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.     

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.     

Analyzing surface EMG signals to determine relationship between jaw imbalance and arm strength loss

ABSTRACT: BACKGROUND: This study investigated the relationship between dental occlusion and arm strength; in particular, the imbalance in the jaw can cause loss in arm strength phenomenon. One of the goals of this study was to record the maximum forces that the subjects can resist against the pull-down force on their hands while biting a spacer of adjustable height on the right or left side of the jaw. Then EMG measurement was used to determine the EMG-Force relationship of the jaw, neck and arms muscles. This gave us useful insights on the arms strength loss due to the biomechanical effects of the imbalance in the jaw mechanism. METHODS: In this study to determine the effects of the imbalance in the jaw to the strength of the arms, we conducted experiments with a pool of 20 healthy subjects of both genders. The subjects were asked to resist a pull down force applied on the contralateral arm while biting on a firm spacer using one side of the jaw. Four different muscles -- masseter muscles, deltoid muscles, bicep muscles and trapezoid muscles -- were involved. Integrated EMG (iEMG) and Higuchi fractal dimension (HFD) were used to analyze the EMG signals. RESULTS: The results showed that (1) Imbalance in the jaw causes loss of arm strength contra-laterally; (2) The loss is approximately a linear function of the height of the spacers. Moreover, the iEMG showed the intensity of muscle activities decreased when the degrees of jaw imbalance increased (spacer thickness increased). In addition, the tendency of Higuchi fractal dimension decreased for all muscles. CONCLUSIONS: This finding indicates that muscle fatigue and the decrease in muscle contraction level leads to the loss of arm strength.     

Relationship between muscle fatigue and oxygen uptake during cycle ergometer exercise with different ramp slope increments.

The surface electromyogram (EMG) from active muscle and oxygen uptake (VO2) were studied simultaneously to examine changes of motor unit (MU) activity during exercise tests with different ramp increments. Six male subjects performed four exhausting cycle exercises with different ramp slopes of 10, 20, 30 and 40 W.min-1 on different days. The EMG signals taken from the vastus lateralis muscle were stored on a digital data recorder and converted to obtain the integrated EMG (iEMG). The VO2 was measured, with 20-s intervals, by the mixing chamber method. A non-linear increase in iEMG against work load was observed for each exercise in all subjects. The break point of the linear relationship of iEMG was determined by the crossing point of the two regression lines (iEMGbp). Significant differences were obtained in the exercise intensities corresponding to maximal oxygen uptake (VO2max) and the iEMGbp between 10 and 30, and 10 and 40 W.min-1 ramp exercises (P < 0.05). However, no significant differences were obtained in VO2max and VO2 corresponding to the iEMGbp during the four ramp exercises. With respect to the relationship between VO2 and exercise intensity during the ramp increments, the VO2-exercise intensity slope showed significant differences only for the upper half (i.e. above iEMGbp). These results demonstrated that the VO2max and VO2 at which a nonlinear increase in iEMG was observed were not varied by the change of ramp slopes but by the exercise intensity corresponding to VO2max and the iEMGbp was varied by the change of ramp slopes.(ABSTRACT TRUNCATED AT 250 WORDS)     

青藏高原不同草地利用方式对土壤粒径分形特征的影响

研究青藏高原草地土壤粒径结构分形特征,为该地区土壤质量评价和生态恢复提供科学依据。以青藏高原4种高寒草地(放牧、围栏禁牧、围栏禁牧+补植、未干扰)为对象,采用分形理论,研究不同利用方式对高寒草地土壤颗粒组成及分形特征的影响,明确土壤粒径分形特征的影响因素。结果表明：与放牧和围栏禁牧+补植相比,围栏禁牧草地中黏粒和粉粒体积分数分别增加了60%—91.1%、43.5%—80.1%,禁牧能够促进土壤砂粒向黏粒和粉粒转变。不同草地利用方式对分形维数有显著影响,单重分形维数D值依次为放牧草地<围栏禁牧+补植草地<未干扰草地=围栏禁牧草地,多重分形维数,包括信息维数D₁、信息维数/容量维数比值D₁/D₀和关联维数D₂依次为放牧草地<围栏禁牧+补植草地<围栏禁牧草地<未干扰草地。单重分形维数D与土壤黏粒、粉粒呈极显著正相关(P<0.01);砂粒、黏粒、粉粒、有机碳和全氮是多重分形维数的限制因素。信息维数D₁、信息维数/容量维数比值D₁...     

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     

分子进化研究：Ⅱ.5SrRNA序列的分形与分子进化的关系

本文根据分形理论的原理和方法,在对现行的计算核酸序列分维的方法进行修改的基础上,对各类生物的80余种5SrRNA序列的分维进行了计算,并结合耗散结构理论就其分维与分子进化的关系问题进行了研究和探讨。作者认为,5SrRNA序列的分维与其分子进化间的关系是一种复杂的非线性关系,在分子进化的过程中,序列的分维表现为随机涨落。     

Hemispheric asymmetry non-linear analysis of EEG during emotional responses from idiopathic Parkinson’s disease patients

Recent studies show right hemisphere has a unique contribution to emotion processing. The present study investigated EEG using non-linear measures during emotional processing in PD patients with respect to motor symptom asymmetry (i.e., most affected body side). We recorded 14-channel wireless EEGs from 20 PD patients and 10 healthy age-matched controls (HC) by eliciting emotions such as happiness, sadness, fear, anger, surprise and disgust. PD patients were divided into two groups, based on most affected body side and unilateral motor symptom severity: left side-affected (LPD, n = 10) or right side-affected PD patients (RPD, n = 10). Nonlinear analysis of these emotional EEGs were performed by using approximate entropy, correlation dimension, detrended fluctuation analysis, fractal dimension, higher order spectra, hurst exponent (HE), largest Lyapunov exponent and sample entropy. The extracted features were ranked using analysis of variance based on F value. The ranked features were then fed into classifiers namely fuzzy K-nearest neighbor and support vector machine to obtain optimal performance using minimum number of features. From the experimental results, we found that (a) classification performance across all frequency bands performed well in recognizing emotional states of LPD, RPD, and HC; (b) the emotion-specific features were mainly related to higher frequency bands; and (c) predominantly LPD patients (inferred right-hemisphere pathology) were more impaired in emotion processing compared to RPD, as showed by a poorer classification performance. The results suggest that asymmetric neuronal degeneration in PD patients may contribute to the impairment of emotional communication.     

Non-linear coupling of atrial activation processes during atrial fibrillation in humans

The activation patterns underlying the electrical activity of the heart during atrial fibrillation (AF) are not entirely random. The aim of this study was to assess the local organization of the activation processes during AF by estimating the non-linear coupling between activation sequences (ASs) in two atrial sites. To quantitatively estimate the degree of non-linear coupling we extracted two indices based on a multivariate embedding procedure and on the estimation of the correlation dimension (CD) and correlation entropy (CE), termed independence of complexity and of independence of predictability, respectively. We analysed AS in two atrial sites in 30 informed subjects during chronic AF of type I, II and III (Wells' classification), ten 6-s-long episodes of each type. Surrogates were used to reject the hypothesis that the time series were generated by linear stochastic dynamics. We estimated CD and CE according to the coarse-grained approach, which leads to a fixed high value for the embedding dimension in all the analysed ASs, and a typical value for the distance between the two ASs in the phase space. Various degrees of organization, ranging from completely synchronized to fully de-coupled signals, were observed: significant degrees of non-linear coupling were found in segments belonging in types I and II AF, whereas type III electrograms always turned out to be weakly coupled. This finding links the morphology of single electrograms to the synchronization between pairs of closely spaced electrograms. Our bivariate approach suggests that the measurement of organization during AF should be based on the estimation of the non-linear coupling between two sites. This approach appears to be more reliable and sensitive than non-linear analysis of single electrograms or linear analysis of their coupling.     

A fractal model for the characterization of mycelial morphology

A new technique based on a fractal model has been developed for the quantification of the macroscopic morophology of mycelia. The morphological structuring is treated as a fractal object, and the fractal dimension, determined by an ultrasonic scattering procedure developed for the purpose, serves as a quantitative morphological index. Experimental observations reported earlier and simulations of mycelial growth, carried out using a probabilistic-geometric growth model developed for the purpose, both validate the applicability of the fractal model. In experiments with three different species, the fractal dimensions of pelletous structures were found to be in the range 1.45-2.0 and those of filamentous structures were in the range 1.9-2.7, with values around 2.0 representing mixed morphologies. Fractal dimensions calculated from simulated mycelia are in rough agreement with these ranges. The fractal dimension is also found to be relatively insensitive to the biomass concentration, as seen by dilution of the original broths. The relation between morphology and filtration properties of the broths has also been studied. The fractal dimension shows a strong correlation with the index of cake compressibility and with the Kozeny constant, two filtration parameters that are known to be morphology dependent. This technique could thus be used to develop correlations between the morphology, represented by the fractal dimension, and important morphology-dependent process variables. (c) 1993 John Wiley & Sons, Inc.     

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...     

Linear and non-linear analysis of cardiac health in diabetic subjects

Diabetes is a chronic disease characterized by hyperglycaemia, which leads to specific long-term complications: retinopathy, neuropathy, nephropathy and cardiomyopathy. Analysis of cardiac health using heart rate variation (HRV) has become a popular method to assess the activities of the autonomic nervous system (ANS). It is beneficial in the assessment of cardiac abnormalities, because of its ability to capture fast fluctuations that may be an indication of sympathetic and vagal activity.This paper documents work on the analysis of both normal and diabetic heart rate signals using time domain, frequency domain and nonlinear techniques. The study is based on data from 15 patients with diabetes and 15 healthy volunteers. Our results show that non-linear analysis of HRV is superior compared to time and frequency methods. Non-linear parameters namely,correlation dimension (CD), approximate entropy (ApEn), sample entropy (SampEn) and recurrence plot properties (REC and DET), are clinically significant.     

Ontogenetic changes in the fractal geometry of the bronchial tree in Rattus norvegicus

Respiration and metabolism change dramatically over the course of the development of vertebrates. In mammals these changes may be ascribed to organogenesis and differentiation of structures involved in gas exchange and transport and the increase in size. Since young as well as mature individuals must be well-designed if the species is to survive, the physiological changes during the development should be matched with geometrical or structural adjustments of the respiratory system. The aim of this study was to evaluate changes in the fractal geometry of the bronchial tree during the postnatal development of the rat. The average fractal dimension of the bronchial tree of the rats was 1.587, but that of juveniles was larger than that of the adults. We found a significant negative correlation between age and fractal dimension. This correlation could be considered be misleading because of the difficulty of separating age/body size effects. Nevertheless, because fractal dimensions of the bronchial tree of rabbits and humans are known to be similar, 1.58 and 1.57 respectively, the body size effect may be nil. To our knowledge, this is the first report of ontogenetic changes in the fractal dimension of the bronchial tree in mammals.     

Microstructural characterization of chitosan and alginate films by microscopy techniques and texture image analysis

The aim of this work is to characterize the microstructure of chitosan and alginate edible films by microscopy techniques and texture image analysis. Edible films were obtained by solution casting and solvent evaporation. The microscopy techniques used in this work were: light, environmental scanning electron and atomic force microscopy. Textural features and fractal dimension were extracted from the images. Entropy and fractal dimension were more useful to evaluate the complexity and roughness of films. The highest values of entropy and fractal dimension corresponded to alginate/chitosan, followed of alginate and chitosan films. An entropy/fractal dimension ratio, proposed here, was useful to characterize the degree of image complexity and roughness of edible films at different magnifications. It was possible to postulate that microscopy techniques combined with texture image analysis are efficient tools to quantitatively evaluate the surface morphology of edible films made of chitosan and alginate.     

A stochastic attractor participates in chymotrypsin catalysis. A new facet of enzyme catalysis

The previously observed discrete levels of vibrational parameters of chymotrypsin and tosyl-chymotrypsin were analyzed by the methods of non-linear dynamics in order to investigate their origin. The fractal dimensionality of the step sequence was determined using the correlation function and the Farey-tree method. These methods yielded the same value and indicated the presence of a "Devil's Staircase", i.e. the existence of a stochastic attractor. The latter was assigned to the substrate-mobilizable conformation. The attractor dimension of the catalytic site in the acylated state was found to be indistinguishable from that of the substrate mobilizable conformation. A "Devil's Staircase" signals the transition from the regular to the stochastic regime. This transition is shared by critical phenomena and may be a prerequisite for catalysis.     

Relationship between work and electromyographic activity during repeated leg muscle contractions in orienteers

Contraction work (CW) was recorded for each of 200 repetitive isokinetic plantar flexions (1.05 rad.s-1) and knee extensions (1.57 rad.s-1) in 14 elite male orienteers. Simultaneous recordings of integrated electromyograms (iEMG) were obtained from the 3 parts of triceps surae and from 3 superficial portions of quadriceps femoris. CW in both muscle groups decreased significantly during the first 30 contractions (the fatigue phase), followed by a steady state level. The relative steady state level was higher for the plantar flexors (70 +/- 17%) than for the knee extensors (56 +/- 12%). For quadriceps a significant increase in iEMG occurred during the first 10 contractions followed by a decrease, whereas the iEMG of the plantar flexors showed a gradual decrease to the steady state level, which was similar for the two muscle groups (71-72%). The chosen expression of output/input balance (CW/iEMG) was constant throughout the plantarflexion test but decreased during the initial 20 knee extensions down to 82%. Thus, the fatigue phase of the knee extensions appeared to be divided into two; the first part had decreases in both CW and CW/iEMG and the second part with a decrease in CW alone. In contrast the plantar flexors only showed the characteristics of the second part.     

Pair-preferences: a Quantitative Measure of Regularities in Protein Sequences

Abstract

We present here the results obtained by applying several different methods to quantitatively measure regularities in protein sequences based on pair-preferences. We have studied the distribution of amino acid residues, singly as well as in pairs in a large data base and have attempted this task. We confirmed the existence of well-defined pair-preferences in proteins which were shown to be remarkably absent in simulated random sequences of similar amino acid distribution. The analysis of the sequences from the SWISS-PROT data base using simple statistical tests, Fourier analysis, fractal analysis and statistical thermodynamical tests were used to derive parameters to define a natural sequence. As a consequence of the existence of pair-preferences, parameters like fractal dimension (D), spectral exponent (β), scaling parameter (H) and entropy (statistical) were found to be characteristic for natural sequences. For a reference state we chose a randomised state devoid of any pair-preference. The pair-preferences qualified well to be used as quantitative measures of regularities in protein sequences.     

Modelling applicability of fractal analysis to efficiency of soil exploration by roots

BACKGROUND AND AIMS: Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion-limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested. MODEL: The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2.5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length. KEY RESULTS: Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three-dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity. CONCLUSIONS: These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.     

Exercise alters fractal dimension and spatial correlation of pulmonary blood flow in the horse.

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) and spatial correlations. On average, the fractal dimension decreased with exercise (trot 1.216 to gallop 1.173; P < 0. 05) despite a variable fractal dimension at rest. Spatial correlation of flow to neighboring pieces increased with exercise (trot 0.57 +/- 0.074 to gallop 0.73 +/- 0.051) and was inversely correlated with fractal dimension, indicating better spatial correlation as blood flow distribution becomes more uniform. This is the first study to document a change in fractal dimension as a result of increasing pulmonary blood flow. Spatial differences in response to vasoregulatory mediators may play a role in this phenomenon.