Fractal Dimension Analysis Research Articles

Dependence of reaction time in hydrothermal synthesis of MoS2 quantum dots: An investigation using optical tools and fractal analysis

The article discusses the novel fractal nature of hydrothermally synthesized Molybdenum Disulfide (MoS2) Quantum Dots (QDs), where the key parameter controlling the process is the 'reaction time’. This parameter is adjusted from 7 to 30 h, including five intermediate values, while keeping all other synthesis conditions constant. The study employs various structural, morphological, and optical techniques, including X-ray diffraction (XRD), X-ray photoelectron Spectroscopy (XPS), High-Resolution Transmission Electron Microscopy (HRTEM) equipped with Selected Area Electron Diffraction (SAED), Scanning Transmission Electron Microscopy (STEM), UV–Vis, and photoluminescence (PL) spectroscopy to track the evolution of MoS2 samples with changing reaction times. The average size of the QDs exhibits a trend of increase followed by a decrease with longer reaction times. This trend is also compared with band gap calculations. STEM images indicate that shorter reaction times lead to the formation of MoS2 sheets, while extended reaction times cause these sheets to fragment into MoS2 QDs. The concept of “compactness” in the system is explored and analyzed using fractal analysis, a statistical tool. The observations from PL, absorption, and STEM align with the time-evolved fractal dimensional analysis, demonstrating the synthesis dynamics.

Local electrical characteristic of memristor structure in a high-resistance state obtained using electrostatic force microscopy: Fractal and multifractal dynamics of surface

A heterostructure BiFeO3/TiO2(Nt)Ti (BFOT) was obtained by the atomic layer deposition (ALD) method. After thermal treatment, the redistribution of Fe/Ti atoms forms an Aurivillius intermediate layered phase, and local charge capture centers are formed in the sample. Due to cationic non-stoichiometry, the BFO film exhibits p-type conductivity, while the nanotubes exhibit n-type conductivity due to oxygen vacancies. It was observed that lateral displacement of the sample can lead to ferroelectric switching, which can, in turn, affect the transition of the memristive structure from high-resistance (HRS) to low-resistance states (LRS). The hysteresis suppression tends to transition to an ohmic character and depends on the amplitude, frequency, and duration of the periodic signal. It has been found that compensation of static charge during resistive switching can affect the transport properties of the material. Fractal dimension analysis showed an acceleration of structure restructuring with increasing voltage, possibly contributing to the transition from an insulator to a metal in certain areas of the film volume. The joint analysis of piezoresponse force microscopy (PFM), electrostatic force microscopy (EFM), and fractal/multifractal dynamics showed a correlation between surface static charge and piezopotential. The new methodology described in this work can help understand the resistive switching processes in ferroelectric/semiconductor memristive structures.

Influence of post-heat treatment with super β transus temperature on the tensile behaviour of LPBF processed Ti6Al4V

This paper investigates the tensile behaviour of Laser powder bed fusion (LPBF) processed Ti6Al4 V samples under three build orientations. The effect of microstructural changes from the post-heat treatments (PHTs – 850 °C, 950 °C 1050 °C) was assessed. The microstructural characterization was performed using optical microscopy, X-ray diffraction, and SEM techniques. The tensile tests were performed using a uniaxial universal testing machine (UTM). The fractal dimension analysis was performed on the fractured surfaces using ImageJ software integrated with an open-source MultiFrac plug-in. The PHT at a higher temperature (i.e., 1050 °C) induces a higher amount of β phase than the other PHTs. The PHT performed at 1050 °C exhibited α-Widmanstatten microstructure consisting of elongated β and a small amount of α. The PHT induces an isotropic behaviour in the LPBF-processed samples. However, the ductility of specimens subjected to PHT at 1050 °C showed ∼ 67%, 40%, and 177% improvement under horizontal (0°), inclined (45°), and vertical (90°) orientations than as-printed samples. Further fractal dimension analysis corroborates well with the ductility values of PHT samples. Therefore, the combination of fractography analysis and fractal dimension approach can be a promising methodology towards fractured surface characterization of additively manufactured metal parts.

Chaos in a tunneling universe

Abstract A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum dynamics, captured by new quasiclassical methods. Chaotic dynamics in the early universe, described by such models, implies that a larger set of initial values of an expanding branch can be probed.

Natural bentonite as an internal curing agent in the production of eco-friendly ultra-high performance concrete with low autogenous shrinkage

This study investigated the use of natural bentonite as a green internal curing agent to prepare eco-friendly ultra-high performance concrete (UHPC) with low autogenous shrinkage and excellent heavy metal ions solidification properties. A method based on the pore fractal dimension analysis was used for assessing the performance of UHPC. Results showed the use of bentonite as a replacement of cement could effectively reduce the autogenous shrinkage through its internal curing effect without compromising the compressive strength and workability of UHPC. The UHPC containing 4% bentonite showed the best volume stability and durability, with a 26.9% reduction in the autogenous shrinking compared to the control UHPC. The addition of bentonite further improved ion penetration resistance and solidification of heavy metal ion owing to its ion exchange capacity. However, the enhancement effect decreased when the bentonite content was too high due to the volume change of bentonite. Two kinds of pore classification dimensions, Dmin and Dmax, were obtained from NMR results to build good correlations with the autogenous shrinkage and durability, respectively. Finally, the ecological evaluation demonstrated that the designed UHPC with bentonite had relatively low environmental impact compared to other internal curing material, which was promising to generate a cleaner product in the near future.

White matter integrity in bipolar disorder investigated with diffusion tensor magnetic resonance imaging and fractal geometry

BackgroundGrowing evidence suggests the presence of white matter (WM) alterations in bipolar disorder (BD). In this study we aimed to investigate the state of WM structures, in terms of tissue integrity and morphological complexity, in BD patients compared to healthy controls (HC), in an attempt to better elucidate the microstructural changes associated with BD. MethodsWe collected a dataset of 399 Diffusion Tensor Magnetic Resonance Imaging (167 BD and 232 healthy controls) images, acquired at five different sites, which was processed with Tract-Based Spatial Statistics (TBSS) and fractal analysis. ResultsThe TBSS analysis demonstrated significantly lower FA values in the BD group. Diffusion abnormalities were primarily located in the temporo-parietal network. The Fractal Dimension (FD) analysis did not reveal consistent significant differences in the morphological complexity of WM structures between the groups. When the FD values of patients were considered individually, it is possible to notice some localized significant deviations from the healthy population. LimitationsDTI sequences have not been harmonized before acquisition, samples' sizes are heterogeneous. ConclusionsThis study, by applying both TBSS and FD analyses, allows to evaluate diffusion and structural alterations of WM at the same time. The evaluation of WM integrity from these two different perspectives could be useful to better understand the pathophysiological and morphological changes underpinning bipolar disorder.

Evaluation of the effect of class II fixed orthodontic treatment on the periradicular bone structure of endodontically treated mandibular molar teeth using fractal dimension analysis

Aim: The aim of this study was to investigate whether changes in periradicular tissues with orthodontic movement of root canal-treated teeth differ from those without root canal treatment using fractal dimension analysis (FA). Methodology: A retrospective archive study was performed using panoramic radiographs taken before (T1) and after (T2) fixed orthodontic treatment. Panoramic radiographs of a total of 32 mandibular 1st and 2nd molar teeth were divided into groups: Group 1 (n:17), the control group, comprised radiographs of mandibular 1st or 2nd teeth without root canal treatment, and Group 2 (n:15) comprised radiographs of 1st or 2nd mandibular molars with root canal treatment. Fractal analyses were performed in four different regions—the periapical, bifurcation, mesial periapical, and distal periapical regions—of the mandibular molar teeth included in the study for a total of 128 analyses. Results: In the control group, orthodontic treatment did not make a statistically significant difference to the fractal dimension values in the four regions of the tooth (p > 0.05). In the endodontically treated group, the fractal dimension values of the mesial periapical regions increased statistically significantly after orthodontic treatment (p < 0.05). Conclusion: The FA values of this study showed that more biological interaction occurred in the root canal treatment group and in the mesial periapical region. Thus, it is important to keep orthodontic force within the tooth’s physiological limits to avoid damaging the tooth in the periapical areas where stress accumulates during orthodontic treatment. How to cite this article: Küçükkaraca E, Sarıçam E. Evaluation of the effect of class II fixed orthodontic treatment on the periradicular bone structure of endodontically treated mandibular molar teeth using fractal dimension analysis. Int Dent Res 2023;13(S1):38-43. https://doi.org/10.5577/idr.2023.vol13.s1.6 Linguistic Revision: The English in this manuscript has been checked by at least two professional editors, both native speakers of English.

Novel Fractal-Based Sub-RPE Compartment OCT Radiomics Biomarkers Are Associated With Subfoveal Geographic Atrophy in Dry AMD.

The purpose of this study was to quantitatively characterize the shape of the sub-retinal pigment epithelium (sub-RPE, i.e., space bounded by RPE and Bruch's membrane) compartment on SD-OCT using fractal dimension (FD) features and evaluate their impact on risk of subfoveal geographic atrophy (sfGA) progression. This was an IRB-approved retrospective study of 137 subjects with dry age-related macular degeneration (AMD) with subfoveal GA. Based on sfGA status at year five, eyes were categorized as "Progressors" and "Non-progressors". FD analysis allows quantification of the degree of shape complexity and architectural disorder associated with a structure. To characterize the structural irregularities along the sub-RPE surface between the two groups of patients, a total of 15 shape descriptors of FD were extracted from the sub-RPE compartment of baseline OCT scans. The top four features were identified using minimum Redundancy maximum Relevance (mRmR) feature selection method and evaluated with Random Forest (RF) classifier using three-fold cross validation from the training set (N = 90). Classifier performance was subsequently validated on the independent test set (N = 47). Using the top four FD features, a RF classifier yielded an AUC of 0.85 on the independent test set. Mean fractal entropy (p-value = 4.8e-05) was identified as the most significant biomarker; higher values of entropy being associated with greater shape disorder and risk for sfGA progression. FD assessment holds promise for identifying high-risk eyes for GA progression. With further validation, FD features could be potentially used for clinical trial enrichment and assessments for therapeutic response in dry AMD patients.

A CLIMATIC PREDICTABILITY INDEX FOR SOUTH WEST MONSOON SEASON IN DIFFERENT DISTRICTS OF WEST BENGAL WITH APPLICATION OF FRACTAL DIMENSION ANALYSIS

A CLIMATIC PREDICTABILITY INDEX FOR SOUTH WEST MONSOON SEASON IN DIFFERENT DISTRICTS OF WEST BENGAL WITH APPLICATION OF FRACTAL DIMENSION ANALYSIS

Fractal dimension analysis of resting state functional networks in schizophrenia from EEG signals.

Fractal dimension (FD) has been revealed as a very useful tool in analyzing the changes in brain dynamics present in many neurological disorders. The fractal dimension index (FDI) is a measure of the spatiotemporal complexity of brain activations extracted from EEG signals induced by transcranial magnetic stimulation. In this study, we assess whether the FDI methodology can be also useful for analyzing resting state EEG signals, by characterizing the brain dynamic changes in different functional networks affected by schizophrenia, a mental disorder associated with dysfunction in the information flow dynamics in the spontaneous brain networks. We analyzed 31 resting-state EEG records of 150 s belonging to 20 healthy subjects (HC group) and 11 schizophrenia patients (SCZ group). Brain activations at each time sample were established by a thresholding process applied on the 15,002 sources modeled from the EEG signal. FDI was then computed individually in each resting-state functional network, averaging all the FDI values obtained using a sliding window of 1 s in the epoch. Compared to the HC group, significant lower values of FDI were obtained in the SCZ group for the auditory network (p < 0.05), the dorsal attention network (p < 0.05), and the salience network (p < 0.05). We found strong negative correlations (p < 0.01) between psychopathological scores and FDI in all resting-state networks analyzed, except the visual network. A receiver operating characteristic curve analysis also revealed that the FDI of the salience network performed very well as a potential feature for classifiers of schizophrenia, obtaining an area under curve value of 0.83. These results suggest that FDI is a promising method for assessing the complexity of the brain dynamics in different regions of interest, and from long resting-state EEG signals. Regarding the specific changes associated with schizophrenia in the dynamics of the spontaneous brain networks, FDI distinguished between patients and healthy subjects, and correlated to clinical variables.

Particle size distribution of aggregate effects on the dynamic compressive behavior of cement waste rock backfill

Cement waste rock backfill (CWRB) is an essential component of green mining. Recent studies have demonstrated that the CWRB can slow surface settlement and provide economic advantages. However, there has been only limited research into the susceptibility of CWRB to dynamic impacts such as rock bursts, especially as mining depth increases. This study aims to investigate the dynamic peak stress, elastic modulus, and dissipated energy of CWRB specimens using a split Hopkinson pressure bar system. The results demonstrated that the responses of aggregate with different particle size distributions to the system’s impact strain rate (ISR) were inconsistent. Specifically, the highest dynamic peak stress of 23.71 MPa was achieved for the CWRB (Talbot index = 0.6) at a low ISR (30 s−1–35 s−1) and 62.33 MPa for the CWRB (Talbot index = 0.4) at a high ISR (40 s−1–50 s−1). A strain nephogram and fractal dimension analysis further suggested that the CWRB (Talbot index = 0.4, 0.6) could continue to provide partial compressive resistance after impact. Moreover, a compressive model was developed to determine the “change point” between the low and high ISR. The model indicated that different particle size distributions influenced the porosity, and at a high ISR, the pore structures further worsened the dynamic compressive behavior of CWRB. This study not only enhances our understanding of the compressive performance of CWRB under dynamic impact, but also contributes to the safety and efficiency of filling mining operations. In addition, it offers a theoretical explanation of the effects on the dynamic compressive behavior of CWRB.

Characterization of shear behavior and damage mechanism of periodic thermal loading sandstone based on NMR technique

We conducted research on the influence of periodic thermal loading on the shear behavior of sandstone through a series of direct shear tests with the aid of acoustic emission techniques. By capturing the evolution in pore structure with nuclear magnetic resonance technology and fractal theory to analyze the damage mechanism. The shear testing reveals that the periodic heating and air cooling sample exhibits a lower shear resistance compared to the continuous heating rock, with more pronounced differences observed in the water cooling samples. The peak shear strength and stiffness are greatly influenced by temperature and thermal loading methods, while the ultimate shear strength remains largely unaffected. Compared to samples with less severe damage, the acoustic emission macrocracking proportion of sandstone with more damage after thermal loading is more significant, corresponding to a smaller b-value. The study of the evolution in pore structure shows that mesopores and macropores exhibit favorable fractal characteristics distinct from micropores. The fractal dimension of mesopores and macropores are observed to be influenced by heating temperature and periodic thermal loading, as evidenced by their negative correlation with the thermal damage variable. After thermal loading, there was a negative correlation between porosity and fractal dimension in mesopores and macropores, indicating that the more severe the damage to the pore structure, the smaller the fractal dimension. The shear strength of periodic thermal loaded sandstone is closely related to the evolution of fractal dimension. The presence of thermal enhancement at 400 °C has been confirmed for the first time through fractal dimension analysis.

Fractal Dimension Analysis of Surface Roughness for Paper and Paperboard

Fractal Dimension Analysis of Surface Roughness for Paper and Paperboard

Pore structure characterization of solvent extracted shale containing kerogen type III during artificial maturation: Experiments and tree-based machine learning modeling

Shale samples with type III kerogen from the Damoguaihe formation were exposed to hydrous and anhydrous pyrolysis (HP and AHP) in the temperature range of 300–450 °C. Next, soluble organic matter (OM) and the liquid yield were removed from the pyrolyzates after each step of thermal maturation. N2 adsorption tests were performed to assess the pore structures of the samples. Furthermore, deconvolution and fractal dimension analyses were executed to unveil pore clusters and discern the complexity of the pore network within each sample. Finally, two tree-based machine learning algorithms, random forest (RF) and extra trees (ET) were applied to model the N2 adsorption/desorption data of pyrolyzates to predict pore structure variations. Based on the results, HP pyrolyzates had higher bitumen reflectance (BRo%) values than AHP ones at all temperature sequences, which confirms water controls thermal maturity. AHP pyrolyzates exhibited larger average pore diameters across all temperatures, while HP pyrolyzates displayed higher BET surface areas in contrast to AHP pyrolyzates. Also, the average pore diameter of HP pyrolyzates with soluble OM and liquid yield extracted did not change significantly during thermal maturation, while the average pore diameter of AHP ones increased, peaking at 400 °C in post-mature stage. The largest total pore volume of HP samples was observed at the end of the wet gas window, while this was observed for AHP samples in the dry gas window. Three mesopore and four macropore clusters were identified in the original sample. Moreover, pore clusters of the pyrolyzates underwent diverse changes during thermal maturation, without following a specific trend, influenced by both temperature and pyrolysis conditions. Abundance of micropores, finer mesopores (2–10 nm), and a smaller average pore diameter in HP pyrolyzates compared to the AHP is the main reason for the higher fractal dimensions showing a more complex pore structure and/or rougher pore surface. Intelligence modeling exhibited that RF outperformed ET in estimating N2 adsorbed/desorbed volumes for the samples. Ultimately, sensitivity analysis revealed that water exerted a more significant influence on pore development in shales during thermal progression, outweighing the impact of temperature.

Experimental investigation and intelligent modeling of pore structure changes in type III kerogen-rich shale artificially matured by hydrous and anhydrous pyrolysis

The occurrence and enrichment of shale plays are highly controlled by pore characteristics of the formation. In this study, an immature sample rich in kerogen type III from the Damoguaihe formation, Hailar Basin in China is subjected to hydrous and anhydrous pyrolysis (HP and AHP) across an extensive temperature range (300–450 °C). Next, low-pressure N2 adsorption analysis was conducted on the pyrolyzate of each maturity stage to study the pore structures’ evolution during thermal maturity simulation. Moreover, deconvolution and fractal dimension analyses were implemented to study pore families and the complexity of pores within the shale samples. Finally, radial basis function (RBF) neural networks optimized by four evolutionary approaches were applied for modeling N2 adsorption data obtained from the HP and AHP samples. According to the results, the original shale sample and all pyrolyzates obtained with HP and AHP scenarios exhibited type IV isotherm with H3 hysteresis loops. As a whole, BET surface area, micro-, meso- and total pore volume of HP pyrolyzates were higher than AHP ones. The unheated shale sample had seven families containing three mesopore and four macropore groups. Although all pyrolyzates obtained from the pyrolysis had families with similar means, their pore volumes were entirely different, which proves that the pore structure of samples undergoes changes during thermal maturation and the presence of water can also enforce these changes. Both fractal dimensions showed a direct relationship with BET surface area and a negative correlation with the average pore diameter of shale samples. The RBF model optimized by differential evolution (DE) delivered a mean absolute percent relative error (MAPRE) value of 4.84% and determination coefficient (R2) of 0.9946 for the total data set, which outperforms other RBF models in predicting N2 adsorption/desorption tests of pyrolyzates. The outcome of sensitivity analysis suggested that the N2 adsorption/desorption behavior of the pyrolyzates was mostly affected by relative pressure and the pyrolysis type (HP or AHP). Ultimately, the results clearly revealed that the effect of water on the pores' alteration of shales with type III kerogen is greater than the effect of temperature or thermal maturity itself.

Study on the effect of flocculation morphology on the floatability of talc flocs and the adhesion mechanism with air bubbles

This study investigates the impact of floc morphology on flotation by preparing two types of flocs with similar apparent particle sizes but different aggregation degrees through varying the stirring speed. Flotation tests were conducted on the two flocs, revealing that flocs with higher aggregation degrees demonstrated superior floatability and higher flotation rate constants. Fractal dimension and AFM analysis indicated that flocs with higher aggregation degrees exhibited higher fractal dimensions, displaying a more circular and compact overall morphology, as well as a more regular and uniform surface morphology. XPS and contact angle tests showed that, for flocs with comparable particle sizes, an increase in fractal dimension led to increased adsorption of flocculant (PEO) on the surface, accompanied by enhanced hydrophobicity. Further analysis of the induction time for particle-bubble attachment and coverage angle demonstrated that flocs with higher fractal dimensions had shorter induction times and larger coverage angles, indicating faster attachment between flocs and bubbles. These findings suggest that flocs with higher fractal dimensions can acquire greater kinetic energy in a flow field, enabling them to more effectively disrupt the hydration film on the bubble surface and adhere to the bubble surface, thereby enhancing floatability.

Corner flow effect on the relative permeability of two-phase flow in nano-confined porous media

Relative permeability is a critical factor clarifying the multiphase flow behavior in nano-porous media. However, most studies have focus on the circle flow, neglecting the corner flow effect. Therefore, in this work, a comprehensive relative permeability model considering the corner flow effect is proposed. We integrated the corner flow with the immiscible flow model and the confined liquid-gas phase equilibrium with the near-miscible flow model. Then it was validated against the experimental measured data, indicating the proposed model can well describe the two-phase flow in the confined space. Subsequently, sensitivity analysis of corner number, fractal dimension, minimum radius, and viscosity ratio were conducted. Results show that the corner flow effect is noticeable when corner number is less than 8. Under the optimal pore radius of 2 × 10−5 m, the gas relative permeability increases from 0.4909 to 0.9274 with corner number raising from 4 to 10. Under critical oil phase saturation of 0.175, increase of fraction dimension, minimum radius, and viscosity ratio leads to the significant decrease of oil relative permeability and increase of gas relative permeability. In addition, nano-confinement effect and CO2 injection will reduce the interfacial tension and increase the near-miscible relative permeability. When CO2 injection increase to 100% under oil saturation of 0.4084, the increment of oil relative permeability is nearly 67.2%. Interfacial intension-based interpolation method indicates that the confined fluid is more likely to be miscible than the bulk fluid. This relative permeability model provides deeper understandings of two-phase flow in the nano-porous media, which is benefit for the better development of unconventional reservoirs.

Concurrent influence of geological parameters on the integrated nano-pore structure and discretized pore families of the petroliferous Cambay shale assessed through multivariate dependence measure

Heterogeneous nanopore structure and distribution regulate the gas trapping, desorption kinetics, and diffusion in shale matrices. In shale, pores range from continuous micro- and mesopore size distributions, varying with organic (total organic matter-TOC) and inorganic constituents (clay content, Fe-bearing minerals, quartz, etc.). Previous research only showed a linear relationship of pore parameters with these intrinsic properties of shale, which limits our understanding of the concurrent influence of multiple intrinsic rock properties. As a result, in this work, we established multivariate dependency of nanopore structure, distribution, and complexity (from low-pressure N2 and CO2 sorption and small-angle scattering; SAXS/MSANS) in the previously little-studied Cambay shales and provided a better tool (partial least square regression) for analyzing the simultaneous effect of intrinsic shale properties on multiply connected pore-parameters. Furthermore, we discretized continuous pore-size distribution into individual pore families using deconvolution to understand the pore space better. Additionally, predicted shale formation environment in terms of deposition probability (P+) and dissolution probability (P−) using a dynamic model of the fractal interface by precipitation and dissolution. Our findings indicate that the Cambay shales have a high potential for future hydrocarbon exploration (S2: 2.42–12.04 mg HC/g rock), “very good” (2-4 wt.%) to “excellent” (&amp;gt;4 wt.%) TOC content, and thermally mature type II–III admixed and type III kerogen. Deconvolution of the micro- and mesopore size distributions reveals that pore width (w) ranges ∼15.30–35 nm occupies greater than 50% of the total pore volume, and its pore volume increases with the presence of quartz, Fe-bearing minerals, and clay content. However, pores with w∼ 3.60–15.30 nm increase exclusively with TOC. In the micro- and early mesopore region, pore volume decreases with TOC from w∼ 0.30–0.75 nm and increases with TOC from w∼ 0.75–3.60 nm. Furthermore, TOC in shale increases the specific surface area and pore volume (micro-, meso-, and total pores), enhancing both sorption and free gas storage capacities. Cambay shales were likely deposited in three distinct environments, with precipitation probability (P+) values of 1, 0.7–0.8, and 0.5, as revealed by a fractal dimension (Ds) analysis of multiple samples.

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.

Pore structure and fractal dimension analysis of ancient city wall bricks in China

Comprehensive quantitative characterization of the pore structures of ancient city wall bricks is important for predicting the durability of historical masonry buildings. However, in most previous studies, only one or two methods were used to analyse the pore structures of fired clay bricks. In this study, mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), and low-field nuclear magnetic resonance (LF-NMR) were used to characterize the pore structure and fractal dimension of nine different ancient city wall bricks. The results show that the surface relaxivity of ancient bricks measured via the Hahn spin echo (HSE) in LF-NMR ranged from 1.55 to 1.75 μm/s. Furthermore, the porosity of the blue bricks measured via LF-NMR were much lower than that obtained via the gravimetric method owing to a higher number of paramagnetic iron mineral phases. LTNA was not suitable for describing pore size distribution of ancient bricks as the pore diameters were mainly concentrated in the range of 100–1000 nm. The pore structures of ancient bricks in dried and water-saturated states were different, the pore size of the white bricks obtained via LF-NMR was smaller than the MIP-derived pore-throat size by a factor of approximately 2.