Measurement Of Fractal Dimension Research Articles

Assessment of mandibular trabecular structure and cervical vertebral maturation using fractal analysis.

Changes in bone trabeculae occur during skeletal maturation. Fractal analysis is a technique for assessing changes in the internal structure of the bone. The aim of this study was to investigate correlation of bone trabeculation measured on panoramic and lateral cephalometric radiographs with cervical vertebral maturation stages (CVMS). CVMS was evaluated on lateral cephalometric radiographs of 120 individuals aged 6 to 18 years. The subjects were divided into 6 groups (n= 20 each) according to CVMS. On panoramic and lateral cephalometric radiographs, fractal dimension (FD) analyses were performed in mandibular corpus, gonial and condylar regions and cervical vertebral bodies (C2, C3, C4). FD measurements from the mandibular corpus region bilaterally and C2-C4 vertebral bodies showed significant positive correlations with CVMS (r= 0.418, r= 0.412, r= 0.324, r= 0.304, r= 0.263, respectively). Significant differences were found in the FD values of the right/left mandibular corpus and C2 and C3 vertebrae compared to CVMS (P< 0.001, P< 0.001, P= 0.005, P= 0.019, respectively). Significant positive moderate correlations between the FD values of the right and left mandibular corpus and CVMS suggest that fractal analysis may be useful in determining skeletal maturity stage. The significant FD values obtained from the right/left mandibular corpus, and C2 and C3 vertebra indicate that the complexity of the internal trabecular structure increases with maturation.

Fractal dimensions and machine learning for detection of Parkinson’s disease in resting-state electroencephalography

Parkinson’s disease (PD) is an incurable neurological disorder that degenerates the cerebrospinal nervous system and hinders motor functions. Electroencephalography (EEG) signal analysis can provide reliable information regarding PD conditions. However, EEG is a complex, multichannel, and nonlinear signal with noise that problematizes identifying PD symptoms. A few studies have employed fractal dimension (FD) to extract distinguishing PD features from EEG signals. However, no exploratory study exists, as per our knowledge, on the efficiency of the different FD measures. We aim to conduct a comparative analysis of the various FDs that, as feature extraction measures, can discriminate PD patients who are ON and OFF medication from healthy controls using ML architecture. This study has implemented and analyzed several techniques for segmentation, feature extraction, and ML models. The results show that k-nearest neighbors (KNN) classifier with Higuchi FD and 90% overlap for segmented window delivers the highest accuracies, yielding a mean accuracy of 99.65±0.15%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.65\\pm 0.15\\%$$\\end{document} for PD patients ON medication and 99.45±0.18%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.45\\pm 0.18\\%$$\\end{document} for PD patients OFF medication, respectively. The model accurately identifies the signs of the disease in resting-state EEG with almost equivalent accuracy in both OFF and ON medication patients. To enhance the interpretability in our study, we leveraged XGB’s feature importance to generate brain topographic plots. This integration of explainable AI (XAI) enhanced the transparency and comprehensibility of our model’s classifications. Additionally, a comparison between the performance of FD and a few entropy measures has also been drawn to validate the significance of FD as a superior feature extraction measure. This study contributes to the body of knowledge with an architectural pipeline for detecting PD in resting-state EEG while emphasizing fractal dimension as an effective way of extracting salient features from EEG signals.

3D Fractal Dimension Analysis: Prognostic Value of Right Ventricular Trabecular Complexity in Participants with Arrhythmogenic Cardiomyopathy.

Arrhythmogenic cardiomyopathy (ACM) is characterized by progressive myocardial fibro-fatty infiltration accompanied by trabecular disarray. Traditionally, two-dimensional (2D) instead of 3D fractal dimension (FD) analysis has been used to evaluate trabecular disarray. However, the prognostic value of trabecular disorder assessed by 3D FD measurement remains unclear. To investigate the prognostic value of right ventricular trabecular complexity in ACM patients using 3D FD analysis based on cardiac MR cine images. Retrospective. 85 ACM patients (mean age: 45 ± 17 years, 52 male). 3.0T/cine imaging, T2-short tau inversion recovery (T2-STIR), and late gadolinium enhancement (LGE). Using cine images, RV (right ventricular) volumetric and functional parameters were obtained. RV trabecular complexity was measured with 3D fractal analysis by box-counting method to calculate 3D-FD. Cox and logistic regression models were established to evaluate the prognostic value of 3D-FD for major adverse cardiac events (MACE). Cox regression and logistic regression to explore the prognostic value of 3D-FD. C-index, time-dependent receiver operating characteristic (ROC) curves and area under the ROC curve (AUC) to evaluate the incremental value of 3D-FD. Intraclass correlation coefficient for interobserver variability. P < 0.05 indicated statistical significance. 26 MACE were recorded during the 60 month follow-up (interquartile range: 48-67 months). RV 3D-FD significantly differed between ACM patients with MACE (2.67, interquartile range: 2.51 ~ 2.81) and without (2.52, interquartile range: 2.40 ~ 2.67) and was a significant independent risk factor for MACE (hazard ratio, 1.02; 95% confidence interval: 1.01, 1.04). In addition, prognostic model fitness was significantly improved after adding 3D-FD to RV global longitudinal strain, LV involvement, and 5-year risk score separately. The myocardial trabecular complexity assessed through 3D FD analysis was found associated with MACE and provided incremental prognostic value beyond conventional ACM risk factors. 4 TECHNICAL EFFICACY: Stage 1.

Fractal Neurodynamics.

The neuronal ongoing electrical activity in the brain network, the neurodynamics, reflects the structure and functionality of generating neuronal pools. The activity of neurons due to their excitatory and inhibitory projections is associated with specific brain functions. Here, the purpose was to investigate if the local ongoing electrical activity exhibits its characteristic spectral and fractal features in wakefulness and sleep across and within subjects. Moreover, we aimed to show that measures typical of complex systems catch physiological features missed by linear spectral analyses. For this study, we concentrated on the evaluation of the power spectral density (PSD) and Higuchi fractal dimension (HFD) measures. Relevant clinical impact of the specific features of neurodynamics identification stands primarily in the potential of classifying cortical parcels according to their neurodynamics as well as enhancing the effectiveness of neuromodulation interventions to cure symptoms secondary to neuronal activity unbalances.

Fractal analysis and radiomorphometric indices: comparison of mandibular bone structure changes on digital panoramic radiographs of smokers

Purpose: The purpose of the study was to assess how smoking affected the mandibular bone structure using a variety of radiomorphometric indices and fractal dimension (FD) analysis.&#x0D; &#x0D; Materials and methods: 56 patients (28 smokers and 28 non-smokers) were included in this retrospective study. In the trabecular bone of the mandible, eight areas of interest of 45x45 pixels were chosen, and fractal dimension analysis was carried out. All digital panoramic radiographs were used to measure the mandibular index and mandibular cortical width. All values were compared between groups. Utilizing the Shapiro-Wilk and Mann-Whitney U tests, collected data were evaluated.&#x0D; &#x0D; Results: There was a statistically significant difference between the groups in ROI4 and ROI8, but not in the mean FD values of ROI1, ROI2, ROI3, ROI5, ROI6 and ROI7 in the mandibular trabecular bone. No statistically significant differences between groups were seen for PMI and MCW measures (p &gt; .05). The intraclass correlation coefficient (ICC) values for the FD, PMI and MCW measurements were excellent.&#x0D; &#x0D; Conclusion: The trabecular bone structures of the anterior of the mental foramen and the condyle were different in smokers. There was no difference in cortical bone structures.

Identifying and differentiating dementias with EEG fractal dimension distributions

AbstractBackgroundAlzheimer’s disease dementia (AD‐dementia) and non‐AD dementia have both been associated with decreases in fractal dimension and spectral slowing in electroencephalography (EEG). Here, we describe a set of EEG features ‐ Fractal Dimension Distributions (FDD) ‐ which quantifies the stability of fractal dimensions over time within specific frequency bands. We compare the performance of models trained using this FDD feature to models using age, spectral power, or overall fractal dimension.MethodWe analyzed resting‐state data from older adults (age M = 71, range = 55‐86) with subjective cognitive impairment (SCI; N = 97, 59 female) or dementia (N = 51, 32 female), including 38 with AD (N = 33). We calculated the Fractal Dimension Distributions (FDD) by first computing the Higuchi fractal dimension within moving windows, then summarizing the distribution of these fractal values using the mean and standard deviation within standard frequency bands. Finally, we trained regularized logistic regression models to classify participants as having SCI or dementia, and as having SCI or AD‐dementia. We compared the performance of models using FDD or standard measures of fractal dimension. Models were evaluated using balanced accuracy, weighted sensitivity, and weighted specificity calculated using 5‐fold cross‐validation.ResultFor SCI vs Dementia, the model using FDD (accuracy = 74%, sensitivity = 67%, specificity = 81%, p &lt; .001) had higher accuracy, sensitivity, and specificity than models trained on age, standard measures of fractal dimension, or spectral power. Similarly, the model trained to predict SCI vs AD‐Dementia was most accurate when using FDD (accuracy = 73%, sensitivity = 59%, specificity = 97%, p &lt; .005). The features useful for discriminating SCI from Dementia partially overlapped with the features useful for discriminating SCI from AD‐Dementia.ConclusionOur novel feature, FDD, outperforms standard measures of fractal dimensions or spectral band power at discriminating between SCI and dementia. Moreover, FDD may help to distinguish between AD and other varieties of dementia.

A novel approach to documenting water diffusion in ancient obsidian artifacts via the complexity analysis of microscope images

The diffusion of water through the surface of archaeological obsidian is mainly a temperature-dependent and concentration driven phenomenon that forms the basis of the hydration dating (OHD) method. For the first time, we apply a novel fractal approach, which explores the various attributes of images linked to the variation in water concentration and structural deficiencies within the hydrated layer. The microscopic images of hydrated layers on two obsidian specimens from Africa spanning thousands of years have been investigated. Seven complexity measures of fractal dimension (succolarity, lacunarity, correlation dimension, local connected fractal dimension (LCFD), fractal fragmented index (FFI), entropy and normalized Kolmogorov complexity (TIFF-LZW)), were applied to the hydration layer images. It was found that the effective determination of diffusion depth mainly comes from the application of succolarity, FFI and LCFD fractal indices, plus the structural deficiencies at the surface and the misconnected lacunas at the interface of the water diffusion layer and unaltered obsidian. The difference between fractal dimensions of the hydrated area and the non-hydrated images turned out to be a crucial quantitative parameter. Accordingly, we found that especially the succolarity, which is based on the capacity of a water fluid to percolate through the obsidian area in a given direction, was critical to determine the characteristics of the obsidian hydration layer. The FFI and LCFD estimate the compaction/fragmentation and connectivity, respectively. Therefore, the fractals play an important role in understanding the general diffusion in solids theory and the study aims at providing a new direction in the OHD and diffusion fields concerning the complex dynamic systems and structures which display a fractal pattern.

Assessment and Comparison of Nonlinear Measures in Resting-State Magnetoencephalograms in Alzheimer's Disease and Mild Cognitive Impairment.

Nonlinear dynamical measures, such as fractal dimension (FD), entropy, and Lempel-Ziv complexity (LZC), have been extensively investigated individually for detecting information content in magnetoencephalograms (MEGs) from patients with Alzheimer's disease (AD). To compare systematically the performance of twenty conventional and recently introduced nonlinear dynamical measures in studying AD versus mild cognitive impairment (MCI) and healthy control (HC) subjects using MEG. We compared twenty nonlinear measures to distinguish MEG recordings from 36 AD (mean age = 74.06±6.95 years), 18 MCI (mean age = 74.89±5.57 years), and 26 HC subjects (mean age = 71.77±6.38 years) in different brain regions and also evaluated the effect of the length of MEG epochs on their performance. We also studied the correlation between these measures and cognitive performance based on the Mini-Mental State Examination (MMSE). The results obtained by LZC, zero-crossing rate (ZCR), FD, and dispersion entropy (DispEn) measures showed significant differences among the three groups. There was no significant difference between HC and MCI. The highest Hedge's g effect sizes for HC versus AD and MCI versus AD were respectively obtained by Higuchi's FD (HFD) and fuzzy DispEn (FuzDispEn) in the whole brain and was most prominent in left lateral. The results obtained by HFD and FuzDispEn had a significant correlation with the MMSE scores. DispEn-based techniques, LZC, and ZCR, compared with HFD, were less sensitive to epoch length in distinguishing HC form AD. FuzDispEn was the most consistent technique to distinguish MEG dynamical patterns in AD compared with HC and MCI.

Assessment of correlation between hand-wrist maturation and cervical vertebral maturation: a fractal analysis study

BackgroundTo investigate whether fractal dimension (FD) measurements from hand-wrist radiographs and lateral cephalometric radiographs are correlated with each other and with skeletal maturation stages.MethodsIn this retrospective study conducted on hand-wrist and lateral cephalometric radiographs obtained from patients between 2017 and 2023, hand-wrist maturation stages (HWMS) and cervical vertebral maturation stages (CVMS) of 144 subjects (6 to 17 years of age) were assessed radiographically. The participants were divided into nine groups (n = 16 each) based on HWMS. Fractal analysis was performed on the radiographs of the radius, the middle finger phalanges (proximal, medial and distal), and the cervical vertebral bodies (C2, C3, C4). Mean and standard deviation values, Spearman’s and Pearson correlation analyses, one-way ANOVA, Kruskal-Wallis H tests and Mann-Whitney-U test were used to evaluate the data.ResultsPositive correlations were found between the FD values of the radius and HWMS or CVMS (r = .559, P = .001, r = .528 P = .001 respectively). The FD values of the radius were positively correlated with those of all cervical vertebrae (C2, C3, C4), proximal and medial phalanges as well as age. FD values measured from the proximal phalanx, medial phalanx and radius showed significant differences among both HWMS and CVMS (P < .05). HWMS was strongly correlated with CVMS (r = .929, P = .001). Age was strongly correlated with HWMS (r = .795, P = .001) and CVMS (r = .756, P = .001). There was a significant difference in terms of age distribution among HWMS and CVMS (P < .05).ConclusionsFD measurements on hand-wrist radiographs can provide useful information for the assessment of skeletal maturation stage. Especially, FD measurements from the radius are important and more reliable to predict skeletal maturation stage.

Dynamical fractal: Theory and case study

Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but none for this specific problem, nor extrapolating the future trend. In the first part of this paper, we construct a theoretical framework for analyzing dynamic (changing) fractals and extrapolating their future trends based on their fractal dimension—a measure of the complexity of the fractal. We believe this approach holds enormous potential for applications in analyzing changing fractals in the real world, such as urban growth, cells, cancers, etc., all of which are invaluable to research. This theoretical framework may shed light on a factor overlooked in past research: the trend of how fractals change. In the second part of this paper, we apply this theoretical framework to study the urbanization of Boston. We compare several maps and measurements of fractal dimensions, produce code11https://github.com/yinj66/fractal-dimension. that reads the maps and divides the city into subsections, and ultimately graph the fractal dimension over time using both differential and difference equations. Finally, we postulate the logistic equation as a model to fit the evolution of the fractal dimension, as well as the total population derived from census data, which serves as a component for comparing dynamical fractals.

(Invited) Using Molecular Dynamics Simulations to Relate Morphology to Water and Ion Dynamics in Hydrated Ion-Conducting Polymers

Hydrated ion-containing polymer membranes are used as electrolytes in a variety of applications, including in fuel cells and in alkaline batteries. Achieving high conductivity in hydrated, ion-conducting polymers typically requires the hydrophobic backbone of the polymers to be nano-phase separated from the hydrophilic domains so that the ions (protons or hydroxide ions) have well-defined water domains for efficient transport. The ion transport thus depends strongly on the hydration level and on the detailed morphology of the hydrophilic domains. It is often difficult to determine the morphology of these domains experimentally. I will present results from atomistic molecular dynamics (MD) simulations that reveal the domain morphology in various ionic polymers. Increasing water content generally leads to an increase in the characteristic spacing between hydrophilic domains. However, this swelling can be obscured in X-ray scattering due to a loss of scattering contrast between the hydrophobic and hydrophilic domains. The MD simulations reveal that the systems are nano-phase separated, even when X-ray scattering appears to indicate otherwise. Calculated and measured scattering profiles are in good qualitative agreement. I will discuss several methods to characterize the water domain morphology in more detail, including various measures of pore size distributions, surface areas, and fractal dimension. Water and ion diffusivities calculated from the MD simulations follow the experimentally-measured trends in conductivity and are consistent with changes in the nanoscale morphology with changing water content. I will discuss the implications of the results for the future design of ion-conducting polymers for use as membranes in electrochemical devices.This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE’s National Nuclear Security Administration under contract DE-NA-0003525. Figure 1

Image simulation and realism evaluation for mammography and tomosynthesis based on the detailed breast phantom

The virtual image system is a key component of virtual clinical trials (VCTs) which can be utilized to evaluate and improve medical imaging devices. The main limitation of VCTs in the Chinese female breast is the lack of detailed structure in the breast model employed in the Chinese specification for testing of quality control in mammography. In this paper, based on Chinese female breast parameters, detailed breast phantoms with different glandularity (fatty, glandular, dense) and compressed breast thicknesses (CBT) (2–7 cm) were generated. Digital mammography (DM) and digital breast tomosynthesis (DBT) projections for these phantoms were simulated with clinical system configuration. Compressed breast volumes were reconstructed through DBT projections with different angles. Power spectrum analysis and fractal dimension measurement were applied for simulated and clinical images. The results show that the average power law exponents and standard deviation (DM, DBT) for clinical and simulated images were (3.26 ± 0.29, 3.33 ± 0.42) and (3.63 ± 0.25, 3.18 ±0.36) respectively. The average fractal dimensions and standard deviation (DM, DBT) for clinical and simulated images were (2.36 ± 0.03, 2.41 ± 0.05) and (2.10 ± 0.01, 2.26 ± 0.06) respectively. We constructed two virtual imaging systems for DM and DBT and obtained the imaging data based on the three-dimensional (3D) detailed breast phantoms. These results indicate that the texture indexes of simulated images are similar to that of the clinical images, and validate that these breast phantoms are suitable for imaging in VCTs requiring realistic anatomy with the Chinese female population. Results also show that the values of power law exponents for clinical and simulated images in DM and DBT are positively correlated with the value of breast glandularity, but the values of fractal dimensions keep steady for different glandularity.

Assessing the Sensitivity of OCT-A Retinal Vasculature Metrics.

The purpose of this study was to examine the sensitivity of quantitative metrics of the retinal vasculature derived from optical coherence tomography angiography (OCT-A) images. Full retinal vascular slab OCT-A images were obtained from 94 healthy participants. Capillary loss, at 1% increments up to 50%, was simulated by randomly removing capillary segments (1000 iterations of randomized loss for each participant at each percent loss). Thirteen quantitative metrics were calculated for each image: foveal avascular zone (FAZ) area, vessel density, vessel complexity index (VCI), vessel perimeter index (VPI), fractal dimension (FD), and parafoveal intercapillary area (PICA) measurements with and without the FAZ (mean PICA, summed PICA, PICA regularity, and PICA standard deviation [PICA SD]). The sensitivity of each metric was calculated as the percent loss at which 80% of the iterations for a participant fell outside of two standard deviations from the sample's normative mean. The most used OCT-A metrics, FAZ area and vessel density, were not significantly different from normative values until 27.69% and 16.00% capillary loss, respectively. Across the remaining metrics, metric sensitivity ranged from 6.37% (PICA SD without FAZ) to 39.78% (Summed PICA without FAZ). The sensitivity of vasculature metrics for detecting random capillary loss varies substantially. Further efforts simulating different patterns of capillary loss are needed for comparison. Additionally, mapping the repeatability of metrics over time in a normal population is needed to further define metric sensitivity. Quantitative metrics vary in their ability to detect vascular abnormalities in OCT-A images. Metric choice in screening studies will need to balance expected capillary abnormalities and the quality of the OCT-A images being used.

Fractal dimension: analyzing its potential as a neuroimaging biomarker for brain tumor diagnosis using machine learning.

Purpose: The main purpose of this study was to comprehensively investigate the potential of fractal dimension (FD) measures in discriminating brain gliomas into low-grade glioma (LGG) and high-grade glioma (HGG) by examining tumor constituents and non-tumorous gray matter (GM) and white matter (WM) regions. Methods: Retrospective magnetic resonance imaging (MRI) data of 42 glioma patients (LGG, n = 27 and HGG, n = 15) were used in this study. Using MRI, we calculated different FD measures based on the general structure, boundary, and skeleton aspects of the tumorous and non-tumorous brain GM and WM regions. Texture features, namely, angular second moment, contrast, inverse difference moment, correlation, and entropy, were also measured in the tumorous and non-tumorous regions. The efficacy of FD features was assessed by comparing them with texture features. Statistical inference and machine learning approaches were used on the aforementioned measures to distinguish LGG and HGG patients. Results: FD measures from tumorous and non-tumorous regions were able to distinguish LGG and HGG patients. Among the 15 different FD measures, the general structure FD values of enhanced tumor regions yielded high accuracy (93%), sensitivity (97%), specificity (98%), and area under the receiver operating characteristic curve (AUC) score (98%). Non-tumorous GM skeleton FD values also yielded good accuracy (83.3%), sensitivity (100%), specificity (60%), and AUC score (80%) in classifying the tumor grades. These measures were also found to be significantly (p < 0.05) different between LGG and HGG patients. On the other hand, among the 25 texture features, enhanced tumor region features, namely, contrast, correlation, and entropy, revealed significant differences between LGG and HGG. In machine learning, the enhanced tumor region texture features yielded high accuracy, sensitivity, specificity, and AUC score. Conclusion: A comparison between texture and FD features revealed that FD analysis on different aspects of the tumorous and non-tumorous components not only distinguished LGG and HGG patients with high statistical significance and classification accuracy but also provided better insights into glioma grade classification. Therefore, FD features can serve as potential neuroimaging biomarkers for glioma.

Fractal dimension analysis of different mandibular regions in familial Mediterranean fever patients: A cross-sectional retrospective study.

Familial Mediterranean fever (FMF) is a genetic condition that may cause loss of bone mineral density (BMD) due to chronic inflammation. Previously, fractal dimension (FD) analysis values of mandibular cortical bone were shown to be lower in osteoporosis. Therefore, FD might be considered as an auxiliary tool to refer patients for dual-energy x-ray absorptiometry (DXA), which is the gold standard for BMD measurement. The purpose of this cross-sectional retrospective study was to evaluate trabecular and cortical microarchitecture of the mandible with FD analysis on panoramic radiographs in a subpopulation of FMF. Also, the effect of colchicine use was investigated. Forty-three FMF patients, aged between 10.8 and 71.2 years, and age- and gender-matched control group consisting of patients, who had no systemic diseases, were included. Demographic information such as age and gender, and colchicine use were recorded. In terms of age, the patients were classified as <30 and 30< years. On each panoramic radiographs five regions of interest were selected on the mandible as: 1- premolar, 2- molar, 3- angular, 4- condylar, and 5- basal cortical bone regions on right (R) and left (L) sides. Statistical significance was accepted at p<0.05 level. Intra- and inter-observer agreements demonstrated good to excellent consistency. In FMF patients, L3 and L4 values were higher, whereas L5 values were lower (p<0.05) than the control group. In terms of age, the difference between groups was insignificant in FMF patients (p>0.05), whereas in control group R3 and L4 values were higher in the 30< age group (p<0.05). Regarding gender and colchicine use, the difference between groups was insignificant (p>0.05). FMF disease might be a candidate for referral to DXA examination based on decreased bone density in the mandibular cortex detected by FD measurements on routine panoramic radiographs. Further studies are warranted to ascertain this relationship.

Relationship analysis of surface roughness measurements on coatings using AFM and fractal dimension by mesoscopic model methods

Surface coating is a method used for protection against corrosion and environmental impact for metals. In the case of solid surfaces, coatings can be achieved by radio-frequency magnetron sputtering or other corrosion-resistant substances, which may involve the deposition of one or more layers, depending on the procedure involved, modifying the morphology of the surface and surface area. This work aims to study the relationship of two surface morphological methods through roughness and fractal dimension measurements in top-surface coatings, bilayer Ti/WTiN/WTiC (named as n = 1); multilayer [Ti/WTiN/WTiC] (named as n = 40) deposited by RF-magnetron sputtering. The measurements were obtained by profilometer and image processing pixel intensity. The topography of each coating exhibited texture with impurities as domes distributed in small cluster island types. The surface roughness were 9.42 and 18.63 nm; fractal dimension measurements were 2.55 and 2.32, respectively, with a low correlation between roughness and fractal dimension. The R-squared analysis exhibited a good relationship between the fractal dimension values, tending linear regression negative. The result of factorial design 22 confirmed the performance correlation and linear regression analyses. The fractal dimension measurements by the optical method can be great potential to evaluate surface roughness complementary in applications such as laboratories and even in scale industrial. Thus the result of statistical treatment shows high accuracy in the measurements.

Quantitative Brain MRI Metrics Distinguish Four Different ALS Phenotypes: A Machine Learning Based Study.

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease whose diagnosis depends on the presence of combined lower motor neuron (LMN) and upper motor neuron (UMN) degeneration. LMN degeneration assessment is aided by electromyography, whereas no equivalent exists to assess UMN dysfunction. Magnetic resonance imaging (MRI) is primarily used to exclude conditions that mimic ALS. We have identified four different clinical/radiological phenotypes of ALS patients. We hypothesize that these ALS phenotypes arise from distinct pathologic processes that result in unique MRI signatures. To our knowledge, no machine learning (ML)-based data analyses have been performed to stratify different ALS phenotypes using MRI measures. During routine clinical evaluation, we obtained T1-, T2-, PD-weighted, diffusion tensor (DT) brain MRI of 15 neurological controls and 91 ALS patients (UMN-predominant ALS with corticospinal tract CST) hyperintensity, n = 21; UMN-predominant ALS without CST hyperintensity, n = 26; classic ALS, n = 23; and ALS patients with frontotemporal dementia, n = 21). From these images, we obtained 101 white matter (WM) attributes (including DT measures, graph theory measures from DT and fractal dimension (FD) measures using T1-weighted), 10 grey matter (GM) attributes (including FD based measures from T1-weighted), and 10 non-imaging attributes (2 demographic and 8 clinical measures of ALS). We employed classification and regression tree, Random Forest (RF) and also artificial neural network for the classifications. RF algorithm provided the best accuracy (70-94%) in classifying four different phenotypes of ALS patients. WM metrics played a dominant role in classifying different phenotypes when compared to GM or clinical measures. Although WM measures from both right and left hemispheres need to be considered to identify ALS phenotypes, they appear to be differentially affected by the degenerative process. Longitudinal studies can confirm and extend our findings.

Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry

Diatoms are one of the main species of interest due to their possible impact on the maintenance of ecosystems, as well as their photosynthetic capacity and biotechnological applications. Reliable, easy, rapid identification of diatoms remains a highly desirable goal to avoid the difficulty for experts in the visual analysis of frustules; a method commonly used to compare the distinctive traits of diatoms, such as ornaments and the marks from images taken by optical and electronic microscopy for identification. This study proposed three simple morphometric methods based on fractal dimension measurements in conjunction with 2D cross-correlation parameters to analyze diatom images. This novel approach demonstrates the differentiation feasibility between a wide variety of diatom species with heterogeneity in their structures and shapes, which could possibly expand the application of this preprocessing process for the identification of new types of images or other biological species.

Accessibility of the surface fractal dimension during film growth.

Fractal properties on self-affine surfaces of films growing under nonequilibrium conditions are important in understanding the corresponding universality class. However, measurement of the surface fractal dimension has been intensively investigated and is still very problematic. In this work, we report the behavior of the effective fractal dimension in the context of film growth involving lattice models believed to belong to the Kardar-Parisi-Zhang (KPZ) universality class. Our results, which are presented for growth in a d-dimensional substrate (d=1,2) and use the three-point sinuosity (TPS) method, show universal scaling of the measure M, which is defined in terms of discretization of the Laplacian operator applied to the height of the film surface, M=t^{δ}g[Θ], where t is the time, g[Θ] is a scale function, δ=2β,Θ≡τt^{-1/z},β, and z are the KPZ growth and dynamical exponents, respectively, and τ is a spatial scale length used to compute M. Importantly, we show that the effective fractal dimensions are consistent with the expected KPZ dimensions for d=1,2, if Θ≲0.3, which include a thin film regime for the extraction of the fractal dimension. This establishes the scale limits in which the TPS method can be used to accurately extract effective fractal dimensions that are consistent with those expected for the corresponding universality class. As a consequence, for the steady state, which is inaccessible to experimentalists studying film growth, the TPS method provided effective fractal dimension consistent with the KPZ ones for almost all possible τ, i.e., 1≲τ<L/2, where L is the lateral size of the substrate on which the deposit is grown. In the growth of thin films, the true fractal dimension can be observed in a narrow range of τ, the upper limit of which is of the same order of magnitude as the correlation length of the surface, indicating the limits of self-affinity of a surface in an experimentally accessible regime. This upper limit was comparatively lower for the Higuchi method or the height-difference correlation function. Scaling corrections for the measure M and the height-difference correlation function are studied analytically and compared for the Edwards-Wilkinson class at d=1, yielding similar accuracy for both methods. Importantly, we extend our discussion to a model representing diffusion-dominated growth of films and find that the TPS method achieves the corresponding fractal dimension only at steady state and in a narrow range of the scale length, compared to that found for the KPZ class.

FRACTAL DIMENSION TECHNIQUES FOR ANALYSIS OF CARDIAC AUTONOMIC NEUROPATHY (CAN)

Identifying Cardiac Autonomic Neuropathy (CAN) in the early stages of proliferation demands more prominent techniques with a reliable significance of identification. CAN being a subclinical consequence that is the leading cause of death in individuals with diabetes mellitus (DM), which is common among one in four people above an average age of 45 years, calls for a more dependable technique for analysis. This study investigates the complexity in prominent time segments (RR, QT and ST) of ECG using different entropy measures and four nonlinear fractal dimension (FD) measures including box counting, Petrosian, Higuchi’s and Katz’s methods. Measures of statistical significance were implemented using Wilcoxon, Mann–Whitney and Kruskal–Wallis tests. The results of the study provide an original approach to diagnostics that reveals the fact that, instead of analyzing the signal running for the whole length, complexity measures can be achieved, if the intervals of the signal are studied including a combination of features rather than any one feature considered for diagnosis. A significance level of [Formula: see text] is achieved in more segments of ECG considered at intervals of time compared to one data recorded at the 20th minute between CAN+ and CAN− groups for both FD and entropy. Neural Network (NN) classification shows the accuracies of 84.61% and 60% in FD and entropy, respectively, computed every fifth minute. The accuracies from the model for the data collected at the 20th minute for FD and entropy are 50.22% and 30.33%, respectively, between the groups.