Mitotic chromosomes are self-entangled and disentangle through a topoisomerase-II-dependent two-stage exit from mitosis.

The topological state of chromosomes determines their mechanical properties, dynamics, and function. Recent work indicated that interphase chromosomes are largely free of entanglements. Here, we use Hi-C, polymer simulations, and multi-contact 3C and find that, by contrast, mitotic chromosomes are self-entangled. We explore how a mitotic self-entangled state is converted into an unentangled interphase state during mitotic exit. Most mitotic entanglements are removed during anaphase/telophase, with remaining ones removed during early G1, in a topoisomerase-II-dependent process. Polymer models suggest a two-stage disentanglement pathway: first, decondensation of mitotic chromosomes with remaining condensin loops produces entropic forces that bias topoisomerase II activity toward decatenation. At the second stage, the loops are released, and the formation of new entanglements is prevented by lower topoisomerase II activity, allowing the establishment of unentangled and territorial G1 chromosomes. When mitotic entanglements are not removed in experiments and models, a normal interphase state cannot be acquired.

Multifractality in spin glasses.

We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Unique ice dendrite morphology on state-of-the-art oil-impregnated surfaces.

Due to its multifaceted impact in various applications, icing and ice dendrite growth has been the focus of numerous studies in the past. Dendrites on wetting (hydrophilic) and nonwetting (hydrophobic) surfaces are sharp, pointy, branching, and hairy. Here, we show a unique dendrite morphology on state-of-the-art micro/nanostructured oil-impregnated surfaces, which are commonly referred to as slippery liquid-infused porous surfaces or liquid-infused surfaces. Unlike the dendrites on traditional textured hydrophilic and hydrophobic surfaces, the dendrites on oil-impregnated surfaces are thick and lumpy without pattern. Our experiments show that the unique ice dendrite morphology on lubricant-infused surfaces is due to oil wicking into the porous dendritic network because of the capillary pressure imbalance between the surface texture and the dendrites. We characterized the shape complexity of the ice dendrites using fractal analysis. Experiments show that ice dendrites on textured oil-impregnated surfaces have lower fractal dimensions than those on traditional lotus leaf-inspired air-filled porous structures. Furthermore, we developed a regime map that can be used as a design guideline for micro/nanostructured oil-impregnated surfaces by capturing the complex effects of oil chemistry, oil viscosity, and wetting ridge volume on dendrite growth and morphology. The insights gained from this work inform strategies to reduce lubricant depletion, a major bottleneck for the transition of micro/nanostructured oil-impregnated surfaces from bench-top laboratory prototypes to industrial use. This work will assist the development of next-generation depletion-resistant lubricant-infused ice-repellent surfaces.

Aluminum Cayley trees as scalable, broadband, multiresonant optical antennas.

An optical antenna can convert a propagative optical radiation into a localized excitation and the reciprocal. Although optical antennas can be readily created using resonant nanoparticles (metallic or dielectric) as elementary building blocks, the realization of antennas sustaining multiple resonances over a broad range of frequencies remains a challenging task. Here, we use aluminum self-similar, fractal-like structures as broadband optical antennas. Using electron energy loss spectroscopy, we experimentally evidence that a single aluminum Cayley tree, a simple self-similar structure, sustains multiple plasmonic resonances. The spectral position of these resonances is scalable over a broad spectral range spanning two decades, from ultraviolet to midinfrared. Such multiresonant structures are highly desirable for applications ranging from nonlinear optics to light harvesting and photodetection, as well as surface-enhanced infrared absorption spectroscopy.

Hippocampal Theta and Episodic Memory.

Computational models of rodent physiology implicate hippocampal theta as a key modulator of learning and memory (Buzsáki and Moser, 2013; Lisman and Jensen, 2013), yet human hippocampal recordings have shown divergent theta correlates of memory formation. Herweg et al. (2020) suggest that decreases in memory-related broadband power mask narrowband theta increases. Their survey also notes that the theta oscillations appear most prominently in contrasts that isolate memory retrieval processes and when aggregating signals across large brain regions. We evaluate these hypotheses by analyzing human hippocampal recordings captured as 162 neurosurgical patients (n = 86 female) performed a free recall task. Using the Irregular-Resampling Auto-Spectral Analysis (IRASA) to separate broad and narrowband components of the field potential, we show that (1) broadband and narrowband components of theta exhibit opposite effects, with broadband signals decreasing and narrowband theta increasing during successful encoding; (2) whereas low-frequency theta oscillations increase before successful recall, higher-frequency theta and alpha oscillations decrease, masking the positive effect of theta when aggregating across the full band; and (3) the effects of theta on memory encoding and retrieval do not differ between reference schemes that accentuate local signals (bipolar) and those that aggregate signals globally (whole-brain average). In line with computational models that ascribe a fundamental role for hippocampal theta in memory, our large-scale study of human hippocampal recordings shows that 3-4 Hz theta oscillations reliably increase during successful memory encoding and before spontaneous recall of previously studied items.SIGNIFICANCE STATEMENT Analyzing recordings from 162 participants, we resolve a long-standing question regarding the role of hippocampal theta oscillations in the formation and retrieval of episodic memories. We show that broadband spectral changes confound estimates of narrowband theta activity, thereby accounting for inconsistent results in the literature. After accounting for broadband effects, we find that increased theta activity marks successful encoding and retrieval of episodic memories, supporting rodent models that ascribe a key role for hippocampal theta in memory function.

Fractal feature selection model for enhancing high-dimensional biological problems.

The integration of biology, computer science, and statistics has given rise to the interdisciplinary field of bioinformatics, which aims to decode biological intricacies. It produces extensive and diverse features, presenting an enormous challenge in classifying bioinformatic problems. Therefore, an intelligent bioinformatics classification system must select the most relevant features to enhance machine learning performance. This paper proposes a feature selection model based on the fractal concept to improve the performance of intelligent systems in classifying high-dimensional biological problems. The proposed fractal feature selection (FFS) model divides features into blocks, measures the similarity between blocks using root mean square error (RMSE), and determines the importance of features based on low RMSE. The proposed FFS is tested and evaluated over ten high-dimensional bioinformatics datasets. The experiment results showed that the model significantly improved machine learning accuracy. The average accuracy rate was 79% with full features in machine learning algorithms, while FFS delivered promising results with an accuracy rate of 94%.

Improving morphological and functional properties of enteric neuronal networks in vitro using a novel upside-down culture approach.

The enteric nervous system (ENS) comprises millions of neurons and glia embedded in the wall of the gastrointestinal tract. It not only controls important functions of the gut but also interacts with the immune system, gut microbiota, and the gut-brain axis, thereby playing a key role in the health and disease of the whole organism. Any disturbance of this intricate system is mirrored in an alteration of electrical functionality, making electrophysiological methods important tools for investigating ENS-related disorders. Microelectrode arrays (MEAs) provide an appropriate noninvasive approach to recording signals from multiple neurons or whole networks simultaneously. However, studying isolated cells of the ENS can be challenging, considering the limited time that these cells can be kept vital in vitro. Therefore, we developed an alternative approach cultivating cells on glass samples with spacers (fabricated by photolithography methods). The spacers allow the cells to grow upside down in a spatially confined environment while enabling acute consecutive recordings of multiple ENS cultures on the same MEA. Upside-down culture also shows beneficial effects on the growth and behavior of enteric neural cultures. The number of dead cells was significantly decreased, and neural networks showed a higher resemblance to the myenteric plexus ex vivo while producing more stable signals than cultures grown in the conventional way. Overall, our results indicate that the upside-down approach not only allows to investigate the impact of neurological diseases in vitro but could also offer insights into the growth and development of the ENS under conditions much closer to the in vivo environment.NEW & NOTEWORTHY In this study, we devised a novel approach for culturing and electrophysiological recording of the enteric nervous system using custom-made glass substrates with spacers. This allows to turn cultures of isolated myenteric plexus upside down, enhancing the use of the microelectrode array technique by allowing recording of multiple cultures consecutively using only one chip. In addition, upside-down culture led to significant improvements in the culture conditions, resulting in a more in vivo-like growth.

Network medicine in ovarian cancer: topological properties to drug discovery.

Network medicine provides network theoretical tools, methods and properties to study underlying laws governing human interactome to identify disease states and disease complexity leading to drug discovery. Within this framework, we investigated the topological properties of ovarian cancer network (OCN) and the roles of hubs to understand OCN organization to address disease states and complexity. The OCN constructed from the experimentally verified genes exhibits fractal nature in the topological properties with deeply rooted functional communities indicating self-organizing behavior. The network properties at all levels of organization obey one parameter scaling law which lacks centrality lethality rule. We showed that $\langle k\rangle $ can be taken as a scaling parameter, where, power law exponent can be estimated from the ratio of network diameters. The betweenness centrality $C_B$ shows two distinct behaviors one shown by high degree hubs and the other by segregated low degree nodes. The $C_B$ power law exponent is found to connect the exponents of distributions of high and low degree nodes. OCN showed the absence of rich-club formation which leads to the missing of a number of attractors in the network causing formation of weakly tied diverse functional modules to keep optimal network efficiency. In OCN, provincial and connector hubs, which includes identified key regulators, take major responsibility to keep the OCN integrity and organization. Further, most of the key regulators are found to be over expressed and positively correlated with immune infiltrates. Finally, few potential drugs are identified related to the key regulators.

Local fractal dimension of collagen detects increased spatial complexity in fibrosis.

Increase of collagen content and reorganization characterizes fibrosis but quantifying the latter remains challenging. Spatially complex structures are often analyzed via the fractal dimension; however, established methods for calculating this quantity either provide a single dimension for an entire object or a spatially distributed dimension that only considers binary images. These neglect valuable information related to collagen density in images of fibrotic tissue. We sought to develop a fractal analysis that can be applied to 3-dimensional (3D) images of fibrotic tissue. A fractal dimension map for each image was calculated by determining a single fractal dimension for a small area surrounding each image pixel, using fiber thickness as the third dimension. We found that this local fractal dimension increased with age and with progression of fibrosis regardless of collagen content. Our new method of distributed 3D fractal analysis can thus distinguish between changes in collagen content and organization induced by fibrosis.

Brain Dynamics Complexity as a Signature of Cognitive Decline in Parkinson's Disease.

BACKGROUND: Higuchi's fractal dimension (FD) captures brain dynamics complexity and may be a promising method to analyze resting-state functional magnetic resonance imaging (fMRI) data and detect the neuronal interaction complexity underlying Parkinson's disease (PD) cognitive decline. OBJECTIVES: The aim was to compare FD with a more established index of spontaneous neural activity, the fractional amplitude of low-frequency fluctuations (fALFF), and identify through machine learning (ML) models which method could best distinguish across PD-cognitive states, ranging from normal cognition (PD-NC), mild cognitive impairment (PD-MCI) to dementia (PDD). Finally, the aim was to explore correlations between fALFF and FD with clinical and cognitive PD features. METHODS: Among 118 PD patients age-, sex-, and education matched with 35 healthy controls, 52 were classified with PD-NC, 46 with PD-MCI, and 20 with PDD based on an extensive cognitive and clinical evaluation. fALFF and FD metrics were computed on rs-fMRI data and used to train ML models. RESULTS: FD outperformed fALFF metrics in differentiating between PD-cognitive states, reaching an overall accuracy of 78% (vs. 62%). PD showed increased neuronal dynamics complexity within the sensorimotor network, central executive network (CEN), and default mode network (DMN), paralleled by a reduction in spontaneous neuronal activity within the CEN and DMN, whose increased complexity was strongly linked to the presence of dementia. Further, we found that some DMN critical hubs correlated with worse cognitive performance and disease severity. CONCLUSIONS: Our study indicates that PD-cognitive decline is characterized by an altered spontaneous neuronal activity and increased temporal complexity, involving the CEN and DMN, possibly reflecting an increased segregation of these networks. Therefore, we propose FD as a prognostic biomarker of PD-cognitive decline. © 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

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

BACKGROUND: 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. PURPOSE: To investigate the prognostic value of right ventricular trabecular complexity in ACM patients using 3D FD analysis based on cardiac MR cine images. STUDY TYPE: Retrospective. POPULATION: 85 ACM patients (mean age: 45 ± 17 years, 52 male). FIELD STRENGTH/SEQUENCE: 3.0T/cine imaging, T2-short tau inversion recovery (T2-STIR), and late gadolinium enhancement (LGE). ASSESSMENT: 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). STATISTICAL TESTS: 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. RESULTS: 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. DATA CONCLUSION: The myocardial trabecular complexity assessed through 3D FD analysis was found associated with MACE and provided incremental prognostic value beyond conventional ACM risk factors. EVIDENCE LEVEL: 4 TECHNICAL EFFICACY: Stage 1.

Fractal Analysis of Left Ventricular Trabeculae in Patients with End-Stage Renal Disease: A Random Survival Tree Analysis.

BACKGROUND: The complexity of left ventricular (LV) trabeculae is related to the prognosis of several cardiovascular diseases. PURPOSE: To evaluate the prognostic value of LV trabecular complexity in patients with end-stage renal disease (ESRD). STUDY TYPE: Prospective outcome study. POPULATION: 207 participants on maintenance dialysis, divided into development (160 patients from 2 centers) and external validation (47 patients from a third center) cohorts, and 72 healthy controls. FIELD STRENGTH: 3.0T, steady-state free precession (SSFP) and modified Look-Locker imaging sequences. ASSESSMENT: All participants had their trabecular complexity quantified by fractal analysis using cine SSFP images. Patients were followed up every 2 weeks until April 2023, or endpoint events happened. Random Forest (RF) and Cox regression models including age, diabetes, LV mass index, mean basal fractal dimension (FD), and left atrial volume index, were developed to predict major adverse cardiac events (MACE). Patients were divided into low- and high-risk groups based on scores derived from the RF model and survival compared. STATISTICAL TESTS: Receiver operating characteristic curve analysis; Kaplan-Meier survival analysis with log rank tests; Harrel's C-index to assess model performance. A P value <0.05 was considered statistically significant. RESULTS: Fifty-five patients (26.57%) experienced MACE during a median follow-up time of 21.83 months. An increased mean basal FD (≥1.324) was associated with a significantly higher risk of MACE. The RF model (C-index: 0.81) had significantly better discrimination than the Cox regression model (C-index: 0.74). Participants of the external validation dataset classified into the high-risk group had a hazard of experiencing MACE increased by 12.29 times compared to those in the low-risk group. DATA CONCLUSION: LV basal FD was an independent predictor for MACE in patients with ESRD. Reliable risk stratification models could be generated based on LV basal FD and other MRI variables using RF analysis. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY: Stage 2.

Prognostic value of right ventricular trabecular complexity in patients with arrhythmogenic cardiomyopathy.

OBJECTIVES: The present study aimed to investigate the incremental prognostic value of the right ventricular fractal dimension (FD), a novel marker of myocardial trabecular complexity by cardiac magnetic resonance (CMR) in patients with arrhythmogenic cardiomyopathy (ACM). METHODS: Consecutive patients with ACM undergoing CMR were followed up for major cardiac events, including sudden cardiac death, aborted cardiac arrest, and appropriate implantable cardioverter defibrillator intervention. Prognosis prediction was compared by Cox regression analysis. We established a multivariable model supplemented with RV FD and evaluated its discrimination by Harrell's C-statistic. We compared the category-free, continuous net reclassification improvement (cNRI) and integrated discrimination index (IDI) before and after the addition of FD. RESULTS: A total of 105 patients were prospectively included from three centers and followed up for a median of 60 (48, 66) months; experienced 36 major cardiac events were recorded. Trabecular FD displayed a strong unadjusted association with major cardiac events (p < 0.05). In the multivariable Cox regression analysis, RV maximal apical FD maintained an independent association with major cardiac events (hazard ratio, 1.31 (1.11-1.55), p < 0.002). The Hosmer-Lemeshow goodness of fit test displayed good fit (X2 = 0.68, p = 0.99). Diagnostic performance was significantly improved after the addition of RV maximal apical FD to the multivariable baseline model, and the continuous net reclassification improvement increased 21% (p = 0.001), and the integrated discrimination index improved 16% (p = 0.045). CONCLUSIONS: In patients with ACM, CMR-assessed myocardial trabecular complexity was independently correlated with adverse cardiovascular events and provided incremental prognostic value. CLINICAL RELEVANCE STATEMENT: The application of FD values for assessing RV myocardial trabeculae may become an accessible and promising parameter in monitoring and early diagnosis of risk factors for adverse cardiovascular events in patients with ACM. KEY POINTS: • Ventricular trabecular morphology, a novel quantitative marker by CMR, has been explored for the first time to determine the severity of ACM. • Patients with higher maximal apical fractal dimension of RV displayed significantly higher cumulative incidence of major cardiac events. • RV maximal apical FD was independently associated with major cardiac events and provided incremental prognostic value in patients with ACM.

Non-invasive differential diagnosis of teratomas from other intracranial germ cell tumours using MRI-based fractal and radiomic analyses.

OBJECTIVES: The histologic subtype of intracranial germ cell tumours (IGCTs) is an important factor in deciding the treatment strategy, especially for teratomas. In this study, we aimed to non-invasively diagnose teratomas based on fractal and radiomic features. MATERIALS AND METHODS: This retrospective study included 330 IGCT patients, including a discovery set (n = 296) and an independent validation set (n = 34). Fractal and radiomic features were extracted from T1-weighted, T2-weighted, and post-contrast T1-weighted images. Five classifiers, including logistic regression, random forests, support vector machines, K-nearest neighbours, and XGBoost, were compared for our task. Based on the optimal classifier, we compared the performance of clinical, fractal, and radiomic models and the model combining these features in predicting teratomas. RESULTS: Among the diagnostic models, the fractal and radiomic models performed better than the clinical model. The final model that combined all the features showed the best performance, with an area under the curve, precision, sensitivity, and specificity of 0.946 [95% confidence interval (CI): 0.882-0.994], 95.65% (95% CI: 88.64-100%), 88.00% (95% CI: 77.78-96.36%), and 91.67% (95% CI: 78.26-100%), respectively, in the test set of the discovery set, and 0.944 (95% CI: 0.855-1.000), 85.71% (95% CI: 68.18-100%), 94.74% (95% CI: 83.33-100%), and 80.00% (95% CI: 58.33-100%), respectively, in the independent validation set. SHapley Additive exPlanations indicated that two fractal features, two radiomic features, and age were the top five features highly associated with the presence of teratomas. CONCLUSION: The predictive model including image and clinical features could help guide treatment strategies for IGCTs. CLINICAL RELEVANCE STATEMENT: Our machine learning model including image and clinical features can non-invasively predict teratoma components, which could help guide treatment strategies for intracranial germ cell tumours (IGCT). KEY POINTS: • Fractals and radiomics can quantitatively evaluate imaging characteristics of intracranial germ cell tumours. • Model combing imaging and clinical features had the best predictive performance. • The diagnostic model could guide treatment strategies for intracranial germ cell tumours.

Prognostic value of left ventricular trabeculae fractal analysis in patients with dilated cardiomyopathy.

BACKGROUND: The prognostic value of left ventricular (LV) myocardial trabecular complexity on cardiovascular magnetic resonance (CMR) in dilated cardiomyopathy (DCM) remains unknown. This study aimed to evaluate the prognostic value of LV myocardial trabecular complexity using fractal analysis in patients with DCM. METHODS: Consecutive patients with DCM who underwent CMR between March 2017 and November 2021 at two hospitals were prospectively enrolled. The primary endpoints were defined as the combination of all-cause death and heart failure hospitalization. The events of cardiac death alone were defined as the secondary endpoints.LV trabeculae complexity was quantified by measuring the fractal dimension (FD) of the endocardial border based on fractal geometry on CMR. Cox proportional hazards regression and Kaplan-Meier survival analysis were used to examine the association between variables and outcomes. The incremental prognostic value of FD was assessed in nested models. RESULTS: A total of 403 patients with DCM (49.31 ± 14.68 years, 69% male) were recruited. After a median follow-up of 43 months (interquartile range, 28-55 months), 87 and 24 patients reached the primary and secondary endpoints, respectively. Age, heart rate, New York Heart Association functional class >II, N-terminal pro-B-type natriuretic peptide, LV ejection fraction, LV end-diastolic volume index, LV end-systolic volume index, LV mass index, presence of late gadolinium enhancement, global FD, LV mean apical FD, and LV maximal apical FD were univariably associated with the outcomes (all P < 0.05). After multivariate adjustment, LV maximal apical FD remained a significant independent predictor of outcome [hazard ratio = 1.179 (1.116, 1.246), P < 0.001]. The addition of LV maximal apical FD in the nested models added incremental prognostic value to other common clinical and imaging risk factors (all <0.001; C-statistic: 0.84-0.88, P < 0.001). CONCLUSION: LV maximal apical FD was an independent predictor of the adverse clinical outcomes in patients with DCM and provided incremental prognostic value over conventional clinical and imaging risk factors.

Local neurodynamics as a signature of cortical areas: new insights from sleep.

Sleep crucial for the animal survival is accompanied by huge changes in neuronal electrical activity over time, the neurodynamics. Here, drawing on intracranial stereo-electroencephalographic (sEEG) recordings from the Montreal Neurological Institute (MNI), we analyzed local neurodynamics in the waking state at rest and during the N2, N3, and rapid eye movement (REM) sleep phases. Higuchi fractal dimension (HFD)-a measure of signal complexity-was studied as a feature of the local neurodynamics of the primary motor (M1), somatosensory (S1), and auditory (A1) cortices. The key working hypothesis, that the relationships between local neurodynamics preserve in all sleep phases despite the neurodynamics complexity reduces in sleep compared with wakefulness, was supported by the results. In fact, while HFD awake > REM > N2 > N3 (P < 0.001 consistently), HFD in M1 > S1 > A1 in awake and all sleep stages (P < 0.05 consistently). Also power spectral density was studied for consistency with previous investigations. Meaningfully, we found a local specificity of neurodynamics, well quantified by the fractal dimension, expressed in wakefulness and during sleep. We reinforce the idea that neurodynamic may become a new criterion for cortical parcellation, prospectively improving the understanding and ability of compensatory interventions for behavioral disorders.

Using fractal dimension analysis to assess the effects of normal aging and sex on subregional cortex alterations across the lifespan from a Chinese dataset.

Fractal dimension (FD) is used to quantify brain structural complexity and is more sensitive to morphological variability than other cortical measures. However, the effects of normal aging and sex on FD are not fully understood. In this study, age- and sex-related differences in FD were investigated in a sample of 448 adults age of 19-80 years from a Chinese dataset. The FD was estimated with the surface-based morphometry (SBM) approach, sex differences were analyzed on a vertex level, and correlations between FD and age were examined. Generalized additive models (GAMs) were used to characterize the trajectories of age-related changes in 68 regions based on the Desikan-Killiany atlas. The SBM results showed sex differences in the entire sample and 3 subgroups defined by age. GAM results demonstrated that the FD values of 51 regions were significantly correlated with age. The trajectories of changes can be classified into 4 main patterns. Our results indicate that sex differences in FD are evident across developmental stages. Age-related trajectories in FD are not homogeneous across the cerebral cortex. Our results extend previous findings and provide a foundation for future investigation of the underlying mechanism.

Adsorption of Cd(II) ions on magnetic graphene oxide/cellulose modified with ß-cyclodextrin: Analytical interpretation via statistical physics modeling and fractal like kinetic approach.

In the present study, ß-cyclodextrin modified magnetic graphene oxide/cellulose (CN/IGO/Cel) was fabricated for removal of Cd(II) ions. The material was characterized through various analytical techniques like FTIR, XRD, TGA/DTA, SEM, TEM, and XPS. The point of zero charge of the material was obtained as 5.38. The controllable factors were optimized by Taguchi design and optimum values were: adsorbent dose-16 mg, equilibrium time-40 min, and initial concentration of Cd(II) ions-40 mg/L. The material shows high adsorption capacity (303.98 mg/g). The good fitting of Langmuir model to adsorption data (R2 = 0.9918-0.9936) revealed the monolayer coverage on adsorbent surface. Statistical physics model M 2 showed best fitting to adsorption data (R2 > 0.997), suggesting the binding of Cd(II) ions occurred on two different receptor sites (n). Stereographically n > 1 confirming vertical multi-molecular mechanisms of Cd(II) ions adsorption on CN/IGO/Cel surface. The adsorption energies (E1 = 23.71-28.95 kJ/mol; E2 = 22.69-29.38 kJ/mol) concluded the involvement of physical forces for Cd(II) ions adsorption. Kinetic data fitted well to fractal-like pseudo first-order model (R2 > 0.9952), concluding the adsorption of Cd(II) ions occurred on energetically heterogeneous surface. The kinetic analysis shows that both the film-diffusion and pore-diffusion were responsible for Cd(II) ions uptake. XPS analysis was utilized to explain the adsorption mechanism of Cd(II) ions onto CN/IGO/Cel.

Evaluation of Bone Mineral Changes in Panoramic Radiographs of Hypothyroid and Hyperthyroid Patients Using Fractal Dimension Analysis.

Objective Hyperthyroidism and hypothyroidism are endocrinopathies that cause a decrease in bone mineral density. The aim of this study is to investigate possible bone changes in the mandible caused by hyperthyroidism and hypothyroidism using fractal analysis (FA) on panoramic radiographs. Material and Methods Panoramic radiographs of a total of 180 patients, including 120 patient groups (60 hyperthyroid, 60 hypothyroid) and 60 healthy control groups, were used. Five regions of interests (ROI) were determined from panoramic radiographs and FA was performed. ROI1: geometric midpoint of mandibular notch and mandibular foramen, ROI2: geometric midpoint of mandibular angle, ROI3: anterior of mental foramen, ROI4: basal cortical area from distal mental foramen to distal root of first molar, ROI5: geometric center of mandibular foramen and mandibular ramus. Results While a significant difference was observed between the patient and control groups regarding ROI1 and ROI2 (p < 0.05); there was no significant difference between the groups in relation to ROI3, ROI4, and ROI5. All FA values were lower in the hyperthyroid group than in the hypothyroid group. Conclusion Fractal analysis proves to be an effective method for early detection of bone mass changes. In the present study, it was concluded that while the mandibular cortical bone was intact, trabecular rich regions were affected by osteoporosis caused by thyroid hormones. Necessary precautions should be taken against the risk of osteoporosis in patients with thyroid hormone disorders.

Optical coherence tomography angiography macular biomarkers of peripheral retinal ischemia in diabetic macular edema: secondary endpoints from the clinical study "FOVEA".

PURPOSE: To investigate the relationship between the macular values of fractal dimension (FD) and lacunarity (LAC) on optical coherence tomography angiography (OCTA) images and the presence of peripheral retina non-perfusion areas (NPAs) on fluorescein angiography (FA) in patients with treatment-naïve diabetic macular edema (DME). METHODS: Fifty patients with treatment-naïve DME underwent a full ophthalmic examination, including best-corrected visual acuity measurement, FA, spectral-domain optical coherence tomography, and OCTA. Specifically, FA was performed to detect the presence of retinal NPAs, whereas fractal OCTA analysis was used to determine macular FD and LAC values at the level of the superficial and deep capillary plexus (SCP and DCP). FA montage frames of the posterior pole and peripheral retina, as well as macular OCTA slabs of the SCP and DCP, were obtained. RESULTS: Thirty (60%) eyes with FA evidence of peripheral retinal NPAs in at least one quadrant showed significantly lower FD and higher LAC in both SCP and DCP, when compared with eyes presenting a well-perfused peripheral retina. Furthermore, macular FD and LAC values were found to be significantly associated with the extent of retinal NPAs. CONCLUSIONS: Macular FD and LAC of both SCP and DCP seem to be strongly associated with the extent of peripheral retinal NPAs, thus suggesting that may be useful predictive biomarkers of peripheral ischemia in treatment-naïve DME eyes.