Changes In Fractal Dimension Research Articles

Fractal Analysis of Mandible in Panoramic Radiographs of Patients Received Radiotherapy for Nasopharyngeal Carcinoma

PurposeThis study aimed to assess the impact of radiotherapy on the internal structure complexity of mandibular cortical and trabecular bone and to determine the duration required for a return to healthy values post-radiotherapy. Materials and MethodsPanoramic radiographs from patients undergoing radiotherapy for nasopharyngeal carcinoma were analyzed before and after treatment. Four groups were formed based on post-radiotherapy radiography timing (0-6 months, 6-12 months, 12-24 months, and 24-36 months), comprising a total of 59 cases and 118 radiographs. Fractal analysis was conducted on four bilateral regions (ROI) in both trabecular and cortical bone on each radiograph. Additionally, measurements of inferior alveolar canal width and mandibular cortical width were performed. Mean and maximum radiation dose values to the mandible were measured, and their correlation with changes in fractal dimension, inferior alveolar canal width, and mandibular cortical width values was assessed. ResultsFractal dimension values in regions over trabecular bone showed a statistically significant decrease in all groups, although no significant difference was observed among the four groups. In ROI-4 from cortical bone, a significant fractal dimension decrease was noted in all groups except the 0-6 month group. The magnitude of fractal dimension decrease was higher in the 12-24 and 24-36 month groups compared to the 0-6 month group. inferior alveolar canal width and mandibular cortical width values significantly decreased post-radiotherapy in all groups, with a consistent decrease across the groups. ConclusionsRadiotherapy induces a reduction in the internal complexity of trabecular and cortical bone structures in the mandible. Osteoradionecrosis risk persists even three years post-radiotherapy, suggesting a cautious approach to interventional procedures on the bone.

Low-temperature treatment optimization for diesel-contaminated kaolin: Mutual impacts of generated pyrolytic carbon and particle agglomeration

Efficiency improvement in low-temperature treatment for diesel-contaminated sites is urgent because changes in soil properties and the generation of new substance during the remediation process can influence the duration and energy utilization. This paper focuses on low-temperature treatment optimization based on the mutual impacts of pyrolytic carbon and kaolin aggregation. Results reveal that the peak mass loss rate occurred between 100–150°C, with minimal loss beyond 200°C. Samples thermally treated at 150–200°C exhibited darker colors, indicating pyrolytic carbon formation, corroborated by x-ray photoelectron spectroscopy (XPS), fourier transform infrared spectroscopy (FTIR), and three-dimensional fluorescence spectrum (3D-EEM) analyses. Additionally, diesel contamination influenced the fractal dimension of aggregates by influencing adhesion forces (<10000 mg/kg) and forming liquid bridges (≥10000 mg/kg) in untreated kaolin, resulting in an initial increase and subsequent fall in fractal dimension with increasing concentration. Decline rates of pollutant gas concentration were closely correlated with fractal dimension changes under thermal conditions due to pollutant volatilization and pyrolytic carbon formation. Based on the consistency between fractal dimension and decline rate, two critical remediation concentrations (C0) and temperatures (T0) indices were identified to optimize the low-temperature remediation.

Experimental study on dynamic mechanical properties of multidirectional constrained water-bearing coal samples under dynamic-static coupling loading

The objective of this study is to investigate the dynamic mechanical properties of coal and rock under deep water conditions. The research employs an enhanced Split Hopkinson Pressure Bar (SHPB) testing system. Five sets of dynamic impact experiments were conducted on coal samples under varying loading conditions to analyse the changes in dynamic strength, energy dissipation, fractal dimension and other characteristics of coal samples under different water content states were analyzed. The experimental results demonstrate that: (1) Under specific strain rate conditions, the dynamic strength of saturated coal samples is lower than that of natural coal samples. As the strain rate gradually increases, the bonding force generated by free water and the Stefan effect jointly act, and the peak strength of saturated coal samples under high strain rate loading conditions is higher than that of natural coal samples. (2) Under certain strain rate conditions, the absorption energy of saturated coal samples is approximately 10% to30% lower than that of natural coal samples, and deformation hysteresis phenomenon occurs in natural coal samples, thereby improving the dynamic strength of natural coal samples relative to saturated coal samples; (3) The fractal dimension of saturated coal samples with a specific strain rate under three-dimensional dynamic static combination loading is higher than that of natural coal samples, and the percentage of small particle coal samples with debris is higher than that of natural coal samples; Finally, based on the HJC model, some coal samples were selected to simulate the coal rock failure characteristics during the triaxial loading process using ANSYS/LS-DYNA, and their stress–strain curves and failure morphology diagrams were obtained. The discrepancy between the numerical simulation and the experimental results was less than 10%, thereby further elucidating and corroborating the coal failure process and dynamic mechanical characteristics.

Heterogeneity properties and permeability of shale matrix at nano-scale and micron-scale

Heterogeneity of shale pores at nano-scale and micrometer-scale is of great significance to gas transport properties. In this study, the pore structure of shale samples from lower Silurian Longmaxi Formation in the Sichuan basin is investigated by field emission-scanning electron microscopy (FE-SEM) and x-ray micro-computed tomography (Xμ-CT) technology. Based on fractal theory, the lacunarity is introduced to describe the clustering degree of pores in shale matrix, which can compensate for the limitations of fractal dimension. Combining lacunarity with fractal dimension allows for quantification of subtle differences in pore spatial distribution. For FE-SEM images at nano-scales, the fractal dimension changes in a “U” shape, while lacunarity changes in a “∩” shape. For Xμ-CT images at micrometer-scale, both the fractal dimension and lacunarity change in a logarithmic function. Lacunarity at both nano-scale and micrometer-scale linearly decreases with the increase in fractal dimension. By three-dimensional (3D) pore network modeling analysis, the structure properties of the connected pores, such as the number of pores and throats, pore diameter, pore volume, pore surface, throat length, and coordination number, are quantitatively calculated, and these structure parameters show strong heterogeneity. The average coordination number of the connected pores ranges in 2.92–4.36. This indicates that these pores in shale matrix have poor connectivity. The permeability varies from 0.06 to 0.17 μm2 in two-dimensional (2D) Xμ-CT images but from 3.20 to 34.99 μm2 in a 3D structure. The permeability in the 3D structure is about two order higher in magnitude than that in the 2D Xμ-CT images.

Rock damage and fracture characteristics considering the interaction between holes and joints

The work studied the damage and fracture characteristics of granite samples with circular holes and parallel fractures of different lengths under uniaxial compression conditions. Acoustic emission (AE) monitoring and digital image correlation (DIC) were used to analyze the dynamic changes of AE parameters, the evolution characteristics of the deformation field on the sample surface, and the correlation between the fractal dimension and the fracture geometry parameters. A computational model was proposed for evaluating the intensity factor of the fracture tip in a double-fracture structure with holes. The interaction between the fractures was considered to reveal the complex law of the intensity factor and the fracturing angle with the fracture geometry. The changes in AE parameters and fractal dimension indicated the influence of fracture extension on the damage mode of samples. Besides, the fracture length affected the micro-fracture behavior. The surface displacement and strain characteristics of samples revealed the modulation effect of the fracture length on the failure mode. The inclination angle, length, holes, and size of the fractures’ friction coefficient significantly affected the evolution of the intensity factor, which in turn regulated the changes in the fracture angle. The work offers a novel quantitative analytical approach and a theoretical framework for comprehending the damage and failure mechanisms of porous and fractured rocks through extensive experimentation and theoretical analysis. It holds significant practical relevance in geological engineering, mining, and tunnel construction.

Pore-fracture structures and seepage flow characteristics during spontaneous coal combustion based on CT 3D reconstruction

To study the evolution characteristics of the pore-fracture structures and seepage properties of coal in the process of spontaneous combustion, a high-temperature tube furnace was used to heat the coal samples. The coal samples were scanned using Xray-CT scanning technology, and the CT 3D reconstruction technology was used to extract the 3D pore structure and equivalent pore network model of each group of coal samples. Firstly, the specific surface area and volume of pore cleavage is statistically characterized; the change rules of Ep, Et, Lc, and Cn are quantitatively analyzed. At 200 °C, the coal body produces a large number of pore fractures, the development of coal samples is more significant, and the pore-specific surface area and the number of pore throats reached their maximum value. In addition, the changes of fractal dimension, porosity, connectivity, and permeability of coal with temperature were discussed, and the best permeability of the coal was achieved at 200 °C. The connectivity and permeability were weakened with the further increase of temperature, and the structural changes had a close influence on the gas seepage pressure and seepage flow rate. The results of the study provide important engineering guidance for deepening fire prevention in coalfields.

Effects of supercritical CO2 fluids on pore structure and fractal characteristics of bituminous coal

Enhanced coalbed methane recovery with CO2 coal seam storage (CO2-ECBM) technology is an important way to achieve China's strategic goals of carbon peak and carbon neutrality. Presently, to date there has been rarely research conducted on the effect of coal sample scale on pore structure under supercritical CO2 (ScCO2) fluids. In this study, a high-pressure geological environment simulation system was adopted to analyze coal samples of different scales for ScCO2 saturation. Subsequently, low-pressure nitrogen gas adsorption (LP-N2GA), mercury intrusion porosimetry (MIP), and low-field nuclear magnetic resonance (LF-NMR) were used to analyze the pore structure and fractal dimension changes in saturated coal samples at different scales. The experimental results show that the mesopore ratios of cylindrical and granular coal decrease by an average of 1.68% and 2.30%, respectively, after the saturation of ScCO2. The proportion of macropores in cylindrical coal increased by an average of 5.50% after ScCO2 saturation, while the proportion of macropores in granular coal changed by 176.86% compared to cylindrical coal. The fractal dimension of the ScCO2 saturated coal samples obtained with LP-N2GA, MIP, and LF-NMR all show a decreasing trend, again confirming the modification of the coal pore surface by ScCO2. Finally, a conceptual model is presented to analyze the mechanism of the effect of coal sample scale on the pore structure under ScCO2. The difference in the transport paths of ScCO2 molecules at different coal scales is the main reason for the difference in the evolution of the pore structure. In addition, the impact of the amount of adsorption obtained in the laboratory using coal samples of different scales on the assessment of the CO2 storage capacity was discussed. Therefore, the results of this study are expected to provide a reference for the CO2 storage capacity assessment of the CO2-ECBM project.

Compaction and shear characteristics of recycled construction & demolition aggregates in subgrade: Exploring particle breakage and shape effects

Recycling construction and demolition (C&D) wastes into useable aggregates in subgrade applications offers significant sustainability benefits. However, the characteristics of recycled aggregates, including particle morphology, crushing strength, and shear behavior, differ substantially from natural aggregates. This paper presented an extensive experimental study on the compaction and mechanics performances of recycled concrete and brick aggregates, with a particular focus on the effects of particle breakage and shape characteristics. The compaction of recycled aggregate specimens comprising three structural types was evaluated using heavy Marshall compaction (HMC) and Superpave gyratory compaction (SGC). The compaction characteristics and particle breakage were examined, enabling a profound understanding of the compaction mechanisms associated with both methods. Furthermore, triaxial shear tests were performed to scrutinize the influences of particle shape, compaction degree, and confining pressure on shear characteristics. Results showed that after 80 gyratory rotations in SGC, the compaction degree of recycled aggregates aligned with the targeted results obtained from HMC. Changes in fractal dimension after compaction exhibited direct correlations with the two-dimensional shape distribution. Axial coefficient, fractal dimension and confining pressure most strongly influenced shear strength. In light of these insights, prediction models for shear strength parameters were proposed using multiple regression analysis. Overall, the study provides valuable insights into the relationships between aggregate morphology, compaction response, breakage behavior, and shear performance. These findings can facilitate optimized design and construction using recycled aggregates to advance sustainable infrastructure development.

Neuroimaging Insights: Structural Changes and Classification in Ménière's Disease.

This study aimed to comprehensively investigate the neuroanatomical alterations associated with idiopathic Ménière's disease (MD) using voxel-based morphometry and surface-based morphometry techniques. The primary objective was to explore nuanced changes in gray matter volume, cortical thickness, fractal dimension, gyrification index, and sulcal depth in MD patients compared with healthy controls (HC). Additionally, we sought to develop a machine learning classification model utilizing these neuroimaging features to effectively discriminate between MD patients and HC. A total of 55 patients diagnosed with unilateral MD and 70 HC were enrolled in this study. Voxel-based morphometry and surface-based morphometry were employed to analyze neuroimaging data and identify structural differences between the two groups. The selected neuroimaging features were used to build a machine learning classification model for distinguishing MD patients from HC. Our analysis revealed significant reductions in gray matter volume in MD patients, particularly in frontal and cingulate gyri. Distinctive patterns of alterations in cortical thickness were observed in brain regions associated with emotional processing and sensory integration. Notably, the machine learning classification model achieved an impressive accuracy of 84% in distinguishing MD patients from HC. The model's precision and recall for MD and HC demonstrated robust performance, resulting in balanced F1-scores. Receiver operating characteristic curve analysis further confirmed the discriminative power of the model, supported by an area under the curve value of 0.92. This comprehensive investigation sheds light on the intricate neuroanatomical alterations in MD. The observed gray matter volume reductions and distinct cortical thickness patterns emphasize the disease's impact on neural structure. The high accuracy of our machine learning classification model underscores its diagnostic potential, providing a promising avenue for identifying MD patients. These findings contribute to our understanding of MD's neural underpinnings and offer insights for further research exploring the functional implications of structural changes.

Evolution of fractal characteristics in shales with increasing thermal maturity: Evidence from neutron scattering, N2 physisorption, and FE-SEM imaging

Fractal dimension analysis has become an essential tool to assess the pore structure of various porous geomaterials including shale rock. In this regard, changes of fractal dimension during the thermal maturation of organic rich shale could represent the evolution of its pore structure. To this end, complementary tests were conducted on six organic rich shale samples that are in a wide range of thermal maturity (equivalent Ro values of 0.52–3.53 %). Fractal dimensions were obtained from small-angle neutron scattering (SANS), N2 physisorption, and field emission-scanning electron microscopy (FE-SEM) data. Herein, surface fractal dimensions were calculated from the N2 adsorption isotherms using the Frenkel–Halsey–Hill method, which was found between 2.46 and 2.71. Power-law exponents (E) of the SANS profiles varied from 2.75 to 3.48, indicating that both surface fractals and mass fractals would characterize the shale samples. As thermal maturity progressed, the fractal dimension shifted from surface to mass fractal while further analyses suggested this was caused by changes in the number density of pores (NDP) of various pore-size ranges. Ultimately, the pore size of the samples during such transition decreased with the increase of Ro.

Using Fractal Theory to Study the Influence of Movable Oil on the Pore Structure of Different Types of Shale: A Case Study of the Fengcheng Formation Shale in Well X of Mahu Sag, Junggar Basin, China

This study investigated the influence of movable oil on the pore structure of various shale types, analyzing 19 shale samples from Well X in the Mahu Sag of the Junggar Basin. Initially, X-ray diffraction (XRD) analysis classified the shale samples. Subsequently, the geochemical properties and pore structures of the samples, both pre and post oil Soxhlet extraction, were comparatively analyzed through Total Organic Carbon (TOC) content measurement, Rock-Eval pyrolysis, and nitrogen adsorption experiments. Additionally, fractal theory quantitatively described the impact of movable oil on the pore structure of different shale types. Results indicated higher movable oil content in siliceous shale compared to calcareous shale. Oil extraction led to a significant increase in specific surface area and pore volume in all samples, particularly in siliceous shale. Calcareous shale predominantly displays H2–H3 type hysteresis loops, indicating a uniform pore structure with ink-bottle-shaped pores. Conversely, siliceous shale exhibited diverse hysteresis loops, reflecting its complex pore structure. The fractal dimension in calcareous shale correlated primarily with pore structure, exhibiting no significant correlation with TOC content before or after oil extraction. Conversely, the fractal dimension changes in siliceous shale samples do not have a clear correlation with either TOC content or pore structure, suggesting variations may result from both TOC and pore structure.

Initiation mechanism of shallow loess slope sliding under coupling effect of train vibration and rainfall

The large-scale construction and operation of the railway in Northwestern China has resulted in some geological disasters in recent times. Among them, the shallow sliding of the loess railway slope caused by the coupling effect of train vibration and rainfall has been a frequent occurrence, causing heavy losses of life and property. Accordingly, this is a major problem an needs an urgent solution. Therefore, this study used acceleration, pressure, moisture, and displacement monitoring equipment, among others, to conduct physical simulation experiments and theoretical analysis on the instability and sliding process of loess railway slopes under the coupling effect of train vibration and rainfall. The research results indicate that acceleration gradually decreases downward along the slope, and the pore water pressure and volumetric water content increase with the increase in rainfall infiltration. The slope displacement exhibits a phased increase after the initial slip. As vibration energy builds up, the slope bottom undergoes rapid structural damage and tensile shear coupled instability failure, followed by slip. Before sliding, both the crack density and fractal dimension of the slope have an active area, that is, a sliding slope area, which continues to expand upward under the cumulative effect of vibration energy. The failure process is divided into three stages according to the changes in macrodeformation, pressure, water content, displacement, and fractal dimension of the slope model: crack development stage, local liquefaction sliding stage, and slip propagation stage. This research elucidates the initiation mechanism of loess railway slope sliding under the coupling effect of train vibration and rainfall and provides a theoretical basis for predicting loess slope disasters under train vibration and providing adequate warning.

Fast Arc Detection Technology Based on Fractal Dimension for SADA Slip Ring in Satellite Power System

The solar array drive assembly (SADA) slip ring is a critical link that provides electrical power and electric signal transmission between solar arrays and satellite power systems, which is prone to arc faults in the space environment. If these arc faults cannot be detected and eliminated quickly enough, they will seriously threaten the safety of the satellite power system and the satellite. In this paper, a fast arc detection method based on fractal dimension is proposed that adapts to different operating modes of power systems. The detection method collects the current differential signal data flowing through the SADA slip ring, and, according to the trend of the fractal dimension change in this signal, the fault identification algorithm is designed for different operating modes of the power system to achieve real-time and rapid identification of arc faults. Finally, the effectiveness of the proposed method is demonstrated using test data under several different fault conditions.

Influence of water coupling coefficient on the blasting effect of red sandstone specimens

This study investigates the impact of different water coupling coefficients on the blasting effect of red sandstone. The analysis is based on the theories of detonation wave and elastic wave, focusing on the variation in wall pressure of the blasting holes. Using DDNP explosive as the explosive load, blasting tests were conducted on red sandstone specimens with four different water coupling coefficients: 1.20, 1.33, 1.50, and 2.00. The study examines the morphologies of the rock specimens after blasting under these different water coupling coefficients. Additionally, the fractal dimensions of the surface cracks resulting from the blasting were calculated to provide a quantitative evaluation of the extent of rock damage. CT scanning and 3D reconstruction were performed on the post-blasting specimens to visually depict the extent of damage and fractures within the rock. Additionally, the volume fractal dimension and damage degree of the post-blasting specimens are calculated. The findings are then combined with numerical simulation to facilitate auxiliary analysis. The results demonstrate that an increase in the water coupling coefficient leads to a reduction in the peak pressure on the hole wall and the crushing zone, enabling more of the explosion energy to be utilized for crack propagation following the explosion. The specimens exhibited distinct failure patterns, resulting in corresponding changes in fractal dimensions. The simulated pore wall pressure–time curve validated the derived theoretical results, whereas the stress cloud map and explosion energy-time curve demonstrated the buffering effect of the water medium. As the water coupling coefficient increases, the buffering effect of the water medium becomes increasingly prominent.

Study on Voids and Seepage Characteristics within Rock Fracture after Shear Dislocation Viewing from CT Test and Numerical Modeling

In rock mass engineering, stress balance changes often cause the relative slip of fractures along a wall surface, impacting the seepage behavior of fluid in the fractures. Using computer tomography (CT) scanning, spatial models of fractures with dislocations ranging from 0 to 10 mm were created to explore the relationship between changes in fracture dislocation and changes in fluid flow behavior, respectively. The spatial fractal dimension of cavity distribution within the fractures was calculated using a thin-plate filling approach to characterize the complexity of the fracture cavity distribution. The fluid flow within the dislocation fractures was then simulated using COMSOL, and the effect of cavity alterations in the form of dislocation on the fluid seepage behavior was analyzed using the spatial fractal. The results show that the values of mechanical aperture after dislocation of the fracture obtained by a CT test are normally distributed, the distribution range of mechanical aperture gradually widens with an increase in the dislocation distance, and the average mechanical aperture increases on a logarithmic curve. The relative spatial fractal dimension decreases gradually with an increase in dislocation distance, and the interconnected pathways within the fracture decrease; in addition, it is observed that the change in the relative spatial fractal dimension is closely correlated with the change in the mean mechanical aperture. Numerical simulations of dislocation fracture seepage found that the permeability increases nonlinearly with increasing dislocation distance. When the dislocation distance reaches 5 mm, nonlinear behaviors such as eddy currents occur, and the influence range of eddy currents gradually expands with the increase in dislocation distance under the influence of the boundary. Moreover, the inertia coefficient B in the Forchheimer equation and the critical hydraulic gradient Jc, which can describe the nonlinear seepage characteristics, show a power function decreasing trend with increasing dislocation distance, and the fluid in the fracture is more likely to produce nonlinear flow.

Temporal Dynamics of Tree Crown Fractal Dimension in Two Species of Deciduous Oaks

Fractal dimension (D) can be used to characterise temporal changes of crown architecture of individual trees. Our goal in this study was to analyse seasonal changes in tree crown fractal dimension of two species of deciduous oaks (Quercus castanea and Q. obtusata) coexisting in a natural forest in central Mexico using low cost sampling, and relate these changes to morphological attributes and environmental variables.Every two months, from May 2017 to September 2018, for each oak species, we photographed fixed portions of the crowns of individual trees, measured their trunk diameters, and obtained average temperature and accumulated precipitation data recorded for the sampling date. From the obtained images, we calculated D values by the semivariogram method using three different variability estimators (square increment, isotropic, and transect variation).We identified a positive correlation between D and temperature, and a negative correlation between temperature and crown cover.The fractal dimension (D) of crowns of two deciduous oak species changes according to the tree’s phenological stage. D values varied through time in relation to tree crown phenological variation, but not with crown cover dimension. We propose a model of annual D value fluctuation in deciduous trees, characterised by two high complexity peaks and two low complexity valleys, corresponding to the effects on crown cover of annual periods of leaf abscission and development.

Effect of Heating Emissions on the Fractal Size Distribution of Atmospheric Particle Concentrations

Excessive particle concentrations during heating periods, which greatly affect people’s physical and mental health and their normal lives, continue to be a concern. It is more practical to understand and analyze the relationship between the fractal dimension and particle size concentration distribution of atmospheric particulate matter before and after adjusting heating energy consumption types. The data discussed and analyzed in this paper were collected by monitoring stations and measured from 2016 to 2018 in Xi’an. The data include fractal dimension and particle size concentration changes in the atmospheric particulate matter before and after adjusting the heating energy consumption types. The results indicate that adjusting the heating energy consumption types has a significant impact on particulate matter. The average concentration of PM2.5 decreased by 26.4 μg/m3. The average concentration of PM10 decreased by 31.8 μg/m3. At the same time, the different particle sizes showed a downward trend. The particles ranging from 0.265 to 0.475 μm demonstrated the maximum decrease, which was 8.80%. The heating period in Xi’an mainly involves particles ranging from 0 to 0.475 μm. The fractal dimensions of the atmospheric particulate matter before and after adjusting the heating energy consumption types were 4.809 and 3.397, respectively. After adjusting the heating energy consumption types, the fractal dimension decreased by 1.412. At that time, the proportions of particle sizes that were less than 1.0 μm, 2.0 μm, and 2.5 μm decreased by 1.467%, 0.604%, and 0.424%, respectively. This paper provides new methods and a reference value for the distribution and effective control of atmospheric particulate matter by adjusting heating energy consumption types.

Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons.To investigate fractal resonance, we first determine the degree to which neurons are fractal and the impact of this fractality on their functionality. By analyzing three-dimensional images of rat hippocampal neurons, we find that the way their dendrites fork and weave through space is important for generating their fractal-like behavior. By modeling variations in neuron connectivity along with the associated energetic and material costs, we highlight how the neurons' fractal dimension optimizes these constraints. To simulate neuron interactions with implant interfaces, we distort the neuron models away from their natural form by modifying the dendrites' fork and weaving patterns. We find that small deviations can induce large changes in fractal dimension, causing the balance between connectivity and cost to deteriorate rapidly. We propose that implant surfaces should be patterned to match the fractal dimension of the neurons, allowing them to maintain their natural functionality as they interact with the implant.

Fractal Dimension Studies of the Brain Shape in Aging and Neurodegenerative Diseases.

The fractal dimension is a morphometric measure that has been used to investigate the changes of brain shape complexity in aging and neurodegenerative diseases. This chapter reviews fractal dimension studies in aging and neurodegenerative disorders in the literature. Research has shown that the fractal dimension of the left cerebral hemisphere increases until adolescence and then decreases with aging, while the fractal dimension of the right hemisphere continues to increase until adulthood. Studies in neurodegenerative diseases demonstrated a decline in the fractal dimension of the gray matter and white matter in Alzheimer's disease, amyotrophic lateral sclerosis, and spinocerebellar ataxia. In multiple sclerosis, the white matter fractal dimension decreases, but conversely, the fractal dimension of the gray matter increases at specific stages of disease. There is also a decline in the gray matter fractal dimension in frontotemporal dementia and multiple system atrophy of the cerebellar type and in the white matter fractal dimension in epilepsy and stroke. Region-specific changes in fractal dimension have also been found in Huntington's disease and Parkinson's disease. Associations were found between the fractal dimension and clinical scores, showing the potential of the fractal dimension as a marker to monitor brain shape changes in normal or pathological processes and predict cognitive or motor function.

The Quantitative Method for Following Radiologic Healing in Endodontic Retreatment; 1-Year Follow-up Study

Objectives: This study aimed to quantitatively evaluate the changes in the internal bone structure at the periapical bone regions after retreatment in endodontics using fractal analysis method on periapical radiographs.&#x0D; Materials and Methods: 29 single-rooted, asymptomatic, single-visit retreatment teeth with apical lesion were included in the study. All teeth included in the study were selected from the maxilla anterior region. Periapical radiograph (T0) was taken for baseline diagnosis at the start of retreatment. Second periapical follow-up radiograph (T1) of the patients was taken at the end of 1 year. The first evaluation phase of the 1-year results of endodontic retreatment is based on the periapical index (PAI). Fractal dimension (FD) was calculated by box-counting method. The paired-sample t-test was used to compare T0 and T1 FDs. The independent samples t-test was employed to compare FD changes between the sexes. The significance level was set to 0.05.&#x0D; Results: PAI scores were found to be statistically significantly decreased in T1 radiographs compared to T0 (p