2.4 EEG Signal Processing and Data Analysis Methods

Clinical researchers have used various statistical methods in conjunction with visual analysis to evaluate EEG data.  Generally, the goal is to relate certain physiological behavior to particular patterns present in the EEG.  One commonly used statistical method is called principal components factor analysis [Gevins, 1987; Trejo and Shensa, 1993].  In this method, the objective is to find a small set of variables called factors (e.g. frequency bins, discrete portions of the time series, etc.) that are maximally uncorrelated with each other and account for most of the variance in the data.  The "best" set of factors is referred to as the principal component factors, which are more likely to be related to the physical condition that is manifested in the data.  Decision and hypothesis testing methods are another class of statistical methods commonly used.  These methods include many techniques, such as:  analysis of variance (ANOVA) tests, multiple regression analysis, and statistical pattern recognition [Gevins, 1987].  In statistical pattern recognition methods, the clinician tries to choose individual features and combinations of features that are important for clinical hypothesis testing.  Stepwise discriminant analysis (SDA) is one pattern recognition method that has been successful in classifying sleep stages and in event-related potential signal analysis.

As mentioned previously, spectral analysis is often used in the analysis of EEGs because the presence of particular frequency bands may be related to specific behavior (e.g. sleep, drowsiness).  The Fourier transform displays power contained in the signal at individual frequencies.  Because the EEG signal is non-stationary, it is necessary to window consecutive data segments and perform consecutive transforms to track the temporal changes in the frequency content of the signal.  These changes are typically viewed on a 3-dimensional graph called a spectrogram or waterfall plot.  Choice of window length, window type, and overlap rate between adjacent data segments are critical to the successful extraction of subtle frequency shifts in the data whose exact temporal nature is unknown [Gevins, 1987; Schiff, 1994].

Several filtering methods have also been used to examine particular frequency bands of interest, including the design of lowpass and bandpass filters.  During the data collection phase, analog IIR (infinite impulse response) filters are used for anti-aliasing and "noise removal" from the EEG signal.  During post-processing analysis, both IIR filters (usually a digital implementation of the analog design) and FIR (finite impulse response) filters are used for signal analysis.  Since advanced analysis typically takes place in the digital domain, frequency-domain designed FIR filters are often used because of their ease of design, ability to design linear phase, and ease of implementation.

Matched filtering used to detect the presence of signal s(t) in the presence of white Gaussian noise n(t) using the model: y(t)=s(t)+n(t)  is another method which optimizes the signal-to-noise ratio.  This approach is useful when the desired signal properties (usually expressed in the frequency domain), S(w), that are to be detected are known a-priori.  The desired signal s(t) is transformed into the frequency-domain S(w) and the complex-conjugate of that transform S*(w)=S(-w) (because s(t) is real) is stored as a reference waveform.  The noisy input signal y(t) is transformed into the frequency domain Y(w) to determine the spectral content of the input signal.  The input Fourier spectrum is then multiplied by the stored reference conjugate waveform and then inverse transformed back to the time domain.  This multiplication in the frequency-domain by the reference waveform will enhance the desired signal components (contained in the reference) and remove the unwanted components (this is a non-causal operation because it involves time reversal of s(t) and batch-processing of the data).  The output product can then be compared to a threshold to determine the presence or absence of the desired signal.

Wavelet theory is another methodology for spectral analysis and filter synthesis.  Wavelets are specially designed signals that have compact support (i.e. are finite duration in the time domain).  Sets of wavelets are used to approximate a signal, where each wavelet is constructed from a basic wavelet by scaling (dilation or compression) and translation (shifting).  The windowed or short-time Fourier transform (STFT) has a fixed analysis window length, and consequently, it will be able to capture many more periods of a sinusoid at higher frequencies than at lower frequencies.  Therefore, the spectral estimate will be increasingly poorer for lower frequencies.  The wavelet transform uses a variable length analysis window that is shorter for higher frequencies and longer for lower frequencies and is designed to capture the same number of periods for any frequency sine wave.  Recent efforts of EEG analysis during sleep and drowsiness have implemented wavelet algorithms as a substitute for windowed Fourier transforms.  Wavelets have recently been applied to analyze ERP's in an attempt to correlate the time-frequency information contained in these signals with human performance measures [Trejo and Shensa, 1993].

Still other researchers are looking at nonlinear characteristics in the EEG signals such as changes in the dimensionality of the signal (indicating periodic, quasi periodic, or chaotic characteristics) as a possible indicator of drowsiness [Pijn, 1991; Pritchard, 1992; Pritchard, 1995].

The analysis of EEGs generally involves the opinions of experienced expert clinicians in conjunction with mathematical methods in an off-line data analysis procedure.  However, there have also been some attempts to automate EEG analysis in the fields of diagnostic sleep scoring and seizure detection.  Automated analysis methods are used to detect the EEG rhythmic activity for the classification of sleep stages [Smith, 1987], for counting spikes and wave complexes [Principe and Smith, 1985; Ktonas, 1987], and for monitoring in intensive care units [Lopes da Silva and Storm van Leeuwen, 1987].

Waveform detection and sleep stage classification are important in the diagnosis of sleep disorders.  Smith et al. [1985, 1987] developed an expert system to classify sleep stages with the knowledge base developed from the experience of sleep researchers and clinicians.  Various analytical methods (lowpass and bandpass filtering, FFTs, zero-crossing and period/amplitude analysis, matched filtering for detecting sleep spindles, pattern recognition, multiple regression analysis) are used to process the data, which is then used by the expert (rule-based) system to reach a decision.  Smith [1987] has claimed a 90% agreement between the computer and human assessments for waveform detection and an 80% agreement for sleep staging.

Several researchers considered automated detection of drowsiness in a waking EEG in the late sixties, including Matousek [1967], Kellaway and Maulsby [1967], and Johnson et al. [1969].  Kellaway observed that increased ratios of theta to alpha activity, increased activity in the 17.5 to 25 Hz range, and increased alpha variability were sensitive indicators of drowsiness.  Johnson found that waking could consistently be distinguished from stage 1 sleep in both high and low-alpha subjects with increased theta-band spectral intensity and decreased percentages of alpha band activity measured relative to the spectral intensity integrated over the entire band.  Gevins et al. [1977] used some of the previous research results to detect drowsiness by setting thresholds based on alert, waking data for each patient using linearly weighted ratios of delta to alpha and theta to alpha spectral intensity from 4 posterior electrode placements.  These ratios were computed on 0.5 to 2 second data epochs to be responsive to transient fluctuations in the level of drowsiness.  Each individual served as his/her own control through the use of an initial, awake calibration period to automatically define the ratio thresholds.  Drowsiness episodes were detected 92% of the time in the training data set and 84% of the episodes were found in the testing data set.  For individuals with low levels of alpha activity, they suggested using theta and/or delta band spectral intensities to better distinguish waking from drowsiness.

The results of Gevins et al. (1987) were much improved over previous results in distinguishing waking from stage 1 sleep.  The authors concluded that this improved accuracy was due to the following factors:  a supervised waking calibration period to set decision thresholds individually; a short time epoch for evaluating transient features; multiple electrodes placed bilaterally and including coverage of the occipital region; and a heuristically determined combination of several tentative "microdecisions" to form the final decision of drowsiness onset or offset.  The first and last of these factors are perhaps most important for improved accuracy in drowsiness detection.  Both of these factors can be incorporated in the current research by recording an "alert" state baseline EEG for each individual, and then using a combination of analytical techniques and measures to reach a final decision on drowsiness.

The EEG associated with arousal is also important in our work.  Even though the EEG during arousal may be different than it is during dozing, the theta to alpha ratio has been reported to decrease with increasing arousal [Matousek, 1967].  This suggests that this ratio may also be useful for detecting arousal.  The abrupt fall-off of alpha spectral intensity with arousal [Kellaway and Maulsby, 1967] would probably be another good indicator.

Expert systems and pattern recognition methods have been employed in the automated detection of phasic and tonic EEG patterns [Ktonas, 1987; Ktonas and Gosalia, 1981].  Phasic EEG patterns are events such as spindles and epileptogenic sharp transients (spikes and sharp waves during seizures).  Examples of tonic EEG patterns include trains of spike-and-wave occurrences, and waxing and waning of alpha activity.  Ktonas has stressed the importance of both time- and frequency-domain analysis to improve waveform detection accuracy.  Time-domain analysis can be used to identify patterns that exist for brief periods and to remove artifacts.  Frequency-domain methods can incorporate filtering to isolate the power density of a signal in particular frequency bands or to detect nonstationarities in the signal, or the FFT can be used to compute the power density of components in frequency bands that were not obvious from analysis of the time signal.

The expert system is advantageous because of its flexible rule base that can utilize various analytical measures and the experience of expert clinicians.  It can also help to capture fuzziness and the qualitative aspects of a clinician.  Ktonas has also noted that real-time spike and sharp wave detection is currently feasible on a UNIX workstation [Ktonas, 1993].  Expert systems have also been used by other researchers for sleep stage classification and artifact removal [Chang et al., 1989; Ifeachor et al., 1990].

Another technique used more recently is the development of artificial neural networks (ANNs) to learn EEG signal patterns for automated sleep stage classification [Roberts and Tarassenko, 1992].  ANNs have also been used to learn patterns in event-related potential (ERP) signals in an attempt to predict human performance [Trejo and Shensa, 1993].  ANNs often require large sets of training data, however they have the capabilities of implementing extremely nonlinear decision boundaries that can enhance classification and thereby improve the decision/detection characteristics of the system.

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