Active fractal networks with stochastic force monopoles and force dipoles: Application to subdiffusion of chromosomal loci.

Motivated by the well-known fractal packing of chromatin, we study the Rouse-type dynamics of elastic fractal networks with embedded, stochastically driven, active force monopoles and force dipoles that are temporally correlated. We compute, analytically-using a general theoretical framework-and via Langevin dynamics simulations, the mean square displacement (MSD) of a network bead. Following a short-time superdiffusive behavior, force monopoles yield anomalous subdiffusion with an exponent identical to that of the thermal system. In contrast, force dipoles do not induce subdiffusion, and the early superdiffusive MSD crosses over to a relatively small, system-size-independent saturation value. In addition, we find that force dipoles may lead to "crawling" rotational motion of the whole network, reminiscent of that found for triangular micro-swimmers and consistent with general theories of the rotation of deformable bodies. Moreover, force dipoles lead to network collapse beyond a critical force strength, which persists with increasing system size, signifying a true first-order dynamical phase transition. We apply our results to the motion of chromosomal loci in bacteria and yeast cells' chromatin, where anomalous sub-diffusion, MSD∼tν with ν≃0.4, was found in both normal and cells depleted of adenosine triphosphate (ATP), albeit with different apparent diffusion coefficients. We show that the combination of thermal, monopolar, and dipolar forces in chromatin is typically dominated by the active monopolar and thermal forces, explaining the observed normal cells vs the ATP-depleted cells behavior.

Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study.

AIMS: This cross-sectional retrospective study was conducted to assess the differences in the microarchitecture of the trabecular bone of the posterior mandibular region at dentulous and edentulous sites with the help of fractal dimension (FD) and lacunarity using cone-beam computed tomography (CBCT). MATERIALS AND METHODS: Ninety CBCT scans were analyzed for the purpose of the present study. Inclusion criteria included subjects with unilaterally missing mandibular molars or premolars and an with intact contralateral opposing tooth. The coronal view of the dentulous and edentulous sites was used, and the region of interest (ROI) was selected 2.6 mm below the apex of the tooth present. These images were then transferred to ImageJ Software, and fractal analysis was done using the box-counting method of the FracLac plug-in. A paired samples t-test was performed to compare the means of FD and lacunarity, and a Kendall correlation was performed to check correlations. A p-value less than 0.05 was considered to indicate statistical significance. RESULTS: Statistical analysis revealed that the mean FD of the edentulous side was significantly greater than that of the dentulous side (p-value = 0.011). Additionally, the mean lacunarity of the edentulous side was marginally significantly greater than that of the dentulous side (p-value = 0.089). A significant negative correlation was detected between the FD and lacunarity of the edentulous region (p-value = 0.017), and a marginally significant negative correlation was detected between edentulous lacunarity and dentulous lacunarity (p-value = 0.081). CONCLUSION: The differences in occlusal forces exerted in dentulous and edentulous regions can lead to a change in the trabecular pattern of the bone in these regions. This change in the microarchitecture of bones can be detected by FD and lacunarity, which can further help us assess changes pre- and post-implant. CLINICAL SIGNIFICANCE: The advanced technology, the assessment of microarchitecture of the bone has been made easy, using FD and lacunarity, as done in the present study. This analysis can further aid us in both pre- and post-implant analysis to prevent failure of the implant. How to cite this article: Bhoraskar M, Denny C, Srikant N, et al. Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study. J Contemp Dent Pract 2024;25(6):581-587.

Nanoscale pore structure and fractal characteristics of lacustrine shale: A case study of the Upper Cretaceous Qingshankou shales, Southern Songliao Basin, China.

The Upper Cretaceous Qingshankou Formation's lacustrine shales in the Songliao Basin are among China's most promising shale oil reservoirs. To elucidate their pore and fractal characteristics, a comprehensive set of analyses encompassing total organic carbon (TOC), X-ray diffraction (XRD), and low-temperature N2 adsorption (LTNA), Rock-Eval pyrolysis experiments and two-dimensional nuclear magnetic resonance (2D-NMR) were conducted. Using the Frenkel-Halsey-Hill (FHH) method, fractal dimensions (D) were calculated, and their relationship with pore metrics and shale compositions were explored. Two distinct fractal dimensions, D1 (0 < P/P0 < 0.5) and D2 (0.5

Mpox outbreak: Time series analysis with multifractal and deep learning network.

This article presents an overview of an mpox epidemiological situation in the most affected regions-Africa, Americas, and Europe-tailoring fractal interpolation for pre-processing the mpox cases. This keen analysis has highlighted the irregular and fractal patterns in the trend of mpox transmission. During the current scenario of public health emergency of international concern due to an mpox outbreak, an additional significance of this article is the interpretation of mpox spread in light of multifractality. The self-similar measure, namely, the multifractal measure, is utilized to explore the heterogeneity in the mpox cases. Moreover, a bidirectional long-short term memory neural network has been employed to forecast the future mpox spread to alert the outbreak as it seems to be a silent symptom for global epidemic.

An optimal fast fractal method for breast masses diagnosis using machine learning.

This article introduces a fast fractal method for classifying breast cancerous lesions in mammography. While fractal methods are valuable for extracting information, they often come with a high computational load and time consumption. This paper demonstrates that extracting optimal fractal information and focusing only on valuable information for classification not only improves computation speed and reduces process load but also enhances classification accuracy. To achieve this, we define an objective function based on accurate classification of benign and malignant masses to identify the best scale. Instead of extracting information from all nine scales, we extract and employ information solely from the best scale for classification. We validate the obtained scales using three classifiers: Support Vector Machine (SVM), Genetic Algorithm (GA), and Deep Learning (DL), which confirm the effectiveness of the proposed method. Comparative analysis with other studies reveals improved classification performance with the presented method.

The relationship between radiomorphometric indices and fractal dimension analysis: a cone-beam computed tomography study.

The purpose of this study is to evaluate the relationship between radiomorphometric indices and fractal dimension (FD) analysis in jawbone radiographic density using Cone-Beam Computed Tomography (CBCT). The study included 87 CBCT datasets from dental patients aged 50-79. Four radiomorphometric indices (Computed Tomography Cortical Index (CTCI), Computed Tomography Mental Index (CTMI), Computed Tomography Index-Superior (CTI-S), and Computed Tomography Index-Inferior (CTI-I)) along with age, gender, remaining teeth, and mandibular bone height were evaluated. FD was assessed in trabecular bone near the mental foramen (ROI 1) and on the mandibular cortical bone (ROI 2). Relationships between indices and variables were analyzed using Pearson chi-square, Fisher's exact, one-way ANOVA, Kruskal-Wallis, and Spearman's rho tests. ANOVA showed significant differences in mandibular bone height (p = .004) and FD at ROI 2 (p = .000) across three mandibular cortex types (C1, C2, C3). Spearman's rho indicated significant correlations between FD at ROI 2 and CTMI, CTI-S, CTI-I (p = .000), and between mandibular bone height and CTMI (p = .010). The correlations of FD at ROI 2 ranged from strongest to weakest with CTCI, CTMI, CTI-S, and CTI-I. High-risk osteoporosis radiomorphometric indices are associated with FD analysis of cortical bone.

Analysis of bone quality formation in sinus lifts with immediate implants.

Sinus lift surgeries are part of the daily practice of dentists. This study evaluates the long-term structure of the bone placed in sinus lifts through the fractal dimension. We conducted a retrospective study on a sample of 35 patients with 51 sinus lifts performed using a lateral window approach and filling material placement. We radiologically analyzed the graft bone to observe its evolution up to one and a half years after the surgical procedure. The obtained results were the average area of the sinuses analyzed was 1401.96 mm2, with a mean area occupied by the filling material of 297.75 mm2. Significant differences are observed when comparing the fractal dimension values obtained on the initial day and one year after prosthesis loading. Similarly, when comparing the values of the area occupied by the biomaterial at the start day and one year after prosthesis loading, significant differences are also obtained (p-value < 0.001). In conclusion, the filling material used in the lateral window sinus lift procedure undergoes significant resorption and shows changes in the fractal dimension.

For a Theory of the Psychotherapeutic Process: Epistemology of Recursion and Relational Fractality.

Psychotherapy is a relational process that emerges from the meeting of two people. There is an ontological difference between the individual psychopathology of the patient and relational therapy; the present work aims to overcome the patient-centric conception of psychotherapy, restoring the dyadic nature of the therapy through the interpretation of the psychological interview as a fractal process. Recursion, namely the application of the same logical operator to the result of the operation itself, is presented here as the basic procedural element of psychotherapy. The paper is divided into two parts: The first has epistemological nature and focuses on complexity theory and cybernetics: Edgar Morin and recursion as a process of existence, Heinz von Foerster and epistemology as second-order praxis. From the thought of Gregory Bateson, it is here postulated the self-similarity of the content and structure of the mind, to the point of conceptualizing the dyadic relationship as a Mind of a different logical type compared to the individual mind. The second part of the present work introduces two intellectual tools designed to conceptualize psychotherapy as a fractal process: the psychopathological hologram, useful for clinical work although of a non-clinical nature, that consists in a fraction of the patient's experiential flow, while the psychotherapeutic string is presented here as the basic recursive element of psychotherapeutic process.

Morphological changes of cerebral gray matter in spinocerebellar ataxia type 3 using fractal dimension analysis.

Spinocerebellar ataxia type 3 (SCA3), or Machado-Joseph disease, presents as a cerebellar cognitive affective syndrome (CCAS) and represents the predominant SCA genotype in Taiwan. Beyond cerebellar involvement, SCA3 patients exhibit cerebral atrophy. While prior neurodegenerative disease studies relied on voxel-based morphometry (VBM) for brain atrophy assessment, its qualitative nature limits individual and region-specific evaluations. To address this, we employed fractal dimension (FD) analysis to quantify cortical complexity changes in SCA3 patients. We examined 50 SCA3 patients and 50 age- and sex-matched healthy controls (HC), dividing MRI cerebral gray matter (GM) into 68 auto-anatomical subregions. Using three-dimensional FD analysis, we identified GM atrophy manifestations in SCA3 patients. Results revealed lateral atrophy symptoms in the left frontal, parietal, and occipital lobes, and fewer symptoms in the right hemisphere's parietal and occipital lobes. Focal areas of atrophy included regions previously identified in SCA3 studies, alongside additional regions with decreased FD values. Bilateral postcentral gyrus and inferior parietal gyrus exhibited pronounced atrophy, correlating with Scale for the Assessment and Rating of Ataxia (SARA) scores and disease duration. Notably, the most notable focal areas were the bilateral postcentral gyrus and the left superior temporal gyrus, serving as imaging biomarkers for SCA3. Our study enhances understanding of regional brain atrophy in SCA3, corroborating known clinical features while offering new insights into disease progression.

Analysis of the difference between Alzheimer's disease, mild cognitive impairment and normal people by using fractal dimensions and small-world network.

This research examined the distinctions in brain network characteristics among individuals with Alzheimer's disease (AD), mild cognitive impairment (MCI), and a control group. Magnetic resonance imaging (MRI) and mini-mental state examination (MMSE) data were retrieved from the Alzheimer's Disease Neuroimaging Initiative (ANDI) database, comprising 40 subjects in each group. Correlation maps for evaluating brain network connectivity were generated using fractal dimension (FD) analysis, a method capable of quantifying morphological changes in cortical and cerebral regions. Employing graph theory, each parcellated brain region was represented as a node, and edges between nodes were utilized to compute small-world network properties for each group. In the comparison between control and AD demonstrated the significantly lower FD values (P<0.05) in temporal lobe, motor cortex, part of occipital and parietal, hippocampus, amygdala, and entorhinal cortex, which present the atrophy. Similarly, comparing control group to MCIs, regions closely associated with memory, such as the hippocampus, showed significantly lower FD values. Furthermore, both AD and MCI groups displayed diminished connectivity and decreased network efficiency. In conclusion, fractal dimension (FD) analysis illustrate the progression of structural declination from mild cognitive impairment (MCI) to Alzheimer's disease (AD). Additionally, structural small-world network analysis presents itself as a potential method for assessing network efficiency and the progression of AD. Moving forward, further clinical assessments are warranted to validate the findings observed in this study.

Evaluation of cyst treatment technique, cyst type, size differences and healing by fractal analysis.

AIM: The aim of the study was to evaluate the trabeculation increase of treated mandibular cysts. MATERIAL AND METHOD: The study included 26 female and 33 male patients (age mean: 38,4 years) with cysts larger than 3 cm in the posterior region of the mandible who were admitted to the same center. Two groups in treatment technique: marsupialization (n = 29) and enucleation (n = 30). Four groups in cyst types: dentigerous cyst (n = 21), keratocyst (n = 19), radicular cyst (n = 15) and residual cyst (n = 4). Cyst size was divided into two categories: smaller than 5.5 cm (n = 31) and larger than 5.5 cm (n = 28). Panoramic radiographs (PR) of the patients were analyzed at the beginning, 6. month and 12. month. RESULT: At the end of the treatment, there was no statistically significant difference in terms of Fractal Analysis (FA) between patients treated with marsupialization and enucleation, but considering that the cysts in the marsupialization group were larger in size, a faster increase in FA was observed in the marsupialization group. When the cysts were grouped according to their size, it was observed that healing tissues in cysts smaller than 5.5 cm reached normal FA values faster, while healing in the middle of cysts larger than 5.5 cm took more time. CONCLUSIONS: FA is a reproducible and reliable method. In large cysts, marsupialization results in a faster recovery, but FA values at the end of treatment are similar to the enucleation group. Cysts larger than 5.5 cm show a more rapid increase in Fractal Dimension (FD). The centre of the cysts is the area that heals the latest. Studies with larger sample sizes are needed to evaluate the difference in healing between cyst types. CLINICAL TRIAL NUMBER: Clinical trial number: Not applicable.

Impact of L-PRF on pain and healing outcomes in lower third molar surgery: a randomized split-mouth trial.

This study explored the effects of L-PRF on pain, soft tissue healing, periodontal condition, and post-extraction bone repair of mandibular third molars (3Ms). A randomized, prospective, triple-blind, split-mouth clinical trial was conducted with 34 volunteers. Eligible patients were randomly allocated into two treatments: G1 (without L-PRF), G2 (alveoli filled with L-PRF), in which the removal of bilateral 3Ms was performed at the same surgical time. Outcomes were assessed according to a visual analogue scale (pain), soft tissue scoring system (wound healing), periodontal probing of mandibular second molar. Bone repair was determined by volumetric analysis (ITK-SNAP software) and fractal analysis (ImageJ software). An intention-to-treat approach to Statistical analysis was used. L-PRF reduced pain in the 7-day postoperative follow-up (p = 0.019) and not only improved soft tissue healing after 1 month of follow-up (p = 0.021), but also probing depth (distal face) in 3 months postoperatively (p = 0.011). Significant alveolar reduction occurred in 3 months after surgery in both treatments (p < 0.05), however, this was more significant in G1 (p = 0.016). The fractal dimension showed no statistical differences. L-PRF improved postoperative clinical parameters of pain, soft tissue healing, and periodontal condition, suggesting that it has a beneficial effect on preserving the alveolar ridge and accelerating the initial repair process.

Effects of thinning on structural complexity of Larix olgensis plantation.

In this paper, we collected the individual tree point cloud data in the plots of Larix olgensis plantations with different thinning intensities in Mengjiagang Forest Farm, applied the fractal analysis theory to extract box dimensions (Db) on MATLAB platform, and characterized the structural complexity of L. olgensis. We assessed the effect of different thinning intensities and tree attributes on the structural complexity of L. olgensis. The results showed significant differences in L. olgensis Db between control (CK: 1.68±0.07), low and medium intensity thinning (T1, T2, T3: 1.74±0.07), and high intensity thinning (T4: 1.81±0.06), which indicated that the thinning intensity increased tree structural complexity. For trunk attribute, the diameter at breast height and tree height was significantly positively correlated with Db, while the height-to-diameter ratio was significantly negatively correlated with Db. For canopy attribute, crown volume, surface area, projected area, and crown diameter was significantly positively correlated with Db. Hegyi competition index was significantly negatively correlated with Db in the control and low-moderate-intensity thinning treatments, but not significantly correlated with Db in the high-intensity thinning treatment. It indicated that thinning influenced L. olgensis structural complexity, with trunk attribute and canopy attribute as the main drivers of L. olgensis structural complexity.

Bioinspired Functional Composites for Enhanced Thermally Conductivity via Fractal-Growth CuNP Fillers.

Thermal conduction for electronic devices has attracted extensive attention in light of the development of 5G communication. Thermally conductive materials with high thermal conductivity and extensive mechanical flexibility are extremely desirable in practical applications. However, the construction of efficient interconnected conductive pathways and continuous conductive networks is inadequate for either processing or actual usage in existing technologies. In this work, spherical copper nanoparticles (S-CuNPs) and urchin-inspired fractal-growth CuNPs (U-CuNPs), thermally conductive metal fillers induced by ionic liquids, were fabricated successfully through the electrochemical deposition method. Compared to S-CuNPs, the U-CuNPs shows larger specific surface contact area, thus making it easier to build a continuous conductive pathway network in the corresponding U-CuNPs/liquid silicone rubber (LSR) thermally conductive composites. The optimal loading of CuNP fillers was determined by evaluating the rheological performance of the prepolymer and the mechanical properties and thermal conductivity performances of the composites. When the filler loading is 150 phr, the U-CuNPs/LSR produces optimal mechanical properties (e.g., tensile strength and modulus), thermal conductivity (above 1000% improvement compared to pure LSR), and heating/cooling efficiency. The enhanced thermal conductivity of U-CuNPs/LSR was also confirmed through the finite element analysis (FEA) overall temperature distribution, indicating that U-CuNPs with larger specific surface contact areas exhibit more advantages in forming a continuous network in composites than S-CuNPs, making U-CuNPs/LSR a promising and competitive alternative to traditional flexible thermally interface materials.

Neuro-evolutionary evidence for a universal fractal primate brain shape.

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of df = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future.

Many of the brain's essential functions ­ from decision-making to movement ­ take place in its outer layer known as the cerebral cortex. The shape of the cerebral cortex varies significantly between species. For instance, in humans, it is folded in to grooves and ridges, whereas in other animals, including mice, it is completely smooth. The structure of the cortex can also differ within a species, and be altered by aging and certain diseases. This vast variation can make it difficult it to characterize and compare the structure of the cortex between different species, ages and diseases. To address this, Wang et al. developed a new mathematical model for describing the shape of the cortex. The model uses a method known as coarse graining to erase, or 'melt away', any cortical folds or structures smaller than a given threshold size. As this threshold increases, the cortex becomes progressively smoother. The relationship between surface areas and threshold sizes indicates the fractal dimension ­ that is, how fragmented the cortex is across different scales. Wang et al. applied their model to the brain scans of eleven primates, including humans, and found the fractal dimension of the cortex was almost exactly 2.5 for all eleven species. This suggests that the cortices of the different primates follow a single fractal shape, which means the folds of each cortex have a similar branching pattern. Although there were distinctions between the species, they were mainly due to the different ranges of fold sizes in each cortex. The model revealed that the broader the range of fold sizes, the more folded the brain ­ but the fractal pattern remains the same. The brain melting method created by Wang et al. provides a new way to characterise cortical shape. Besides revealing a hitherto hidden regularity of nature, they hope that in the future their new method will be useful in assessing brain changes during human development and ageing, and in diseases like Alzheimer's and epilepsy.

Left atrial appendage thrombus is associated with a higher fractal dimension in patients with atrial fibrillation.

PURPOSE: To assess the anatomical complexity of the left atrial appendage (LAA) using fractal dimension (FD) based on cardiac computed tomography angiography (CTA) and the association between LAA FD and LAA thrombosis. MATERIALS AND METHODS: Patients with atrial fibrillation (AF) who underwent both cardiac CTA and transesophageal echocardiography (TEE) between December 2018 and December 2022 were retrospectively analyzed. Patients were categorized into normal (n = 925), circulatory stasis (n = 82), and thrombus groups (n = 76) based on TEE results and propensity score matching (PSM) was performed for subsequent analysis. FD was calculated to quantify the morphological heterogeneity of LAA. Independent risk factors for thrombus were screened using logistic regression. The diagnostic performance of FD and CHA2DS2-VaSc score for predicting thrombus was evaluated using the area under the receiver operating characteristics curve (AUC). RESULTS: LAA FD was higher in the thrombus group (1.61 [1.49, 1.70], P < 0.001) than in the circulatory stasis (1.33 [1.18, 1.47]) and normal groups (1.30 [1.18, 1.42]) both before and after PSM. LAA FD was also an independent risk factor in the thrombus (OR [odds ratio] = 570,861.15 compared to normal, 41,122.87 compared to circulatory stasis; all P < 0.001) and circulatory stasis group (OR = 98.87, P = 0.001) after PSM. The diagnostic performance of LAA FD was significantly better than the CHA2DS2-VaSc score in identifying thrombus. CONCLUSIONS: Patients with high LAA FD are more likely to develop LAA thrombus, and the use of FD provides an effective method for assessing the risk of thrombosis in AF patients, thereby guiding individualized clinical treatment.

Exploring anisotropic mechanical properties of lobster claw exoskeleton through fractal models.

The outstanding mechanical properties of lobster claw exoskeletons are intricately tied to their internal microstructure. Investigating this relationship can offer vital insights for designing high-performance additive manufacturing structures. Fractal theory, with its fractional dimensional perspective, suits the complexity of real-world phenomena. Our study examines fully hydrated lobster claw exoskeletons using a multifaceted approach: four-point bending tests, scanning electron microscopy observations, and fractal models. Test results reveal superior mechanical properties in longitudinal specimens. Scanning electron microscopy shows non-uniform fiber helical structures and porous elements in the exoskeleton. Fracture mechanisms involve both breaking fiber fragments perpendicular to the cross-section and tearing between these fragments. The observed crack propagation paths exhibit statistical self-similarity. Consequently, we develop fractal models for the crack propagation paths in longitudinal and transverse specimens, calculating crack extension forces. Using the box-counting method and its improved variant, we determine the fractal dimensions of specimen sections. The fractal dimension of longitudinal models exceeds that of transverse models, and calculated crack extension forces are higher in longitudinal models. These findings align well with experimental data, demonstrating fractal theory's efficacy in analyzing the lobster claw exoskeleton's anisotropic mechanical properties.

Analysis of a class of fractal hybrid fractional differential equation with application to a biological model.

Recently, the area devoted to fractional calculus has given much attention by researchers. The reason behind such huge attention is the significant applications of the mentioned area in various disciplines. Different problems of real world processes have been investigated by using the concepts of fractional calculus and important and applicable outcomes were obtained. Because, there has been a lot of interest in fractional differential equations. It is brought on by both the extensive development of fractional calculus theory and its applications. The use of linear and quadratic perturbations of nonlinear differential equations in mathematical models of a variety of real-world problems has received a lot of interest. Therefore, motivated by the mentioned importance, this research work is devoted to analyze in detailed, a class of fractal hybrid fractional differential equation under Atangana- Baleanu- Caputo ABC derivative. The qualitative theory of the problem is examined by using tools of non-linear functional analysis. The Ulam-Hyer's (U-H) type stability criteria is also applied to the consider problem. Further, the numerical solution of the model is developed by using powerful numerical technique. Lastly, the Wazewska-Czyzewska and Lasota Model, a well-known biological model, verifies the results. Several graphical representations by using different fractals fractional orders values are presented. The detailed discussion and explanations are given at the end.

Evaluation of mandibular trabecular bone by fractal analysis in pediatric patients with hypodontia of the mandibular second premolar tooth.

BACKGROUND: It is still unclear whether the trabecular structure of the jaw is different in individuals with hypodontia than in those without hypodontia; this is important for clinicians. The aim was to determine whether the mandibular trabecular bone structure of children and adolescents with hypodontia differs from the control group by using the fractal analysis (FA) method in this study. METHODS: A total of 138 panoramic radiographs of 69 cases and 69 control subjects (mean age 13.2 ± 10.1) were evaluated. The age and gender of subjects in the case and control groups were matched. Three regions of interest (ROIs) were selected from the panoramic radiographs. ROI1 refers to the center of the ramus rising above the mandibular foramen. ROI2 refers to the area between the apical level of the mandibular molar and the upper border of the mandibular canal. ROI3, the missing tooth region, refers to the apical third of the mesial side of the erupting or fully erupted permanent mandibular first molar. Mann-Whitney U and Wilcoxon tests were used. p < 0.05 was accepted for the significance value. RESULTS: The mean fractal dimension (FD) values of ROI1, ROI2, and ROI3 were 1,25, 1,20, and 1,13, respectively. The means FD values obtained from the ramus region were higher than the other regions (p < 0.05). The FD values did not differ significantly according to gender and age (p > 0.05). The FD values of the case group were lower than the control group for ROI3 (p < 0.05). CONCLUSION: The results of this study showed that the mandibular trabecular bone quality of pediatric patients with one missing tooth was different from the healthy group. The difference in the mean FD values from the ROIs indicates that the ramus has a denser structure than the mandibular corpus. Clinicians should factor this into their dental treatment planning process.

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.