Box-counting Method Research Articles

Fractal dimension analysis of lightning discharges of various types based on a comprehensive literature review

In this study, photographic records of natural lightning flashes obtained from high-speed video camera observations are analyzed based on an extensive literature review. The purpose of this work is to estimate the fractal dimension of lightning discharges and to analyze and evaluate the effect of lightning type (downward and upward flashes during their propagation as well as return strokes) and lightning polarity (negative and positive). Three methods of fractal dimension estimation are employed namely the: (i) box-counting, (ii) sandbox, and (iii) correlation method, utilizing algorithms developed in MATLAB software. Appropriate image processing techniques are employed to guarantee precision in fractal dimension estimation. A thorough discussion is conducted by comparing the estimated fractal dimension values with those previously documented in the relevant literature based on field observations. The mean fractal dimension of downward negative leaders for the three methods (1.18, 1.31, 1.38) aligns well with previous studies, while positive downward leaders exhibit lower values (1.08, 1.15, 1.26), denoting a reduced branching behavior; upward leaders demonstrate slightly higher fractal dimensions than downward ones. Additionally, an attempt to correlate the lightning return stroke peak current with the fractal dimension is made. The outcomes of this research may assist in facilitating precise modeling of the lightning attachment phenomenon, thereby contributing to the development of safer lightning protection systems.

Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study.

This cross-sectional retrospective study was conducted to assess the differences in the microarchitecture of the trabecular bone of the posterior mandibular region at dentulous and edentulous sites with the help of fractal dimension (FD) and lacunarity using cone-beam computed tomography (CBCT). Ninety CBCT scans were analyzed for the purpose of the present study. Inclusion criteria included subjects with unilaterally missing mandibular molars or premolars and an with intact contralateral opposing tooth. The coronal view of the dentulous and edentulous sites was used, and the region of interest (ROI) was selected 2.6 mm below the apex of the tooth present. These images were then transferred to ImageJ Software, and fractal analysis was done using the box-counting method of the FracLac plug-in. A paired samples t-test was performed to compare the means of FD and lacunarity, and a Kendall correlation was performed to check correlations. A p-value less than 0.05 was considered to indicate statistical significance. Statistical analysis revealed that the mean FD of the edentulous side was significantly greater than that of the dentulous side (p-value = 0.011). Additionally, the mean lacunarity of the edentulous side was marginally significantly greater than that of the dentulous side (p-value = 0.089). A significant negative correlation was detected between the FD and lacunarity of the edentulous region (p-value = 0.017), and a marginally significant negative correlation was detected between edentulous lacunarity and dentulous lacunarity (p-value = 0.081). The differences in occlusal forces exerted in dentulous and edentulous regions can lead to a change in the trabecular pattern of the bone in these regions. This change in the microarchitecture of bones can be detected by FD and lacunarity, which can further help us assess changes pre- and post-implant. The advanced technology, the assessment of microarchitecture of the bone has been made easy, using FD and lacunarity, as done in the present study. This analysis can further aid us in both pre- and post-implant analysis to prevent failure of the implant. How to cite this article: Bhoraskar M, Denny C, Srikant N, et al. Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study. J Contemp Dent Pract 2024;25(6):581-587.

Patient´s perception of spatial complexity in emergency spaces of a hospital in China: a method for stakeholders to improve design and management

ABSTRACT The focus of medical facility users has shifted from prioritizing epidemic prevention to prioritizing experience after COVID-19, particularly in the emergency department (ED) of a large-scale Chinese hospital. The current visual elements of the emergency department provide a negative perception to the patients who visit the department. The study aims to optimize the ED's spatial design by understanding how visual elements affect patients' perception of spatial complexity. The methodology involved recreating a patient's typical path through the ED using data from the hospital information system (HIS), capturing images at 70 location nodes, and calculating the fractal dimensions of these images using the box-counting method. Visual elements were categorized into eight groups, and their fractal dimensions and proportions within the images were analyzed. A breakpoint graph was developed to track changes in spatial complexity perception as patients move through the ED. Statistical analysis, including correlation and one-way ANOVA, revealed that spatial attributes and lighting conditions significantly impact spatial complexity. From the results, grouping analysis was conducted on the visual elements of the horizontal surfaces, vertical surfaces, ceiling, furniture, and vegetation. Further optimization was proposed. In conclusion, this study highlights the importance of visual elements in emergency spaces, directly influencing users' perception of spatial complexity. The relationship between spatial complexity and fractal dimension is further emphasized. Stakeholders and designers can use the findings of this study as references to make informed decisions to improve the user's experience in the healthcare-built environment.

Fractal of tensile fracture morphology of 5083 aluminum alloy sheet and its relationship with tensile properties

In this paper, the mechanical properties of 5083 aluminum alloy sheet were put under tensile test at different temperatures, and the fracture form and basic law of fracture were qualitatively analyzed. The program of fractal fracture morphology by the box-counting method was developed based on the fractal principle. We calculated the fractal dimension of the material at different temperatures, determined its relationship with tensile deformation properties at different temperatures, and established a quantitative theoretical relationship. The results show that the fractal dimension of 5083 aluminum alloy sheet at different tensile deformation temperatures is between 1.77 and 1.79 and the fractal dimension, yield strength, and tensile strength decrease with the growing deformation temperature. At the same tensile deformation temperature, the higher the magnification, the greater the fractal dimension of the scanning electron microscopy image.

Exploring anisotropic mechanical properties of lobster claw exoskeleton through fractal models

The outstanding mechanical properties of lobster claw exoskeletons are intricately tied to their internal microstructure. Investigating this relationship can offer vital insights for designing high-performance additive manufacturing structures. Fractal theory, with its fractional dimensional perspective, suits the complexity of real-world phenomena. Our study examines fully hydrated lobster claw exoskeletons using a multifaceted approach: four-point bending tests, scanning electron microscopy observations, and fractal models. Test results reveal superior mechanical properties in longitudinal specimens. Scanning electron microscopy shows non-uniform fiber helical structures and porous elements in the exoskeleton. Fracture mechanisms involve both breaking fiber fragments perpendicular to the cross-section and tearing between these fragments. The observed crack propagation paths exhibit statistical self-similarity. Consequently, we develop fractal models for the crack propagation paths in longitudinal and transverse specimens, calculating crack extension forces. Using the box-counting method and its improved variant, we determine the fractal dimensions of specimen sections. The fractal dimension of longitudinal models exceeds that of transverse models, and calculated crack extension forces are higher in longitudinal models. These findings align well with experimental data, demonstrating fractal theory's efficacy in analyzing the lobster claw exoskeleton's anisotropic mechanical properties.

Efficacy of the CALM® Algorithm in Reducing Motion-Induced Artifacts in CBCT Imaging: A Fractal Dimension Analysis of Trabecular Bone.

The primary goal of this investigation was to ascertain the efficacy of the CALM® motion artifact reduction algorithm in diminishing motion-induced blurriness in Cone Beam Computed Tomography [CBCT] images. The assessment was conducted through Fractal Dimension [FD] analysis of the trabecular bone. A desiccated human mandible was subjected to Planmeca ProMax 3D® scanning under eight distinct protocols, marked by variations in motion presence [at 5, 10, and 15 degrees] and the deployment of CALM®. In every scan, five distinct regions of interest [ROIs] were designated for FD analysis, meticulously avoiding tooth roots or cortical bone. The FD was computed employing the box-counting method with Image-J 1.53 software. Our findings reveal that a 5-degree motion does not significantly disrupt FD analysis, while a 10-degree motion and beyond exhibit statistical differences and volatility among the sites and groups. A decreased FD value, signifying a less intricate or "rough" bone structure, correlated with amplified motion blurriness. The utilization of CALM® software seemed to counteract this effect in some instances, reconciling FD values to those akin to the control groups. Nonetheless, CALM®'s efficacy differed across sites and motion degrees. Interestingly, at one site, CALM® application in the absence of motion resulted in FD values considerably higher than all other groups. The study indicates that motion, particularly at 10 degrees or more, can considerably impact the FD analysis of trabecular bone in CBCT images. In some situations, the CALM® motion artifact reduction algorithm can alleviate this impact, though its effectiveness fluctuates depending on the site and degree of motion. This underscores the necessity of factoring in motion and the employment of artifact reduction algorithms during the interpretation of FD analysis outcomes in CBCT imaging. More research is necessary to refine the application of such algorithms and to comprehend their influence on different sites under varying motion degrees.

Application of computer vision techniques to damage detection in underwater concrete structures

Underwater concrete structure crack detection and structural health condition assessment based on image processing is a challenging task. The complex underwater environment and severe image degradation seriously affect the accuracy of crack detection. To solve these problems, a monocular vision and image-enhanced fractal-based fractal science based on computer vision and image processing techniques are proposed to carry out a non-contact detection study of underwater concrete cracks. In this study, a four-level structural health condition was established to assist in underwater crack measurement and safety assessment. The box-counting method was used as a practical tool to calculate the fractal dimension. To verify the effective distance of the algorithm, three distances of 0.5 m,0.8 m, and 1.2 m were set. The results show that the method proposed in this study can effectively detect cracks in submerged concrete members within 0.6 m and help managers correctly determine the health of the structure using the fractal dimension.

Mapping the composite nature of clay matrix in mudstones: integrated micromechanics profiling by high-throughput nanoindentation and data analysis

AbstractMudstones and shales serve as natural barrier rocks in various geoenergy applications. Although many studies have investigated their mechanical properties, characterizing these parameters at the microscale remains challenging due to their fine-grained nature and susceptibility to microstructural damage introduced during sample preparation. This study aims to investigate the micromechanical properties of clay matrix composite in mudstones by combining high-speed nanoindentation mapping and machine learning data analysis. The nanoindentation approach effectively captured the heterogeneity in high-resolution mechanical property maps. Utilizing machine learning-based k-means clustering, the mechanical characteristics of matrix clay, brittle minerals, as well as measurements on grain boundaries and structural discontinuities (e.g., cracks) were successfully distinguished. The classification results were validated through correlation with broad ion beam-scanning electron microscopy images. The resulting average reduced elastic modulus (Er) and hardness (H) values for the clay matrix were determined to be 16.2 ± 6.2 and 0.5 ± 0.5 GPa, respectively, showing consistency across different test settings and indenter tips. Furthermore, the sensitivity of indentation measurements to various factors was investigated, revealing limited sensitivity to indentation depth and tip geometry (when comparing Cube corner and Berkovich tip in a small range of indentation depth variations), but decreased stability at lower loading rates. Box counting and bootstrapping methods were applied to assess the representativeness of parameters determined for the clay matrix. A relatively small dataset (indentation number = 60) is needed to achieve representativeness, while the main challenges is to cover a representative mapping area for clay matrix characterization. Overall, this study demonstrates the feasibility of high-speed nanoindentation mapping combined with data analysis for micromechanical characterization of the clay matrix in mudstones, paving the way for efficient analysis of similar fine-grained sedimentary rocks.

Analysis of fractal dimension of lymphocytes exposed to different doses of ionizing radiation through box counting method

Analysis of fractal dimension of lymphocytes exposed to different doses of ionizing radiation through box counting method

Linear fractal evolution characteristics of rock crack distributions during loading process

To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.

Characterization of pore model and percolation simulation of bulk grain pile porous media

AbstractTo ensure the quality of grain storage, researchers have developed a variety of models for the morphological structure of bulk grain piles. However, traditional characterization methods suffer from issues such as inaccurate models, limited size ranges, and low precision. In this study, x‐ray computed tomography was employed for the first time to capture real three‐dimensional (3D) images, revealing the surface porosity distribution ranging from 30% to 38% along the slice direction and a fractal dimension primarily distributed between 1.45 and 1.47. Moreover, the box counting method was used to determine the representative elementary volume (REV) comprising 600 × 600 × 600 pixels, effectively characterizing pore structure using porosity as an index. Connectivity analysis of the REV was conducted by integrating the refined central axis method and the 3D watershed algorithm. Equivalent diameters of connected pores were mainly distributed between 0.5 and 3.5 mm, with an average pore diameter of 2.22 ± 0.02 mm, an average coordination number of 7.04 ± 0.07, and an average tortuosity of 1.58 ± 0.01. Based on the characteristic parameters of connected pores, an equivalent pore network model (EPNM) was reconstructed for numerical simulation of single‐phase percolation of bulk grain pile. In addition, the constructed experimental platform demonstrates that the constructed EPNM closely corresponds to the real pore structure of the seed body, accurately reflecting pore–throat size, connectivity, and morphological characteristics within the grain pile. Furthermore, this research model can be applied to the study of gas flow, heat transfer, and mass transfer within porous media.

Residual strength of porous alumina ceramics and fractal characterization of their crack patterns after thermal shocks

Thermal shock behaviors of porous alumina samples with different porosities (4.6–16.0 %) and mean grain sizes (2.72–5.02 μm) were investigated under different quenching temperatures. The slit island method was used to analyze the structures of the pores. The effect of the pore structure on the thermal shock resistance of alumina ceramics was described quantitatively. The results revealed that the thermal shock resistance decreased when the fractal dimension of the pores increased. Alumina ceramic strips with a porosity and mean grain size of 4.6 % and 5.02 μm, respectively, were fabricated using raw powders with a mean particle size of ∼0.3 μm. These samples possessed the highest residual strength ratio (∼46.16 % at 600 °C) and critical temperature difference (∼262 °C). In addition, the fractal characterization of cracks on the surfaces of the alumina ceramics after thermal shock was carried out using the box-counting dimension method. In addition, we investigated the correlation between the mechanical properties and fractal dimensions of the surface cracks. The box-counting dimension increased with crack propagation and negatively correlated with the residual strength. Furthermore, the propagation rate of the surface cracks decreased as the temperature difference increased, resulting in a decrease in the growth rate of the fractal dimension.

A Comparison of Evaluation Methodologies of the Fractal Dimension of Premixed Turbulent Flames in 2D and 3D Using Direct Numerical Simulation Data

AbstractA Direct Numerical Simulation (DNS) database of statistically planar flames ranging from the wrinkled flamelets to the thin reaction zones regime and DNS data for a Bunsen premixed flame representing the wrinkled flamelets regime have been utilised to evaluate the fractal dimensions of flame surfaces using the filtering dimension method, the box-counting algorithm and the correlation dimension approach. The fractal dimension evaluated based on the fully resolved three-dimensional data has been found to be reasonably approximated by adding unity to the equivalent fractal dimension evaluated based on two-dimensional projections irrespective of the methodology of extracting fractal dimension. This indicates that the flame surface can be approximated as a self-similar fractal surface for the range of Karlovitz and Damköhler numbers considered here. While all methods, provide results identical to each other for benchmark problems, it has been found that the fractal dimension evaluation based on box-counting method provides almost identical results as that obtained using the filtering dimension method for both three and two dimensions, while the fractal dimensions based on the correlation dimension tend to be slightly smaller. The findings of the current analysis have the potential to be used to reliably estimate the actual fractal dimension in 3D based on experimentally obtained 2D binarised reaction progress variable field. The inner cut-off scales estimated based on all three methodologies yield comparable results in terms of order of magnitude with the box-counting method predicting a smaller value of inner cut-off scale in comparison to other methods. The execution times for fractal dimension extraction based on filtering dimension and box-counting methodologies are found to be comparable but the correlation dimension method is found to be considerably faster than the two alternative approaches and provides results consistent with theoretical bounds in all cases.

A quantitative study of the microstructure of Indian Gondwana shale: a fractal and algebraic topology approach

This paper covers a novel micro-level application of image processing in understanding the topological and petrophysical properties of Indian Gondwana shale using X-ray computed microtomography images. The complexity and randomness in the pore system are explained through the concept of fractal dimension (FD). In this paper, a quantitative analysis of 2D and 3D fractal dimensions of pores, grains and interfaces was performed for Indian Gondwana shale, using the box-counting method. A pore network is formed by the connection of many subpore clusters, each with a different volume. Hence, an image segmentation algorithm was applied to label different subclusters, and subsequently an analysis of FD was carried out on such subclusters of pores and grains. We implemented a novel application of Betti numbers (B0, B1 and B2) and Euler characteristics on our sample and calculated the possible flow channels of the sample. The FD of grains was found to be greater than the FD of the pore–grain interfaces, while the FD of pores was found to have the smallest value. Consequently, we also observed how the FD of both pores and grains was majorly controlled by the largest subcluster, and during fluid intrusion we observed a significant decrease in the FD of pores. Finally, the pore network with a larger B0 and larger difference of B1 was proved to be best for the storage of hydrocarbons and for fluid movement along more flow channels.

Microwave irradiation-induced deterioration of rock mechanical properties and implications for mechanized hard rock excavation

In this study, a novel microwave-water cooling-assisted mechanical rock breakage method was proposed to address the issues of severe tool wear at elevated temperatures, poor rock microwave absorption, and excessive microwave energy consumption. The investigation object was sandstone, which was irradiated at 4 kW microwave power for 60 s, 180 s, 300 s, and 420 s, followed by air and water cooling. Subsequently, uniaxial compression, Brazilian tension, and fracture tests were conducted. The evolution of damage in sandstone was measured using active and passive nondestructive acoustic detection methods. The roughness of the fracture surfaces of the specimens was quantified using the box-counting method. The damage mechanisms of microwave heating and water cooling on sandstone were discussed from both macroscopic and microscopic perspectives. The experimental results demonstrated that as the duration of the microwave irradiation increased, the P-wave velocity, uniaxial compressive strength (UCS), elastic modulus (E), tensile strength, and fracture toughness of sandstone exhibited various degrees of weakness and were further weakened by water cooling. Furthermore, an increase in the microwave irradiation duration enhanced the damaging effect of water cooling. The P-wave velocity of the sandstone was proportional to the mechanical parameters. Microwave heating and water cooling weakened the brittleness of the sandstone to a certain extent. The fractal dimension of the fracture surface was correlated with the duration of microwave heating, and the water-cooling treatment resulted in a rougher fracture surface. An analysis of the instantaneous cutting rate revealed that water cooling can substantially enhance the efficiency of microwave-assisted rock breakage.

Cross-correlation between the multifractal spectra of the solar wind magnetic field from Parker Solar Probe and Solar Orbiter

Abstract The solar wind, a plasma emanating from the Sun and extending throughout the universe, continues to be a subject of intense study. This study focused on examining the multifractal spectra of the solar wind’s magnetic field in regions proximal and distal to the Sun, leveraging data collected by the Parker Solar Probe and Solar Orbiter satellites, respectively. Utilizing the box-counting method within multifractal analysis has provided insights into the distinctive characteristics of each satellite, including singularity exponents and multifractal spectra. However, the cross-correlation observed between the spectra obtained by both satellites has prompted further inquiry into its physical implications. This suggests the need for a more comprehensive investigation to elucidate the underlying dynamics driving these correlations and their significance in our understanding of solar wind behavior. Continued research in this area holds promise for advancing our comprehension of solar phenomena and their broader implications.

The effect of mentoplate application on the condyle

BackgroundThe aim of the study was to investigate the changes occurring in the mandibular condyle by using mentoplate together with rapid maxillary expansion (MP-RME) treatment in the correction of skeletal class III relationship, using fractal analysis (FA).MethodsThe sample consisted of 30 individuals (8–11 years) diagnosed with skeletal Class III malocclusion who underwent MP-RME treatment. Archival records provided cone-beam computed tomography (CBCT) images taken at two intervals: before MP-RME treatment (T0) and after treatment (T1). The CBCT images were obtained using standardized settings to ensure consistency in image quality and resolution. The trabecular structures in the bilateral condyles at both T0 and T1 were analyzed using FA. The FA was performed on these condylar images using the Image J software. The region of interest (ROI) was carefully selected in the condyle to avoid overlapping with cortical bone, and the box-counting method was employed to calculate the fractal dimension (FD). Statistical analysis was conducted to compare the FD values between T0 and T1 and to evaluate gender differences. The statistical significance was determined using paired t-tests for intra-group comparisons and independent t-tests for inter-group comparisons, with a significance level set at p < 0.05.ResultsThe analysis revealed no statistically significant differences in the trabecular structures of the condyles between T0 and T1 (p > 0.05). However, a significant gender difference was observed in FA values, with males exhibiting higher FA values in the left condyle compared to females at both T0 and T1 (p < 0.05). Specifically, the FA values in the left condyle increased from a mean of 1.09 ± 0.09 at T0 to 1.13 ± 0.08 at T1 in males, whereas in females, the FA values remained relatively stable with a mean of 1 ± 0.09 at T0 and 1.03 ± 0.11 at T1.ConclusionThe findings indicate that MP-RME therapy does not induce significant alterations in the trabecular structure of the mandibular condyle. These results suggest the treatment’s safety concerning the structural integrity of the condyle, although the observed gender differences in FA values warrant further investigation.

Analysis and Characterization of Micro–Nano Pores in Coal Reservoirs of Different Coal Ranks

Coalbed methane represents a promising source of clean and efficient unconventional energy. The intricate network of micro–nano pores within coal serves as the primary adsorption space for gas, contributing to the complexity of gas migration channels. In this study, based on the box-counting method, three coal samples representing low, medium, and high ranks were subjected to high-precision micro-CT scanning and nano-CT scanning to generate three-dimensional (3D) pore network models using Avizo visualization software. This facilitated the accurate and quantitative characterization of the micro–nano pore structures within coal reservoirs. The results indicated that the face rate distribution range of each sample was large, indicating relatively strong heterogeneity in each sample. The volume fractal dimension of each sample, determined through micro–nano-CT scanning, was around 2.5, while the surface fractal dimension exhibited oscillatory characteristics with moderate uniformity. The pore equivalent radius and throat equivalent radius distributions were unimodal across all the samples, with the micro-CT scanning revealing a concentration primarily within the range of 100–400 μm for the pore equivalent radius and within 200 μm for the throat equivalent radius. Conversely, the nano-CT scanning exhibited concentrations primarily within the range of 500–2500 nm for the pore equivalent radius and within 2000 nm for the throat equivalent radius. The analysis of the 3D reconstruction structures indicated that the middle-rank coal exhibited more developed large–medium pores compared with the low-rank and high-rank coal, while the low-rank and high-rank coal exhibited relatively more micro–small pores. Furthermore, the low-rank coal exhibited the fewest number of pores but the largest average pore equivalent radius and throat radius. Additionally, the middle–high-rank coal exhibited a relatively larger number of pores. Despite the complex topological structures observed in each sample, a significant proportion indicated a coordination number of 0–20, indicating excellent connectivity within the coal samples. This study is conducive to the optimization of coalbed methane surface development blocks and the formulation of reasonable development plans.

Cortex and White Matter of the Cerebral Hemispheres: Anatomical Correlations and Age-Related Changes Measured with Fractal Analysis

Aim. The aim of the present study was to determine the fractal dimension (FD) values of the cortex and white matter of the cerebral hemispheres using fractal analysis of two-dimensional magnetic resonance images, explore the anatomical correlations of the cortex and white matter FD, and study age-associated changes in the cortex and white matter. Methods. Two-dimensional brain magnetic resonance images of 100 apparently healthy individuals of both genders (44 males and 56 females) aged 18-86 years were studied. Five sections of each participant’s brain were selected (4 coronal and 1 axial). After image segmentation, the FD values and sectional areas of the cortex and white matter were determined. Fractal analysis was conducted using a two-dimensional variant of the box-counting method. Results. The FD values of the cortex and white matter varied across the five brain sections analyzed. Specifically, the cortex exhibited a decrease in the FD, whereas the white matter showed an increase in the FD in the coronal sections along the rostro-caudal direction. The FD values obtained from different sections displayed weak to moderate correlations. Additionally, no significant differences were observed in the FD values of the cortex and white matter between males and females. However, the sectional area values of the cortex and white matter were slightly higher in males as compared to females. Furthermore, a negative correlation was identified between the FD values of the cortex and white matter of the cerebral hemispheres, while sectional areas did not exhibit significant correlations. The cortex FD positively correlated with the gyrification index, whereas the white matter FD showed a negative correlation with this parameter. Additionally, both the FD and sectional area values of the cortex displayed strong and moderate negative correlations with age, respectively. In contrast, the FD and sectional area values of the white matter demonstrated weak negative correlations with age. Males showed stronger correlations of the studied parameters with age across the majority of the analyzed sections compared to females, although these differences were not statistically significant. Conclusions. In this study, a negative correlation was found between the cortex and white matter FD values, influenced by anatomical factors such as the degree of gyrification. While the cortex FD values significantly decreased with age, age-related changes in the white matter FD values were relatively weak.

Fractal Analysis of Trabecular Alveolar Bone with Intrabony and Furcation Defects Using Periapical Dental Radiographs

Objective: Fractal analysis (FA) is a non-invasive method that quantitatively measures complex patterned geometric structures present throughout the image. Trabecular morphology of the alveolar bone and the changes occurring in the trabeculae in case of periodontitis can be detected with this method. To examine the periodontal defects in human skull bones using the FA, to compare them with healthy alveolar bone regions. Methods: Furcation and intrabony defects were artificially created in the mandible alveolar bones (n:24). Periapical X-ray images of alveolar bone regions containing teeth with defects were taken using the parallel technique. Fractal analysis was performed by box-counting method using Image J software on images from areas containing healthy and defective trabecular bone. Results: No statistically significant difference was found between the fractal values of healthy tissue and bifurcation defetcs and between the healthy tissue and intrabony defects (p&gt;0.05). Conclusion: Many factors may have affected the outcomes; patient selection, imaging methods, sample size, Region of interest (ROI) selection-location and size, individual and anatomical variations. These variables need to be standardized as much as possible and the limitations of the method need to be improved.