Fractal Analysis Research Articles

Dissolution kinetics and heterogeneous evolution of dolomite with different pore structures

Mesogenetic dissolution is a critical process in the evolution and preservation of pore spaces in carbonate reservoirs. While limestone dissolution has been extensively studied, there is a lack of research on the dissolution kinetics of dolomite reservoirs, particularly regarding differences in dissolution mechanisms and heterogeneity evolution across various pore structures. This study aims to investigate diagenesis processes and heterogeneity evolution patterns in dolomites with different pore structures by simulating reservoir dissolution using organic acids generated during kerogen cracking. Flow system dissolution experiments were conducted on four dolomites with varying pore structures in 0.2% acetic acid under high-temperature (T = 40–160 °C) and high-pressure (P = 10–50 MPa) conditions. The chemical composition of the fluid and pore structure images were analyzed using ICP-OES and X-ray computed microtomography, respectively. Pore size distribution and evolution were assessed through digital cores based on Micro-CT analysis, while fractal and multifractal analyses were employed to quantify the evolution of pore structure heterogeneity. The findings highlight the importance of an effective combination of early material base and subsequent organic acid dissolution in the formation and maintenance of deep, high-quality dolomite reservoirs.

Assessment of the Trabecular Bone Microstructure Surrounding Impacted Maxillary Canines Using Fractal Analysis on Cone-Beam Computed Tomography Images.

To assess the impact of the presence or position (buccal/palatal) of impacted canines on trabecular bone density using fractal analysis (FA) on cone-beam computed tomography (CBCT) images, and to compare the results with a control group without impacted canines. This retrospective study included 41 patients with unilateral impacted canines (30 palatal, 11 buccal) and a control group of 39 patients who underwent surgically assisted rapid maxillary expansion. All patients had CBCT images recorded for diagnostic and treatment purposes. Cross-sectional CBCT images were obtained between the first and second premolars on both sides of the patients' maxilla. From these images, fractal dimension (FD) was measured in a 20 × 20 pixel region of interest in the trabecular bone using the ImageJ software. The FD values were significantly higher on the impacted side in the impacted canine group (p = 0.02). Within the impacted canine group, a significant increase in FD was observed on the impacted side in the buccal-impacted subgroup (p = 0.02), while no significant difference was observed in the palatal-impacted subgroup (p > 0.05). According to the results of our study, there is an association between the position of the impacted canine and trabecular bone density. An increased trabecular bone density may play a role in the etiology of buccally impacted canines. Clinicians should consider anchorage planning, and appropriate force level, during the forced eruption of buccally impacted canines with high surrounding bone density, to minimize undesirable movements and achieve optimal treatment outcomes.

Alveolar bone healing patterns in chronic kidney failure and kidney transplant recipients: A pixel intensity and fractal analyses.

To assess and compare radiographically the alveolar bone after tooth extractions in individuals with chronic kidney failure undergoing hemodialysis (CKFh), those submitted to kidney transplantation (KT), and those without kidney disease (CG) by using fractal analysis (FA) and pixel intensity (PI). Periapical radiographs of 48 CKFh individuals (87 extracted teeth), 12 KT individuals (26 extracted teeth and 29 control individuals [76 extracted teeth] were analyzed at 7 and 60 days after tooth extraction. Fractal dimension (FD) and PI were assessed to evaluate the alveolar trabecular bone structural complexity and mineral content. The difference in FD values between the 7th and 60th postoperative days in KT individuals (0.03±0.08) was significantly lower compared to those of CKFh individuals (0.09±0.10) and controls (0.15±0.06). As for the difference in PI values, KT (4.55±10.24) and CKFh groups (9.88±15.90) showed significantly lower values compared to those of the control group (17.93±11.86) in the same period. These results indicate a lower gain in the trabecular bone complexity and bone density in the alveolus of KT individuals compared to the other groups. Overall mineral content and thickness of the bone in the plane of the x-ray beam were lower in KT and CKFh individuals compared to controls, reflecting the need for careful consideration in recommending rehabilitation with dental implants for these patients. Particular attention should be given to the potential challenges in oral rehabilitation of KT patients.

Factors Controlling Differences in Morphology and Fractal Characteristics of Organic Pores of Longmaxi Shale in Southern Sichuan Basin, China

Shale gas is a prospective cleaner energy resource and the exploration and development of shale gas has made breakthroughs in many countries. Structure deformation is one of the main controlling factors of shale gas accumulation and enrichment in complex tectonic areas in southern China. In order to estimate the shale gas capacity of structurally deformed shale reservoirs, it is necessary to understand the systematic evolution of organic pores in the process of structural deformation. In particular, as the main storage space of high-over-mature marine shale reservoirs, the organic matter pore system directly affects the occurrence and migration of shale gas; however, there is a lack of systematic research on the fractal characteristics and deformation mechanism of organic pores under the background of different tectonic stresses. Therefore, to clarify the above issues, modular automated processing system (MAPS) scanning, low-pressure gas adsorption, quantitative evaluation of minerals by scanning (QEMSCAN), and focused ion beam scanning electron microscopy (FIB-SEM) were performed and interpreted with fractal and morphology analyses to investigate the deformation mechanisms and structure of organic pores from different tectonic units in Silurian Longmaxi shale. Results showed that in stress concentration areas such as around veins or high-angle fractures, the organic pore length-width ratio and the fractal dimension are higher, indicating that the pore is more obviously modified by stress. Under different tectonic backgrounds, the shale reservoir in Weiyuan suffered severe denudation and stronger tectonic compression during burial, which means that the organic pores are dominated by long strip pores and slit-shaped pores with high fractal dimension, while the pressure coefficient in Luzhou is high and the structural compression is weak, resulting in suborbicular pores and ink bottle pores with low fractal dimension. The porosity and permeability of different forms of organic pores are also obviously different; the connectivity of honeycomb pores with the smallest fractal dimension is the worst, that of suborbicular organic pores is medium, and that of long strip organic pores with the highest fractal dimension is the best. This study provides more mechanism discussion and case analysis for the microscopic heterogeneity of organic pores in shale reservoirs and also provides a new analysis perspective for the mechanism of shale gas productivity differences in different stress–strain environments.

Single-Particle Crushing Test of Coated Calcareous Sand Based on MICP

Calcareous sand is a crucial construction material for island and reef development and reinforcing it using Microbially Induced Calcite Precipitation (MICP) technology is a promising new method. This study employed 3D scanning technology to assess changes in the particle size and morphology of MICP-treated, coated calcareous sand particles. Single-particle crushing tests were conducted to analyze their crushing strength, crushing energy, crushing modes, and fragment fractal dimensions. The results indicated that MICP treatment significantly increased particle size, surface area, and volume, while reducing flatness. At a cementation solution concentration of 1 mol/L, both crushing strength and crushing energy were optimized. The coated particles exhibited three crushing modes: explosive crushing, mixed crushing, and splitting crushing. Thicker coatings led to a tendency for particles to break into larger fragments through the mixed and splitting crushing modes. Fractal analysis revealed that coating thickness directly affects the local crushing characteristics of the particles.

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.

The use of fractal analysis to assess the influence of electrospark alloying on the durability indicators of hydraulic hammer parts

Abstract. Statement of the problem. In order to increase the wear resistance and fatigue strength of the material of hydraulic hammer parts, it is not always advisable to change the traditional technology of manufacturing the part and, in particular, the methods of its heat treatment. Different types of finishing are applied only specifically to the given product. In some cases, it is worth applying surface strengthening of the product. Purpose and problem statement. The purpose of the work is to evaluate the impact of electrospark alloying on the durability indicators of hydraulic hammer parts. In order to achieve the set goal, it is necessary to: develop modes of electrospark alloying; conduct an analysis of the location of damage zones and their nature on parts strengthened by electrospark alloying, identical to those observed on tested parts manufactured without additional strengthening and with the use of LTO; Apply fractal analysis to evaluate the impact of electrospark alloying on the durability indicators of hydraulic hammer parts. Research material and methods. All details were strengthened by electrospark alloying with tungsten. The power of the processing current was 1 kW. The peak, in addition to strengthening with tungsten, was additionally processed by electrospark alloying with chromium at a current of 1.5 kW. The surfaces processed by electrospark alloying were ground to obtain the roughness of the strengthened surfaces of parts R and 04–08. Experimental results and their discussion. During the micro-examination of areas strengthened by electrospark alloying, which are outside the load zone during the test, it was established that the areas strengthened by electrospark alloying on the body and sleeve have a thickness of 10–40 μm and a hardness of Н V 600–650. On the strikers, the initial thickness of the hardened layer is 20 μm with a hardness of НV 600–650. The strengthened zones in the cross-section have the appearance of arc-shaped, embedded surface layers of metal parts, phases. There are no structural changes under this zone in the main metal. Conclusions. The results of tests of parts strengthened by electrospark alloying show that the wear resistance of the parts is increased by 1.3 times compared to the original state of the parts. Fractal models were obtained, which can be interpreted as a knowledge base for monitoring the strength indicators of the striker body, which allow monitoring its residual resource during operation. It was established that the strength indicators increase when the fractal dimension of the sorbite component increases, since it has better strength indicators compared to the original ferrite-pearlite structure. Indicators of pairwise correlation coefficients of the obtained models are fixed in the interval of values 0.6779...0.9254.

Fractal formalism in crystallized-Ge via Al induced crystallization under ion irradiation

The fractal characterization of polycrystalline-Ge formed via Al induced crystallization under ion irradiation is presented. The polycrystalline (p-) Al (50 nm)/amorphous (a-) Ge (50 nm) is irradiated using 1000 keV Xe+ ions with fluences of 7 × 1014 ions/cm2, 3 × 1015 ions/cm2 and 1 × 1016 ions/cm2 followed by post-thermal annealing at 200 °C. The pristine (i.e., as-prepared) sample is also thermally annealed for comparison purposes. The X-ray diffraction measurement confirms the crystallization of Ge after thermal annealing in both pristine and ion irradiated samples whereas only ion irradiation does not show any crystallization of Ge. The optical micrograph and field emission scanning electron microscopy (FE-SEM) images show dotted like structures on the surface of the film which are found to increase with increasing ion fluence. The Rutherford backscattering spectrometry and energy dispersive X-ray spectroscopy confirm the layer exchange phenomena at the interface in the p-Al/a-Ge bilayer system with Ge crystallization. The fractal analyses have been carried out on FE-SEM images which confirms the Ge fractals formation due to crystallization of Ge followed by layer exchange. The fractal dimension and hurst exponent are calculated and found that the surface roughness decreases with increasing ion fluence up to the fluence of 3 × 1015 ions/cm2 and then increases at higher fluence.

Statistical fractal analysis in testing the Hypotheses with imprecise data

A new statistical hypothesis testing procedure using fractal analysis, incorporating the concept of lacunarity for interval population parameters when the sample data are real intervals, is introduced. The decision rules for accepting or rejecting the null and alternative hypotheses are provided, along with testing procedures and numerical examples. Additionally, the proposed tests are extended to statistical hypotheses involving fuzzy data samples with lacunarity.

Application of Fractal Dimension for Cardiac Arrhythmias Classification

Fractal analysis is crucial for understanding complex, irregular patterns found in nature, finance, and various scientific fields. It helps to reveal self-similarity, where structures repeat at different scales, providing insights into chaotic systems like weather patterns, stock markets, and biological growth. By applying fractal analysis, researchers can model phenomena that traditional geometric methods cannot easily describe, enabling better predictions and deeper comprehension of dynamic systems. The Fractals are a fascinating mathematical tool for modeling the roughness of nature and understanding structure of such complex objects. They are considered a tool for understanding the world. In general, fractal objects are characterized by the fractal dimension. The application of fractal geometry to the analysis of ECG time series data is examined in this paper. A method based on the assessment of the Fractal Dimension (FD) of ECG recordings is suggested for the identification of cardiac diseases. In this work, and in order to exploit the fractal dimension to analyze fractal signals, the notion of fractal dimension is defined by presenting methods for calculating this dimension such as Higuchi algorithm, Katz method, regularization, box-counting etc… Each of them has its own advantages and disadvantages. This study has shown that the electrocardiogram (ECG) is a fractal signal. This allows to classify heartbeats founded on the concept of fractals. The main aim is to develop a digital technique to analyze ECG signals in order to make an accurate diagnosis of cardiovascular diseases.

Effects of rock pore and micromorphology on electromagnetic radiation characteristics

Electromagnetic radiation (EMR) is a crucial tool for monitoring and early warning of underground engineering disasters. Investigating the inherent pore characteristics of rocks is essential for a comprehensive understanding of the EMR phenomenon. The EMR was monitored during various types of rock splitting failures. The pore structure and micromorphology of rocks are studied using quantitative methods such as mercury intrusion porosimetry, fractal analysis, and the Gray Level Co-occurrence Matrix (GLCM). Results indicate that the fractal dimension of red sandstone is significantly lower than the other three rocks. The fractal complexity increases sequentially from red sandstone to marble, granite, and limestone. As the fractal dimension decreases, the signal waveform characteristics of the four rocks become more complex before the main fracture, with a significant increase in signals during the compaction and elasticity stages. Higher fractal dimensions lead to a shift in energy and count from elasticity stage to the post-peak stage. The main fracture amplitudes of the four rocks generally exhibited a consistent pattern, following the sequence of granite > marble > limestone > red sandstone. The main fracture amplitude decreases with increasing complexity of the rock's pore micromorphology. Rock pore characteristics affect frequency domain characteristics by influencing rock strength and crack expansion. An increase in the average pore diameter tends to decrease both the main and center frequencies.

Arbor vitae cerebelli: Fractal properties and their quantitative assessment by novel “contour scaling” fractal analysis method (an anatomical study)

BackgroundArbor vitae cerebelli (tree-like branching white matter of the cerebellum) has a complex spatial configuration that is challenging to assess using conventional morphometric methods. This study proposes a fractal approach to describe and quantify the anatomy of Arbor vitae cerebelli. For this purpose, a new “contour scaling” method for fractal analysis of cerebellar white matter was developed. Material and methodsThe cerebella of 100 cadavers (50 male and 50 female) who died from causes unrelated to brain pathology, aged 20–95 years, were examined. Mid-sagittal sections of the cerebellar vermis were studied. The fractal dimension values of the cerebellar white matter were determined using both the developed fractal analysis method and the conventional “box counting” method, along with measurements of non-fractal parameters including cerebellar weight, area and perimeter of the vermis cross-section, perimeter-to-area ratio, and circularity. ResultsConsidering the cerebellar white matter as a tree-like fractal, it was found to have 7 or 8 primary branches, which subdivide into 10-18 second-iteration branches, 19–38 third-iteration branches, and 34–53 fourth-iteration branches. Females more often had 8 primary branches compared to males, while males had a greater number of branches in the second to fourth iterations. The mean fractal (Hausdorff) dimension was 1.697 (1.721 in males, 1.674 in females, P = 0.01). The fractal dimension correlated most strongly with the perimeter and area of the vermis cross-section and had no significant relationship with age. ConclusionThe fractal (Hausdorff) dimension, determined using the novel “contour scaling” method, quantitatively assesses the degree of branching of the cerebellar white matter. An increase in the absolute size of the cerebellum leads to a higher degree of branching of its white matter and an increase in the number of its constitutive components – white matter branches and folia.

Comprehensive linear and nonlinear heart rate variability normative data in children.

The autonomic nervous system (ANS) is critical in regulating involuntary bodily functions, including heart rate. Heart rate variability (HRV) reflects the complex interplay between the ANS and humoral factors, making it a valuable noninvasive tool for assessing autonomic function. While HRV has been extensively studied in adults, normative data for HRV in children, primarily based on long-term rhythm recordings, are limited. This study aimed to establish comprehensive normative data for HRV in children. In this retrospective study, we examined 24-h Holter monitors of children aged 1day to 18years, divided into six age groups, at Nemours Children's Health in Orlando, Florida, spanning the years 2013-2023. HRV analysis encompassed time-domain, frequency-domain, and nonlinear indices. Holter data for a total of 247 patients in six age groups were included. An age-related uptrend was observed in all time- and frequency-domain variables except the normalized unit of low-frequency power. Entropy analysis revealed contradictory results among different entropy techniques. Sample and approximate entropy analyses were consistent and showed less complexity and more predictability of HRV with decreasing heart rate, while Shannon entropy analysis showed the opposite. Fractal detrended fluctuation analysis exhibited significant decreases across the age groups, suggestive of diminishing self-similarity of HRV patterns. Control of heart rate and HRV is a highly complex process and requires further study for a better understanding. It seems that no single parameter can fully elucidate the entire process. A combination of time-domain, frequency-domain, and nonlinear indices may be necessary to explain HRV behavior in the growing body.

Microglial morphological/inflammatory phenotypes and endocannabinoid signaling in a preclinical model of periodontitis and depression

BackgroundDepression is a chronic psychiatric disease of multifactorial etiology, and its pathophysiology is not fully understood. Stress and other chronic inflammatory pathologies are shared risk factors for psychiatric diseases, and comorbidities are features of major depression. Epidemiological evidence suggests that periodontitis, as a source of low-grade chronic systemic inflammation, may be associated with depression, but the underlying mechanisms are not well understood.MethodsPeriodontitis (P) was induced in Wistar: Han rats through oral gavage with the pathogenic bacteria Porphyromonas gingivalis and Fusobacterium nucleatum for 12 weeks, followed by 3 weeks of chronic mild stress (CMS) to induce depressive-like behavior. The following four groups were established (n = 12 rats/group): periodontitis and CMS (P + CMS+), periodontitis without CMS, CMS without periodontitis, and control. The morphology and inflammatory phenotype of microglia in the frontal cortex (FC) were studied using immunofluorescence and bioinformatics tools. The endocannabinoid (EC) signaling and proteins related to synaptic plasticity were analyzed in FC samples using biochemical and immunohistochemical techniques.ResultsUltrastructural and fractal analyses of FC revealed a significant increase in the complexity and heterogeneity of Iba1 + parenchymal microglia in the combined experimental model (P + CMS+) and increased expression of the proinflammatory marker inducible nitric oxide synthase (iNOS), while there were no changes in the expression of cannabinoid receptor 2 (CB2). In the FC protein extracts of the P + CMS + animals, there was a decrease in the levels of the EC metabolic enzymes N-acyl phosphatidylethanolamine-specific phospholipase D (NAPE-PLD), diacylglycerol lipase (DAGL), and monoacylglycerol lipase (MAGL) compared to those in the controls, which extended to protein expression in neurons and in FC extracts of cannabinoid receptor 1 (CB1) and to the intracellular signaling molecules phosphatidylinositol-3-kinase (PI3K), protein kinase B (Akt) and extracellular signal-regulated kinase 1/2 (ERK1/2). The protein levels of brain-derived neurotrophic factor (BDNF) and synaptophysin were also lower in P + CMS + animals than in controls.ConclusionsThe combined effects on microglial morphology and inflammatory phenotype, the EC signaling, and proteins related to synaptic plasticity in P + CMS + animals may represent relevant mechanisms explaining the association between periodontitis and depression. These findings highlight potential therapeutic targets that warrant further investigation.Graphical

Mechanisms of Proppant Transport in Rough Fractures of Offshore Unconventional Reservoirs: Shale and Tight Sandstone

After hydraulic fracturing, unconventional reservoirs frequently encounter challenges related to limited effective proppant support distance and suboptimal proppant placement. Due to the strong heterogeneity of offshore reservoirs, which causes varying fracture roughnesses depending on different lithologies, a systematic study of the relationship between roughness and proppant transport could optimize operational parameters. This study incorporates the box dimension method for fractal dimension analysis to quantify roughness in auto-correlated Gaussian distributed surfaces created by true triaxial tests. Combined with the numerical analysis of (computational fluid dynamics) CFD-DEM (discrete element method) for bidirectional coupling, the laws of proppant deposition and transport processes within fractures with different roughnesses are obtained through comparative verification simulations. The results show that for rougher fractures of shale, the proppants are transported farther, but at JRC_52, (joint roughness coefficient), where there may be plugging in curved areas, there is a risk of near-well blockages. Compared to the smooth model, fluctuations in JRC_28 (tight sandstone) drastically increase turbulent kinetic energy within the fracture, altering particle transport dynamics. Moreover, smaller proppants (d/w ≤ 0.3) exhibit better transport capacity due to gravity, but the conductivity of the proppant is limited when the particles are too small. A d/w of 0.4 is recommended to guarantee transport capacity and proppant efficiency near the well. Additionally, proppants injected sequentially from small to large in shale fractures offer optimal propping effects, and can take advantage of the better transport capacity of smaller proppants in rough fractures. The large proppant (d/w = 0.8) is primarily deposited by gravity and forms a sloping sand bed, which subsequently ensures the aperture of the fractures. This research provides a fresh perspective on the influence of fracture roughness on proppant transport in offshore unconventional reservoirs and offers valuable considerations for the order of proppant injection.

Mechanical behaviors of metakaolin-based foamed geopolymer (MKFG) under dynamics loading

In this study, metakaolin-based foam geopolymer (MKFG) with densities of 400 kg/m3, 600 kg/m3, and 800 kg/m3 were prepared. The effect of weak links on the dynamic mechanical behavior, damage morphology, and energy absorption capacity (SEAp) of the MKFG was studied by X-CT analysis, Split Hopkinson Pressure Bar (SHPB) test, and fractal analysis. The results show that the connected porosity of MKFG rises with decreasing density. The sensitivity of the damage level to strain rate decreases with elevated connected porosity, which is because the stress concentrations caused by weak links. The amplifying effect of strain rate on the dynamic compressive strength of MKFG diminishes as the connected porosity increases. The sensitivity of SEAp to the damage level rises with a decrease in the connected porosity. Finally, the simulation results corroborate that the distribution of connected pores has a significant influence on the damage process of the MKFG.

Targeting high-potential mineral prospects in the Ezzhiliga region, Moroccan central massif, using spectral data from the ASTER sensor

This research paper introduces a comprehensive methodology for assessing hydrothermal alteration zones and structural complexity in the Ezzhiliga region, situated in the Hercynian Central Massif of Morocco. The approach utilizes ASTER imagery as the primary data source. The main objectives were to identify and analyze these geological features and then create a potential map for mineral exploration by integrating fuzzy logic and fractal concentration area analysis. Band ratios (RBD) and principal component analysis (PCA) were employed to detect and map argillic, phyllic, propylitic, and iron oxide alteration zones. Additionally, structural lineaments were extracted from the PC1 imagery to understand the structural pattern of the survey area. The incorporation of hydrothermal alteration zones and structural lineaments was achieved through the application of a fuzzy logic model, resulting in the generation of a mineral favorability map. The fuzzy logic model was customized to combine hydrothermal alteration and lineaments density maps, effectively eliminating false spectral anomalies induced by various interference factors. This map was then analyzed using the fractal concentration-area (C-A) model, which separated the anomaly from the geological background and generated a final mineral potential map. Analysis of fractal concentration-area was employed to define thresholds with greater precision, enhancing the reliability of mineral prospectivity assessments. Furthermore, laboratory analyses were performed to verify the outcomes of the mineral potential map. The obtained results revealed a significant affinity with the field data and indicated that the highly prospective zones are perfectly limited in spatial extent and generally associated with the contact of the Zaër granitic pluton with the metamorphic host rock, except for the anomaly identified to the southeast of the study area, along a major NE-SW trending fault.

Nanobubbles in Ultrapure Water Can Self-Propel.

Nanobubbles are sub- micron-sized gas entities that find applications in a wide range of scientific fields. Typically, they are thought to diffuse according to Brownian motion. We report the existence of self-propelled motion of oxygen bulk nanobubbles in ultrapure water at body temperature. Their motion, to a large extent, is self-affine; there are different scaling exponents along the x- and y-axes as well as for the lateral displacement. We use fractal analysis, and we calculate the structure function, the normalised velocity autocorrelation function, the skewness, and the kurtosis. All descriptors attest the existence of a quasi-Gaussian stochastic process, which is classified as fractional Brownian motion. More than 50 \% of the trajectories along the x-axis follow superdiffusion, while this amount drops to 30 \% for motion along the y-axis as a result of the asymmetry of the field of view.

Exploring swine oviduct anatomy through micro-computed tomography: a 3D modeling perspective.

The oviduct plays a crucial role in the reproductive process, serving as the stage for fertilization and the early stages of embryonic development. When the environment of this organ has been mimicked, it has been shown to enhance in vitro embryo epigenetic reprogramming and to improve the yield of the system. This study explores the anatomical intricacies of two oviduct regions, the uterotubal junction (UTJ) and the ampullary-isthmic junction (AIJ) by using micro-computed tomography (MicroCT). In this study, we have characterized and 3D-reconstructed the oviduct structure, by measuring height and width of the oviduct's folds, along with the assessments of fractal dimension, lacunarity and shape factor. Results indicate distinct structural features in UTJ and AIJ, with UTJ displaying small, uniformly distributed folds and high lacunarity, while AIJ shows larger folds with lower lacunarity. Fractal dimension analysis reveals values for UTJ within 1.189-1.1779, while AIJ values range from 1.559-1.770, indicating differences in structural complexity between these regions. Additionally, blind sacs or crypts are observed, akin to those found in various species, suggesting potential roles in sperm sequestration or reservoir formation. These morphological differences align with functional variations and are essential for developing an accurate 3D model. In conclusion, this research provides information about the oviduct anatomy, leveraging MicroCT technology for detailed 3D reconstructions, which can significantly contribute to the understanding of geometric-morphological characteristics influencing functional traits, providing a foundation for a biomimetic oviduct-on-a-chip.

Applications of fractal analysis techniques in magnetic resonance imaging and computed tomography for stroke diagnosis and stroke-related brain damage: a narrative review

The fractal analysis technique has emerged as a novel and promising method in mathematical analysis, providing valuable insights across various fields of neuroimaging. The fractal analysis technique allows for the quantitative characterization of complex geometric structures that traditional Euclidean geometry-based morphometric methods fail to describe adequately. This review provides an overview of the principles, characteristics, and main applications of the fractal analysis technique, focusing on its applications and perspectives in stroke diagnosis based on neuroimaging data. In stroke research, the fractal analysis technique has been used to characterize brain tissue, pathological foci, and the vascular network, providing critical diagnostic and prognostic information. Researchers have applied the fractal analysis technique to brain lesions resulting from ischemic strokes to conduct geometric analyses of lesion shapes, indicating its diagnostic and prognostic values. Fractal properties have been used to study the texture of lesions, healthy tissue, and penumbra zones, which is essential for determining the presence and boundaries of damaged brain tissue. Additionally, fractal analysis of intracerebral hemorrhages has shown that hemorrhage geometry is correlated with prognosis and survival rates. This method has been used to assess cortex and white matter configurations in stroke patients, highlighting brain remodeling and compensatory changes. It has also been proven effective in detecting morphological alterations in brain structures during transient ischemic attacks. Moreover, fractal analysis of the brain vasculature revealed changes associated with ischemic stroke and hemorrhage. Overall, the fractal analysis technique in brain magnetic resonance imaging and computed tomography is an informative and sensitive imaging analysis method that, with further development, can significantly improve stroke diagnosis and prognosis on the basis of neuroimaging data.