New and robust method for trabecular bone texture based on fractal dimension

Zehani, Soraya; Ouahabi, Abdeldjalil; Oussalah, Mourad; Mimi, Malika; Taleb‐Ahmed, Abdelmalik

doi:10.1109/iecon.2016.7793619

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…Biological systems have been studied under the fractal perspective (Copley et al, 2012 ; Wedman et al, 2015 ; Lennon et al, 2016 ; Stankovic et al, 2016 ). There are reports suggesting that the fractal dimension discriminates between healthy and pathological conditions (Hiroshima et al, 2016 ; Zehani et al, 2016 ; Müller et al, 2017 ; Zhang et al, 2017 ; Popovic et al, 2018 ). In the cardiac context, structural remodeling generates significant fractal dimension variations (Zouein et al, 2014 ; Captur et al, 2016 ).…”

Section: Introductionmentioning

confidence: 99%

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

et al. 2018

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The mechanisms of atrial fibrillation (AF) are a challenging research topic. The rotor hypothesis states that the AF is sustained by a reentrant wave that propagates around an unexcited core. Cardiac tissue heterogeneities, both structural and cellular, play an important role during fibrillatory dynamics, so that the ionic characteristics of the currents, their spatial distribution and their structural heterogeneity determine the meandering of the rotor. Several studies about rotor dynamics implement the standard diffusion equation. However, this mathematical scheme carries some limitations. It assumes the myocardium as a continuous medium, ignoring, therefore, its discrete and heterogeneous aspects. A computational model integrating both, electrical and structural properties could complement experimental and clinical results. A new mathematical model of the action potential propagation, based on complex fractional order derivatives is presented. The complex derivative order appears of considering the myocardium as discrete-scale invariant fractal. The main aim is to study the role of a myocardial, with fractal characteristics, on atrial fibrillatory dynamics. For this purpose, the degree of structural heterogeneity is described through derivatives of complex order γ = α + jβ. A set of variations for γ is tested. The real part α takes values ranging from 1.1 to 2 and the imaginary part β from 0 to 0.28. Under this scheme, the standard diffusion is recovered when α = 2 and β = 0. The effect of γ on the action potential propagation over an atrial strand is investigated. Rotors are generated in a 2D model of atrial tissue under electrical remodeling due to chronic AF. The results show that the degree of structural heterogeneity, given by γ, modulates the electrophysiological properties and the dynamics of rotor-type reentrant mechanisms. The spatial stability of the rotor and the area of its unexcited core are modulated. As the real part decreases and the imaginary part increases, simulating a higher structural heterogeneity, the vulnerable window to reentrant is increased, as the total meandering of the rotor tip. This in silico study suggests that structural heterogeneity, described by means of complex order derivatives, modulates the stability of rotors and that a wide range of rotor dynamics can be generated.

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Section: Introductionmentioning

confidence: 99%

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

et al. 2018

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“…In our case, the use of wavelets enhances the contours, which minimizes the impact of information loss in medical imaging, mainly in tumor detection [12][13][14][15]. Moreover, bandelets are 2nd-generation wavelets and the corresponding transform is an orthogonal multi-resolution transform that is able to capture the geometric content of images and surfaces.…”

Section: Introductionmentioning

confidence: 99%

Medical Video Coding Based on 2nd-Generation Wavelets: Performance Evaluation

et al. 2019

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The operations of digitization, transmission and storage of medical data, particularly images, require increasingly effective encoding methods not only in terms of compression ratio and flow of information but also in terms of visual quality. At first, there was DCT (discrete cosine transform) then DWT (discrete wavelet transform) and their associated standards in terms of coding and image compression. The 2nd-generation wavelets seeks to be positioned and confronted by the image and video coding methods currently used. It is in this context that we suggest a method combining bandelets and the SPIHT (set partitioning in hierarchical trees) algorithm. There are two main reasons for our approach: the first lies in the nature of the bandelet transform to take advantage of capturing the geometrical complexity of the image structure. The second reason is the suitability of encoding the bandelet coefficients by the SPIHT encoder. Quality measurements indicate that in some cases (for low bit rates) the performance of the proposed coding competes with the well-established ones (H.264 or MPEG4 AVC and H.265 or MPEG4 HEVC) and opens up new application prospects in the field of medical imaging.

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“…It has been shown that real systems exhibit nonlinear behaviors (Garcia‐Ruiz et al, 2012; Meakin, 1998), examples of fields where these behaviors can be observed are: pluvimetry (García‐Marín, 2007), texture food (Serrano et al, 2019), medical signal and image analysis (Baish & Jain, 2000; dos Santos Menezes et al, 2021; Hua et al, 2009; Jud et al, 2016; Lopes & Betrouni, 2009; N'Diaye et al, 2013; Reishofer et al, 2018; Silvetti & Delrieux, 2010), and porous media (Ehlers & Wagner, 2019; Jiang & Tchelepi, 2019; Shen et al, 2018) the latest one is of our interest. Actually, scientific communications on porous systems cover multiple disciplines of science and engineering, some examples are: materials science and fluid dynamics (Calvo‐Guirado et al, 2019; Ehlers & Wagner, 2019; Hosseinikhah et al, 2020) thermodynamics (Alizadeh et al, 2021; Sheikholeslami et al, 2019) and biological systems (Khazayinejad et al, 2021; Kosari & Vafai, 2021), for instance; bones (Alves et al, 2017; Borowska et al, 2015; Camargo et al, 2016; Harrar et al, 2011; Hua et al, 2009; Koh et al, 2012; Sanchez‐Molina et al, 2013; Xiao et al, 2020; Zehani et al, 2016) and teeth (Nezafat et al, 2019; Solaymani et al, 2018, 2020)—on which we focus on. Teeth and bones share some similarities like mineral composition (calcium phosphate) and both contain internally living porous tissue, but the main difference between them is that bones can regenerate by their own, unlike teeth (Okazaki, 2021).…”

Section: Introductionmentioning

confidence: 99%

Multifractal approach for a biological porous media: Human dentin case

Sánchez‐Chávez,

Flores‐Cano,

Santiago‐Hernández

et al. 2023

Microscopy Res & Technique

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A multifractal characterization to human dentin porosity is made. Micrographs of human dentin samples gotten from scanning electron microscopy (SEM) were studied in order to characterize porosity. We got the generalized dimensions (multifractal moments) for pore space and matrix skeleton on gray scale and binary images for samples of both gender. For the case, we found that superficial porosity is linked to mass fractal dimension in an approximately linear relationship as for binary images. In addition, probability density distribution (PDD) for pore diameters is found a normal PDD type. Other quantities of interest like mean, standard deviation, maximum and minimum pore diameters, voit ratios, and percentage of chemical composition are reported.Research Highlights SEM sample, images and procedure for multifractal analysis are detailed. Micro patterns in grayscale are multifractal and in binary scale are monofractals. Superficial porosity is relate to mass fractal dimension approximately linearly. From the porosity values, voit ratios are determined. Pores diameters obey a normal PDD.

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New and robust method for trabecular bone texture based on fractal dimension

Cited by 6 publications

References 19 publications

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

Atrial Rotor Dynamics Under Complex Fractional Order Diffusion

Medical Video Coding Based on 2nd-Generation Wavelets: Performance Evaluation

Multifractal approach for a biological porous media: Human dentin case

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