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.

Evaluation of fractal analysis and radiomorphometric measurements of mandibular bone structure in bruxism and non-bruxism paediatric patients.

OBJECTIVES: The goal of this examination was to compare the impact of probable sleep/awake bruxism on the mandibular trabecular bone structure by fractal analysis (FA) with digital panoramic radiograph (DPR) and radiomorphometric measurements in paediatric patients with bruxism. METHODS: The examination included 130 participants with 63 patients with probable sleep/awake bruxism and 67 control groups. Bilateral regions of interest (ROI) in three regions were examined as ROI1: mandibular ramus, ROI2: mandibular angulus, ROI3: anterior to the molar teeth. Radiomorphometric measurements were taken of the mandibular cortical width (MCW), panoramic mandibular index (PMI), and mandibular cortical index (MCI). p < 0.05 was approved for statistical significance. RESULTS: The ROI-1, ROI-2, and ROI-3 values were defined to be statistically significantly high in the bruxism group (p < 0.05). No significant difference was found between the groups in the other values (p > 0.05). There was no difference in the age and gender for any of the parameters (p > 0.05). CONCLUSION: In children and adolescents, the mandibular trabecular bone can be affected by bruxism. FA can be used as an auxiliary method for finding the mandibular trabecular differences of patients with bruxism in paediatric dentistry just as it can for adults.

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.

Alveolar bone healing patterns in chronic kidney failure and kidney transplant recipients: A pixel intensity and fractal analyses.

AIMS: To assess and compare radiographically the alveolar bone after tooth extractions in individuals with chronic kidney failure undergoing hemodialysis (CKFh), those submitted to kidney transplantation (KT), and those without kidney disease (CG) by using fractal analysis (FA) and pixel intensity (PI). METHODS AND RESULTS: Periapical radiographs of 48 CKFh individuals (87 extracted teeth), 12 KT individuals (26 extracted teeth and 29 control individuals [76 extracted teeth] were analyzed at 7 and 60 days after tooth extraction. Fractal dimension (FD) and PI were assessed to evaluate the alveolar trabecular bone structural complexity and mineral content. The difference in FD values between the 7th and 60th postoperative days in KT individuals (0.03 ± 0.08) was significantly lower compared to those of CKFh individuals (0.09 ± 0.10) and controls (0.15 ± 0.06). As for the difference in PI values, KT (4.55 ± 10.24) and CKFh groups (9.88 ± 15.90) showed significantly lower values compared to those of the control group (17.93 ± 11.86) in the same period. These results indicate a lower gain in the trabecular bone complexity and bone density in the alveolus of KT individuals compared to the other groups. CONCLUSIONS: Overall mineral content and thickness of the bone in the plane of the x-ray beam were lower in KT and CKFh individuals compared to controls, reflecting the need for careful consideration in recommending rehabilitation with dental implants for these patients. Particular attention should be given to the potential challenges in oral rehabilitation of KT patients.

Effect of Fixed and Removable Functional Therapy on Mandibular Anterior Bone Structures: A Fractal Analysis Study.

(1) Background and aim: The effects of functional therapies on dentoalveolar and skeletal structures have been investigated in orthodontics for many years. The aim of this retrospective study was to evaluate the changes caused by fixed and removable functional therapy in the mandibular anterior trabecular structures using fractal dimension (FD) analysis. (2) Methods: A total of 60 patients with skeletal and dental class II malocclusion were included in the study and three groups were formed: the untreated control group (CG), the Forsus fatigue-resistant device group (FFRDG), and the Monoblock group (MBG). Bone areas of interest determined in the buccoapical of the mandibular incisors and the symphysis in the lateral cephalometric radiographs taken before (T0) and after (T1) functional therapy were evaluated using FD analysis. The relationship between the FD and IMPA (Incisor Mandibular Plane Angle) angles was evaluated. Parametric and nonparametric tests were used in statistical analysis according to normality distribution. The statistical significance level was determined as p < 0.05. (3) Results: There was no statistically significant difference between the FD values of all groups at T0 (p > 0.05). At T1, buccoapical FD values were significantly lower in FFRDG and MBG compared to the control group (p < 0.05), while symphyseal FD values were not found to be significant (p > 0.05). The IMPA angle was significantly lower in the FFRDG and MBG than in the control group at T0, while it was higher at T1 (p < 0.05). While a significant negative correlation was observed between the IMPA angle and buccoapical FD values in both FFRDG and MBG (p < 0.05), it was not observed with the symphysis FD values (p > 0.05). (4) Conclusions: Trabecular changes caused by functional therapy in the mandibular anterior bone can be evaluated on lateral cephalometric radiographs with FD analysis. It was concluded that orthodontists should ensure controlled changes in the IMPA angle during functional therapy, especially for the decreases in FDs seen in the buccoapical alveolar region due to the forward movement of the mandibular incisors.

Plasminogen activator inhibitor-1 mediates cerebral ischemia-induced astrocytic reactivity.

Although ischemia increases the abundance of plasminogen activator inhibitor-1 (PAI-1), its source and role in the ischemic brain remain unclear. We detected PAI-1-immunoreactive cells with morphological features of reactive astrocytes in the peri-ischemic cortex of mice after an experimentally-induced ischemic lesion, and of a chimpanzee that suffered a naturally-occurring stroke. We found that although the abundance of PAI-1 increases 24 hours after the onset of the ischemic injury in a non-reperfusion murine model of ischemic stroke, at that time-point there is no difference in astrocytic reactivity and the volume of the ischemic lesion between wild-type (Wt) animals and in mice either genetically deficient (PAI-1-/-) or overexpressing PAI-1 (PAI-1Tg). In contrast, 72 hours later astrocytic reactivity and the volume of the ischemic lesion were decreased in PAI-1-/- mice and increased in PAI-1Tg animals. Our immunoblottings and fractal analysis studies show that the abundance of astrocytic PAI-1 rises during the recovery phase from a hypoxic injury, which in turn increases the abundance of glial fibrillary acidic protein (GFAP) and triggers morphological features of reactive astrocytes. These studies indicate that cerebral ischemia-induced release of astrocytic PAI-1 triggers astrocytic reactivity associated with enlargement of the necrotic core.

Fractal geometry of culprit coronary plaque images within optical coherence tomography in patients with acute coronary syndrome vs stable angina pectoris.

The main cause of acute coronary syndrome (ACS) is plaque rupture and thrombus formation. However, it has not been fairly successful to identify vulnerable plaque to rupture using conventional parameters of intravascular imaging modalities. Fractal analysis is one of the mathematical models to examine geometrical features of picture image using a specific parameter called as fractal dimension (FD) which suggests geometric complexity of the image. This study examined FD of the optical coherence tomography (OCT)-derived images of the culprit plaque in patients with ACS vs stable angina pectoris (SAP) to evaluate the feasibility of FD for identifying vulnerable coronary plaques prone to provoke ACS distinguished from stable plaques only provoking SAP. We examined 65 cases (34 ACS patients, 31 SAP patients) in which the culprit lesion was imaged by OCT before percutaneous coronary intervention in patients with ACS and SAP. The culprit plaque lesion in the ACS group had a significantly larger mean lipid arc (203.8 ± 39.4° vs 152.3 ± 34.5°, p < 0.001) and a larger lipid plaque length (12.6 ± 5.1 mm vs 7.7 ± 2.7 mm, p < 0.001) and a thinner fibrous cap thickness (75.3 ± 22.3 µm vs 134.8 ± 53.2 µm, p < 0.001) than those in the SAP group. The prevalence of OCT-derived macrophage infiltration (Mph) in the entire culprit coronary vessel as well as that of the OCT-derived thin-cap fibroatheroma (TCFA) at the culprit lesion were significantly greater in the ACS group than those in the SAP group, respectively (Mph: 61.8% vs 35.5%, p = 0.048; TCFA: 44.1% vs 6.4%, p < 0.001). The FD of culprit plaque in the ACS group was significantly greater than in the SAP group (2.401 ± 0.073 vs 2.341 ± 0.051, p < 0.001). In multivariate regression analysis, the presence of Mph was a significant determinant of FD (regression coefficient estimate 0.049, CI 0.018-0.079, p = 0.002). The FD of OCT-derived image of culprit coronary plaque in the ACS group was significantly greater than that in the SAP group, indicating that the culprit plaque in ACS were structurally more complex. Therefore, fractal analysis of coronary OCT images might be clinically useful for identifying coronary plaques prone to provoke ACS.

Modern methods of neuroanatomical and neurophysiological research.

Our article explores a variety of modern research techniques employed in neuroanatomy and neurophysiology. We highlight the use of computer technologies, image analysis methods, and innovative approaches that expand our understanding of anatomical structures. The techniques we discuss include fractal analysis, the Pickworth method, scanning microscopy, and advanced computer image processing systems. Fractal analysis, in particular, offers a unique perspective on brain structures and functions and is a key tool in neuroanatomical research. We also focus on its application in neuroanatomical studies, particularly in cases of Alzheimer's disease and epilepsy. These modern research methods not only enhance our knowledge but also have significant clinical potential. Their use in diagnosing neurological diseases like Alzheimer's and epilepsy promises faster and more accurate diagnoses. We emphasize the combination of multiple methods for improved quality of anatomical structure imaging.

Tracking and modeling the movement of Queensland fruit flies, Bactrocera tryoni, using harmonic radar in papaya fields.

Determining movement parameters for pest insects such as tephritid fruit flies is critical to developing models which can be used to increase the effectiveness of surveillance and control strategies. In this study, harmonic radar was used to track wild-caught male Queensland fruit flies (Qflies), Bactrocera tryoni, in papaya fields. Experiment 1 continuously tracked single flies which were prodded to induce movement. Qfly movements from this experiment showed greater mean squared displacement than predicted by both a simple random walk (RW) or a correlated random walk (CRW) model, suggesting that movement parameters derived from the entire data set do not adequately describe the movement of individual Qfly at all spatial scales or for all behavioral states. This conclusion is supported by both fractal and hidden Markov model (HMM) analysis. Lower fractal dimensions (straighter movement paths) were observed at larger spatial scales (> 2.5 m) suggesting that Qflies have qualitatively distinct movement at different scales. Further, a two-state HMM fit the observed movement data better than the CRW or RW models. Experiment 2 identified individual landing locations, twice a day, for groups of released Qflies, demonstrating that flies could be tracked over longer periods of time.

Radiographic texture of the trabecular bone of the proximal phalanx in horses with metacarpophalangeal osteoarthritis.

Osteoarthritis (OA) is a prevalent condition in horses, leading to changes in trabecular bone structure and radiographic texture. Although fractal dimension (FD) and lacunarity have been applied to quantify these changes in humans, their application in horses remains nascent. This study evaluated the use of FD, bone area fraction (BA/TA), and lacunarity in quantifying trabecular bone differences in the proximal phalanx (P1) in 50 radiographic examinations of equine metacarpophalangeal joints with varying OA degrees. In the dorsopalmar view, regions of interest were defined in the trabecular bone of the proximal epiphysis, medial and lateral to the sagittal groove of P1. Lower BA/TA values were observed medially in horses with severe OA (P=0.003). No significant differences in FD and lacunarity were found across OA degrees (P>0.1). FD, BA/TA, and lacunarity were not effective in identifying radiographic texture changes in the P1 trabecular bone in horses with different metacarpophalangeal OA degrees.

Novel Use of Fractal Analysis for Quantifying Polymethylmethacrylate Distribution Patterns in Osteoporotic and Malignant Vertebral Compression Fractures Following Vertebroplasty.

Purpose: Fractal analysis is a mathematical tool which allows the evaluation of complex microstructural features within materials that cannot be expressed in traditional geometric terms. The purpose of this study is to quantify the differences in polymethylmethacrylate intravertebral cement spatial distribution patterns following vertebroplasty using fractal analysis through the examination of osteoporotic and malignant compression fractures. Methods: Frontal and lateral post-vertebroplasty radiographs were evaluated from 29 patients with osteoporotic and malignant compression fractures who underwent vertebroplasty. The individually treated vertebra were divided into osteoporotic (n = 35) and malignant groups (n = 41). Images underwent segmentation, thresholding, and binarization prior to fractal analysis. Fractal dimension and lacunarity values were derived from the region of interest in treated vertebrae using the "box-counting" and "gliding-box" techniques respectively using ImageJ. The mean values of both parameters were compared between the 2 groups. Results: The mean fractal dimension was significantly higher in the malignant vertebral compression fracture group (1.53 ± 0.08) compared to the osteoporotic group (1.34 ± 0.17; P < .001). Similarly, mean lacunarity values were significantly higher in the malignant fracture group (0.50 ± 0.09) compared to the osteoporotic group (0.37 ± 0.10; P < .001). Conclusions: Fractal dimension and lacunarity values of cement spatial distribution patterns obtained from the post-vertebroplasty radiographs can differentiate between benign osteoporotic and malignant vertebral compression fractures. This novel technique may be useful for evaluating cement spatial distribution patterns in spine augmentation procedures, although further research is warranted in this area.

Accurate identification of individuals with subjective cognitive decline using 3D regional fractal dimensions on structural magnetic resonance imaging.

BACKGROUND AND OBJECTIVE: Accurate identification of individuals with subjective cognitive decline (SCD) is crucial for early intervention and prevention of neurodegenerative diseases. Fractal dimensionality (FD) has emerged as a robust and replicable measure, surpassing traditional geometric metrics, in characterizing the intricate fractal geometrical properties of brain structure. Nevertheless, the effectiveness of FD in identifying individuals with SCD remains largely unclear. A 3D regional FD method can be suggested to characterize and quantify the spatial complexity of the precise gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD. METHODS: This study introduces a novel integer ratio based 3D box-counting fractal analysis (IRBCFA) to quantify regional fractal dimensions (FDs) in structural magnetic resonance imaging (MRI) data. The innovative method overcomes limitations of conventional box-counting techniques by accommodating arbitrary box sizes, thereby enhancing the precision of FD estimation in small, yet neurologically significant, brain regions. RESULTS: The application of IRBCFA to two publicly available datasets, OASIS-3 and ADNI, consisting of 520 and 180 subjects, respectively. The method identified discriminative regions of interest (ROIs) predominantly within the limbic system, fronto-parietal region, occipito-temporal region, and basal ganglia-thalamus region. These ROIs exhibited significant correlations with cognitive functions, including executive functioning, memory, social cognition, and sensory perception, suggesting their potential as neuroimaging markers for SCD. The identification model trained on these ROIs demonstrated exceptional performance achieving over 93 % accuracy on the discovery dataset and exceeding 87 % on the independent testing dataset. Furthermore, an exchange experiment between datasets revealed a substantial overlap in discriminative ROIs, highlighting the robustness of our method across diverse populations. CONCLUSION: Our findings indicate that IRBCFA can serve as a valuable tool for quantifying the spatial complexity of gray matter, providing insights into cognitive aging and aiding in the automated identification of individuals with SCD. The demonstrated generalizability and robustness of this method position it as a promising tool for neurodegenerative disease research and offer potential for clinical applications.

EVALUATION OF MANDIBULAR TRABECULAR AND CORTICAL STRUCTURE BY FRACTAL ANALYSIS IN HYPERLIPIDEMIA AND HYPERTENSION PATIENTS.

INTRODUCTION: This study aimed to evaluate the mandibular trabecular and cortical changes in patients with hyperlipidemia (HL) and/or hypertension (HT) using fractal dimension (FD) analysis, mandibular cortical width (MCW), panoramic mandibular index (PMI) and mandibular cortical index (MCI). MATERIALS AND METHODS: Panoramic radiographs of 100 patients were evaluated. FD measurement of three region of interest (ROI) including the angulus, corpus and interdental bone area were made. MCW, PMI and MCI were also measured and noted. RESULTS: Angulus, corpus and interdental FD values were significantly lower in three disease groups than the control group. Angulus, corpus, and interdental FD values were significantly lower in the HL+HT group than in the HL group and HT group. MCW value was significantly lower in the HL group, HT group, and HL+HT group than the control group. The cortical index C1 was more common in the control group while C2 was more common in the HT, HL and HL+HT group. CONCLUSION: The fact that FD was significantly lower in the HL+HT group compared to the HL and HT groups indicates the positive effect of their association on bone loss and quality. FD measurements on images obtained using a direct digital panoramic system can be used for treatment planning and follow-up of patients with HL and/or HT.

Fractal analysis of left ventricular trabeculae in heart failure with preserved ejection fraction patients with multivessel coronary artery disease.

OBJECTIVES: Endocardial trabeculae undergo varicose changes and hyperplasia in response to hemodynamic influences and are a variable phenotype reflecting changes in disease. Fractal analysis has been used to analyze the complexity of endocardial trabeculae in a variety of cardiomyopathies. The aim of this paper was to quantify the myocardial trabecular complexity through fractal analysis and to investigate its predictive value for the diagnosis of heart failure with preserved ejection fraction (HFpEF) in patients with multivessel coronary artery disease (CAD). METHODS: The retrospective study population consisted of 97 patients with multivessel CAD, 39 of them were diagnosed with HFpEF, while 46 healthy volunteers were recruited as controls. Fractal dimension (FD) was obtained through fractal analysis of endocardial trabeculae on LV short-axis cine images. Logistic regression analyses were used to confirm the predictors and compare different prediction models. RESULTS: Mean basal FD was significantly higher in patients with HFpEF than in patients without HFpEF or in the healthy group (median: 1.289; IQR: 0.078; p < 0.05). Mean basal FD was also a significant independent predictor in univariate and multivariate logistic regression (OR: 1.107 and 1.043, p < 0.05). Furthermore, adding FD to the prediction model improved the calibration and accuracy of the model (c-index: 0.806). CONCLUSION: The left ventricular FD obtained with fractal analysis can reflect the complexity of myocardial trabeculae and has an independent predictive value for the diagnosis of HFpEF in patients with multivessel CAD. Including FD into the diagnostic model can help improve the diagnosis. CRITICAL RELEVANCE STATEMENT: Differences show in the complexity of endocardial trabeculae in multivessel coronary artery disease patients, and obtaining fractal dimensions (FD) by fractal analysis can help identify heart failure with preserved ejection fraction (HFpEF) patients. KEY POINTS: The complexity of myocardial trabeculae differs among patients with multivessel coronary artery disease. Left ventricular fractal dimensions can reflect the complexity of the myocardial trabecular. Fractal dimensions have predictive value for the diagnosis of heart failure with preserved ejection fraction.

Radiologic evaluation of associated symptoms and fractal analysis of unilateral dens invaginatus cases.

OBJECTIVE: The aim of this study is to determine the age-based prevalence of dens invaginatus cases and to learn the radiologic findings. In addition, fractal analysis of the periapical regions of unilateral dens invaginatus cases and contralateral teeth was performed to determine the effect of possible microleakage on fractal dimension. METHODS: A total of 136 patients (170 teeth) identified in panoramic radiographs taken for diagnostic purposes between January 2018 and December 2023 at our Department of Oral and Maxillofacial Radiology were included in the study. Data were analysed using IBM SPSS V23. The Chi-square test was used for comparing categorical variables between groups. The relationship between the FD values calculated around the apexes of the teeth with unilateral dens invaginatus and the contralateral teeth was analyzed by paired t test. A significance level of p < 0.050 was adopted. RESULTS: The mean age of the cases was calculated as 28.1 (8-63) years. 66 (48.5%) of the cases were female, and 70 (51.1%) were male. The lateral incisor was the most affected tooth among these cases. Bilateral cases were observed in 34 patients. Type 2 was detected in 93 patients, Type 1 in 35 patients, and Type 3 dens invagination in 8 patients. Dens invaginatus cases were observed in 134 maxillary and 2 mandibular teeth. Periapical lesions were seen in 22 of these cases. CONCLUSIONS: Dens invaginatus cases are a congenital anomaly encountered at any age. Early diagnosis is crucial to prevent the loss of pulp vitality due to these invaginations. It should be noted that these invaginations can affect both jaws. However, due to the prevalence of occurrence in the maxillary anterior teeth and asymptomatic nonvitality, particular attention should be paid to evaluating this region.

Degenerative Temporomandibular Disorders: An Assessment of Bone Trabecular Structure Using Fractal Analysis in Digital Panoramic Radiographs.

Introduction Fractal analysis has proved to be a salient tool to quantitatively assess the qualitative changes in the bone trabeculae of patients with hyperparathyroidism, osteoporosis, and various temporomandibular disorders, including osteoarthritis (OA) and rheumatoid arthritis of temporomandibular joint (TMJ), in several previous studies. The purpose of this study was to use fractal analysis to assess alterations in the trabecular pattern of the mandibular condyle in patients with degenerative temporomandibular disorders. Materials and methods This study comprised 98 subjects with 49 subjects in the study group and 49 subjects in the control group, aged 18-50 years. Age and sex in the control group were matched to those in the case group. The subjects were assessed clinically with the Diagnostic Criteria for Temporomandibular Disorders. Digital panoramic X-ray equipment with set parameters of 70 kvp, 8 mA, and 16-second exposure duration was used to take panoramic radiographs. Fractal analysis was done and the calculated fractal dimension value was obtained using ImageJ version 1.48 software (National Institutes of Health, Bethesda, MD). The same observer used Muir and Goss's method to rate the total degenerative changes in the condylar surfaces, which were substantiated by the calculated fractal dimension value. The data were statistically analyzed. Results The results revealed a significant difference (p-value = 0.041) between the mean fractal value in the case group's (1.35) and the control group's (1.38) left sides whereas the differences in the mean fractal values between the case and control groups on the right side was not significant (p-value = 0.49). Conclusion It is recommended to use the fractal dimension value and the total degenerative severity score together to quantify degenerative changes in the TMJ OA rather than exclusively relying on fractal value.

BP neural network-based analysis of the applicability of NMF in side-step cutting.

Background: Although the spatio-temporal structure of muscle activation in cutting have been studied extensively, including time-varying motor primitives and time-invariant motor modules under various conditions, the factorisation methods suitable for cutting are unclear, and the extent to which each factorisation method loses information about movement during dimensionality reduction is uncertain. Research question: To clarify the extent to which NMF, PCA and ICA retain information about movement when downscaling, and to explore the factorisation method suitable for cutting. Methods: The kinematic data during cutting was captured with a Vicon motion capture system, from which the kinematic features of the pelvic centre of mass were calculated. NMF, PCA and ICA were used to obtain muscle synergies based on sEMG of the cutting at different angles, respectively. A back propagation neural network was constructed using temporal component of synergy as input and the kinematics data of pelvic as output. Calculation of the Hurst index using fractal analysis based on the temporal component of muscle synergy. Results: The quality of sEMG reconstruction is significantly higher with ICA (P < 0.01) than with NMF and PCA for the cutting. The NMF reconstruction has a high degree of preservation of movement, whereas the ICA loses movement information about the most of the swing phase, and the PCA loses information related to the change of direction. Hurst index less than 0.5 for all three angles of cutting. Significance: NMF is suitable for extracting muscle synergies in all directions of cutting. Information related to movement may be lost when using PCA and ICA to extract the synergy of cutting. The high individual variability of muscle synergy in cutting may be responsible for the loss of movement information in muscle synergy.

Three-Dimensional Fractal Analysis of the Interstitial Cells of Cajal Networks of Gastrointestinal Tissue Specimens.

Introduction: Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks. Methods: In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach. Results: The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05). Conclusions: The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.

Fractal Analysis in Clinical Neurosciences: An Overview.

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.