Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals

Multi-scale fractal Fourier Ptychographic microscopy to assess the dose-dependent impact of copper pollution on living diatoms

Accumulation of bioavailable heavy metals in aquatic environment poses a serious threat to marine communities and human health due to possible trophic transfers through the food chain of toxic, non-degradable, exogenous pollutants. Copper (Cu) is one of the most spread heavy metals in water, and can severely affect primary producers at high doses. Here we show a novel imaging test to assay the dose-dependent effects of Cu on live microalgae identifying stress conditions when they are still capable of sustaining a positive growth. The method relies on Fourier Ptychographic Microscopy (FPM), capable to image large field of view in label-free phase-contrast mode attaining submicron lateral resolution. We uniquely combine FPM with a new multi-scale analysis method based on fractal geometry. The system is able to provide ensemble measurements of thousands of diatoms in the liquid sample simultaneously, while ensuring at same time single-cell imaging and analysis for each diatom. Through new image descriptors, we demonstrate that fractal analysis is suitable for handling the complexity and informative power of such multiscale FPM modality. We successfully tested this new approach by measuring how different concentrations of Cu impact on Skeletonema pseudocostatum diatom populations isolated from the Sarno River mouth.

A novel method for identifying aerobic granular sludge state using sorting, densification and clarification dynamics during the settling process

Aerobic granular sludge is one of the most promising biological wastewater treatment technologies, yet maintaining its stability is still a challenge for its application, and predicting the state of the granules is essential in addressing this issue. This study explored the potential of dynamic texture entropy, derived from settling images, as a predictive tool for the state of granular sludge. Three processes, traditional thickening, often overlooked clarification, and innovative particle sorting, were used to capture the complexity and diversity of granules. It was found that rapid sorting during settling indicates stable granules, which helps to identify the state of granules. Furthermore, a relationship between sorting time and granule heterogeneity was identified, helping to adjust selection pressure. Features of the dynamic texture entropy well correlated with the respirogram, i.e., R2 were 0.86 and 0.91 for the specific endogenous respiration rate (SOURe) and the specific quasi-endogenous respiration rate (SOURq), respectively, providing a biologically based approach for monitoring the state of granules. The classification accuracy of models using features of dynamic texture entropy as an input was greater than 0.90, significantly higher than the input of conventional features, demonstrating the significant advantage of this approach. These findings contributed to developing robust monitoring tools that facilitate the maintenance of stable granular sludge operations.

Qualitative and quantitative comparisons of type 1 macular neovascularizations between pachychoroid neovasculopathy and neovascular age-related macular degeneration using optical coherence tomography angiography

OBJECTIVES

To compare qualitative and quantitative features of type 1 macular neovascularizations (MNV) in pachychoroid neovasculopathy (PNV) and neovascular age-related macular degeneration (nAMD).

METHODS

Forty-three treatment-naive eyes of 41 PNV patients and 40 treatment-naive eyes of 38 patients with nAMD were included. The patients were classified as PNV or nAMD according to the presence of pachychoroid features and soft/reticular drusen. Presence of central trunk and maturity of the MNV were evaluated on optical coherence tomography angiography (OCTA) images. MNV area, vessel density (VD), total vessel length (VL), number of intersection points (IPs), fractal dimension (FD), and lacunarity (LAC) were calculated using ImageJ software and FracLac plugin.

RESULTS

The mean age was 56.8 ± 8.7 years in PNV and 70.4 ± 8.8 years in neovascular AMD groups (p < 0.001). Compared to nAMD, the presence of central trunk was less frequent in PNV (48.8% vs 77.5%, p = 0.007). Immature MNV pattern was observed more frequently in PNV eyes than nAMD (41.9% vs 20.0%, p = 0.009). PNV cases had significantly lower median MNV area [0.913(1.115) vs 2.542(3.273) mm²], total VL [14.84 (20.46) vs 36.34 (44.68) mm], number of IPs [104(140) vs 335(417.3)], and FD [1.56(0.10) vs 1.59(0.11)] comparing to nAMD cases (p < 0.001, p = 0.001, p < 0.001, p = 0.043 respectively). However, the mean VD (42.4 ± 6.8 vs 42.9 ± 9.0%) and the median LAC values [0.42 (0.09) vs 0.42 (0.09)] did not differ significantly between groups (p = 0.776, p = 0.526, respectively).

CONCLUSION

Morphological and quantitative differences exist in type 1 neovascular lesions. Type 1 MNVs in the PNV group are characterized by a smaller and less complex structure.

Edible oil based optical clearing for optical coherence tomography angiography imaging

In optical imaging, optical clearing agents are commonly used to enhance the structural details of a sample. The current study investigates how to use it to improve the data obtained by an optical coherence tomography angiography system. A natural edible oil with no chemical base has been used for optical clearing. In-vivo testing on mice and humans yielded excellent optical clearing. Using computational techniques, the improvement in angiography signal caused by the optical clearing agent is investigated qualitatively and quantitatively. Compared to the control group, applying the edible oil-based optical clearing agent demonstrated improved vessel percentage and refined vascular signal intensity along depth.

A triangular model of fractal growth with application to adsorptive spin-coating of polymers

Over the last 40 years, applied mathematicians and physicists have proposed a number of mathematical models that produce structures exhibiting a fractal dimension. This work has coincided with the discovery that objects with fractal dimension are relatively common in the natural and human-produced worlds. One particularly successful model of fractal growth is the diffusion limited aggregation (DLA) model, a model as notable for its simplicity as for its complex and varied behavior. It has been modified and used to simulate fractal growth processes in numerous experimental and empirical contexts. In this work, we present an alternative fractal growth model that is based on a growing mass that bonds to particles in a surrounding medium and then exerts a force on them in an iterative process of growth and contraction. The resulting structure is a spreading triangular network rather than an aggregate of spheres, and the model is conceptually straightforward. To the best of our knowledge, this model is unique and differs in its dynamics and behavior from the DLA model and related particle aggregation models. We explore the behavior of the model, demonstrate the range of model output, and show that model output can have a variable fractal dimension between 1.5 and 1.83 that depends on model parameters. We also apply the model to simulating the development of polymer thin films prepared using spin-coating which also exhibit variable fractal dimensions. We demonstrate how the model can be adjusted to different dewetting conditions as well as how it can be used to simulate the modification of the polymer morphology under solvent annealing.

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.

A Self-Similarity Logic May Shape the Organization of the Nervous System

From the morphological point of view, the nervous system exhibits a fractal, self-similar geometry at various levels of observations, from single cells up to cell networks. From the functional point of view, it is characterized by a hierarchical organization in which self-similar structures (networks) of different miniaturizations are nested within each other. In particular, neuronal networks, interconnected to form neuronal systems, are formed by neurons, which operate thanks to their molecular networks, mainly having proteins as components that via protein-protein interactions can be assembled in multimeric complexes working as micro-devices. On this basis, the term "self-similarity logic" was introduced to describe a nested organization where, at the various levels, almost the same rules (logic) to perform operations are used. Self-similarity and self-similarity logic both appear to be intimately linked to the biophysical evidence for the nervous system being a pattern-forming system that can flexibly switch from one coherent state to another. Thus, they can represent the key concepts to describe its complexity and its concerted, holistic behavior.

The Morphology of Brain Neurons: The Box-Counting Method in the Quantitative Analysis of 2D Images

This chapter begins by showing the difference between fractal geometry and fractal analysis. The text shows the difference between mathematical and natural fractals and how they are best defined by explaining the concept of fractal analysis. Furthermore, the text presents the most famous technique of fractal analysis: the box-counting method. Defining this method and showing the methodology that leads to the precise value of the fractal (i.e., the box) dimension is done by demonstrating the images of human dentate neurons. A more detailed explanation of the methodology was presented in the previous version of this chapter.This version promotes the notion of monofractal analysis and shows how three types of the same neuronal images can quantify four image properties. The results showed that monofractal parameters successfully quantified four image properties in three nuclei of the cerebellum. Finally, the author discusses the results of this chapter and previously published conclusions. The results show how the monofractal parameters discriminate images of neurons from the three nuclei of the human cerebrum. These outcomes are discussed along with the results of previous studies.

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.

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Model aggregated 2D suspensions in shear and compression: From a fluid layer to an auxetic interface?

HYPOTHESIS

Particle-laden interfaces play a crucial role in engineering stability of multiphase systems. However, a full understanding of the mechanical properties in shear and compression, especially in relation to the underlying microstructural changes, is as yet lacking. In this study, we investigate the interfacial rheological moduli in heterogeneous networks of aggregated 2D suspensions using different deformation modes and relate these moduli to changes in the microstructure.

EXPERIMENTS

Interfacial rheological experiments were conducted at different surface coverages and clean kinematic conditions, namely in (i) simple shear flow in a modified double wall-ring geometry and (ii) isotropic compression in a custom-built radial trough, while monitoring the evolution of the microstructure.

FINDINGS

The compressive moduli increase non-monotonically with decreasing void fraction, reflecting the combined effect of aggregate densification and reduction of void structures, with rotation of rigid clusters playing a significant role in closing voids. However, the shear moduli increase monotonically, which correlates with the increase in fractal dimension of the aggregates making up the backbone network. We also observe that these interfaces act as 2D auxetic materials at intermediate coverages, which is surprising given their amorphous structure. This finding has potential implications for the resilience of particle-coated bubbles or droplets subjected to time-varying compression-expansion deformations.

The mandibular bone structure in children by fractal dimension and its correlation with pixel intensity values: a pilot study

OBJECTIVES

To identify a normal pattern of mandibular trabecular bone in children based on the fractal dimension (FD), and its possible correlation with pixel intensity (PI) values, to facilitate the early diagnosis of possible diseases and/or future bone alterations.

MATERIALS AND METHODS

The 50 panoramic images were selected and divided into two groups, according to the children's age: 8-9 (Group 1; n = 25) and 6-7 (Group 2; n = 25). For FD and PI analyses, three regions of interest (ROIs) were selected, and their mean values were evaluated for each ROI, according to each group, using the t test for independent samples and the model of generalized estimation equations (GEE). Subsequently, these mean values were correlated by the Pearson test.

RESULTS

Comparing the groups, FD and PI did not differ from each other for any of the measured regions (p > 0.00). It was observed that in the mandible branch (ROI1), FD and PI means were 1.26 ± 0.01 and 81.0 ± 2.50, respectively. In the mandible angle (ROI2), the means were 1.21 ± 0.02 (FD) and 72.8 ± 2.13 (PI); and in the mandible, cortical (ROI3) values of FD = 1.03 ± 0.01 and PI = 91.3 ± 1.75 were obtained. There was no correlation between FD and PI in any of the analyzed ROI (r < 0.285). The FD means of ROI1 and ROI2 did not differ from each other (p = 0.053), but both were different from ROI3 (p < 0.00). All PI values differed from each other (p < 0.00).

CONCLUSION

The bone trabeculate pattern in 6-9-year-old children presented FD between 1.01 and 1.29. Besides that, there was no significant correlation between FD and PI.

Microglial morphometric analysis: so many options, so little consistency

Quantification of microglial activation through morphometric analysis has long been a staple of the neuroimmunologist's toolkit. Microglial morphological phenomics can be conducted through either manual classification or constructing a digital skeleton and extracting morphometric data from it. Multiple open-access and paid software packages are available to generate these skeletons via semi-automated and/or fully automated methods with varying degrees of accuracy. Despite advancements in methods to generate morphometrics (quantitative measures of cellular morphology), there has been limited development of tools to analyze the datasets they generate, in particular those containing parameters from tens of thousands of cells analyzed by fully automated pipelines. In this review, we compare and critique the approaches using cluster analysis and machine learning driven predictive algorithms that have been developed to tackle these large datasets, and propose improvements for these methods. In particular, we highlight the need for a commitment to open science from groups developing these classifiers. Furthermore, we call attention to a need for communication between those with a strong software engineering/computer science background and neuroimmunologists to produce effective analytical tools with simplified operability if we are to see their wide-spread adoption by the glia biology community.

Fractal dimension, lacunarity, and cortical thickness in the mandible: Analyzing differences between healthy men and women with cone-beam computed tomography

Purpose

The objective of this study was to assess the fractal dimension, lacunarity, trabecular microarchitecture parameters, and cortical linear measurements in the mandibles of male and female individuals to identify differences between them.

Materials and Methods

In total, 116 cone-beam computed tomography scans of healthy individuals of different ages (57 men and 59 women, aged between 20 and 60 years) were selected. The following bone parameters were measured: 1) buccal, lingual, and basal cortical bone thickness in 5 standard parasagittal sections (the midline, the left and right sides of the lower lateral incisors, and the left and right sides of the lower canines); 2) the bone volume fraction of 10 sequential axial sections from each patient by creating a volume of interest in the area between the lower canines; and 3) fractal dimension and lacunarity using grayscale images of the same region of the volume of interest in the anterior mandible. Spearman correlation coefficients and the Mann-Whitney test were used.

Results

A significant and positive correlation was found between age and cortical thickness, especially in the region of the central incisors. Significant differences between sexes in terms of fractal dimension, lacunarity, and bone volume were found. Women revealed lower fractal dimension values and higher lacunarity and bone volume ratio values than men.

Conclusion

Fractal dimension, lacunarity, trabecular bone volume, and cortical thickness were different between men and women of different ages.

Spontaneous clustering of exfoliated two-dimensional materials at the air-water interface

HYPOTHESIS

Coating approaches which trap nanoparticles at an interface have become popular for depositing single-layer films from nanoparticle dispersions. Past efforts concluded that concentration and aspect ratio dominate the impact on aggregation state of nanospheres and nanorods at an interface. Although few works have explored the clustering behaviour of atomically thin, two-dimensional materials, we hypothesize that nanosheet concentration is the dominant factor leading to a particular cluster structure and that this local structure impacts the quality of densified Langmuir films.

EXPERIMENTS

We systematically studied cluster structures and Langmuir film morphologies of three different nanosheets, namely chemically exfoliated molybdenum disulfide, graphene oxide and reduced graphene oxide.

FINDINGS

We observe cluster structure transitions from island-like domains to more linear networks in all materials as dispersion concentration is reduced. Despite differences in material properties and morphologies, we obtained the same overall correlation between sheet number density (A/V) in the spreading dispersion and cluster fractal structure (d_f) is observed, with reduced graphene oxide sheets showing a slight delay upon transitioning into a lower-density cluster. Regardless of assembly method, we found that cluster structure impacts the attainable density of transferred Langmuir films. A two-stage clustering mechanism is supported by by considering the spreading profile of solvents and an analysis of interparticle forces at the air-water interface.

A highly generalized classifier for osteoporosis radiography based on multiscale fractal, lacunarity, and entropy distributions

Background: Osteoporosis is a common degenerative disease with high incidence among aging populations. However, in regular radiographic diagnostics, asymptomatic osteoporosis is often overlooked and does not include tests for bone mineral density or bone trabecular condition. Therefore, we proposed a highly generalized classifier for osteoporosis radiography based on the multiscale fractal, lacunarity, and entropy distributions. Methods: We collected a total of 104 radiographs (92 for training and 12 for testing) of lumbar spine L4 and divided them into three groups (normal, osteopenia, and osteoporosis). In parallel, 174 radiographs (116 for training and 58 for testing) of calcaneus from health and osteoporotic fracture groups were collected. The texture feature data of all the radiographs were pulled out and analyzed. The Davies-Bouldin index was applied to optimize hyperparameters of feature counting. Neighborhood component analysis was performed to reduce feature dimension and increase generalization. A support vector machine classifier was trained with only the most effective six features for each binary classification scenario. The accuracy and sensitivity performance were estimated by calculating the area under the curve. Results: Interpretable feature trends of osteoporotic pathological changes were depicted. On the spine test dataset, the accuracy and sensitivity of binary classifiers were 0.851 (95% CI: 0.730-0.922), 0.813 (95% CI: 0.718-0.878), and 0.936 (95% CI: 0.826-1) for osteoporosis diagnosis; 0.721 (95% CI: 0.578-0.824), 0.675 (95% CI: 0.563-0.772), and 0.774 (95% CI: 0.635-0.878) for osteopenia diagnosis; and 0.935 (95% CI: 0.830-0.968), 0.928 (95% CI: 0.863-0.963), and 0.910 (95% CI: 0.746-1) for osteoporosis diagnosis from osteopenia. On the calcaneus test dataset, they were 0.767 (95% CI: 0.629-0.879), 0.672 (95% CI: 0.545-0.793), and 0.790 (95% CI: 0.621-0.923) for osteoporosis diagnosis. Conclusion: This method showed the capacity of resisting disturbance on lateral spine radiographs and high generalization on the calcaneus dataset. Pixel-wise texture features not only helped to understand osteoporosis on radiographs better but also shed new light on computer-aided osteopenia and osteoporosis diagnosis.

The fractal brain: scale-invariance in structure and dynamics

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

New insights into the evaluation criteria for high-quality deep marine shale gas reservoirs in the Longmaxi formation: Evidence from organic matter pore development characteristics

Porosity, total organic carbon content, brittle mineral content, and gas content are now the primary references for classifying and evaluating marine shale gas reservoirs in China. Is there a more effective and appropriate reservoir classification scheme for deep marine shale? The Longmaxi Formation in Luzhou, southern Sichuan Basin, China, is the main object of study. Quantitative analysis and modeling using data from field emission scanning electron microscopy, nitrogen adsorption, and logging were used to characterize organic matter (OM) pore multi-scale development and reveal the relationship between OM pore and the high-quality reservoirs. Microscopic and macroscopic indications from OM pores show that a large number of OM pores were developed in high-quality reservoirs. OM surface porosity occupancy of the high-quality reservoir in the Luzhou area was more than 60%. OM porosity occupancy was more than 50%. The nitrogen adsorption–desorption hysteresis loops demonstrate the development of bottleneck and wedge-shaped OM pores. Characterization of multi-scale pore structure by box dimension, pore volume and specific surface area. It is found that the key to the formation of high-quality reservoirs was the massive development of OM mesopores in siliceous shale and the relatively homogeneity structure, which was conducive to the enrichment and migration of shale gas. Furthermore, the improved model decreased the relative error in predicting the OM porosity by about 32.5%. The use of OM porosity occupancy for high-quality reservoir classification was better, and the results were consistent with geological understanding. OM porosity occupancy showed that the area from Lunanxi to Luzhou to Rongchang to Jiangjin was the key exploration area for high-quality reservoirs in southern Sichuan. This study is expected to provide a new idea for OM pore modeling analysis and deep marine shale gas reservoir classification.

The Fractal Viewpoint of Tumors and Nanoparticles

Even though the promising therapies against cancer are rapidly improved, the oncology patients population has seen exponential growth, placing cancer in 5th place among the ten deadliest diseases. Efficient drug delivery systems must overcome multiple barriers and maximize drug delivery to the target tumors, simultaneously limiting side effects. Since the first observation of the quantum tunneling phenomenon, many multidisciplinary studies have offered quantum-inspired solutions to optimized tumor mapping and efficient nanodrug design. The property of a wave function to propagate through a potential barrier offer the capability of obtaining 3D surface profiles using imaging of individual atoms on the surface of a material. The application of quantum tunneling on a scanning tunneling microscope offers an exact surface roughness mapping of tumors and pharmaceutical particles. Critical elements to cancer nanotherapeutics apply the fractal theory and calculate the fractal dimension for efficient tumor surface imaging at the atomic level. This review study presents the latest biological approaches to cancer management based on fractal geometry.

Polymer Physics-Based Classification of Neurons

Recognizing that diverse morphologies of neurons are reminiscent of structures of branched polymers, we put forward a principled and systematic way of classifying neurons that employs the ideas of polymer physics. In particular, we use 3D coordinates of individual neurons, which are accessible in recent neuron reconstruction datasets from electron microscope images. We numerically calculate the form factor, F(q), a Fourier transform of the distance distribution of particles comprising an object of interest, which is routinely measured in scattering experiments to quantitatively characterize the structure of materials. For a polymer-like object consisting of n monomers spanning over a length scale of r, F(q) scales with the wavenumber [Formula: see text] as [Formula: see text] at an intermediate range of q, where [Formula: see text] is the fractal dimension or the inverse scaling exponent ([Formula: see text]) characterizing the geometrical feature ([Formula: see text]) of the object. F(q) can be used to describe a neuron morphology in terms of its size ([Formula: see text]) and the extent of branching quantified by [Formula: see text]. By defining the distance between F(q)s as a measure of similarity between two neuronal morphologies, we tackle the neuron classification problem. In comparison with other existing classification methods for neuronal morphologies, our F(q)-based classification rests solely on 3D coordinates of neurons with no prior knowledge of morphological features. When applied to publicly available neuron datasets from three different organisms, our method not only complements other methods but also offers a physical picture of how the dendritic and axonal branches of an individual neuron fill the space of dense neural networks inside the brain.

Blood supply to the superficial fascia of the abdomen: An anatomical study

The aim of this study was to examine data demonstrating that Scarpa's fascia, a superficial fascia of the anterior abdominal wall, is a vascularized tissue. Specimens of the fascia of seven volunteers undergoing abdominoplasty surgical procedures at the Plastic Surgery Unit of the University of Padova Medical Center were collected. Fractal analysis and quantitative assessment of the vascular network of the fascia was carried out, exploiting the presence of blood in the vessels. Each sample was divided and processed for histological/immunohistochemical analysis (into 5 micron-paraffin embedded sections and cryo-sectioned free-floating samples) as well as for electron microscopy study. A rich vascular pattern forming a fine, dense meshwork with an area percentage of 6.20% ± 2.10% von Willebrand factor stained vessels was noted in all the specimens of the fascia examined; the area percentage of the αSMA-stained vessels was 2.93% ± 1.80%. The diameters of the vessels fell between the 13 and 65 μm range; the network was composed of arteries, veins, capillaries and lymphatic segments. Topological results showed that the vascular network within Scarpa's fascia is well branched (segments: 6615 ± 3070 and 8.40 ± 3.40 per mm² ; crossing points: 3092 ± 1490 and 3.40 ± 1.90 per mm² ). Fractal analysis (fractal dimension = 1.063 ± 0.10; lacunarity = 0.60 ± 0.10) revealed that this particular vascular network has an optimal spatial distribution and homogeneity occupying the entire space of the superficial fascia. These findings could undoubtedly be useful to plastic surgeons as well as to pain management specialists.

Shannon entropy as a reliable score to diagnose human fibroelastic degenerative mitral chords: A micro-ct ex-vivo study

This paper is aimed at identifying by means of micro-CT the microstructural differences between normal and degenerative mitral marginal chordae tendineae. The control group is composed of 21 normal chords excised from 14 normal mitral valves from heart transplant recipients. The experimental group comprises 22 degenerative fibroelastic chords obtained at surgery from 11 pathological valves after mitral repair or replacement. In the control group the superficial endothelial cells and spongiosa layer remained intact, covering the wavy core collagen. In contrast, in the experimental group the collagen fibers were arranged as straightened thick bundles in a parallel configuration. 100 cross-sections were examined by micro-CT from each chord. Each image was randomized through the K-means machine learning algorithm and then, the global and local Shannon entropies were obtained. The optimum number of clusters, K, was estimated to maximize the differences between normal and degenerative chords in global and local Shannon entropy; the p-value after a nested ANOVA test was chosen as the parameter to be minimized. Optimum results were obtained with global Shannon entropy and 2≤K≤7, providing p < 0.01; for K=3, p = 2.86·10^-3. These findings open the door to novel perioperative diagnostic methods in order to avoid or reduce postoperative mitral valve regurgitation recurrences.

Fractional Spiking Neuron: Fractional Leaky Integrate-and-Fire Circuit Described with Dendritic Fractal Model

As dendrites are essential parts of neurons, they are crucial factors for neuronal activities to follow multiple timescale dynamics, which ultimately affect information processing and cognition. However, in the common SNN (Spiking Neural Networks), the hardware-based LIF (Leaky Integrate-and-Fire) circuit only simulates the single timescale dynamic of soma without relating dendritic morphologies, which may limit the capability of simulating neurons to process information. This study proposes the dendritic fractal model mainly for quantifying dendritic morphological effects containing branch and length. To realize this model, We design multiple analog fractional-order circuits (AFCs) which match their extended structures and parameters with the dendritic features. Then introducing AFC into FLIF (Fractional Leaky Integrate-and-Fire) neuron circuits can demonstrate the same multiple timescale dynamics of spiking patterns as biological neurons, including spiking adaptation, inter-spike variability with power-law distribution, first-spike latency, and intrinsic memory. By contrast, it further enhances the degree of mimicry of neuron models and provides a more accurate model for understanding neural computation and cognition mechanisms.

Surface-Based Cortical Measures in Multimodal Association Brain Regions Predict Chess Expertise

The complex structure of the brain supports high-order cognition, which is crucial for mastering chess. Surface-based measures, including the fractional dimension (FD) and gyrification index (GI), may be more sensitive in detecting cortical changes relative to volumetric indexes. For this reason, structural magnetic resonance imaging data from 29 chess experts and 29 novice participants were analyzed using the CAT12 toolbox. FD and GI for each brain region were compared between the groups. A multivariate model was used to identify surface-based brain measures that can predict chess expertise. In chess experts, FD is increased in the left frontal operculum (p < 0.01), and this change correlates with the starting age of chess practice (ρ = −0.54, p < 0.01). FD is decreased in the right superior parietal lobule (p < 0.01). Chess expertise is predicted by the FD in a network of fronto-parieto-temporal regions and is associated with GI changes in the middle cingulate gyrus (p < 0.01) and the superior temporal sulcus (p < 0.01). Our findings add to the evidence that chess expertise is based on the complex properties of the brain surface of a network of transmodal association areas important for flexible high-level cognitive functions. Interestingly, these changes are associated with long-lasting practice, suggesting that neuroplastic effects develop over time.

Mathematical analysis for spatial distribution of vessels, mast cells and adipocytes in superficial fascia

As a novel origin of adipocytes, the superficial fascia, a typical soft connective tissue, has abundant adipocytes and preadipocytes, accompanied by numerous mast cells. Blood vessels pass through the fascia to form a network structure. The more reasonable statistical analysis methods can provide a new method for in-depth study of soft connective tissue by clarifying the spatial distribution relation between cells (point structure) and blood vessels (linear structure). This study adopted the Guidolin et al. statistical analysis methods used by epidemiology and ecology to quantitatively analyze the distribution pattern and correlations among blood vessels, adipocytes, and mast cells. Image-processing software and self-written computer programs were used to analyze images of whole-mounted fascia, and the relevant data were measured automatically. Voronoi's analysis revealed that the vascular network was non-uniformly distributed. In fascia with average area of 3.75 cm2, quantitative histological analysis revealed 81.16% of mast cells and 74.74% of adipocytes distributed within 60 μm of blood vessels. A Spearman's correlation coefficient (rs) of >0.7 showed the co-distribution of the two types of cells under different areas. Ridge regression analysis further revealed the spatial correlation among blood vessels, adipocytes and mast cells. The combination of classical epidemiological analysis and extended computer program analysis can better analyze the spatial distribution relation between cells and vessels and should provide an effective analysis method for study of the histology and morphology of fascia and related connective tissues.

Fractal and textural imaging identify new subgroups of patients with colorectal cancer based on biophysical properties of the cancer cells

Colorectal cancer (CRC) can been sub-divided, based on the generation of tertiary lymphoid structures (TLS), into CRC with a Crohn's like lymphoid reaction (CLR) representing de novo formation of TLSs or CRC lacking TLSs that show Diffuse Inflammatory infiltration (DII). The association between TLS, early treatment initiation and longer survival highlights the need for deeper patient stratification that could lead to more targeted therapies. We hypothesized that such stratification might be achieved by using digital image analyses. Here we retrospectively analyzed 35 CRC patient samples classified as CLR or DII by digital analysis, focusing on the parameters Fractal dimension, Lacunarity and the textural features Angular second momentum, Correlation, Inverse difference momentum and Entropy. Significant differences in the grades of these parameters between the two patient groups provided preliminary data that additional biophysical information can divide CRC into at least 3 subgroups which encompass CLR and DII. Additional studies are needed to test if this sub-classification aids in the selection of targeted therapy for patients with CRC.

Evaluating the effects of orthodontic treatment with clear aligners and conventional brackets on mandibular condyle bone quality using fractal dimension analysis of panoramic radiographs

OBJECTIVE

Orthodontic treatment carried out with clear aligners has become a method that is preferred by patients. In this study, the effect following orthodontic treatment with clear aligners and with conventional brackets, on the mandibular condyle trabecular bone formation is aimed to be examined.

MATERIALS AND METHODS

Thirty two individuals (16 females and 16 males) with a mean age of 16.80 ± 3,10 years who received orthodontic treatment with clear aligners and conventional brackets were included in the study. Individuals included in the study from the archive data were divided into two groups according to treatment types. The mandibular condyle bone quality in the panoramic images taken from the patients before orthodontic treatment (T0) and after orthodontic treatment (T1) has been compared retrospectively. This examination is carried out via the fractal analysis method.

RESULT

The mandibular condyle bone density in individuals that have undergone orthodontic treatment with clear aligners, has been reduced following orthodontic treatment. In individuals that have undergone orthodontic treatment with conventional brackets however the mandibular condyle bone density has increased following treatment (T0) in comparison to before being treated (T1). The mandibular condyle bone density change according to different treatment groups has been found to be statistically different.

CONCLUSION

Orthodontic treatment with clear aligners provides several advantages to patients. However, besides determining the effectiveness of the treatment, complications must also be examined. Application of clear aligners in orthodontic treatment may cause a decrease in bone density in the mandibular condyle. When evaluating orthodontic treatments carried out with clear aligners, the change of the mandibular condyle head bone should be taken into consideration.

Fractal Perspective on the Rapid Maxillary Expansion Treatment; Evaluation of the Relationship Between Midpalatal Suture Opening and Dental Effects

OBJECTIVE

This retrospective study investigates the relationship between the midpalatal suture opening and the dental effects of Rapid Maxillary Expansion (RME) treatment using fractal analysis.

METHODS

The participants of this study were selected from the patients who underwent Cone Beam Computed Tomography(CBCT) scans in 2019 and were treated with banded type Maxillary Expander. This study included 20 participants (with a mean age of 10.64±10.64, ranging from 8 to 13 years): 12 males and 8 females. Patients went through CBCT scan and images taken were analyzed using the ImageJ program. The following parameters were measured and analyzed before and after RME treatment: fractal dimensional value of Midpalatal suture(MPS), Distobuccal(DB), Mesiobuccal(MB), Palatal(P), Total distance, Cortical bone and linear values of External maxilla, Internal maxilla, Palatal roots, distance of Central fosses and angular values of Tipping value of 16 and 26. We used Spearman's nonparametric test for non-normal variables to investigate the correlation between changes in MPS and other variables.

RESULTS

The results showed a strong positive correlation between the MPS and Right MB (0.34, p<0.05) and Left MB (0.59, p<0.05) variables and a strong negative correlation between the MPS and the External maxillary variables (-0.53, p<0.05).

CONCLUSION

The results of the study have shown a strong correlation between right and left MB and External Maxilla. RME caused a reduction in buccal alveolar bone thickness and a slight reduction in MPS thickness in growing patients. Therefore, we suggest that fractal analysis can be used to evaluate the skeletal and dental effects of RME in patients.

A novel injectable fibromodulin-releasing granular hydrogel for tendon healing and functional recovery

A crucial component of the musculoskeletal system, the tendon is one of the most commonly injured tissues in the body. In severe cases, the ruptured tendon leads to permanent dysfunction. Although many efforts have been devoted to seeking a safe and efficient treatment for enhancing tendon healing, currently existing treatments have not yet achieved a major clinical improvement. Here, an injectable granular hyaluronic acid (gHA)-hydrogel is engineered to deliver fibromodulin (FMOD)-a bioactive extracellular matrix (ECM) that enhances tenocyte mobility and optimizes the surrounding ECM assembly for tendon healing. The FMOD-releasing granular HA (FMOD/gHA)-hydrogel exhibits unique characteristics that are desired for both patients and health providers, such as permitting a microinvasive application and displaying a burst-to-sustained two-phase release of FMOD, which leads to a prompt FMOD delivery followed by a constant dose-maintaining period. Importantly, the generated FMOD-releasing granular HA hydrogel significantly augmented tendon-healing in a fully-ruptured rat's Achilles tendon model histologically, mechanically, and functionally. Particularly, the breaking strength of the wounded tendon and the gait performance of treated rats returns to the same normal level as the healthy controls. In summary, a novel effective FMOD/gHA-hydrogel is developed in response to the urgent demand for promoting tendon healing.

Distinct fatty acid redistribution and textural changes in the brain tissue upon the static magnetic field exposure

We observed different outcomes upon the subacute exposure to the 128 mT highly homogeneous static magnetic field (SMF) when its orientation was (i) aligned with the vertical component of the geomagnetic field; (ii) in the opposite direction. We employed the fatty acids (FA) composition and digital image analyses (DIA) to provide insights into the underlying processes and examine the possible weak SMF effects. Swiss-Webster male mice were whole-body exposed for 1 h/day over five days. Brain tissue's thin liquid chromatography resulted in brain FA composition, indicating a possible sequence of changes due to the SMF exposure. Quantitative DIA accurately assessed different image parameters. Delicate textural changes were revealed in the group where pathohistological or biochemical alterations have not been detected. DIA-based biological markers seem to be very promising for studying delicate tissue changes, which results from the high sensitivity and wide availability of DIA.

Controlled assembly of retinal cells on fractal and Euclidean electrodes

Controlled assembly of retinal cells on artificial surfaces is important for fundamental cell research and medical applications. We investigate fractal electrodes with branches of vertically-aligned carbon nanotubes and silicon dioxide gaps between the branches that form repeating patterns spanning from micro- to milli-meters, along with single-scaled Euclidean electrodes. Fluorescence and electron microscopy show neurons adhere in large numbers to branches while glial cells cover the gaps. This ensures neurons will be close to the electrodes’ stimulating electric fields in applications. Furthermore, glia won’t hinder neuron-branch interactions but will be sufficiently close for neurons to benefit from the glia’s life-supporting functions. This cell ‘herding’ is adjusted using the fractal electrode’s dimension and number of repeating levels. We explain how this tuning facilitates substantial glial coverage in the gaps which fuels neural networks with small-world structural characteristics. The large branch-gap interface then allows these networks to connect to the neuron-rich branches.

Fractal Analysis on Surface Topography of Thin Films: A Review

The topographies of various surfaces have been studied in many fields due to the significant influence that surfaces have on the practical performance of a given sample. A comprehensive evaluation requires the assistance of fractal analysis, which is of significant importance for modern science and technology. Due to the deep insights of fractal theory, fractal analysis on surface topographies has been widely applied and recommended. In this paper, the remarkable uprising in recent decades of fractal analysis on the surfaces of thin films, an essential domain of surface engineering, is reviewed. By summarizing the methods used to calculate fractal dimension and the deposition techniques of thin films, the results and trends of fractal analysis are associated with the microstructure, deposition parameters, etc. and this contributes profoundly to exploring the mechanism of film growth under different conditions. Choosing appropriate methods of surface characterization and calculation methods to study diverse surfaces is the main challenge of current research on thin film surface topography by using fractal theory. Prospective developing trends are proposed based on the data extraction and statistics of the published literature in this field.

Pre-Training Without Natural Images

Is it possible to use convolutional neural networks pre-trained without any natural images to assist natural image understanding? The paper proposes a novel concept, Formula-driven Supervised Learning (FDSL). We automatically generate image patterns and their category labels by assigning fractals, which are based on a natural law. Theoretically, the use of automatically generated images instead of natural images in the pre-training phase allows us to generate an infinitely large dataset of labeled images. The proposed framework is similar yet different from Self-Supervised Learning because the FDSL framework enables the creation of image patterns based on any mathematical formulas in addition to self-generated labels. Further, unlike pre-training with a synthetic image dataset, a dataset under the framework of FDSL is not required to define object categories, surface texture, lighting conditions, and camera viewpoint. In the experimental section, we find a better dataset configuration through an exploratory study, e.g., increase of #category/#instance, patch rendering, image coloring, and training epoch. Although models pre-trained with the proposed Fractal DataBase (FractalDB), a database without natural images, do not necessarily outperform models pre-trained with human annotated datasets in all settings, we are able to partially surpass the accuracy of ImageNet/Places pre-trained models. The FractalDB pre-trained CNN also outperforms other pre-trained models on auto-generated datasets based on FDSL such as Bezier curves and Perlin noise. This is reasonable since natural objects and scenes existing around us are constructed according to fractal geometry. Image representation with the proposed FractalDB captures a unique feature in the visualization of convolutional layers and attentions.

Spatial patterns of urbanising landscapes in the North Indian Punjab show features predicted by fractal theory

Understanding and governing human settlement patterns is a major challenge of the urban age. While rural settlements emerge as parts of agricultural landscapes, cities typically evolve in economically strategic locations, and over time form hierarchical systems of cities. Purposeful planning and the collective, self-organized behavior of the inhabitants interact in the development of regional settlement patterns. Since self-organizing systems often produce fractal patterns in nature, this study combines approaches of land use science, city ranking, and urban planning under a fractal theory framework, to analyze the settlement system of the Indian Punjab. Scaling levels were defined by discontinuities in the size distribution of built-up areas (Global Urban Footprint), which correlated to population-based classifications (r = 0.9591). Self-similarity across scales was supported by geo-statistical similarity (p < 0.05) of distances and angles between settlements of successive classes, and the overall fractal dimension of D_B = 1.95. When compared to a modeled Sierpinski Carpet, more than 50% of the settlements met the fractal geometry rules at larger scales. The spatial distribution of small villages, however, deviated, indicating a scale-related shift in organizing principles. Explicitly acknowledging cross-scale relations and self-organisation in regional planning policies may lead to more sustainable settlement structures that are in harmony with natural system properties.

Interactive patches over amyloid-β oligomers mediate fractal self-assembly

The monomeric units of intrinsically disordered proteins self-assemble into oligomers, protofilaments, and eventually fibrils which may turn into amyloid. The aggregation of these proteins is primarily studied in bulk with no restriction on their degrees of freedom. Herein we experimentally demonstrate that amyloid-β (Aβ) aggregation under diffusion-limited conditions leads to its fractal self-assembly. Confocal microscopy and scanning electron microscopy with energy dispersion x-ray analysis were used to confirm that the fractal self-assemblies were formed from Aβ rather than the salt present in the two supporting media: deionized water and phosphate buffered saline. The results from the molecular docking experiments implicated that electrostatic and hydrophobic patches on the solvent-accessible surface area of the Aβ oligomers mediate the fractal self-assembly. These implications were tested with laser light scattering experiments on the oligomers formed by breaking mature fibrils of Aβ through sonication, which were observed to self-assemble into fractals when sonicated solutions were drop casted. The electrostatic interactions modulate the fractal morphologies with pH of the solution, which leads to a morphological phase transition observed through the variation in their fractal dimension. These transitions provide experimental evidence for the existing theoretical framework in terms of different kinetic models. The higher surface-to-volume ratio of these fractal self-assemblies may have applications in drug delivery, biosensing, and other biomedical applications.

The analysis of F-actin structure of mesenchymal stem cells by quantification of fractal dimension

The actin cytoskeleton is indispensable for the motility and migration of all types of cells; therefore, it plays a crucial role in the ability of the tissues to repair. Mesenchymal stem cells are intensively used in regenerative medicine, but usually relatively low percent of transplanted cells reaches the injury. To overcome this evident limitation, researchers try to enhance the motility and migration rate of the cells. As one of the approaches, co-cultivation and preconditioning of stem cells with biologically active compounds, which can cause actin cytoskeleton rearrangements followed by an increase of migratory properties of the cells, could be applied. The observed changes in F-actin structure induced by the compounds require quantitative estimation, and measurement of fluorescence intensity of the F-actin image captured by various microscopic techniques is commonly used nowadays. However, this approach could not always accurately detect the observed changes in the shape and structure of actin cytoskeleton. At this time, the image of F-actin has an irregular geometric pattern, and thus could be considered and characterized as a fractal object. To quantify the re-organization of cellular F-actin in terms of fractal geometry Minkovsky's box-counting method is suitable, but it is not widely used nowadays. We modified and improved the previously described method for fractal dimension measurement, and successfully applied it for the quantification of the F-actin structures of human mesenchymal stem cells.

Antisense therapy in a rat model of Alexander disease reverses GFAP pathology, white matter deficits, and motor impairment

[Figure: see text].

Fractal Design for Advancing the Performance of Chemoresistive Sensors

The rapid advancement of internet of things (IoT)-enabled applications along with connected automation in sensing technologies is the heart of future intelligent systems. The probable applications have significant implications, from chemical process monitoring to agriculture, mining, space, wearable electronics, industrial manufacturing, smart cities, and point-of-care (PoC) diagnostics. Advancing sensor performance such as sensitivity to detect trace amounts (ppb-ppm) of analytes (gas/VOCs), selectivity, portability, and low cost is critical for many of these applications. These advancements are mainly achieved by selecting and optimizing sensing materials by their surface functionalization and/or structural optimization to achieve favorable transport characteristics or chemical binding/reaction sites. Surprisingly, the sensor geometry, shapes, and patterns were not considered as critical parameters, and most of these sensors were designed by following simple planar and interdigitated electrode geometry. In this study, we introduce a new bioinspired fractal approach to design chemoresistive sensors with fractal geometry, which grasp the architecture of fern leaves represented by the geometric group of space-filling curves of fractal patterns. These fractal sensors were printed by an extrusion process on a flexible substrate (PET) using specially formulated graphene ink as a sensing material, which provided significant enhancement of the active surface area to volume ratio and allowed high-resolution fractal patterning along with a reduced current transportation path. To demonstrate the advantages and influence of fractal geometry on sensor performance, here, three different kinds of sensors were fabricated based on different fractal geometrics (Sierpinski, Peano, and Hilbert), and the sensing performance was explored toward different VOC analytes (e.g., ethanol, methanol, and acetone). Among all these fractal-designed sensors including interdigitate sensors, the Hilbert-designed printed sensor shows enhanced sensing properties in terms of fast response time (6 s for 30 ppm), response value (14%), enhanced detection range (5-100 ppm), high selectivity, and low interference to humidity (up to RH 80%) for ethanol at room temperature (20 °C). Moreover, a significant improvement of this sensor performance was observed by applying the mechanical deformation (positive bending) technique. The practical application of this sensor was successfully demonstrated by monitoring food spoilage using a commercial box of strawberries as a model. Based on these presented results, this biofractal biomimetic VOC sensor is demonstrated for a prospective application in food monitoring.

Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

Linear system analysis has been dominating medical and dental research, and most of the research achievements in these fields have come from applying a reductionist view of nature. However, biologic systems are fundamentally nonlinear with highly composite dynamics made up of numerous interacting elements and feedback loops, therefore studying them as linear models may not result in an accurate representation of their true features. The authors reviewed and utilized some of the principles of chaos and nonlinearity and extended them to clinical dentistry, from cracked tooth and flare-up after root canal procedures to the outcome of clinical treatments. Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. The goal of this paper is to present some areas within nonclinical research that we believe will have important roles in the development of future clinical examination methods and therapies.

Postnatal development of inner lamina II interneurons of the rat medullary dorsal horn

ABSTRACT

Pain processing in young mammals is immature. Despite the central role of the medullary dorsal horn (MDH) in processing orofacial sensory information, the maturation of the neurons within the MDH has been largely overlooked. Combining in vitro electrophysiological recordings and 3D morphological analysis over the first postnatal month in rats, we investigated the age-dependent development of the neurons within the inner lamina II (IIi) of the MDH. We show the lamina IIi neuronal population transition into a more hyperpolarized state, with modification of the action potential waveform, and a shift from single spiking, at early postnatal ages, to tonic firing and initial bursting at later stages. These physiological changes are associated with a strong structural remodelling of the neuronal morphology with most of the modifications occurring after the third postnatal week. Among the lamina IIi neuronal population, the subpopulation of interneurons expressing the γ isoform of the protein kinase C (PKCγ+) are key elements for the circuits underlying facial mechanical allodynia. How do they develop from the rest of the lamina IIi constitute an important question that remained to be addressed. Here, we show that PKCγ+ interneurons display electrophysiological changes over time comparable with the PKCγ- population. However, they show a distinctive increase of the soma volume and primary branches length, as opposed to the PKCγ- population. Together, our data demonstrate a novel pattern of late postnatal maturation of lamina IIi interneurons, with a spotlight on PKCγ+ interneurons, that may be relevant for the development of orofacial sensitivity.

Chronic exposure to low concentrations of chlorpyrifos affects normal cyclicity and histology of the uterus in female rats

Chlorpyrifos (CPF), the most used insecticide in Argentina, can act as an endocrine disruptor at low doses. We previously demonstrated that chronic exposure to CPF induces hormonal imbalance in vivo. The aim of this work was to study the effects of low concentrations of CPF (0.01 and 1 mg/kg/day) on the reproductive system of virgin adult rats. In the ovary, we studied the effects of CPF on steroidogenesis by determining steroid hormone content by RIA and CYP11 and CYP19 enzyme expression by qRT-PCR. The estrous cycle was evaluated by microscopic observation of vaginal smear, as well as by changes in uterine histology. In endometrium, we determined the fractal dimension and expression of PCNA, ERα and PR by IHC. Our results showed that chronic exposure to CPF affects ovarian steroid synthesis, causing alterations in the normal cyclicity of animals. In addition, CPF induced proliferative changes in the uterus, suggesting that it could affect reproduction or act as a risk factor in the development of uterine proliferative pathologies.

Structural Fractal Analysis of the Active Site of Acetylcholinesterase in Complexes with Huperzine A, Galantamine, and Donepezil

The fractal dimension (D) of the active site of hAChE in the unliganded state and as part of complexes with hyperzine A, galantamine, and donepezil is calculated using molecular interatomic-distance histograms. Fractal matrices of structural changes (FMSCs) are formed by pairwise comparison of the values of D and by revealing the significance of their differences. FMSCs are found to be used to quantitatively estimate the changes in the structures of the molecules in various states. When analyzing FMSCs, we found that the most significant structural changes are related to the Glu202 amino acid residue. No structural perturbations are revealed in the case of Trp86, Gly122, Ala204, Phe338, Tyr341, Gly448, and Ile451.

Tubular human brain organoids to model microglia-mediated neuroinflammation

Human brain organoids, 3D brain tissue cultures derived from human pluripotent stem cells, hold promising potential in modeling neuroinflammation for a variety of neurological diseases. However, challenges remain in generating standardized human brain organoids that can recapitulate key physiological features of a human brain. Here, we present tubular organoid-on-a-chip devices to generate better organoids and model neuroinflammation. By employing 3D printed hollow mesh scaffolds, our device can be easily incorporated into multiwell-plates for reliable, scalable, and reproducible generation of tubular organoids. By introducing rocking flows through the tubular device channel, our device can perfuse nutrients and oxygen to minimize organoid necrosis and hypoxia, and incorporate immune cells into organoids to model neuro-immune interactions. Compared with conventional protocols, our method increased neural progenitor proliferation and reduced heterogeneity of human brain organoids. As a proof-of-concept application, we applied this method to model the microglia-mediated neuroinflammation after exposure to an opioid receptor agonist. We found isogenic microglia were activated after exposure to an opioid receptor agonist (DAMGO) and transformed back to the homeostatic status with further treatment by a cannabinoid receptor 2 (CB2) agonist (LY2828360). Importantly, the activated microglia in tubular organoids had stronger cytokine responses compared to those in 2D microglial cultures. Our tubular organoid device is simple, versatile, inexpensive, easy-to-use, and compatible with multiwell-plates, so it can be widely used in common research and clinical laboratory settings. This technology can be broadly used for basic and translational applications in inflammatory diseases including substance use disorders, neural diseases, autoimmune disorders, and infectious diseases.

Structural changes in the trabecular bone of the mandibular condyle of growing patients with sagittal jaw discrepancy treated with the twin-block appliance

OBJECTIVE

The objective of this study was to evaluate the structural changes in the trabecular bone of the mandibular condyles in patients treated with the Twin-block functional orthopaedic appliance that act by promoting condylar growth and to compare the fractal dimension (FD) of condylar trabecular bone structure prior to treatment (T0) and after orthopaedic functional treatment (T1).

SETTING AND SAMPLE POPULATION

This retrospective study included panoramic images of 112 individuals with a mean age of 11.04 ± 1.30 years in the study group (32 girls and 24 boys) and 11.6 ± .80 years in the control group (29 girls and 27 boys).

MATERIALS AND METHODS

The standardized region of interest was selected as the right and left condylar areas close to the articulation surfaces from the twin-block (TB) group, which included patients who completed functional orthopaedic treatment and the control group, which included untreated individuals. FD values in the condylar region were analysed from the panoramic radiographs of both groups using a box-counting method with ImageJ software (version 1.52a, US National Institutes of Health).

RESULTS

There was a significant decrease in the FD values of the right (-.038) and left (-.022) condylar region at T0 and T1 in the TB group. Between-group FD comparisons demonstrated that the TB group showed changes in the condylar region (right, P = .004; left, P = .022) compared to the control group.

CONCLUSION

Functional orthopaedic forces caused a decrease in the trabecular structure of the condylar area examined.

Fractal Analysis of the Distribution and Morphology of Pores in Dinosaur Eggshells Collected in Mexico: Implications to Understand the Biomineralization of Calcium Carbonate

In this work, we present an investigation of the surface area and roughness of different dinosaur eggshells of 70 million years old using fractal dimension analysis obtained from atomic force microscopy (AFM) and scanning electron microscopy (SEM) information. We also conduct qualitative analyses on the external and inner surfaces of eggshells, which are mainly composed of calcium carbonate. The morphological characteristics of both surfaces can be revealed by both SEM and AFM techniques. It is observed that the inner surface of the eggshell has greater roughness that increases the surface area due to the vaster number of pores compared to the external face, making, therefore, the fractal dimension also greater. The aim of this contribution is to identify the morphology of the pores, as well as the external and inner surfaces of the eggshells, since the morphology is very similar on both surfaces and will otherwise be difficult to determine with the naked eye by SEM and AFM. In addition, the sole AFM analysis is very complicated for these types of samples due to the intrinsic roughness. However, it needs additional methods or strategies to complete this purpose. This contribution used the fractal dimension to show the same behavior obtained in both SEM and AFM techniques, indicating the fractal nature of the structures.

How neurons exploit fractal geometry to optimize their network connectivity

We investigate the degree to which neurons are fractal, the origin of this fractality, and its impact on functionality. By analyzing three-dimensional images of rat neurons, we show the way their dendrites fork and weave through space is unexpectedly important for generating fractal-like behavior well-described by an ‘effective’ fractal dimension D. This discovery motivated us to create distorted neuron models by modifying the dendritic patterns, so generating neurons across wide ranges of D extending beyond their natural values. By charting the D-dependent variations in inter-neuron connectivity along with the associated costs, we propose that their D values reflect a network cooperation that optimizes these constraints. We discuss the implications for healthy and pathological neurons, and for connecting neurons to medical implants. Our automated approach also facilitates insights relating form and function, applicable to individual neurons and their networks, providing a crucial tool for addressing massive data collection projects (e.g. connectomes).