Empirical mode decomposition of field potentials from macaque V4 in visual spatial attention

Empirical mode decomposition (EMD) has recently been introduced as a local and fully data-driven technique for the analysis of non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. In this article we consider the application of EMD to the analysis of neuronal activity in visual cortical area V4 of a macaque monkey performing a visual spatial attention task. We show that, by virtue of EMD, field potentials can be resolved into a sum of intrinsic components with different degrees of oscillatory content. Low-frequency components in single-trial recordings contribute to the average visual evoked potential (AVEP), whereas high-frequency components do not, but are identified as gamma-band (30–90 Hz) oscillations. The magnitude of time-varying gamma activity is shown to be enhanced when the monkey attends to a visual stimulus as compared to when it is not attending to the same stimulus. Comparison with Fourier analysis shows that EMD may offer better temporal and frequency resolution. These results support the idea that the magnitude of gamma activity reflects the modulation of V4 neurons by visual spatial attention. EMD, coupled with instantaneous frequency analysis, is demonstrated to be a useful technique for the analysis of neurobiological time-series.     

A Flattest Constrained Envelope Approach for Empirical Mode Decomposition

Empirical mode decomposition (EMD) is an adaptive method for nonlinear, non-stationary signal analysis. However, the upper and lower envelopes fitted by cubic spline interpolation (CSI) may often occur overshoots. In this paper, a new envelope fitting method based on the flattest constrained interpolation is proposed. The proposed method effectively integrates the difference between extremes into the cost function, and applies a chaos particle swarm optimization method to optimize the derivatives of the interpolation nodes. The proposed method was tested on three different types of data: ascertain signal, random signals and real electrocardiogram signals. The experimental results show that: (1) The proposed flattest envelope effectively solves the overshoots caused by CSI method and the artificial bends caused by piecewise parabola interpolation (PPI) method. (2) The index of orthogonality of the intrinsic mode functions (IMFs) based on the proposed method is 0.04054, 0.02222±0.01468 and 0.04013±0.03953 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is lower than the CSI method and the PPI method, and means the IMFs are more orthogonal. (3) The index of energy conversation of the IMFs based on the proposed method is 0.96193, 0.93501±0.03290 and 0.93041±0.00429 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is closer to 1 than the other two methods and indicates the total energy deviation amongst the components is smaller. (4) The comparisons of the Hilbert spectrums show that the proposed method overcomes the mode mixing problems very well, and make the instantaneous frequency more physically meaningful.     

Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains

This paper presents a new ECG denoising approach based on noise reduction algorithms in empirical mode decomposition (EMD) and discrete wavelet transform (DWT) domains. Unlike the conventional EMD based ECG denoising approaches that neglect a number of initial intrinsic mode functions (IMFs) containing the QRS complex as well as noise, we propose to perform windowing in the EMD domain in order to reduce the noise from the initial IMFs instead of discarding them completely thus preserving the QRS complex and yielding a relatively cleaner ECG signal. The signal thus obtained is transformed in the DWT domain, where an adaptive soft thresholding based noise reduction algorithm is employed considering the advantageous properties of the DWT compared to that of the EMD in preserving the energy in the presence of noise and in reconstructing the original ECG signal with a better time resolution. Extensive simulations are carried out using the MIT-BIH arrythmia database and the performance of the proposed method is evaluated in terms of several standard metrics. The simulation results show that the proposed method is able to reduce noise from the noisy ECG signals more accurately and consistently in comparison to some of the stateof-the-art methods.     

Fronto-Central Theta Oscillations Are Related to Oscillations in Saccadic Response Times (SRT): An EEG and Behavioral Data Analysis

The phase reset hypothesis states that the phase of an ongoing neural oscillation, reflecting periodic fluctuations in neural activity between states of high and low excitability, can be shifted by the occurrence of a sensory stimulus so that the phase value become highly constant across trials (Schroeder et al., 2008). From EEG/MEG studies it has been hypothesized that coupled oscillatory activity in primary sensory cortices regulates multi sensory processing (Senkowski et al. 2008). We follow up on a study in which evidence of phase reset was found using a purely behavioral paradigm by including also EEG measures. In this paradigm, presentation of an auditory accessory stimulus was followed by a visual target with a stimulus-onset asynchrony (SOA) across a range from 0 to 404 ms in steps of 4 ms. This fine-grained stimulus presentation allowed us to do a spectral analysis on the mean SRT as a function of the SOA, which revealed distinct peak spectral components within a frequency range of 6 to 11 Hz with a modus of 7 Hz. The EEG analysis showed that the auditory stimulus caused a phase reset in 7-Hz brain oscillations in a widespread set of channels. Moreover, there was a significant difference in the average phase at which the visual target stimulus appeared between slow and fast SRT trials. This effect was evident in three different analyses, and occurred primarily in frontal and central electrodes.     

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。     

A Four-Stage Hybrid Model for Hydrological Time Series Forecasting

Hydrological time series forecasting remains a difficult task due to its complicated nonlinear, non-stationary and multi-scale characteristics. To solve this difficulty and improve the prediction accuracy, a novel four-stage hybrid model is proposed for hydrological time series forecasting based on the principle of ‘denoising, decomposition and ensemble’. The proposed model has four stages, i.e., denoising, decomposition, components prediction and ensemble. In the denoising stage, the empirical mode decomposition (EMD) method is utilized to reduce the noises in the hydrological time series. Then, an improved method of EMD, the ensemble empirical mode decomposition (EEMD), is applied to decompose the denoised series into a number of intrinsic mode function (IMF) components and one residual component. Next, the radial basis function neural network (RBFNN) is adopted to predict the trend of all of the components obtained in the decomposition stage. In the final ensemble prediction stage, the forecasting results of all of the IMF and residual components obtained in the third stage are combined to generate the final prediction results, using a linear neural network (LNN) model. For illustration and verification, six hydrological cases with different characteristics are used to test the effectiveness of the proposed model. The proposed hybrid model performs better than conventional single models, the hybrid models without denoising or decomposition and the hybrid models based on other methods, such as the wavelet analysis (WA)-based hybrid models. In addition, the denoising and decomposition strategies decrease the complexity of the series and reduce the difficulties of the forecasting. With its effective denoising and accurate decomposition ability, high prediction precision and wide applicability, the new model is very promising for complex time series forecasting. This new forecast model is an extension of nonlinear prediction models.     

Local Properties of Vigilance States: EMD Analysis of EEG Signals during Sleep-Waking States of Freely Moving Rats

Understanding the inherent dynamics of the EEG associated to sleep-waking can provide insights into its basic neural regulation. By characterizing the local properties of the EEG using power spectrum, empirical mode decomposition (EMD) and Hilbert-spectral analysis, we can examine the dynamics over a range of time-scales. We analyzed rat EEG during wake, NREMS and REMS using these methods. The average instantaneous phase, power spectral density (PSD) of intrinsic mode functions (IMFs) and the energy content in various frequency bands show characteristic changes in each of the vigilance states. The 2nd and 7th IMFs show changes in PSD for wake and REMS, suggesting that those modes may carry wake- and REMS-associated cognitive, conscious and behavior-specific information of an individual even though the EEG may appear similar. The energy content in θ₂ (6Hz-9Hz) band of the 1st IMF for REMS is larger than that of wake. The decrease in the phase function of IMFs from wake to REMS to NREMS indicates decrease of the mean frequency in these states, respectively. The rate of information processing in waking state is more in the time scale described by the first three IMFs than in REMS state. However, for IMF5-IMF7, the rate is more for REMS than that for wake. We obtained Hilbert-Huang spectral entropy, which is a suitable measure of information processing in each of these state-specific EEG. It is possible to evaluate the complex dynamics of the EEG in each of the vigilance states by applying measures based on EMD and Hilbert-transform. Our results suggest that the EMD based nonlinear measures of the EEG can provide useful estimates of the information possessed by various oscillations associated with the vigilance states. Further, the EMD-based spectral measures may have implications in understanding anatamo-physiological correlates of sleep-waking behavior and clinical diagnosis of sleep-pathology.     

Modeling of the effect of modulated electromagnetic radiation on animal cells

Frequency-dependent modifications of intracellular free calcium concentration ([Ca2+]i) in neutrophils exposures to modulated extremely high frequency electromagnetic radiation were analyzed using a special mathematical model for [Ca2+]i oscillations. The model took into account the activation of Ca2+ influx into the cell by cytosolic Ca2+ and Ca(2+)-induced Ca2+ release from intracellular stores. The calcium channels of plasma membrane were chosen as a target for the influence of harmonic signal and additive noise in the model. The model simulation showed that in response to modulating signal, the rise in [Ca2+]i, has frequency dependence and phase dependence in relation to the moment of chemical stimulation. The phase-frequency dependence of the effect was observed at a certain sequence of delivery of chemical stimulus and modulating signal to the cell. At intensities of modulating signals exceeding the threshold, a rise in [Ca2+]i, reaching a level of more than 50% of the initial level, was observed at a frequency of about 1 Hz and in the phase range of 0.3-2.5 radians. The effect was found only at high intensities of chemical stimulus. The additive noise introduced into the system modified qualitatively and quantitatively the phase-frequency characteristics of the cell response to the modulating signal. An increase in noise intensity resulted in a displacement of the average frequency of the band of rise in [Ca2+]i, and then the emergence of a set of bands with a greater Q-factors. The analysis of dynamics of the nonlinear system in terms of the stability theory showed that, as the intensity of chemical stimulus increases, the system transits by means of a series of bifurcations from regular driving to chaotic, and then to oscillations, induced by a modulating harmonic signal. The boundary of the transition of oscillations from chaotic to induced ones corresponds to a specific "threshold" of the intensity of chemical stimulus for the significant rise in [Ca2+]i in response to the modulating signal. The results of the model analysis are in good correspondence with the experimental data obtained earlier, namely, with the effects of modulated extremely high-frequency electromagnetic radiation on neutrophils, which were observed only in the presence of Ca2+ in extracellular medium and at high concentrations of calcium ionophore A23187. Thus, as the characteristic frequency of the quasi-periodic process of calcium signalling in the cell coincides with the frequency of external field, a narrow-band rise in [Ca2+]i is observed, which can result in a modification of the functional activity of the cell.     

Temporal associations between weather and headache: analysis by empirical mode decomposition

Background

Patients frequently report that weather changes trigger headache or worsen existing headache symptoms. Recently, the method of empirical mode decomposition (EMD) has been used to delineate temporal relationships in certain diseases, and we applied this technique to identify intrinsic weather components associated with headache incidence data derived from a large-scale epidemiological survey of headache in the Greater Taipei area.

Methodology/Principal Findings

The study sample consisted of 52 randomly selected headache patients. The weather time-series parameters were detrended by the EMD method into a set of embedded oscillatory components, i.e. intrinsic mode functions (IMFs). Multiple linear regression models with forward stepwise methods were used to analyze the temporal associations between weather and headaches. We found no associations between the raw time series of weather variables and headache incidence. For decomposed intrinsic weather IMFs, temperature, sunshine duration, humidity, pressure, and maximal wind speed were associated with headache incidence during the cold period, whereas only maximal wind speed was associated during the warm period. In analyses examining all significant weather variables, IMFs derived from temperature and sunshine duration data accounted for up to 33.3% of the variance in headache incidence during the cold period. The association of headache incidence and weather IMFs in the cold period coincided with the cold fronts.

Conclusions/Significance

Using EMD analysis, we found a significant association between headache and intrinsic weather components, which was not detected by direct comparisons of raw weather data. Contributing weather parameters may vary in different geographic regions and different seasons.     

Studying properties of neurotransmitter receptors by non-stationary noise analysis of spontaneous postsynaptic currents and agonist-evoked responses in outside-out patches

Chemical synaptic transmission depends on neurotransmitter-gated ion channels concentrated in the postsynaptic membrane of specialized synaptic contacts. The functional characteristics of these neurotransmitter receptor channels are important for determining the properties of synaptic transmission. Whole-cell recording of postsynaptic currents (PSCs) and outside-out patch recording of transmitter-evoked currents are important tools for estimating the single-channel conductance and the number of receptors contributing to the PSC activated by a single transmitter quantum. When single-channel activity cannot be directly resolved, non-stationary noise analysis is a valuable tool for determining these parameters. Peak-scaled non-stationary noise analysis can be used to compensate for quantal variability in synaptic currents. Here, we present detailed protocols for conventional and peak-scaled non-stationary noise analysis of spontaneous PSCs and responses in outside-out patches. In addition, we include examples of computer code for individual functions used in the different stages of non-stationary noise analysis. These analysis procedures require 3-8 h.     

The problem of information value in microvascular networks

A novel methodology of quantitative estimation of the information value in microvascular networks is proposed. The methodology has been developed on the basis of the results of wavelet analysis of skin blood flow oscillations measured by means of laser Doppler flowmetry (LDF) in 30 healthy subjects and 56 patients with hand diseases or consequences of hand injuries. The method is based on the calculation of the relative indices of information preservation, dominance of the preserved information, and information effectiveness. The deviation from the multistable information regimen is the largest in the case of resonance oscillations: the total information quantity is significantly decreased; however, the preservation of dominant information and its effectiveness are improved. The preservation of trophic myogenic information predominates upon reduction of sympathetic influences. An increase in the number of information channels increases only the information quantity, whereas the degree of its preservation varies. Sensory peptidergic nerve fibers are activated in response to local heating of the dorsal forearm skin to 34°C. This information is the most effective at the beginning of the heating, when the blood flow increases to a plateau. The blood flow oscillations represented in the wavelet spectrum of microcirculatory oscillations serve as operators based on effective information. These oscillations not only play the hemodynamic role, but also carry information in microvascular networks.     

Signalling drought in guard cells

A number of environmental conditions including drought, low humidity, cold and salinity subject plants to osmotic stress. A rapid plant response to such stress conditions is stomatal closure to reduce water loss from plants. From an external stress signal to stomatal closure, many molecular components constitute a signal transduction network that couples the stimulus to the response. Numerous studies have been directed to resolving the framework and molecular details of stress signalling pathways in plants. In guard cells, studies focus on the regulation of ion channels by abscisic acid (ABA), a chemical messenger for osmotic stress. Calcium, protein kinases and phosphatases, and membrane trafficking components have been shown to play a role in ABA signalling process in guard cells. Studies also implicate ABA-independent regulation of ion channels by osmotic stress. In particular, a direct osmosensing pathway for ion channel regulation in guard cells has been identified. These pathways form a complex signalling web that monitors water status in the environment and initiates responses in stomatal movements.     

Sensory information in local field potentials and spikes from visual and auditory cortices: time scales and frequency bands

Studies analyzing sensory cortical processing or trying to decode brain activity often rely on a combination of different electrophysiological signals, such as local field potentials (LFPs) and spiking activity. Understanding the relation between these signals and sensory stimuli and between different components of these signals is hence of great interest. We here provide an analysis of LFPs and spiking activity recorded from visual and auditory cortex during stimulation with natural stimuli. In particular, we focus on the time scales on which different components of these signals are informative about the stimulus, and on the dependencies between different components of these signals. Addressing the first question, we find that stimulus information in low frequency bands (<12 Hz) is high, regardless of whether their energy is computed at the scale of milliseconds or seconds. Stimulus information in higher bands (>50 Hz), in contrast, is scale dependent, and is larger when the energy is averaged over several hundreds of milliseconds. Indeed, combined analysis of signal reliability and information revealed that the energy of slow LFP fluctuations is well related to the stimulus even when considering individual or few cycles, while the energy of fast LFP oscillations carries information only when averaged over many cycles. Addressing the second question, we find that stimulus information in different LFP bands, and in different LFP bands and spiking activity, is largely independent regardless of time scale or sensory system. Taken together, these findings suggest that different LFP bands represent dynamic natural stimuli on distinct time scales and together provide a potentially rich source of information for sensory processing or decoding brain activity.     

Hierarchic Stochastic Modelling Applied to Intracellular Ca2+ Signals

Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011) which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to signalling. is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular release events (puffs). We derive analytical expressions for a mechanistic model, based on recent data from live cell imaging, and calculate spike statistics in dependence on cellular parameters like stimulus strength or number of channels. The new approach substantiates a generic model, which is a very convenient way to simulate spike sequences with correct spiking statistics.     

Empirical Mode Decomposition and Wavelet Transform Based ECG Data Compression Scheme

ObjectiveIn health-care systems, compression is an essential tool to solve the storage and transmission problems. In this regard, this paper reports a new electrocardiogram (ECG) data compression scheme which employs sifting function based empirical mode decomposition (EMD) and discrete wavelet transform.MethodEMD based on sifting function is utilized to get the first intrinsic mode function (IMF). After EMD, the first IMF and four significant sifting functions are combined together. This combination is free from many irrelevant components of the signal. Discrete wavelet transform (DWT) with mother wavelet ‘bior4.4’ is applied to this combination. The transform coefficients obtained after DWT are passed through dead-zone quantization. It discards small transform coefficients lying around zero. Further, integer conversion of coefficients and run-length encoding are utilized to achieve a compressed form of ECG data.ResultsCompression performance of the proposed scheme is evaluated using 48 ECG records of the MIT-BIH arrhythmia database. In the comparison of compression results, it is observed that the proposed method exhibits better performance than many recent ECG compressors. A mean opinion score test is also conducted to evaluate the true quality of the reconstructed ECG signals.ConclusionThe proposed scheme offers better compression performance with preserving the key features of the signal very well.     

Empirical mode decomposition based filtering techniques for power line interference reduction in electrocardiogram using various adaptive structures and subtraction methods

Electrocardiogram (ECG) is a vital sign monitoring measurement of the cardiac activity. One of the main problems in biomedical signals like electrocardiogram is the separation of the desired signal from noises caused by power line interference, muscle artifacts, baseline wandering and electrode artifacts. Different types of digital filters are used to separate signal components from unwanted frequency ranges. Adaptive filter is one of the primary methods to filter, because it does not need the signal statistic characteristics. In contrast with Fourier analysis and wavelet methods, a new technique called EMD, a fully data-driven technique is used. It is an adaptive method well suited to analyze biomedical signals. This paper foregrounds an empirical mode decomposition based two-weight adaptive filter structure to eliminate the power line interference in ECG signals. This paper proposes four possible methods and each have less computational complexity compared to other methods. These methods of filtering are fully a signal-dependent approach with adaptive nature, and hence it is best suited for denoising applications. Compared to other proposed methods, EMD based direct subtraction method gives better SNR irrespective of the level of noises.     

A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition

Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony. Action Editor: Carson C. Chow     

Optimal Information Transfer in the Cortex through Synchronization

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.     

Automatic analysis of composite physical signals using non-negative factorization and information criterion

In time-resolved spectroscopy, composite signal sequences representing energy transfer in fluorescence materials are measured, and the physical characteristics of the materials are analyzed. Each signal sequence is represented by a sum of non-negative signal components, which are expressed by model functions. For analyzing the physical characteristics of a measured signal sequence, the parameters of the model functions are estimated. Furthermore, in order to quantitatively analyze real measurement data and to reduce the risk of improper decisions, it is necessary to obtain the statistical characteristics from several sequences rather than just a single sequence. In the present paper, we propose an automatic method by which to analyze composite signals using non-negative factorization and an information criterion. The proposed method decomposes the composite signal sequences using non-negative factorization subjected to parametric base functions. The number of components (i.e., rank) is also estimated using Akaike's information criterion. Experiments using simulated and real data reveal that the proposed method automatically estimates the acceptable ranks and parameters.