showed that the rhombohedron-shaped nanoparticles had a smaller size and a narrower size distribution than the plate-like nanoparticles. The magnetic properties of both shapes were also compared, and the rhombohedron-shaped nanoparticles showed higher magnetic saturation than the plate-like nanoparticles. In total, both studies demonstrate the importance of morphological analysis of nanoparticles for their potential applications. In this work, the use of FD analysis is a novel approach that could be applied to other nanomaterials to determine their uniformity and homogeneity. In several studies, researchers have used different methods, such as FD, for structural and morphological analysis and recommend analyzing the size, dimensions, and morphology of nanomaterials for future research on their structure in terms of uniformity and homogeneity [55].

These findings have important implications for researchers in the fields of material and medical science. FD analysis is a valuable tool for characterizing the properties of nanomaterials and nanocomposites. It provides information on the surface roughness, porosity, and fractal nature of the material, which can be useful for understanding their physical and chemical properties. The use of FD analysis in this study highlights its potential as a nondestructive and noninvasive technique for characterizing nanocomposites for medical imaging applications [56–61].

The results of this study suggest that FD analysis can be used to evaluate the uniformity and homogeneity of nanocomposites for in vitro and in vivo applications, including medical imaging investigations like MRI. By analyzing the size, dimensions, and morphology of the nanocomposites, researchers can gain a better understanding of their structure and properties, which can aid in the design and development of improved materials for medical applications. This study also highlights the importance of carefully analyzing the size, dimensions, and morphology of nanocomposites in order to assess their uniformity and homogeneity, which is critical for their use in medical imaging and other applications. Overall, the findings of this study contribute to our understanding of the properties of nanocomposites and demonstrate the potential of FD analysis as a valuable tool for their characterization.

The study recommended that future research into the structure of nanocomposites should focus on analyzing their size, dimensions, and morphology to improve their uniformity and homogeneity for medical imaging investigations such as MRI. Overall, this study provides insights into the use of fractal analysis to analyze the structure of nanocomposites and highlights the importance of uniformity and homogeneity in their design for medical applications.

4. Conclusion and Interpretations

To our knowledge, this is the first time that a fabricated nanocomposite for MRI has had its SEM image analyzed for FD and other statistical criteria. At the molecular level, the size, dimensions, and morphology of the Gd³⁺/13X/DOX/FA nanocomposite that was made were measured. This was done to see if the range of particles in the SEM images of the nanocomposites showed that they were uniform and homogeneous. Using a segmented SEM image of the nanocomposite, we were able to determine the FDs of 30 randomly chosen particles and use them to do our calculations. The average, minimum, maximum, skewness, and range of the data were used to analyze the SEM image of the nanocomposite. The fractal data analysis metrics FD_avg, FD_sd, and FD_lac were also used. We evaluated the consistency and uniformity of the SEM image by selecting 30 images. Particle morphology, size, and dimension information all be used to calculate FD. All the data support a negative skewness of −0.13904. Based on FD_avg, our maximum and lowest values were 1.9209 and 1.7623. Assuming that the range of the data is limited (in our research, the range is 0.1586), we infer that the particle size and distribution in the SEM image are similar and that these NPs are homogeneous and have high uniformity. The FD_avg demonstrates that the average size of our produced NPs is relatively large. To the contrary, we concluded that the particle sizes and shapes are different since this range is not zero, and our data show an appropriate range. The nanocomposite’s SEM image supports this interpretation. At first glance, the image seemed to be harmonized. When the computations were run, however, it was discovered that the resulting particles were not very uniform. The particles were evenly distributed throughout all surfaces, yet they varied in size, dimensions, and morphology. In conclusion, the nanocomposite exhibited uniform dispersion across all surfaces despite differences in particle sizes and shapes, as evidenced by several fractal data analysis methods. This highlights the importance of structural analysis in nanoscience and provides valuable information on the morphology and uniformity of nanocomposite materials, particularly for future studies on their homogeneity and consistency, especially in applications such as in vitro and in vivo nanocomposites and medical imaging techniques like MRI.

Data Availability

This article contains all of the data produced or analyzed during this investigation. Any further inquiries should be forwarded to the corresponding author.

Conflicts of Interest

The author declares that he/she has no conflict of interest.

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Copyright © 2023 Sadegh Ghaderi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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