Analysis of EEG signals has been a very active arena for the testing and application of new methods of signal analysis. Such interest comes from the desire to understand better patterns of normal and abnormal brain activity. Initially, computational ability limited the analyses to either non-automated or computationally efficient methods. However, many of those methods have survived the modern era of computer analysis and have been used in even the most advanced devices due to their modest requirements for processing power and the already existing data from a large variety of clinical situations. Analyzing a background EEG signal presents many fewer challenges than does analysis of an epileptic seizure. Although all EEGs are typically composed of a number of component frequencies, many of these records have prolonged periods of relative stationarity. In contrast, the ictal EEG is a rapidly changing dynamical signal that poses a number of analytic challenges that make certain methods (e.g. linear or averaging) less than ideal.
The introduction of the Fast-Fourier transform (FFT) algorithm of Cooley and Tukey (Cooley and Tukey, 1965) represented a major advance in the ability to analyze EEG signals and methods based on FFT are still perhaps the most widely used. For the first time, the EEG signals could be decomposed into component frequencies and changes specific to selected frequency bands could be detected. Although visual characterization of EEG frequencies has been part of routine EEG interpretation since inception, FFT made this analysis objective, quantifiable and accessible. FFT is most appropriately applied to relatively stationary signals such as those during general anesthesia or during ICU recordings of background activity (e.g. slow activity). While short time FFT can be applied to ictal events, the method itself is not suited for detailed time analysis.
The EEG during sleep, including the various sleep stages is one that represents evolution of activity, albeit much more gradual and prolonged than that seen during seizures. EEG activity during sleep has been analyzed extensively and frequency bands from 0 to 40 Hz have been correlated with phases of sleep and sleep-related events. Each band of EEG frequencies has been analyzed and correlated with both visual analysis and with sleep stages. Furthermore, cortical and thalamocortical circuits involved in the generation of those frequencies have been investigated to determine if EEG signal frequency can be equated with specific cerebral activity and the location of such activity.
With increased and more readily available computational power, less computationally efficient methods of signal analysis have been applied. Numerous methods based on autoregressive modeling have provided considerable data from ictal EEGs (Franaszczuk et al., 1985; Gath et al., 1992; Franaszczuk and Bergey, 1999). Even more recently, methods based on non-linear dynamics (e.g. chaos) have been applied to the EEG (Stam, 2005). While the original hypothesis of finding a chaotic state in the brain failed, it has been replaced more recently with more realistic goals of detecting and characterizing the associated non-linear dynamics.
Current intracranial EEG (ICEEG) recordings with higher routine sampling rates allow investigation of higher frequencies. Accurate recording of high frequency activity (e.g. >200 Hz) requires not only appropriate sampling, but also special electrodes designed for this activity. There is a growing number of investigations regarding whether or not this activity is an important component of seizure initiation and of the evolutionary dynamic with early studies in 1992 (Allen et al., 1992; Fisher et al., 1992) and more recent studies utilizing instrumentation that facilitates exploration of higher frequency (Traub et al., 2001; Jirsch et al., 2006). However, the definition of high frequency activity is still variable among groups and results are often limited by the number of patients studied.
Early attempts to provide extended information or analysis in the time-frequency domain were limited by the requirements for stationarity of most methods and the problem of interference of the signal components (cross-terms). Zaveri et al., in 1992, described the maturity of the time-frequency analysis applied to EEG signals of seizures and the possible use of specially designed analysis with limited interference (Zaveri et al., 1992). However, probably due to the mathematical complexity of those methods, they were not developed further than the experimental stages. The introduction of the matching pursuit method provided a method that had no such requirements and was not affected by the cross-term problem.
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