Emergence of fractal geometries in the evolution of a metabolic enzyme.

Fractals are patterns that are self-similar across multiple length-scales1. Macroscopic fractals are common in nature2-4; however, so far, molecular assembly into fractals is restricted to synthetic systems5-12. Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpinski triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors, and the results suggest it may have emerged as a harmless evolutionary accident. Our findings expand the space of possible protein complexes and demonstrate that intricate and regulatable assemblies can evolve in a single substitution.

The effect of reef morphology on coral recruitment at multiple spatial scales.

Coral reefs are in decline worldwide, making it increasingly important to promote coral recruitment in new or degraded habitat. Coral reef morphology-the structural form of reef substrate-affects many aspects of reef function, yet the effect of reef morphology on coral recruitment is not well understood. We used structure-from-motion photogrammetry and airborne remote sensing to measure reef morphology (rugosity, curvature, slope, and fractal dimension) across a broad continuum of spatial scales and evaluated the effect of morphology on coral recruitment in three broadcast-spawning genera. We also measured the effect of other environmental and biotic factors such as fish density, adult coral cover, hydrodynamic larval import, and depth on coral recruitment. All variables combined explained 72% of coral recruitment in the study region. Coarse reef rugosity and curvature mapped at ≥2 m spatial resolution-such as large colonies, knolls, and boulders-were positively correlated with coral recruitment, explaining 22% of variation in recruitment. Morphology mapped at finer scales (≤32 cm resolution) was not significant. Hydrodynamic larval import was also positively related to coral recruitment in Porites and Montipora spp., and grazer fish density was linked to significantly lower recruitment in all genera. In addition, grazer density, reef morphology, and hydrodynamic import had differential effects on coral genera, reflecting genus-specific life history traits, and model performance was lower in gonochoric species. Overall, coral reef morphology is a key indicator of recruitment potential that can be detected by remote sensing, allowing potential larval sinks to be identified and factored into restoration actions.

Genetic and functional insights into the fractal structure of the heart.

The inner surfaces of the human heart are covered by a complex network of muscular strands that is thought to be a remnant of embryonic development1,2. The function of these trabeculae in adults and their genetic architecture are unknown. Here we performed a genome-wide association study to investigate image-derived phenotypes of trabeculae using the fractal analysis of trabecular morphology in 18,096 participants of the UK Biobank. We identified 16 significant loci that contain genes associated with haemodynamic phenotypes and regulation of cytoskeletal arborization3,4. Using biomechanical simulations and observational data from human participants, we demonstrate that trabecular morphology is an important determinant of cardiac performance. Through genetic association studies with cardiac disease phenotypes and Mendelian randomization, we find a causal relationship between trabecular morphology and risk of cardiovascular disease. These findings suggest a previously unknown role for myocardial trabeculae in the function of the adult heart, identify conserved pathways that regulate structural complexity and reveal the influence of the myocardial trabeculae on susceptibility to cardiovascular disease.

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%.

Analyzing fractal dimension in electroconvulsive therapy: Unraveling complexity in structural and functional neuroimaging.

BACKGROUND: Numerous studies show that electroconvulsive therapy (ECT) induces hippocampal neuroplasticity, but findings are inconsistent regarding its clinical relevance. This study aims to investigate ECT-induced plasticity of anterior and posterior hippocampi using mathematical complexity measures in neuroimaging, namely Higuchi's fractal dimension (HFD) for fMRI time series and the fractal dimension of cortical morphology (FD-CM). Furthermore, we explore the potential of these complexity measures to predict ECT treatment response. METHODS: Twenty patients with a current depressive episode (16 with major depressive disorder and 4 with bipolar disorder) underwent MRI-scans before and after an ECT-series. Twenty healthy controls matched for age and sex were also scanned twice for comparison purposes. Resting-state fMRI data were processed, and HFD was computed for anterior and posterior hippocampi. Group-by-time effects for HFD in anterior and posterior hippocampi were calculated and correlations between HFD changes and improvement in depression severity were examined. For FD-CM analyses, we preprocessed structural MRI with CAT12's surface-based methods. We explored group-by-time effects for FD-CM and the predictive value of baseline HFD and FD-CM for treatment outcome. RESULTS: Patients exhibited a significant increase in bilateral hippocampal HFD from baseline to follow-up scans. Right anterior hippocampal HFD increase was associated with reductions in depression severity. We found no group differences and group-by-time effects in FD-CM. After applying a whole-brain regression analysis, we found that baseline FD-CM in the left temporal pole predicted reduction of overall depression severity after ECT. Baseline hippocampal HFD did not predict treatment outcome. CONCLUSION: This study suggests that HFD and FD-CM are promising imaging markers to investigate ECT-induced neuroplasticity associated with treatment response.

In Silico Design of Heterogeneous Microvascular Trees Using Generative Adversarial Networks and Constrained Constructive Optimization.

OBJECTIVE: Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo. METHODS: We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension-oriented constrained constructive optimization (LFDO-CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO-CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. RESULTS: The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. CONCLUSIONS: These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology.

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.

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.

Neutron Scattering Analysis of Cryptococcus neoformans Polysaccharide Reveals Solution Rigidity and Repeating Fractal-like Structural Patterns.

Cryptococcus neoformans is a fungal pathogen that can cause life-threatening brain infections in immunocompromised individuals. Unlike other fungal pathogens, it possesses a protective polysaccharide capsule that is crucial for its virulence. During infections, Cryptococcus cells release copious amounts of extracellular polysaccharides (exo-PS) that interfere with host immune responses. Both exo-PS and capsular-PS play pivotal roles in Cryptococcus infections and serve as essential targets for disease diagnosis and vaccine development strategies. However, understanding their structure is complicated by their polydispersity, complexity, sensitivity to sample isolation and processing, and scarcity of methods capable of isolating and analyzing them while preserving their native structure. In this study, we employ small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) for the first time to investigate both fungal cell suspensions and extracellular polysaccharides in solution. Our data suggests that exo-PS in solution exhibits collapsed chain-like behavior and demonstrates mass fractal properties that indicate a relatively condensed pore structure in aqueous environments. This observation is also supported by scanning electron microscopy (SEM). The local structure of the polysaccharide is characterized as a rigid rod, with a length scale corresponding to 3-4 repeating units. This research not only unveils insights into exo-PS and capsular-PS structures but also demonstrates the potential of USANS for studying changes in cell dimensions and the promise of contrast variation in future neutron scattering studies.

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 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.

Fractal characteristics of the trabecular pattern of the mandible in patients with renal transplantation.

OBJECTIVE: In this study, we examined the mandibular trabecular bone structures by performing fractal dimension (FD) analysis in patients who underwent renal transplantation (RTx). METHODS: Our study is an observational study with 69 RTx patients and 35 control group patients. The mean FD values of the patient and control groups were calculated and compared. In addition, biochemical parathyroid hormone (PTH), serum calcium, phosphorus, alkaline phosphatase (ALP), and vitamin-D parameters and FD values of both groups were analyzed. RESULTS: FD values were significantly lower in the patient group than in the healthy group (p < .05). In the RTx group compared to the control group, ALP (90.71 ± 34.25-66.54 ± 16.8, respectively) (p < .001) and PTH (75.76 ± 38.01-38.17 ± 12.39, respectively) (p < .001) values were higher. There was a positive correlation between the FD values and ALP (rspearman  = .305, p = .011) and a negative correlation between FD values and vitamin-D (rspearman  = .287, p = .017) of patients with RTx. CONCLUSION: FD values were found to be lower in patients who underwent RTx compared to the control group. It should be considered that FD analysis can be a method that can be used to evaluate trabecular bone structure in patients undergoing RTx.

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.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series.

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with ρ - 1 / 4 . On the other hand, they tend to be monofractal, and their average scales with ρ - 1 / 2 for high fish densities. These two regimes overlap at critical density ρ c , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

The fractal brain: scale-invariance in structure and dynamics.

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

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.

Correlation between left atrial appendage morphology based on fractal dimension quantification and its hemodynamic parameters in patients with atrial fibrillation.

AIMS: To investigate the relationship between left atrial appendage (LAA) morphology, quantified based on fractal dimension (FD), and LAA hemodynamic parameters in patients with atrial fibrillation (AF), in an effort to reveal the effect of LAA shape on blood flow. MATERIALS AND METHODS: 225 patients with AF who underwent cardiac computed tomography angiography (CTA) and transesophageal echocardiography (TEE) were enrolled. LAA morphology was quantified based on FD on cardiac CTA images, and LAA hemodynamic parameters, including injection fraction (EF), filling peak flow velocity (FV), maximum speed of emptying (PEV), and wall motion velocity (WMV), were assessed using TEE. RESULTS: We divided the patients with AF into two groups based on a mean LAA FD of 1.32: the low FD group (n=124) and the high FD group (n=101). Compared to the low FD group, there were more patients with LAA circulatory stasis/thrombus (P=0.008) in the high FD group, as well as lower LAA FV (P=0.004), LAA PEV (P=0.007), and LAA WMV (P=0.007). LAA FD was an independent and significant determinant of LAA EF (ß = -11.755, P=0.001), LAA FV (ß = -17.364, P=0.004), LAA PEV (ß = -18.743, P<0.001), and LAA WMV (ß = -7.740, P=0.001) in multiple linear regression analysis. CONCLUSIONS: LAA FD is an essential determinant of LAA hemodynamic parameters, suggesting that the relatively complex morphology of the LAA may influence its hemodynamics, which can correlate with embolic events.

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.