Dynamical correlation of non-stationary signals in time domain—A comparative study

In a thorough study, the multitaper (MTM) and the extended continuous wavelet-transform (CWT) coherence-analysis methods were compared in terms of there application in determining the dynamics from the electroencephalogram (EEG) and electromyogram (EMG) signals of patients with Parkinsonian tremor. The main aim of the study in a biological point of view is to analyze whether the basic tremor frequency and its “first harmonic” frequency of Parkinsonian tremor are really harmonically related or are in fact distinct processes.The extension of the CWT is achieved by using a Morlet wavelet as the analysis window with an adjustable relative bandwidth which gives the flexibility in setting a desired frequency resolution. In order to obtain a perspective view of the two methods, they were applied to two different model signals to determine their actual threshold in detecting short-lived changes in the analysis of non-stationary signals and to determine their noise thresholds by adding external noise to the signals to test the reduction in coherence to be not merely due to the random fluctuations in stochastic signals. Beyond applying an autoregressive 2nd-order and a coupled van der Pol model system, however, also true EEG and EMG data from five Parkinson patients were used. The results were compared in terms of the time and frequency resolutions of these two methods, and it was determined that the multitaper method was able to detect reduction in power and coherence as short as 1 s. The extended CWT analysis only revealed gaps that were longer than 3 s.The time gaps in the coherence indicate the loss of connection between the cortex and muscle during the respective time intervals. This more accurate analysis of the MTM was also seen in the dynamical EEG–EMG coherence at the tremor frequency and its “first harmonic” of Parkinsonian patients.In terms of our “biological” aim, this shows distinct prevalence of the corticomuscular coupling at those frequencies over time. Applying this method to biological data reveals important aspects about their dynamics, e.g., the distinct dynamics between basic frequency and “first harmonic” frequency over time in Parkinsonian tremor.     

Cognitive neuroscience of creativity: EEG based approaches

Cognitive neuroscience of creativity has been extensively studied using non-invasive electrical recordings from the scalp called electroencephalograms (EEGs) and event related potentials (ERPs). The paper discusses major aspects of performing research using EEG/ERP based experiments including the recording of the signals, removing noise, estimating ERP signals, and signal analysis for better understanding of the neural correlates of processes involved in creativity. Important factors to be kept in mind to record clean EEG signal in creativity research are discussed. The recorded EEG signal can be corrupted by various sources of noise and methodologies to handle the presence of unwanted artifacts and filtering noise are presented followed by methods to estimate ERPs from the EEG signals from multiple trials. The EEG and ERP signals are further analyzed using various techniques including spectral analysis, coherence analysis, and non-linear signal analysis. These analysis techniques provide a way to understand the spatial activations and temporal development of large scale electrical activity in the brain during creative tasks. The use of this methodology will further enhance our understanding the processes neural and cognitive processes involved in creativity.     

SSVEP Extraction Based on the Similarity of Background EEG

Steady-state Visual Evoked Potential (SSVEP) outperforms the other types of ERPs for Brain-computer Interface (BCI), and thus it is widely employed. In order to apply SSVEP-based BCI to real life situations, it is important to improve the accuracy and transfer rate of the system. Aimed at this target, many SSVEP extraction methods have been proposed. All these methods are based directly on the properties of SSVEP, such as power and phase. In this study, we first filtered out the target frequencies from the original EEG to get a new signal and then computed the similarity between the original EEG and the new signal. Based on this similarity, SSVEP in the original EEG can be identified. This method is referred to as SOB (Similarity of Background). The SOB method is used to detect SSVEP in 1s-length and 3s-length EEG segments respectively. The accuracy of detection is compared with its peers computed by the widely-used Power Spectrum (PS) method and the Canonical Coefficient (CC) method. The comparison results illustrate that the SOB method can lead to a higher accuracy than the PS method and CC method when detecting a short period SSVEP signal.     

Dynamic processes in the human EEG

The possible mechanisms which determine the temporal dynamics of discrete narrow-band spectral components of human EEG recorded by a single electrode in the state of rest were analyzed. The dynamics of short-segment spectra was observed by application of Fast Fourier Transform (FFT) to 5-s EEG epochs successively shifted by 0.32 s. For each subject the matrices were formed and presented in a graphic mode. Matrix rows represented the number of points in each short-segment spectrum, and the columns represented the number of short-segment spectra. The columns reflect the amplitude dynamics of a given frequency, and power transition between the columns reflects the frequency dynamics. The most common type of the amplitude dynamics consisted in short (2-8 s) periods of stable activity of the discrete spectral components replaced by symmetrical bifurcation or confluence of spectral peaks. The obtained results suggest by the presence of both additive and multiplicative mechanisms of oscillatory interactions in the EEG. More detailed analysis of the amplitude-modulated EEG processes is provided by application of some additive features of the FFT to both EEG and computer-simulated signals.     

Power spectral density and coherence analysis of Alzheimer’s EEG

In this paper, we investigate the abnormalities of electroencephalograph (EEG) signals in the Alzheimer’s disease (AD) by analyzing 16-scalp electrodes EEG signals and make a comparison with the normal controls. The power spectral density (PSD) which represents the power distribution of EEG series in the frequency domain is used to evaluate the abnormalities of AD brain. Spectrum analysis based on autoregressive Burg method shows that the relative PSD of AD group is increased in the theta frequency band while significantly reduced in the alpha2 frequency bands, particularly in parietal, temporal, and occipital areas. Furthermore, the coherence of two EEG series among different electrodes is analyzed in the alpha2 frequency band. It is demonstrated that the pair-wise coherence between different brain areas in AD group are remarkably decreased. Interestingly, this decrease of pair-wise electrodes is much more significant in inter-hemispheric areas than that in intra-hemispheric areas. Moreover, the linear cortico-cortical functional connectivity can be extracted based on coherence matrix, from which it is shown that the functional connections are obviously decreased, the same variation trend as relative PSD. In addition, we combine both features of the relative PSD and the normalized degree of functional network to discriminate AD patients from the normal controls by applying a support vector machine model in the alpha2 frequency band. It is indicated that the two groups can be clearly classified by the combined feature. Importantly, the accuracy of the classification is higher than that of any one feature. The obtained results show that analysis of PSD and coherence-based functional network can be taken as a potential comprehensive measure to distinguish AD patients from the normal, which may benefit our understanding of the disease.     

Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, R?ssler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.     

External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System

The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.     

Time Delay and Partial Coherence Analyses to Identify Cortical Connectivities

Recently it has been demonstrated by Albo that partial coherence analysis is sensitive to signal to noise ratio (SNR) and that it will always identify the signal with the highest SNR among the three signals as the main (driving) influence. We propose to use time delay analysis in parallel to partial coherence analysis to identify the connectivities between the multivariate time series. Both are applied to a theoretical model (used by Albo) to analyse the connections introduced in the model. Time delay analysis identifies the connections correctly. We also apply these analyses to the electroencephalogram (EEG) and electromyogram of essential tremor patients and EEG of normal subjects while bimanually tapping their index fingers. Biologically plausible cortico-muscular and cortico-cortical connections are identified by these methods.     

Non-linear and linear forecasting of the EEG time series

The method of non-linear forecasting of time series was applied to different simulated signals and EEG in order to check its ability of distinguishing chaotic from noisy time series. The goodness of prediction was estimated, in terms of the correlation coefficient between forecasted and real time series, for non-linear and autoregressive (AR) methods. For the EEG signal both methods gave similar results. It seems that the EEG signal, in spite of its chaotic character, is well described by the AR model.     

Relationship of spatial synchronization of θ-band bioelectric potentials of human EEG with the success of visual spatial task performance

Students (46 young men) were asked to memorize and reproduce the order and location (on a computer monitor) of signals. Two groups of subjects were formed according to how accurately they reproduced the true location and order of the signals. Subjects of the first group, in contrast to the second group, reproduced the signal location and order at a high accuracy and with few mistakes even in the first trials. EEGs were recorded prior to the test, during memorizing, and after completion of the task. In the initial state and after completion of the task, the two groups did not differ in the EEG θ-rhythm. During memorizing the signal sequence, an increase in the coefficients of coherence was recorded in the EEG θ band of the right brain hemisphere of the first-group of students; this was not characteristic of the second group. Three systems of connection with the foci of activity were determined in the right occipital, central, and frontal cortical areas, where the coherence of the EEG θ band was significantly higher during memorizing in the students that had exhibited a high accuracy of signal reproduction. Since the right hemisphere deals mainly with the perception of visual spatial information and it is more active in processing nonverbal and stereotyped signals, we have suggested that the students of two groups employed different strategies in solving the task during memorizing.     

第一和第二语言Stroop任务中EEG同步化分析

采用基于多元自回归的瞬时EEG相干方法研究了十位汉英双语者执行Stroop任务时脑神经电活动及其功能皮层区的协同作用。结果显示：在β1(13-18Hz)频段,无论是汉语(第一语言,L1)还是英语(第二语言,L2)呈现的刺激,不一致条件的EEG相干值明显大于一致条件的EEG相干值,表明β1频段对刺激类型敏感;与L2相比,L1的Stroop任务中,额一顶区的相干值显著增强。EEG相干值反映了不同脑皮层间的相互作用强度。因此研究结果表明：判断和处理冲突信息(如Stroop的不一致条件)时脑功能皮层区之间的协同作用增强;相对于第二语言,第一语言处理过程中额一顶区之间的通信协作增加。     

Automatic classification of EEG segments and extraction of representative ones by dynamic clusters method

Use of the dynamic clusters method for automatic extraction of compressed information about recorded EEG signal is presented. The computer first divides the record into quasi-stationary segments by means of adaptive segmentation. Second, the extracted segments are classified by a method of dynamic clusters into homogeneous classes. One part of the used clustering algorithm permits to specify and draw the most typical class members, which may represent the whole studied EEG signal and may be used as input for the further phase of the automatic EEG analysis, i.e. for the classification of the whole EEG records. The above procedure was applied to a 75 sec long EEG record of anaesthetized cat intoxicated by CO.     

Time-Dependent Statistical and Correlation Properties of Neural Signals during Handwriting

To elucidate the cortical control of handwriting, we examined time-dependent statistical and correlational properties of simultaneously recorded 64-channel electroencephalograms (EEGs) and electromyograms (EMGs) of intrinsic hand muscles. We introduced a statistical method, which offered advantages compared to conventional coherence methods. In contrast to coherence methods, which operate in the frequency domain, our method enabled us to study the functional association between different neural regions in the time domain. In our experiments, subjects performed about 400 stereotypical trials during which they wrote a single character. These trials provided time-dependent EMG and EEG data capturing different handwriting epochs. The set of trials was treated as a statistical ensemble, and time-dependent correlation functions between neural signals were computed by averaging over that ensemble. We found that trial-to-trial variability of both the EMGs and EEGs was well described by a log-normal distribution with time-dependent parameters, which was clearly distinguished from the normal (Gaussian) distribution. We found strong and long-lasting EMG/EMG correlations, whereas EEG/EEG correlations, which were also quite strong, were short-lived with a characteristic correlation durations on the order of 100 ms or less. Our computations of correlation functions were restricted to the spectral range (13–30 Hz) of EEG signals where we found the strongest effects related to handwriting. Although, all subjects involved in our experiments were right-hand writers, we observed a clear symmetry between left and right motor areas: inter-channel correlations were strong if both channels were located over the left or right hemispheres, and 2–3 times weaker if the EEG channels were located over different hemispheres. Although we observed synchronized changes in the mean energies of EEG and EMG signals, we found that EEG/EMG correlations were much weaker than EEG/EEG and EMG/EMG correlations. The absence of strong correlations between EMG and EEG signals indicates that (i) a large fraction of the EEG signal includes electrical activity unrelated to low-level motor variability; (ii) neural processing of cortically-derived signals by spinal circuitry may reduce the correlation between EEG and EMG signals.     

Concerning the amplitude modulation of the human EEG

Amplitude-modulated processes can be formally presented as a product of two or more sinusoids. This makes it possible to study them by means of analysis of multiplicative phenomena using the Fast Fourier Transform (FFT). To assess the contribution of amplitude EEG modulation to the dynamic of electrical activity of the human brain, the results of the FFT of simulated signals obtained by multiplication of oscillatory processes with different parameters were compared with the results of the FFT of a single EEG recording from a subject at rest. We studied the temporal dynamics of spectral components calculated with different spectral resolution under similar conditions for real and simulated signals. An attempt was made to analyze and interpret the amplitude-modulated EEG processes using the additive properties of the FTT. It was shown that processes of amplitude modulation are present in electrical brain activity and determine the synchronism of changes in time in the majority of frequency components of the EEG spectrum. The presence of the amplitude modulation in bioelectrical processes is of a fundamental nature, since it is a direct reflection of the control, synchronization, regulation, and intersystem interaction in the nervous and other body systems. The study of this modulation gives a clue to the mechanisms of these processes.     

Determination of ultrasound phase velocity in trabecular bone using time dependent phase tracking technique

Ultrasound velocity is one of the key acoustic parameters for noninvasive diagnosis of osteoporosis. Ultrasound phase velocity can be uniquely measured from the phase of the ultrasound signal at a specified frequency. Many previous studies used fast Fourier transform (FFT) to determine the phase velocity, which may cause errors due to the limitations of FFT. The new phase tracking technique applied an adaptive tracking algorithm to detect the time dependent phase and amplitude of the ultrasound signal at a specified frequency. This overcame the disadvantages of FFT to ensure the accuracy of the ultrasound phase velocity. As a result, the new method exhibited high accuracy in the measurement of ultrasound phase velocity of two phantom blocks with the error less than 0.4%. 41 cubic trabecular samples from sheep femoral condyles were used in the study. The phase velocity of the samples using the new method had significantly high correlation to the bulk stiffness of the samples (r = 0.84) compared to the phase velocity measured using fast Fourier transform FFT (r = 0.14). In conclusion, the new method provided an accurate measurement of the ultrasound phase velocity in bone.     

Spatial organization of biopotentials and decision-making time during purposeful mental activity in humans

Features of spatial organization of neocortical potentials were studied in subjects with different decision-making time during performing the task of memorizing and subsequently reproducing, on a monitor screen, a sequence of signals. The subjects with a short decision-making time differed from those with a long decision-making time in a higher level of the intra- and interhemispheric coherence in alpha EEG frequency band different neocortical areas during reproduction of a signal sequence (coherence in the frontal, central and parietal areas; coherence between the right central and the left frontal, central, parietal, occipital and temporal areas; coherence between the left occipital and both the frontal areas).     

Single evoked potential reconstruction by means of wavelet transform

We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach — the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Baar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two condiitons: high signal to noise ratio and clear separation of the EEG and EP spectra. These assumptions are not easy to fulfill, though. Cerutti et al. (1987) modeled background EEG activity by means of an AR process and event related brain activity by ARMA. In this way they were able to find a filter extracting single EP. Nevertheless, their method was not quite free of assumptions, since they since they used averaged EP to define their ARMA filter. In the following we shall briefly describe the method of the multiresolution decomposition and we will apply it to the analysis and reconstruction of single evoked potentials.     

Analysis of EEG signals during epileptic and alcoholic states using AR modeling techniques

Electroencephalogram (EEG) analysis remains problematic due to limited understanding of the signal origin, which leads to the difficulty of designing evaluation methods. In spite of these shortcomings, the EEG is a valuable tool in the evaluation of some neurological disorders as well as in the evaluation of overall cerebral activity. In most studies, which use quantitative EEG analysis, the properties of measured EEG are computed by applying power spectral density (PSD) estimation for selected representative EEG samples. The sample for which the PSD is calculated is assumed to be stationary. This work deals with a comparative study of the PSD obtained from normal, epileptic and alcoholic EEG signals. The power density spectra were calculated using fast Fourier transform (FFT) by Welch's method, auto regressive (AR) method by Yule–Walker and Burg's method. The results are tabulated for these different classes of EEG signals.     

基于EMD的左右手运动想象脑电信号分析研究

基于经验模态分解（EMD）理论,提出一种左右手运动想象脑电信号分析方法。首先利用时间窗对脑电信号数据进行划分,对每段数据通过经验模态分解法将其分解为一组固有模态函数IMF,提取主要信号所在的IMF层去除信号中的噪声。对含有主要信号的几层IMF进行Hilbert变换,得到瞬时频率与对应的瞬时幅值。再提取左右手想象的特定频段mu节律和beta节律的能量信号作为特征,分别利用支持向量机（SVM）和Fisher进行了分类比较。对EMD和小波包在去噪和特征提取进行了比较。结果表明,EMD是一种很有效的去噪方法,经过EMD分解后提取的能量信号在区分左右手想象上更具有优势,识别率高。