Perinatal model of human transition from hypogravity to Earth’s gravity based on nonlinear electromyogram characteristics

Interferential electromyogram (iEMG) was analyzed in healthy newborns (n = 29) during the first 24 h of life as a model of transition from hypogravity (intrauterine immersion) to Earth’s gravity (the postnatal period). Nonlinear methods of iEMG analysis (correlation dimension, entropy, and fractal dimension) reflecting the complexity, chaotic character, and predictability of signals from the leg and arm antagonistic muscles were used. The iEMG fractal dimension was shown to grow in all the muscles as the postnatal period extended, except the m. gastrocnemius during the first 24 h of life. Lower fractal and correlation dimensions and entropy were found to be characteristic of the flexors, especially at a low iEMG amplitude suggesting better congenital programming of the flexors compared to the extensors. It was concluded that the early ontogenesis model can be potentially useful for studying the evolution and the states of antigravity functions.     

Structural complexity in mussel beds: the fractal geometry of surface topography

Seafloor topographic complexity is ecologically important because it provides habitat structure and alters boundary-layer flow over the bottom. Despite its importance, there is little agreement on how to define and measure surface complexity. The purpose of this investigation was to utilize fractal geometry of vertical cross-section profiles to characterize the surface topography of the soft-bottom mussel bed (Mytilus edulis L.) at Bob's Cove, ME, USA. Mussels there have been shown previously to have spatially ordered fractal characteristics in the horizontal plane. Two hypotheses were tested. The first was that the bed surface is fractal over the spatial scale of 1.44-200 mm, with fractal dimension less than or equal to 1.26, the value for the Koch curve, our model for bed profiles. The second was that bed surface topography (i.e., in vertical profile) is less complex than the mussel bed spatial pattern (i.e., aerial view in the horizontal plane). Both hypotheses were supported. Cross-sections of plaster casts of the bed produced 88 surface profiles, all of which were fractal over the entire spatial scale of more two orders of magnitude employed in the analysis. Fractal dimension values (D) for individual profiles ranged from 1.031 to 1.310. Fractal dimensions of entire casts ranged up to mean (1.242+/-0.046) and median (1.251) values similar to 1.26, the theoretical value of the Koch curve. The bed surface was less complex than the bed spatial pattern because every profile had D<1.36, the smallest value previously obtained from aerial views of the bed. The investigation demonstrated for the first time that surface topography of a soft-bottom mussel bed was fractal at a spatial scale relevant to hydrodynamic processes and habitat structure important for benthic organisms. The technique of using cross-section profiles from casts of the bed surface avoided possible underestimates of fractal dimension that can result from other profiling methods reported in the literature. The results demonstrate that fractal dimension can be useful in the analysis of habitat space and water flow over any irregular seafloor surface because it incorporates the size, shape, and scale of roughness elements into a simple, numerical metric.     

Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach

A hybrid differential-discrete mathematical model has been used to simulate biofilm structures (surface shape, roughness, porosity) as a result of microbial growth in different environmental conditions. In this study, quantitative two- and three-dimensional models were evaluated by introducing statistical measures to characterize the complete biofilm structure, both the surface structure and volume structure. The surface enlargement, coefficient of roughness, fractal dimension of surface, biofilm compactness, and solids hold-up were found to be good measures of biofilm structure complexity. Among many possible factors affecting the biofilm structure, the influence of biomass growth in relation to the diffusive substrate transport was investigated. Porous biofilms, with many channels and voids between the "finger-like" or "mushroom" outgrowth, were obtained in a substrate-transport-limited regime. Conversely, compact and dense biofilms occurred in systems limited by the biomass growth rate and not by the substrate transfer rate. The surface complexity measures (enlargement, roughness, fractal dimension) all increased with increased transport limitation, whereas the volume measures (compactness, solid hold-up) decreased, showing the change from a compact and dense to a highly porous and open biofilm.     

La géométrie fractale pour l’analyse de signaux médicaux : état de l’art

The diagnostic interpretation of medical images is a complex task aiming to detect potential abnormalities. One of the most used features in this process is texture which is a key component in the human understanding of images. Many studies were conducted to develop algorithms for texture quantification. The relevance of fractal geometry in medical image analysis is justified by the proven self-similarity of anatomical objects when imaged with a finite resolution. Over the last years, fractal geometry was applied extensively in many medical signal analysis applications. The use of these geometries relies heavily on estimation of the fractal features. Various methods were proposed to estimate the fractal dimension or multifractal spectrum of a signal. This article presents an overview of these algorithms, the way they work, their benefits and limits, and their application in the field of medical signal analysis.     

Curvelet Based Offline Analysis of SEM Images

Manual offline analysis, of a scanning electron microscopy (SEM) image, is a time consuming process and requires continuous human intervention and efforts. This paper presents an image processing based method for automated offline analyses of SEM images. To this end, our strategy relies on a two-stage process, viz. texture analysis and quantification. The method involves a preprocessing step, aimed at the noise removal, in order to avoid false edges. For texture analysis, the proposed method employs a state of the art Curvelet transform followed by segmentation through a combination of entropy filtering, thresholding and mathematical morphology (MM). The quantification is carried out by the application of a box-counting algorithm, for fractal dimension (FD) calculations, with the ultimate goal of measuring the parameters, like surface area and perimeter. The perimeter is estimated indirectly by counting the boundary boxes of the filled shapes. The proposed method, when applied to a representative set of SEM images, not only showed better results in image segmentation but also exhibited a good accuracy in the calculation of surface area and perimeter. The proposed method outperforms the well-known Watershed segmentation algorithm.     

Analysis of fractal dimension of O2A glial cells differentiating in vitro

Fractal dimension is a quantitative measure of morphological complexity. Glial cells of the oligodendrocyte-type 2 astrocyte (O2A) lineage exhibit increasing morphological complexity as they differentiate in vitro. Enriched populations of O2A progenitor cells isolated from neonatal rat cerebral hemispheres or optic nerves were allowed to differentiate in vitro, and their fractal dimensions were measured over time. The fractal dimensions of the maturing cells correlated with perceived complexity; cells with elaborate process branching had larger fractal dimensions than cells with a simpler morphology. An analysis of changes in fractal dimension revealed distinct rates of growth for both oligodendrocytes and type 2 astrocytes. The fractal dimension remained constant over a 10-fold range in optical magnification, demonstrating that cultured O2A glial cells exhibit self-similarity, a defining characteristic of fractal objects. These results illustrate that fractal dimension analysis of maturing cell populations is a useful method for quantitatively describing the process of cell differentiation.     

Surface Roughness Detection of Arteries via Texture Analysis of Ultrasound Images for Early Diagnosis of Atherosclerosis

There is a strong research interest in identifying the surface roughness of the carotid arterial inner wall via texture analysis for early diagnosis of atherosclerosis. The purpose of this study is to assess the efficacy of texture analysis methods for identifying arterial roughness in the early stage of atherosclerosis. Ultrasound images of common carotid arteries of 15 normal mice fed a normal diet and 28 apoE^−/− mice fed a high-fat diet were recorded by a high-frequency ultrasound system (Vevo 2100, frequency: 40 MHz). Six different texture feature sets were extracted based on the following methods: first-order statistics, fractal dimension texture analysis, spatial gray level dependence matrix, gray level difference statistics, the neighborhood gray tone difference matrix, and the statistical feature matrix. Statistical analysis indicates that 11 of 19 texture features can be used to distinguish between normal and abnormal groups (p<0.05). When the 11 optimal features were used as inputs to a support vector machine classifier, we achieved over 89% accuracy, 87% sensitivity and 93% specificity. The accuracy, sensitivity and specificity for the k-nearest neighbor classifier were 73%, 75% and 70%, respectively. The results show that it is feasible to identify arterial surface roughness based on texture features extracted from ultrasound images of the carotid arterial wall. This method is shown to be useful for early detection and diagnosis of atherosclerosis.     

The effects of habitat complexity and hydraulic conditions on the establishment of benthic stream macroalgae

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Lethal effect of chitosan‐Ag (I) films on Staphylococcus aureus as evaluated by electron microscopy

Aim: This article investigated the lethal effect and morphological changes on Staphylococcus aureus strains ATCC 25923 and ATCC 6538P produced by chitosan‐Ag (I) films as observed by electron microscopy. Methods and Results: The antimicrobial activity of films against staphylococci was determined using the broth dilution method and agar diffusion test. Killing curves, transmission and scanning electron microscopy (TEM and SEM) techniques were employed to evaluate the bacterial death and morphological changes in bacterial cells after exposure to chitosan‐Ag (I) films. Films affected the cell structure of Staph. aureus, causing elongation of cells, disaggregation of grape‐like cluster, contraction of bacterial cytoplasm, thickening of cell wall, increase in cell wall roughness, cell disruption with loss of intracellular material, filamentation and bacteriolysis, as seen in the micrographs following 3, 6, 12 and 16 h of incubation. Conclusions: Obtained images clearly show that chitosan‐Ag (I) films have a notable antistaphylococcal activity. Significance and Impact of the Study: Information from this study can be employed in guiding future strategies to improve the design of materials for the food industry packaging.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

Functional significance of variation in bryophyte canopy structure

In most bryophytes, the thickness of boundary layers (i.e., unstirred layers) that surrounds plant surfaces governs rates of water loss. Architectural features of canopies that influence boundary layer thickness affect the water balance of bryophytes. Using field samples (9.3 cm diameter cushions) from 12 populations (11 species) of mosses and liverworts, we evaluated the relationship between canopy structure and boundary layer properties. Canopy structure was characterized using a contact surface probe to measure canopy depth along perpendicular transects at spatial scales ranging from 0.8 to 30 mm on 186 points per sample. Semivariance in depth measurements at different spatial scales was used to estimate three architectural properties: surface roughness (L(r)), the scale of roughness elements (S(r)), and fine-scale surface texture, the latter characterized by the fractal dimension (D) of the canopy profile. Boundary layer properties were assessed by evaporation of ethanol from samples in a wind-tunnel at wind speeds from 0.6 to 4.2 m/s and applied to characterize mass transfer using principles of dynamic similarity (i.e., using dimensionless representations of conductance and flow). In addition, particle image velocimetry (PIV) was used to visualize and quantify flow over two species. All cushions exhibited the characteristics of turbulent as opposed to laminar boundary layers, and conductance increased with surface roughness. Bryophyte canopies with higher L(r) had greater conductances at all wind speeds. Particle image velocimetry analysis verified that roughness elements interacted with flow and caused turbulent eddies to enter canopies, enhancing evaporation. All three morphological features were significantly associated with evaporation. When L(r), S(r), and D were incorporated with a flow parameter into a conductance model using multiple linear regression, the model accounted for 91% of the variation in mass transfer.     

On the Fractal Geometry of DNA by the Binary Image Analysis

The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.     

Postural Stability in Young Adults with Down Syndrome in Challenging Conditions

To evaluate postural control and performance in subjects with Down syndrome (SwDS), we measured postural sway (COP) in quiet stance in four 20-second tests: with eyes open or closed and on hard or foam surface. Ten SwDS and eleven healthy subjects participated, aged 29.8 (4.8) and 28.4 (3.9), respectively. The time-series recorded with the sampling rate of 100 Hz were used to evaluate postural performance (COP amplitude and mean velocity) and strategies (COP frequency, fractal dimension and entropy). There were no intergroup differences in the amplitude except the stance on foam pad with eyes open when SwDS had larger sway. The COP velocity and frequency were larger in SwDS than controls in all trials on foam pad. During stances on the foam pad SwDS increased fractal dimension showing higher complexity of their equilibrium system, while controls decreased sample entropy exhibiting more conscious control of posture in comparison to the stances on hard support surface. This indicated that each group used entirely different adjustments of postural strategies to the somatosensory challenge. It is proposed that the inferior postural control of SwDS results mainly from insufficient experience in dealing with unpredictable postural stimuli and deficit in motor learning.     

Fractal dimension of K1735 mouse melanoma clones and spheroid invasion in vitro

An in vitro tumour-host confrontation method to investigate the invasion behaviour of cancer has been applied to K1735 mouse melanomas. Fluorescently labelled spheroids of cancer cells and host cells were confronted and the temporal course of cancer invasion into the host was investigated using confocal laser scanning microscopy. To improve the quantitative data of this method, the boundary images of the fluorescently labelled confrontation pairs were treated as fractals. The physical and mathematical framework for determination of the fractal capacity dimension is widely used in biology and medicine and has proved to be a very useful tool for describing the cancer invasion process. The fractal capacity dimension determination was carried out by dilation of the binary boundaries of the objects, which were treated as an estimate of the Minkowski-Bouligand dimension. The fractal dimension correlated well with the degree of invasion of the K1735-M2 clone. Control experiments, with host-host confrontations and various K1735 clones with reduced invasiveness, support these results.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

The nonlinear parameters of an interference electromyogram in two-day-old human newborns

The temporal structure of an interference electromyogram (iEMG) was studied in healthy one- and two-day-old human newborns (n = 76) using nonlinear parameters (correlation and fractal dimension, correlation entropy). It was found that the nonlinear parameters of iEMG were time-dependent because they decreased during the first two days of life. These parameters were also sensitive to the muscle function, because the correlation dimension, fractal dimension, and correlation entropy of iEMG of the gastrocnemius muscle differed from the same parameters of other muscles. Some nonlinear parameters were found to be independent of the iEMG amplitude. This model of early ontogenesis is expected to be useful for studying antigravitational activity.     

长江源区高寒草原和高寒草甸土壤粒径分布特征

为探究长江源区主要下垫面土壤空间异质性与粒径分布(PSD)非均匀性,运用分形理论描述高寒草原和高寒草甸2种下垫面土壤粒径分布特征,分析了 2种下垫面土壤的分形维数特征差异及其与土壤颗粒组成的关系.结果表明:研究区土壤颗粒粒径主要分布于100-800 μm,高寒草原土壤单重分形维数(Dv)为2.429～2.508,高寒草...     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

Wavelet packet fractal analysis of neuronal morphology

An image analysis method called two-dimensional wavelet packet analysis (2D WPA) is introduced to quantify branching complexity of neurons. Both binary silhouettes and contour profiles of neurons were analyzed to determine accuracy and precision of the fractal dimension in cell classification tasks. Two-dimensional WPA plotted the slope of decay for a sorted list of discrete wavelet packet coefficients belonging to the adapted wavelet best basis to obtain the fractal dimension for test images and binary representations of neurons. Two-dimensional WPA was compared with box counting and mass-radius algorithms. The results for 2D WPA showed that it could differentiate between neural branching complexity in cells of different type in agreement with accepted methods. The importance of the 2D WPA method is that it performs multiresolution decomposition in the horizontal, vertical, and diagonal orientations.     

Alginate/chitosan hydrogels as perspective transport systems for cefotaxime

This work reports synthesis of pH-responsive alginate/chitosan hydrogel spheres with the average diameter of 2.0 ± 0.05 mm, which contain cefotaxime that is an antibiotic of the cefalosporine group. The spheres provided the cefotaxime encapsulation efficiency of 95 ± 1%. An in vitro release of cefotaxime from the spheres in the media that simulate human biological fluids in peroral delivery conditions was found to be a pH-dependent process. The analysis of cefotaxime release kinetics by the Korsmeyer–Peppas model revealed a non-Fickian mechanism of its diffusion, which may be related to intermolecular interactions occurring between the antibiotic and chitosan. Conductometry, UV spectroscopy, and IR spectroscopy were used to study complexation of chitosan with cefotaxime in aqueous media with varied pH, characterize the composition of the complexes, and calculate their stability constants. The composition of the cefotaxime–chitosan complexes was found to correspond to the 1.0:4.0 and 1.0:2.0 molar ratios of the components at pH 2.0 and 5.6, respectively. Quantum chemical modeling was used to evaluate energy characteristics of chitosan–cefotaxime complexation considering the influence of a solvent.