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.

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.

Assessment of Fractal Synchronization during an Epileptic Seizure.

In this paper, we define fractal synchronization (FS) based on the idea of stochastic synchronization and propose a mathematical apparatus for estimating FS. One major advantage of our proposed approach is that fractal synchronization makes it possible to estimate the aggregate strength of the connection on multiple time scales between two projections of the attractor, which are time series with a fractal structure. We believe that one of the promising uses of FS is the assessment of the interdependence of encephalograms. To demonstrate this approach in evaluating the cross-dependence between channels in a network of electroencephalograms, we evaluated the FS of encephalograms during an epileptic seizure. Fractal synchronization demonstrates the presence of desynchronization during an epileptic seizure.

Evolution of Retinal Neuron Fractality When Interfacing with Carbon Nanotube Electrodes.

Exploring how neurons in the mammalian body interact with the artificial interface of implants can be used to learn about fundamental cell behavior and to refine medical applications. For fundamental and applied research, it is crucial to determine the conditions that encourage neurons to maintain their natural behavior during interactions with non-natural interfaces. Our previous investigations quantified the deterioration of neuronal connectivity when their dendrites deviate from their natural fractal geometry. Fractal resonance proposes that neurons will exhibit enhanced connectivity if an implant's electrode geometry is matched to the fractal geometry of the neurons. Here, we use in vitro imaging to quantify the fractal geometry of mouse retinal neurons and show that they change during interaction with the electrode. Our results demonstrate that it is crucial to understand these changes in the fractal properties of neurons for fractal resonance to be effective in the in vivo mammalian system.

Fractal Dimension, Circularity, and Solidity of Cell Clusters in Liquid-Based Endometrial Cytology Are Potentially Useful for Endometrial Cancer Detection and Prognosis Prediction.

Endometrial cancer (EC) in women is increasing globally, necessitating improved diagnostic methods and prognosis prediction. While endometrial histology is the conventional approach, liquid-based endometrial cytology may benefit from novel analytical techniques for cell clusters. A clinical study was conducted at the University of Fukui Hospital from 2012 to 2018, involving 210 patients with endometrial cytology. The liquid-based cytology images were analyzed using cell cluster analysis with Image J software. Logistic regression, ROC analysis, and survival analysis were employed to assess the diagnostic accuracy and prognosis between cell cluster analysis and EC/atypical endometrial hyperplasia (AEH). Circularity and fractal dimension demonstrated significant associations with EC and AEH, regardless of age and cytology results. The ROC analysis revealed improved diagnostic accuracy when combining fractal dimension with cytology, particularly in menopausal age groups. Lower circularity and solidity were independently associated with poor overall survival, while higher fractal dimension values correlated with poorer overall survival in Grades 2 and 3 endometrial cancers. The combination of circularity and fractal dimension with cytology improved diagnostic accuracy for both EC and AEH. Moreover, circularity, solidity, and fractal dimension may serve as prognostic indicators for endometrial cancer, contributing to the development of more refined screening and diagnostic strategies.

Direct-Acting Oral Anticoagulant/Vitamin K Antagonists: Do They Affect the Trabecular and Cortical Structure of the Mandible?

BACKGROUND: This study aimed to evaluate the mandibular bone structure of patients using oral anticoagulants (OACs) vitamin K antagonist drugs (warfarin) and other OACs including direct oral anticoagulants [(DOACs) apixaban, rivaroxaban, dabigatran, edoxaban]. Analyses were based upon the fractal dimension (FD), the panoramic mandibular index (PMI) and the Klemetti index (KI), which is also known as the mandibular cortical index (MCI). METHODOLOGY: Ninety participants were divided into three groups: group 1: 30 systemically healthy individuals who had not used any anticoagulants before, group 2: 30 individuals using warfarin, and group 3: 30 individuals using DOACs. FD was used to analyze trabecular bone architecture in the condyle, angle, and two sites in the alveolar bone. PMI was used to evaluate the quantity of cortical bone and KI was used to evaluate the cortical bone quality. RESULTS: There was no difference between the groups regarding FD analysis and KI; however, a difference was found between groups 1, 2, and 3 in the PMI (P≤ 0.001). The PMI in group 1 was higher than in groups 2 and 3. CONCLUSION: Mandibular radiomorphometric indices can be used on panoramic radiographs to evaluate the quantity of mandibular cortical bone in patients using oral anticoagulants.

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions.

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

Fractals and Chaos in the Hemodynamics of Intracranial Aneurysms.

Computing the emerging flow in blood vessel sections by means of computational fluid dynamics is an often applied practice in hemodynamics research. One particular area for such investigations is related to the cerebral aneurysms, since their formation, pathogenesis, and the risk of a potential rupture may be flow-related. We present a study on the behavior of small advected particles in cerebral vessel sections in the presence of aneurysmal malformations. These malformations cause strong flow disturbances driving the system toward chaotic behavior. Within these flows, the particle trajectories can form a fractal structure, the properties of which are measurable by quantitative techniques. The measurable quantities are well established chaotic properties, such as the Lyapunov exponent, escape rate, and information dimension. Based on these findings, we propose that chaotic flow within blood vessels in the vicinity of the aneurysm might be relevant for the pathogenesis and development of this malformation.

Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties.

Imagine a world in which damaged parts of the body - an arm, an eye, and ultimately a region of the brain - can be replaced by artificial implants capable of restoring or even enhancing human performance. The associated improvements in the quality of human life would revolutionize the medical world and produce sweeping changes across society. In this chapter, we discuss several approaches to the fabrication of fractal electronics designed to interface with neural networks. We consider two fundamental functions - stimulating electrical signals in the neural networks and sensing the location of the signals as they pass through the network. Using experiments and simulations, we discuss the favorable electrical performances that arise from adopting fractal rather than traditional Euclidean architectures. We also demonstrate how the fractal architecture induces favorable physical interactions with the cells they interact with, including the ability to direct the growth of neurons and glia to specific regions of the neural-electronic interface.

Fractal Resonance: Can Fractal Geometry Be Used to Optimize the Connectivity of Neurons to Artificial Implants?

In parallel to medical applications, exploring how neurons interact with the artificial interface of implants in the human body can be used to learn about their fundamental behavior. For both fundamental and applied research, it is important to determine the conditions that encourage neurons to maintain their natural behavior during these interactions. Whereas previous biocompatibility studies have focused on the material properties of the neuron-implant interface, here we discuss the concept of fractal resonance - the possibility that favorable connectivity properties might emerge by matching the fractal geometry of the implant surface to that of the neurons.To investigate fractal resonance, we first determine the degree to which neurons are fractal and the impact of this fractality on their functionality. By analyzing three-dimensional images of rat hippocampal neurons, we find that the way their dendrites fork and weave through space is important for generating their fractal-like behavior. By modeling variations in neuron connectivity along with the associated energetic and material costs, we highlight how the neurons' fractal dimension optimizes these constraints. To simulate neuron interactions with implant interfaces, we distort the neuron models away from their natural form by modifying the dendrites' fork and weaving patterns. We find that small deviations can induce large changes in fractal dimension, causing the balance between connectivity and cost to deteriorate rapidly. We propose that implant surfaces should be patterned to match the fractal dimension of the neurons, allowing them to maintain their natural functionality as they interact with the implant.

Fractal Fluency: Processing of Fractal Stimuli Across Sight, Sound, and Touch.

People are continually exposed to the rich complexity generated by the repetition of fractal patterns at different size scales. Fractals are prevalent in natural scenery and also in patterns generated by artists and mathematicians. In this chapter, we will investigate the powerful significance of fractals for the human senses. In particular, we propose that fractals with mid-range complexity play a unique role in our visual experiences because the visual system has adapted to these prevalent natural patterns. This adaptation is evident at multiple stages of the visual system, ranging from data acquisition by the eye to processing of this data in the higher visual areas of the brain. Based on these results, we will discuss a fluency model in which the visual system processes mid-complexity fractals with relative ease. This fluency optimizes the observer's capabilities (such as enhanced attention and pattern recognition) and generates an aesthetic experience accompanied by a reduction in the observer's physiological stress levels. In addition to reviewing people's responses to viewing fractals, we will compare these responses to recent research focused on fractal sounds and fractal surface textures. We will extend our fractal fluency model to allow for stimuli across multiple senses.

ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research.

To explore questions asked in neuroscience, neuroscientists rely heavily on the tools available. One such toolset is ImageJ, open-source, free, biological digital image analysis software. Open-source software has matured alongside of fractal analysis in neuroscience, and today ImageJ is not a niche but a foundation relied on by a substantial number of neuroscientists for work in diverse fields including fractal analysis. This is largely owing to two features of open-source software leveraged in ImageJ and vital to vigorous neuroscience: customizability and collaboration. With those notions in mind, this chapter's aim is threefold: (1) it introduces ImageJ, (2) it outlines ways this software tool has influenced fractal analysis in neuroscience and shaped the questions researchers devote time to, and (3) it reviews a few examples of ways investigators have developed and used ImageJ for pattern extraction in fractal analysis. Throughout this chapter, the focus is on fostering a collaborative and creative mindset for translating knowledge of the fractal geometry of the brain into clinical reality.

The Fractal Geometry of the Brain: AnOverview.

The first chapter of this book introduces some history, philosophy, and basic concepts of fractal geometry and discusses how the neurosciences can benefit from applying computational fractal-based analysis. Further, it compares fractal with Euclidean approaches to analyzing and quantifying the brain in its entire physiopathological spectrum and presents an overview of the first section of this book as well.

Fractal analysis of left ventricular trabeculae in post-STEMI: from acute to chronic phase.

PURPOSE: The temporal evolution of ventricular trabecular complexity and its correlation with major adverse cardiovascular events (MACE) remain indeterminate in patients presenting with acute ST elevation myocardial infarction (STEMI). METHODS: This retrospective analysis enrolled patients undergoing primary percutaneous coronary intervention (pPCI) for acute STEMI, possessing cardiac magnetic resonance (CMR) data in the acute (within 7 days), subacute (1 month after pPCI), and chronic phases (6 months after pPCI) from January 2015 to January 2020 at the three participating sites. Fractal dimensions (FD) were measured for the global, infarct, and remote regions of left ventricular trabeculae during each phase. The potential association of FD with MACE was analyzed using multivariate Cox regression. RESULTS: Among the 200 analyzed patients (182 men; median age, 61 years; age range, 50-66 years), 37 (18.5%) encountered MACE during a median follow-up of 31.2 months. FD exhibited a gradual decrement (global FD at acute, subacute, and chronic phases: 1.253 ± 0.049, 1.239 ± 0.046, 1.230 ± 0.045, p < 0.0001), with a more pronounced decrease observed in patients subsequently experiencing MACE (p < 0.001). The global FD at the subacute phase correlated with MACE (hazard ratio 0.89 (0.82, 0.97), p = 0.01), and a global FD value below 1.26 was associated with a heightened risk. CONCLUSION: In patients post-STEMI, the global FD, serving as an indicator of left ventricular trabeculae complexity, independently demonstrated an association with subsequent major adverse cardiovascular events, beyond factors encompassing left ventricular ejection fraction, indexed left ventricular end-diastolic volume, infarct size, heart rate, NYHA class, and post-pPCI TIMI flow. CRITICAL RELEVANCE STATEMENT: In patients who have had an ST-segment elevation myocardial infarction, global fractal dimension, as a measure of left ventricular trabeculae complexity, provided independent association with subsequent major adverse cardiovascular event. KEY POINTS: • Global and regional FD decreased after STEMI, and more so in patients with subsequent MACE. • Lower global FD at the subacute phase and Δglobal FD from acute to subacute phase were associated with subsequent MACE besides clinical and CMR factors. • Global FD at the subacute phase independently correlated with MACE and global FD value below 1.26 was associated with higher risk.

Do Habitat MRI and Fractal Analysis Help Distinguish Triple-Negative Breast Cancer From Non-Triple-Negative Breast Carcinoma.

Purpose: To determine whether multiparametric MRI-based spatial habitats and fractal analysis can help distinguish triple-negative breast cancer (TNBC) from non-TNBC. Method: Multiparametric DWI and DCE-MRI at 3T were obtained from 142 biopsy- and surgery-proven breast cancer with 148 breast lesions (TNBC = 26 and non-TNBC = 122). The contrast-enhancing lesions were divided into 3 spatial habitats based on perfusion and diffusion patterns using K-means clustering. The fractal dimension (FD) of the tumour subregions was calculated. The accuracy of the habitat segmentation was measured using the Dice index. Inter- and intra-reader reliability were evaluated with the intraclass correlation coefficient (ICC). The ability to predict TNBC status was assessed using the receiver operating characteristic curve. Results: The Dice index for the whole tumour was 0.81 for inter-reader and 0.88 for intra-reader reliability. The inter- and intra-reader reliability were excellent for all 3 tumour habitats and fractal features (ICC > 0.9). TNBC had a lower hypervascular cellular habitat and higher FD 1 compared to non-TNBC (all P < .001). Multivariate analysis confirmed that hypervascular cellular habitat (OR = 0.88) and FD 1 (OR = 1.35) were independently associated with TNBC (all P < .001) after adjusting for rim enhancement, axillary lymph nodes status, and histological grade. The diagnostic model combining hypervascular cellular habitat and FD 1 showed excellent discriminatory ability for TNBC, with an AUC of 0.951 and an accuracy of 91.9%. Conclusions: The fraction of hypervascular cellular habitat and its FD may serve as useful imaging biomarkers for predicting TNBC status.

Stride-to-stride fluctuations and temporal patterns of muscle activity exhibit similar responses during walking to variable visual cues.

Incorporating variability within gait retraining approaches has been proposed and shown to lead to positive changes. Specifically, submitting the individuals to walk in synchrony to cues that are temporally organized with a fractal-like patterns, promotes changes at the stride-to-stride fluctuations closer to those typically find in young adults. However, there is still a need to understand the underlying neuromuscular mechanisms associated to such improvement. Thus, this study aimed to investigate whether changes in the temporal structure of the variability in gait patterns are accompanied by changes in muscle activity patterns. Fourteen young individuals walked synchronized to one uncued (UNC) and three cued conditions: isochronous (ISO), fractal (FRC) and random (RND). Inter-stride intervals were determined from an accelerometer placed on the lateral malleoli. Inter-muscle peak intervals were obtained from the electromyographic signal from the gastrocnemius muscle. Fractal scaling, obtained through detrended fluctuation analysis, and coefficient of variation were calculated. Repeated measures ANOVAs were used to identify differences between conditions. Significant main effect was observed for both fractal scaling and coefficient of variation. Both shown no differences between UNC and FRC conditions, while ISO and RND were significantly lower compared to UNC and FRC conditions. In addition, a Pearson's Correlation was used to test the correlation between variables. A strong correlation was found the temporal structure of gait and muscle activity patterns. These findings strengthen the current literature regarding the incorporation of variability within cued approaches. Specifically, it shows that such an approach allows the modification of the neuromuscular processes underlying the stride-to-stride fluctuations.

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.

Being fractal: Embodying antiracism values in course-based participatory action research.

In the winter and spring of 2021, I-a White, female, graduate student-taught a six-month course surrounding the theme: Disrupting Systemic Racism at our University Through Action Research. I was challenged to lead a meaningful course in a two-dimensional virtual space, amidst rising death tolls of the COVID-19 pandemic and the rhythmic beat of calls for racial justice pulsing through our Zoom class periods. This experience opened my eyes as an educator, budding community psychologist, and an antiracist White accomplice. In this critical autoethnographic case study, I recount my experience adapting the community organizing principle of fractals into a pedagogical framework that guided my instructional practices in a community psychology course. In doing so, I echo the call for community psychologists to connect our work more tightly to Black, Indigenous, and people of Color social justice organizers and movements to fortify the field's relevance in the struggle for racial justice.

Assessment of spatiotemporal characteristics of gait, trough the Phyphox® app: a case series.

BACKGROUND: Spatiotemporal characteristics from human locomotion can provide effective clinical metrics to assess motor control and brain function. This case report aims to assess the temporal structure of variability in stride-to-stride time and calculated the intrinsic fractal frame that is hidden below the repetitive structure of physiological gait through the "Phyphox" app. This is an innovative study from the perspective of analyzing gait variables through a mobile app. CASE PRESENTATION: Five older adults Caucasian (3 women; age = 73 ± 10,5 years; body mass = 62,2 ± 15,1 kg; height = 1,56 ± 0,1 m; 2 men; age = 75,5 ± 7,8 years; body mass = 86,3 ± 18,0 kg; height = 1,77 ± 0,1 m) participated in this study. Five participants were asked to walk with a natural cadence, two of the participants presented a value greater than 80 step's/minute (81.14 ± 0.01; 86.67 ± 0.02); and the others had values between 55 and 65 step's/minute (55.20 ± 0.02; 55.78 ± 0.05; 61.02 ± 0.05). Regarding the coefficient of variation, only one participant presented 10.08%. For the total number of steps, three of the participants had values greater than 1000 steps. The variability of these stride-to-stride time has been quantified through detrended fluctuation analysis; one participant presented a value above 1. CONCLUSIONS: This study provides evidence that a smartphone might provide a valid measure to assess the spatiotemporal characteristics of gait.

A guide to Whittle maximum likelihood estimator in MATLAB.

The assessment of physiological complexity via the estimation of monofractal exponents or multifractal spectra of biological signals is a recent field of research that allows detection of relevant and original information for health, learning, or autonomy preservation. This tutorial aims at introducing Whittle's maximum likelihood estimator (MLE) that estimates the monofractal exponent of time series. After introducing Whittle's maximum likelihood estimator and presenting each of the steps leading to the construction of the algorithm, this tutorial discusses the performance of this estimator by comparing it to the widely used detrended fluctuation analysis (DFA). The objective of this tutorial is to propose to the reader an alternative monofractal estimation method, which has the advantage of being simple to implement, and whose high accuracy allows the analysis of shorter time series than those classically used with other monofractal analysis methods.