Evaluation of TMJ bone microarchitecture in malocclusion and tooth loss using fractal dimension analysis.

Collateral circulation is a key determinant of treatment response and outcomes in acute ischemic stroke (AIS), yet its assessment in clinical practice remains limited and subjective. While CT perfusion (CTP) offers insight into tissue viability, its restricted availability and susceptibility to artifacts reduce its practical utility, particularly in smaller centers. As an accessible alternative, we developed and validated an automated quantitative collateral index (qCI) derived from CTA using a deep learning U-Net segmentation framework, and evaluated the ability of CTA-based features to predict post-stroke recovery and functional outcomes. We retrospectively analyzed prospectively collected data from 230 AIS patients who underwent endovascular thrombectomy (EVT) between 2019-2023. CTA scans were segmented using a validated neural network-based vascular extraction model to generate 3D vessel networks and compute morphology metrics (vessel length, branching, fractal dimension, tortuosity). A fully automated qCI was derived through hemispheric comparison of vascular features following spatial registration. Agreement of qCI with clinician grading was quantified. Gradient-boosted decision tree models were trained to predict early neurological deterioration (END), early neurological improvement (ENI), and 90-day modified Rankin Scale (mRS) using (i) CTP-only (core, penumbra, mismatch), (ii) CTA-only (qCI + morphology), and (iii) combined CTA+CTP features. Automated qCI (graded 0-3) showed strong concordance with expert scoring (accuracy 0.863; Pearson R = 0.880; Cohen's κ = 0.786). Dichotomized collateral status achieved 0.938 accuracy (AUROC = 0.945). For 90-day mRS prediction, the CTA-only model outperformed the CTP-only model (AUROC 0.730 vs 0.645) with better calibration (Brier score 0.178 vs 0.295). The combined CTA+CTP model performed best overall (AUROC 0.781), with similar improvements observed for END. CTA-derived features led to significant reclassification gains when added to perfusion-based models. Automated CTA-derived qCI and cerebrovascular morphology provide rapid, objective, and reproducible collateral assessment with high agreement to expert grading. These features outperform perfusion metrics in several predictive tasks and further enhance prognostic accuracy when combined with CTP. Because CTA is widely available, qCI offers a scalable, clinically practical tool for improving stroke outcome prediction, particularly in settings where CTP is unavailable.

Refining nonlinear parameters for evaluating gait stability in subjects with various musculoskeletal disorders: A technical note.

Purpose This study aimed to develop and validate a CT-based nomogram incorporating three-dimensional fractal dimension (FD 3D) to noninvasively predict tumor spread through air spaces (STAS) in stage IA lung adenocarcinoma. Materials and methods A retrospective analysis was performed on 110 patients with stage IA lung adenocarcinoma who underwent surgical resection. CT morphological features and fractal-dimension metrics were collected. Patients were categorized into STAS-positive ( n = 48) and STAS-negative ( n = 62) groups based on pathology. Univariate and multivariate logistic regression analyses were conducted to identify independent predictors of STAS. Receiver operating characteristic (ROC) curve analysis evaluated predictive performance, and a nomogram model was constructed and internally validated. Based on the nomogram score, patients were further stratified into low- and high-risk STAS groups using the optimal cutoff value determined by the maximum Youden index. Results Univariate analysis showed significant differences in consolidation-to-tumor ratio (CTR) ( p < 0.001), morphological irregularity ( p = 0.006), lobulation ( p = 0.039), pleural indentation ( p = 0.004), vascular convergence ( p = 0.010), and FD 3D ( p < 0.001) between groups. Multivariate analysis identified CTR, morphological irregularity, lobulation, and FD 3D as independent predictors of STAS in stage IA lung adenocarcinoma. The nomogram model achieved an area under the curve (AUC) of 0.894 (95%CI: 0.821–0.944; p < 0.001), with a sensitivity of 75.00% and a specificity of 90.32%. At the optimal cutoff value of 0.56, the model demonstrated a positive predictive value (PPV) of 85.71% in the high-risk group ( n = 42, 38.18%) and a negative predictive value (NPV) of 82.35% in the low-risk group ( n = 68, 61.82%), with significant differences in STAS prevalence between groups (85.71% vs. 17.65%, χ 2 = 46.18, p < 0.001). Conclusion The CT-based nomogram integrating FD 3D and key imaging features can noninvasively predict STAS status in stage IA lung adenocarcinoma. This model shows promise for assisting surgical decision-making, though prospective studies are needed to validate its clinical utility.

ABSTRACT The transition toward sustainable materials (SDG12) in the automotive sector necessitates data-driven frameworks. This study proposes a novel hybrid decision-making Exponential TOmada de Decisão Interativa Multicritério (ExpTODIM) framework, to evaluate and rank PALF-based hybrid polymer composites intended for automotive interior door panel applications. The framework integrates Random Forest Regression (RFR) with the Exponential TODIM (ExpTODIM) method under Cartesian form of Complex Fuzzy Decision Weighted Averaging (CFDWA) and Geometric (CFDWG) aggregation schemes. RFR is employed to derive objective, data-driven weights by quantifying the relative importance of nine key mechanical parameters, including tensile strength, flexural modulus, fracture toughness, and impact resistance. Fracture energy (0.1115549), Young’s modulus (0.111553456), and Flexural strength (0.111535261) emerged as the most influential criteria, indicating their strong contribution to overall composite performance. These weights are subsequently used within the ExpTODIM model. Results indicate that the composite fabricated with 0–1 mm/min (0 wt% filler) achieved the highest prospect value (1.00), exhibiting superior tensile and fracture properties essential for stiffness and energy absorption in automotive applications. Comparative sensitivity analyses across criteria weights, attenuation factor (λ), and dominance sensitivity (s) confirmed the robustness of the proposed framework, with RFR–ExpTODIM–CFDWA revealed to be superior compared to with RFR–ExpTODIM–CFDWG.

Thermo-diffusive response of fractal spherical tumors under modified Green-Naghdi heat conduction models.

Combined influence of polymeric and mineral fibres on fresh-state performance and fracture properties of high-performance self-compacting concrete.

In this study, CT scanning technology was combined with ImageJ 1.54r and Avizo 3D 2022 professional image analysis software to quantify porosity. The aim was to reveal the intrinsic correlation between the pore structure characteristics and the macroscopic properties of vegetated concrete. A combination of 3D reconstruction, fractal analysis and multi-parameter regression modelling techniques was utilised to quantify the association between pore parameters and material properties. The mechanistic role of pore structure in regulating the strength-permeability trade-off relationship was elucidated. The results show that: (1) aggregate particle size and porosity are significantly negatively correlated with the compressive strength of vegetated concrete and strongly positively correlated with the water permeability coefficient, while the effects of both of them on the pH value of the material are negligible; (2) the porosity obtained by the image analysis method meets the design requirements of the target porosity, and the deviation between the computed 3D porosity from CT scanning and the 2D sliced porosity is less than 1%. The image analysis porosity is slightly lower than the measured value, a deviation within a reasonable range. (3) There is a robust positive correlation between the fractal dimension of the vegetated concrete structural surface and porosity. With increasing aggregate size, porosity gradually increases, pore network connectivity is significantly enhanced, and the fractal dimension increases correspondingly. (4) Function fitting analysis confirms that the correlation between the connected porosity and the compressive strength and permeability coefficient is more significant than that of the cross-sectional porosity. Specifically, compressive strength is significantly negatively correlated with equivalent pore size and fractal dimension, and the water permeability coefficient is strongly positively correlated with these two parameters. This study can provide important theoretical support and engineering reference for the optimization of the mix proportion and performance control of vegetated concrete.

Evaluation of bone changes in patients born premature using mandibular indices and fractal dimension analysis on dental panoramic radiographs.

This study investigates the performance and microstructure evolution of high-ferrite Portland cement (HFC) concrete under the coupled action of abrasion and freeze-thaw cycles (CAA-FTC). The 3D surface morphology of deteriorated concrete was studied; abrasion depth and volume loss evolution data were collected, while analyzing the abrasion depth fractal dimension. The characteristics of hydration products were determined using mercury intrusion porosimetry and 29Si nuclear magnetic resonance method. The ITZ's micromechanical properties and thickness were investigated via nanoindentation and SEM-EDS. The results show that under the CAA-FTC conditions, concrete deterioration is significantly exacerbated, leading to increased abrasion depth and volume loss compared to single-factor abrasion. A significant inverse relationship between the abrasion depth fractal dimension and abrasion resistance was revealed. Under CAA-FTC conditions, CG1 and CD1 exhibit increased total porosity with enlarged large pore proportions and reduced medium pores, whereas HFC1 outperforms HFC2-based concrete, showing 8.2-26.4% higher abrasion resistance and 6.5-12.0% greater nanoindentation elastic modulus in the ITZ. Regarding the deterioration factors' influence weight, abrasion time exhibits a deterioration weight 4.8 times to 10.0 times greater than freeze-thaw cycling, making the former a dominant factor and the latter a secondary contributor. Mechanistically, freeze-thaw cycles reduce the average molecular chain length of C-S-H gel, increase harmful pores and total porosity, and degrade the ITZ's microstructure, while abrasion causes surface-to-core physical damage and freeze-thaw cycling induces core-to-surface expansive damage. This interaction results in surface scaling, mortar spalling, and structural loosening, significantly reducing physical and mechanical properties of the concrete under study.

Background: Swept-source optical coherence tomography angiography (SS-OCTA) enables rapid assessment of retinal microvasculature. However, cross-platform comparability remains limited by device-specific acquisition and image quality characteristics. This study prospectively compared two novel SS-OCTA systems, DREAM (200 kHz) and BMizar (400 kHz). Methods: Fifty eyes from 25 healthy participants underwent 3 mm × 3 mm macular OCTA imaging with both devices in a single session. Images were analysed using OCTAVA to extract foveal avascular zone (FAZ) area, vessel area density (VAD), total vessel length (TVL), node counts, fractal dimension (FD), median vessel length (MVL) in SCP, and mean vessel diameter (MVD) in DCP. Image quality was assessed using FAZ-noise rate, contrast-to-noise ratio (CNR), and FAZ noise-floor standard deviation. Paired comparisons were performed using Wilcoxon signed-rank tests and Cliff's delta. Results: BMizar acquisition time was shorter than DREAM for the evaluated 3 × 3 mm protocol (median 5.36 s vs. 9.93 s), reflecting differences in A-scan rate and protocol implementation; acquisition time is therefore reported descriptively. In the SCP, DREAM yielded lower VAD (41.9% vs. 48.8%) and fewer nodes (1547 vs. 1879) but exhibited markedly less background noise (noise-floor SD 4.1 vs. 57.9) and substantially higher CNR (16.7 vs. 0.82). DREAM also showed longer MVL (45 vs. 39 µm) and higher FD (1.98 vs. 1.97; δ = 0.90). In the DCP, DREAM demonstrated smaller FAZ areas (0.27 vs. 0.42 mm2), thinner MVD (14 vs. 25 µm), higher node counts (3144 vs. 2301), longer TVL (223.6 vs. 206.2 mm), and higher FD (1.98 vs. 1.97), whereas VAD was higher on BMizar (32.96% for DREAM vs. 49.93% for BMizar). FAZ-noise rates were consistently higher for BMizar in both plexuses. Conclusions: Both devices provide reliable SS-OCTA imaging, but with distinct strengths. DREAM delivers higher vascular continuity and more reliable FAZ and DCP quantification, whereas BMizar achieves faster acquisition at the cost of noise, inflating SCP density and distorting FAZ-based metrics. Awareness of these characteristics is essential to ensure the valid use of OCTA biomarkers in clinical and research applications.

ABSTRACT This study systematically investigates the influence of basalt fiber (BF) content on the deformation patterns and failure mechanisms of Pisha sandstone cement‐soil (PSC) composites under multi‐level cyclic loading (MLCL). Dynamic triaxial tests and X‐ray computed tomography (CT) analysis were employed to evaluate the performance of BF‐PSC specimens. The results indicate that the dynamic shear modulus (DSM) initially increases and then decreases with increasing BF content, while it gradually enhances with rising confining pressure. The damping ratio increases progressively with BF content but decreases with higher confining pressure. Under cyclic loading, failure initiates from both ends toward the center and from the periphery to the interior, with damage progression accelerating exponentially upon crack formation. Based on CT scan results, a mathematical model describing the dynamic failure pattern of BF‐PSC was established using fractal dimension theory, achieving a high fitting degree exceeding 0.98. The optimal BF content was identified as 0.3%, which increased the maximum DSM by up to 37.7% at 60 kPa confining pressure.

Background/Objectives: Accurate diagnosis and staging of periodontitis rely on clinical measurements and radiographic assessment of alveolar bone loss. Methods: Studies published between 1 January 2020 and 31 October 2025 were searched in the Web of Science and PubMed databases in accordance with the PRISMA guidelines. Original research articles that evaluated periodontal pathology on radiographic images using fractal analysis and/or artificial intelligence approaches, with clearly defined methodologies, were included. Due to methodological heterogeneity, a quantitative meta-analysis was not performed, and the findings were summarized using a narrative synthesis approach. Results: Of 346 records, 80 studies (9 fractal, 71 AI) met the inclusion criteria. Fractal analysis studies predominantly calculated the fractal dimension on panoramic or periapical radiographs using the box-counting method. In artificial intelligence studies, the task types mainly comprised classification, segmentation, detection, and hybrid approaches (multi-stage models or models combining multiple tasks). Panoramic and intraoral radiographs were the predominant imaging modalities. Performance metrics were reported across wide ranges (sensitivity 0.23-1.00; accuracy 0.506-1.00; specificity 0.41-0.99; F1 score 0.15-0.99; AUC 0.75-0.99), and in some studies, these metrics were only partially reported. Conclusions: Fractal analysis and artificial intelligence approaches offer objective and reproducible assessment of periodontal bone loss; however, methodological and reporting heterogeneity limit comparability and generalizability. Standardization of ROI definitions, datasets, study designs, and performance reporting is needed to improve clinical applicability. Future research should also explore hybrid models that combine the quantitative microstructural insights of fractal analysis with the automated detection capabilities of artificial intelligence to enhance diagnostic precision.

The preparation of micro-textures on the surface of cutting tool substrates can significantly improve the cutting performance and service life of cutting tools, but different types of micro-textures have different anti-friction and wear-resistant effects. Therefore, in this paper, three types of micro-textures (round pit, V-shaped and groove-shaped) were prepared on the surface of cemented carbide samples and coated with AlCrSiTiN composite coating. A micro-performance testing platform for cemented carbide surfaces was constructed, and fractal dimension and digital image analysis techniques were used to characterise the phase composition, surface morphology, grain size and micro-hardness of cemented carbide surfaces under different preparation parameters. Based on the GRA-TOPSIS evaluation method, the micro-performance and morphology of round pit, V-shaped and groove-shaped cemented carbide surfaces were comprehensively evaluated. Research findings indicate that laser power significantly influences overall performance. The optimal preparation parameters for the three texture types are as follows: Circular pitted texture: p = 35 W, v = 1700 mm/s, n = 7 passes, γ = 17%; V-shaped texture: p = 35 W, v = 300 mm/s, n = 5 passes, γ = 9%; groove-shaped texture: p = 35 W, v = 700 mm/s, n = 7 passes, γ = 17%.

Abstract We develop a fractional-weighted functional-analytic framework for the analysis of chaotic dynamics in which the governing equations remain classical while the geometry of the underlying Hilbert space is modified. Specifically, we introduce a family of fractional scalar products with singular weights derived from the Riemann–Liouville kernel, generating weighted Hilbert spaces that emphasize late-time dynamics and long-term correlations. Within this framework, the fractional parameter $$\alpha $$ α plays a dual role by controlling temporal localization in the scalar product and acting as an effective probe of dynamical complexity. By embedding trajectories of the classical Lorenz system into these spaces, we show that the value $$\alpha _{\min }$$ α min minimizing the normalized fractional norm exhibits a clear nonlinear correlation with the Kaplan–Yorke dimension $$D_{KY}$$ D KY of the attractor, thereby establishing $$\alpha _{\min }$$ α min as a functional proxy for fractal complexity without modifying the underlying dynamics. To support analysis and computation, we construct orthogonal and complete basis systems adapted to the fractional geometry, including weighted Gram–Schmidt bases and Jacobi polynomial expansions, which enable efficient spectral approximation of chaotic signals and reveal intrinsic temporal asymmetries not captured by standard $$L^2$$ L 2 representations. The proposed approach provides new analytical and spectral tools for detecting bifurcations, quantifying chaotic complexity, and representing fractal structure, offering a complementary alternative to existing methods based on fractional-order dynamical models.

Skin nerve activity (SKNA), extracted from electrocardiograms, is a noninvasive surrogate of sympathetic nervous system (SNS) activity. We evaluated whether complexity-based metrics derived from integrated SKNA (iSKNA; 500-1000 Hz) and time-varying SKNA (TVSKNA; 160-1140 Hz) discriminate SNS activation in experimental (n = 23) and clinical dental datasets (n = 49). Experimental tasks included the Valsalva maneuver and thermal grill stimulation; clinical recordings involved cold testing, with exploratory subgroup analyses based on anxiety status. Pain intensity was assessed using a visual analog scale (VAS); clinically significant pain (CSP+) was defined as a VAS score ≥ 4. Approximate entropy, sample entropy, Hjorth mobility and complexity, Katz fractal dimension, and standard deviation were computed. In the experimental dataset, the Valsalva maneuver produced large-to-huge effects (Cohen's d = 1.93-3.46, p < 0.001). Thermal grill tasks showed moderate-to-large effects for adjacent pain levels (|d| = 0.63-0.71). ROC analysis showed strong discrimination for baseline vs. pain (AUC 0.80-0.99) but limited separation between adjacent pain levels (AUC 0.56-0.64). In the clinical dataset, discrimination was strongest for no pain vs. CSP+ (|d| = 0.86-1.17), with higher AUC in severe-anxiety participants (0.81-0.96) than non-severe (0.64-0.75). Complexity measures generally decreased during SNS activation, complementing amplitude-based changes. These findings support combined magnitude- and complexity-based descriptors for characterizing short-term sympathetic activation.

EEG-based biomarkers for psychosis: Comparative performance of support vector machines and deep neural networks.

Abstract Scaling laws in astrophysical systems that involve energy, geometry, and spatiotemporal evolution provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard fractal-diffusive self-organized criticality (FD-SOC) model, which is built on four fundamental assumptions: (i) the dimensionality d = 3, (ii) the fractal dimension D V = d − 1/2 = 2.5, (iii) classical diffusion L ∝ T (1/2) , and (iv) the proportionality of the dissipated energy to the fractal volume, E ∝ V . Based on these assumptions, the FD-SOC model predicts a scaling law of T ∝ E k ∝ E (4/5) = E 0.8 . On the observational side, we find only one case (out of the nine analyzed cases) that is consistent with the FD-SOC model, namely, the scaling law of T ∝ E 0.86±0.03 by A. Araujo &amp; A. Valio. The other eight cases have scaling law coefficients clustered around values of k ≈ 0.3−0.4, which possibly can be explained by nonstandard SOC models, i.e., k = 2/( βD V ), in terms of linear expansion β = 2 and/or Euclidean dimension D V = 3. The relatively low values of time duration ranges may also indicate possible truncation biases.

Abstract To address the challenges of capturing nonlinear degradation behavior and the lack of micro-macro mapping in the evaluation of electrical contact performance for silver-based electrical contact materials,,this study proposes a comprehensive assessment method integrating multidimensional parameters, state-aware weight allocation, and micro-morphology verification. Using an electrical contact performance testing system, multi-condition experiments were conducted on contacts made of different materials. Key parameters such as contact resistance, arc time, and welding force were collected in real time. Variant Multiscale Permutation Entropy was employed to identify performance inflection points, and a Dynamic Weighted Grey Relational Projection (DG-GRP) model was constructed to characterize degradation pathways. The concept of contact difference planes was introduced, integrating fractal dimension and fractal roughness features to analyze the nonlinear correlation between microstructure and performance degradation. Bayesian optimization (BO) is employed to achieve adaptive optimization of key control parameters in the failure penalty factor. Experimental results demonstrate the method's excellent adaptability and robustness across multiple failure modes. It achieves high consistency between microstructure and macro-performance, overcoming limitations of traditional linear evaluation. This establishes a scientifically sound multi-scale assessment system, providing theoretical support for contact material performance evaluation and service life prediction.

In this paper, we shall deal with the long-time dynamics of a nonlinear system of variable coefficient wave equation with a fractional damping, a time varying delay term and a memory term. Many researchers have extensively studied the attractor of wave equation with a memory term or a delay term. However, the study of the attractors of wave equation with both a memory term and a delay term is rarely involved. Hence, we shall discuss the existence of smooth global attractors with finite fractal dimension, the existence of exponential attractors and upper semicontinuity of global attractors for the wave equation with a fractional damping, a time varying delay term and a memory term. More importantly, we apply the fractional damping to overcome the traditional limitations on the coefficients between damping and delay terms.