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Two ranges of dielectric permittivity (k) increase in polymer composites upon the modification of BaTiO3 filler with multiwalled carbon nanotubes (MWCNTs) are shown for the first time. The first increase in permittivity is observed at low MWCNT content in the composite (approximately 0.07 vol.%) without a considerable increase in dielectric loss tangent and electrical conductivity. This effect is determined by the intensification of filler-polymer interactions caused by the nanotubes, which introduce Brønsted acidic centers on the modified filler surface and thus promote interactions with the cyanoethyl ester of polyvinyl alcohol (CEPVA) polymer binder. Consequently, the structure of the composites becomes more uniform: the permittivity increase is accompanied by a decrease in the lacunarity (nonuniformity) of the structure and an increase in scale invariance, which characterizes the self-similarity of the composite structure. The permittivity of the composites in the first range follows a modified Lichtenecker equation, including the content of Brønsted acidic centers as a parameter. The second permittivity growth range features a drastic increase in the dielectric loss tangent and conductivity corresponding to the percolation effect with the threshold at 0.3 vol.% of MWCNTs.
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Introduction: Several functional gastrointestinal disorders (FGIDs) have been associated with the degradation or remodeling of the network of interstitial cells of Cajal (ICC). Introducing fractal analysis to the field of gastroenterology as a promising data analytics approach to extract key structural characteristics that may provide insightful features for machine learning applications in disease diagnostics. Fractal geometry has advantages over several physically based parameters (or classical metrics) for analysis of intricate and complex microstructures that could be applied to ICC networks. Methods: In this study, three fractal structural parameters: Fractal Dimension, Lacunarity, and Succolarity were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy; respectively of three types of gastric ICC network structures from a flat-mount transgenic mouse stomach. Results: The Fractal Dimension of ICC in the longitudinal muscle layer was found to be significantly lower than ICC in the myenteric plexus and circumferential muscle in the proximal, and distal antrum, respectively (both p < 0.0001). Conversely, the Lacunarity parameters for ICC-LM and ICC-CM were found to be significantly higher than ICC-MP in the proximal and in the distal antrum, respectively (both p < 0.0001). The Succolarity measures of ICC-LM network in the aboral direction were found to be consistently higher in the proximal than in the distal antrum (p < 0.05). Conclusions: The fractal parameters presented here could go beyond the limitation of classical metrics to provide better understanding of the structural-functional relationship between ICC networks and the conduction of gastric bioelectrical slow waves.
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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.
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Fractales , HumanosRESUMEN
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.
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PURPOSE: To investigate the relationship between the macular values of fractal dimension (FD) and lacunarity (LAC) on optical coherence tomography angiography (OCTA) images and the presence of peripheral retina non-perfusion areas (NPAs) on fluorescein angiography (FA) in patients with treatment-naïve diabetic macular edema (DME). METHODS: Fifty patients with treatment-naïve DME underwent a full ophthalmic examination, including best-corrected visual acuity measurement, FA, spectral-domain optical coherence tomography, and OCTA. Specifically, FA was performed to detect the presence of retinal NPAs, whereas fractal OCTA analysis was used to determine macular FD and LAC values at the level of the superficial and deep capillary plexus (SCP and DCP). FA montage frames of the posterior pole and peripheral retina, as well as macular OCTA slabs of the SCP and DCP, were obtained. RESULTS: Thirty (60%) eyes with FA evidence of peripheral retinal NPAs in at least one quadrant showed significantly lower FD and higher LAC in both SCP and DCP, when compared with eyes presenting a well-perfused peripheral retina. Furthermore, macular FD and LAC values were found to be significantly associated with the extent of retinal NPAs. CONCLUSIONS: Macular FD and LAC of both SCP and DCP seem to be strongly associated with the extent of peripheral retinal NPAs, thus suggesting that may be useful predictive biomarkers of peripheral ischemia in treatment-naïve DME eyes.