Nonlinear measures of heart rate time series: influence of posture and controlled breathing.

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P < 0.00001), a decrease in predictability (P < 0.00001) and an increase in nonlinearity (P = 0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component.

A chaos-based model for low complexity predictive coding scheme for compression and transmission of electroencephalogram data.

A method for low complexity, low bit rate transmission of EEG (electroencephalogram) data, based on chaotic principles, is presented. The EEG data is assumed to be generated by a non-linear dynamical system of E dimensions. The E dynamical variables are reconstructed from the one-dimensional time series by the process of time-delay embedding. A model of the form X[n + 1] = F(X[n], X[n - 1], ... , X[n - p]) is fitted for the data in the E-dimensional space and this model is used as predictor in the predictive coding scheme for transmission. This model is able to give a reduction of nearly 50% of the dynamic range of the error signal to be transmitted, with a reduced complexity, when compared to the conventionally used linear prediction method. This implies that a reduced bit rate of transmission with a reduced complexity can be obtained. The effects of variation of model parameters on the complexity and bit rate are discussed.

EEG seizure in bilateral ECT is different between low and high stimulus doses.

Melancholic depressive patients referred for ECT were randomized to receive either low dose (n = 20) or high dose (n = 20) stimulus applied bifrontotemporally. The two stimulus groups were comparable on the clinical variables. The EEG seizure was recorded on two channels (right and left frontal), digitized, coded and analyzed offline without knowledge of ECT parameters. EEG seizure was of comparable duration in the two stimulus (high dose and low dose) groups. A new composite measure, Strength-Symmetry-Index (SSI), based on strength and symmetry of seizure EEG was computed using fractal geometry. The SSI of the early-seizure was higher in the high dose than in the low dose ECT group. In a stepwise, logistic regression model, this variable contributed to 65% with correct classification of high dose and low dose ECT seizures.

Strength Symmetry Index: a measure of seizure adequacy in ECT.

Seizure electroencephalography (EEG) was recorded from two channels--right (Rt) and left (Lt)--during bilateral electroconvulsive therapy (ECT) (n = 12) and unilateral ECT (n = 12). The EEG was also acquired into a microcomputer and was analyzed without knowledge of the clinical details. EEG recordings of both ECT procedures yielded seizures of comparable duration. The Strength Symmetry Index (SSI) was computed from the early- and midseizure phases using the fractal dimension of the EEG. The seizures of unilateral ECT were characterized by significantly smaller SSI in both phases. More unilateral than bilateral ECT seizures had a smaller than median SSI in both phases. The seizures also differed on other measures as reported in the literature. The findings indicate that SSI may be a potential measure of seizure adequacy that remains to be validated in future research.

EEG delta band spectral power: differneces between unilateral and bilateral ect seizures.

EEG was recorded from right and left frontal leads during bilateral (n=11) and unilateral (n=l4) ECTs. The seizure EEG was analyzed using East Fourier 'Transform and the spectral power oj the Delta (1-4 Hz) band was computed. The spectral power on both sides was similar in the bilateral ECT. Unilateral ECT produced asymmetry in the early - (first 8 seconds after stimulus offset) and mid - (17-32 seconds after the stimulus offset) siezure phases; the spectral power was lower on the unstimulated hemisphere. Studies to elucidate the relevance of EEG delta band of the seizure to therapeutic potency of ECT are suggested.

ANC schemes for the enhancement of EEG signals in the presence of EOG artifacts.

One of the most important applications of adaptive systems is in noise cancellation using adaptive filters. In this paper, we propose adaptive noise cancellation schemes for the enhancement of EEG signals in the presence of EOG artifacts. The effect of two reference inputs is studied on simulated as well as recorded EEG signals and it is found that one reference input is enough to get sufficient minimization of EOG artifacts. This has been verified through correlation analysis also. We use signal to noise ratio and linear prediction spectra, along with time plots, for comparing the performance of the proposed schemes for minimizing EOG artifacts from contaminated EEG signals. Results show that the proposed schemes are very effective (especially the one which employs Newton's method) in minimizing the EOG artifacts from contaminated EEG signals.

Patterns of attractor dimensions of sleep EEG.

Low dimensional chaos is a property of many physiological oscillatory systems including the brain. Time series of sleep EEG records have been analyzed in the framework of recent developments in nonlinear dynamics. One of the characteristics of a chaotic time series is its attractor dimension. The running attractor dimension of a chaotic time series may reflect changes in states more accurately than manually scored records. In the present study the attractor dimensions of consecutive EEG segments of five sleep records were analyzed. The block of the EEG segment (window) was shifted by various lengths along the entire sleep data of each subject thus producing a running attractor dimension curve for each record. The attractor dimension values for different sleep stages were significantly different. The pattern of the running attractor dimension closely matched the scored hypnograms in these five sleep records.

Use of finite wordlength FIR digital filter structures with improved magnitude and phase characteristics for reduction of muscle noise in EEG signals.

One of the main disturbances in EEG signals is EMG artefacts generated by muscle movements. In the paper, the use of a linear phase FIR digital low-pass filter with finite wordlength precision coefficients is proposed, designed using the compensation procedure, to minimise EMG artefacts in contaminated EEG signals. To make the filtering more effective, different structures are used, i.e. cascading, twicing and sharpening (apart from simple low-pass filtering) of the designed FIR filter. Modifications are proposed to twicing and sharpening structures to regain the linear phase characteristics that are lost in conventional twicing and sharpening operations. The efficacy of all these transformed filters in minimising EMG artefacts is studied, using SNR improvements as a performance measure for simulated signals. Time plots of the signals are also compared. Studies show that the modified sharpening structure is superior in performance to all other proposed methods. These algorithms have also been applied to real or recorded EMG-contaminated EEG signal. Comparison of time plots, and also the output SNR, show that the proposed modified sharpened structure works better in minimising EMG artefacts compared with other methods considered.

Autoregressive spectral array for graphical display of EEG data.

A graphical display of the frequency content of background electroencephalogram (EEG) activity is obtained by calculating the spectral estimates using autocorrelation autoregressive method and the classical Fourier transform method. Display of spectral content of consecutive data segments is made using hidden-line suppression technique so as to get a spectral array. The autoregressive spectral array (ASA) is found to be sensitive to baseline drift. Following baseline correction the autoregressive technique is found to be superior to the Fourier method of compressed spectral array (CSA) in detecting the transitions in the frequencies of the signal. The smoothed ASA gives a better picture of transitions and changes in the background activity. The ASA can be made to adapt to specific changes of dominant frequencies while eliminating unnecessary peaks in the spectrum. The utility of the ASA for background EEG analysis is discussed.

Minimization of EOG artefacts from corrupted EEG signals using a neural network approach.

In this paper, we propose a neural network (NN) approach to the enhancement of EEG signals in the presence of EOG artefacts. We recast the EEG enhancement problem into the optimization framework by developing an appropriate cost function. The cost function is nothing but the energy in the enhanced EEG signal obtained through a nonlinear filter formulation, unlike the conventionally-used linear filter formulation. The minimization property of feedback-type neural networks is exploited to solve this problem. An analysis has been performed to characterize the stationary points of the suggested energy function. The hardware set-up of the developed neural network has also been derived. The optimum nonlinear filter coefficients obtained from this minimization algorithm are used to estimate the EOG artefact which is then subtracted from the corrupted EEG signal, sample by sample, to get the artefact minimized signal. The time plots as the LP spectrum show that the proposed method is very effective. Thus the power and efficacy of the NN approach have been exploited for the purpose of minimizing EOG artefacts from corrupted EEG signals.

Spectral estimation of EEG signals using cascaded inverse filters.

While most of the studies on application of autoregressive (AR) methods to EEG signals have considered direct modelling of EEG data, this paper considers the inverse problem of passing the EEG signal through an inverse filter and shows how such inverse filters when cascaded give an improved spectral estimate of the input data. It is shown how a proper choice of model orders of such cascaded inverse filters leads to better spectral estimation of an EEG signal than by conventional AR filters. An EEG signal, when first passed through a low order inverse filter, actually results in a signal with reduced dynamic range and thus a second inverse filter with higher order gives much better spectral peaks. In fact, such cascading operation reduces the problem of ill conditioning of the autocorrelation matrix thus yielding better results. The analysis has been performed using real EEG data.

A non-linear estimation model for adaptive minimization of EOG artefacts from EEG signals.

In this paper, we propose an adaptive noise cancellation scheme in a novel way for the minimization of electrooculogram (EOG) artefacts from corrupted EEG signals. This method is based on the fact that the transfer function of the biological neuron can be modeled as a sigmoid non-linearity. Comparison of the time plots and the smoothed linear prediction spectra show that the proposed method effectively minimizes the EOG artefacts from corrupted EEG signals. We have also studied the performance of the above scheme for different values of filter order (P) and the convergence factor (mu). Normalised Mean Squared Error (NMSE) has been used as the measure for comparison. The study shows that the NMSE decreases with increase in P and mu (but saturates after certain values of the parameters), thereby implying a better EOG minimization from EEG signals. It is also observed that the EOG minimization scheme with two EOG reference inputs works better than that with one reference input.

Data compression by linear prediction for storage and transmission of EEG signals.

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

A nonlinear perspective in understanding the neurodynamics of EEG.

The developments in nonlinear dynamics and the theory of chaos have considerably altered our perception and analysis of many complex systems, including the brain. This paper reviews the physical and dynamical aspect of brain's electrical activity from this new perspective and indicates possible future directions. The importance of emerging trends of nonlinear dynamics and chaos to neurobiology has been discussed in the context of various states of consciousness and behaviour. In the past, EEG analysis has been confined to descriptive stochastic statistics and any understanding of the transitional process of brain activities was either nonexistent or not amenable for investigation. With the developments in nonlinear dynamics, the chaotic dynamical parameters and trajectory behaviour will find their use as feature detection techniques in EEG. Furthermore, nonlinear dynamics provides a model for EEG generation and temporal prediction which will help in determining the nature of neuronal processes governing various states of brain activity. The formalism of globally coupled dynamic systems will find applications in modelling the transitional states of EEG.

Use of running fractal dimension for the analysis of changing patterns in electroencephalograms.

Running fractal dimensions were measured on four channels of an electroencephalogram (EEG) recorded from a normal volunteer. The changes in the background activity due to eye closure were clearly differentiated by the fractal method. The compressed spectral array (CSA) and the running fractal dimensions of the EEG showed corresponding changes with respect to change in the background activity. The fractal method was also successful in detecting low amplitude spikes and the changes in the patterns in the EEG. The effects of different window lengths and shifts on the running fractal dimension have also been studied. The utility of fractal method for EEG data compression is highlighted.

A mimetic-based frequency domain technique for automatic generation of EEG reports.

This paper describes a novel mimetic technique of using frequency domain approach and digital filters for automatic generation of EEG reports. Digitized EEG data files, transported on a cartridge, have been used for the analysis. The signals are filtered for alpha, beta, theta, and delta bands with digital bandpass filters of fourth-order, cascaded, Butterworth, infinite impulse response (IIR) type. The maximum amplitude, mean frequency, continuity index and degree of asymmetry have been computed for a given EEG frequency band. Finally, searches for the presence of artifacts (eye movement or muscle artifacts) in the EEG records have been made.