Fig. 1
Algorithm for calculation of AEEG. The raw EEG is filtered, rectified, smoothed, and the amplitude displayed as a range on a combined linear/logarithmic compressed time scale
AEEG has been extensively used for evaluating cerebral function in critically ill neonates, including commercially available “cerebral function monitors” that provide AEEG for a limited number of channels. AEEG may be a reliable means to detect background EEG patterns and seizures [10], although, used in isolation without raw EEG, a significant proportion of seizures may be missed (sensitivities of 38–55 % sensitivity for neonatologist trained in interpretation of cerebral function monitors) [11]. Sensitivity of AEEG for seizure detection in cEEG in adult patients has been reported as >80 % [12] (Fig. 2).
Fig. 2
Example of focal seizures on AEEG. AEEG for the left hemisphere and right hemisphere electrode derivation is displayed at the top (note the combined linear and logarithmic scale for amplitude). Three seizures predominantly involving the left hemisphere are shown in this 1 h sample. The bottom panel shows the raw EEG near seizure onset at the time point indicated by the arrowhead
Envelope Trend Analysis
The envelope trend is similar to the AEEG. The raw EEG is filtered to a specified frequency range (commonly 2–6 Hz), and the median amplitude of the waveforms within the frequency range is plotted for a given epoch (e.g., 10–20 s) (Fig. 3). In neonates, envelope trends have been shown to be fairly sensitive for longer seizures, but performed much more poorly for brief seizures and slowly evolving seizures [13].
Fig. 3
Example of focal seizures on envelope trend. Envelope trend for the left and right hemisphere electrode derivations is displayed at the top, showing two seizures predominantly involving the left hemisphere. The bottom panel shows the raw EEG near seizure onset at the time point indicated by the arrowhead
Burst Suppression Ratio
The burst suppression ratio (BSR) is an algorithm designed to follow the depth of sedation during management of status epilepticus or other condition (like elevated intracranial pressure) with anesthetics, where the goal is to place the EEG in a burst suppression pattern. Traditionally, burst suppression is often described by the duration of the periods of suppression and, sometimes, the duration of the intervening bursts. The BSR is simply the percentage of time in a given epoch that the EEG is suppressed (Fig. 4). Thus, an EEG consisting of on average 3 s periods of suppression with 1 s bursts would have a BSR of 75 %. For the purpose of calculating the BSR, suppression is defined as an EEG amplitude below a certain value (e.g., <5 μV) for a minimum duration (e.g., >0.5 s). As with other qEEG tools/trends, the actual mathematical algorithms used for implementation are more complex [14].
Fig. 4
Example of burst suppression ratio. A 1 h sample of the calculated BSR for the left and right hemisphere is displayed at the top. Raw EEG samples from time points A and B (arrows) are shown at the bottom. In (a), the BSR is approximately 70 % indicating fairly large fraction of the sample is suppressed. With reduction in sedation, the BSR drops to around 10–15 % at point B, and the periods of suppression are much briefer. Raw EEG corresponding to time points A and B are shown in panels (a) and (b), respectively
Frequency-Domain qEEG Tools
Rudimentary frequency-domain qEEG tools have been available for decades, including in analog machines. With the advent of digital EEG recordings and the availability of more powerful computers, they have become much more common.
Filtering
Although not commonly thought of as a qEEG tool, filtering of the raw EEG using analog or digital filters to reduce/remove certain frequencies is a form of frequency-domain analysis. This allows for the removal of noise (e.g., 60 Hz interference, high-frequency artifact from muscle activity, and low-frequency artifact from sweat). In addition, the EEG can be filtered to highlight the contribution made by certain frequencies, for example, a band-pass filter from 8 to 13 Hz to look at alpha frequencies or from 12 to 16 Hz to look for spindle activity.
Spectral Analysis
Most frequency-domain analysis relies on Fourier analysis (or spectral analysis). Fourier analysis refers to decomposing a signal (any quantity that varies with time or some other dimension) into simpler pieces – a weighted sum of trigonometric functions, like sine waves, with different frequencies and starting points (phase shifts), referred to as the Fourier series. For periodic signals (those that repeat at some regular interval), this can be done as a series of sine waves that are harmonically related (have frequencies that are integer multiples of the main frequency). For aperiodic signals, the sine waves required to decompose the signal theoretically involve all frequencies. For each frequency, the Fourier series is actually a complex number (having a real and imaginary component, written as a + ib). Rather than talking about the real and imaginary components, the Fourier series is usually expressed in terms of an amplitude (r, size of the sine wave) and a phase (θ, the point in the cycle of the sine wave at which it starts):
For most signals, calculating the Fourier series is mathematically complicated. The computation of the Fourier series was significantly simplified by an algorithm known as the fast Fourier transform (FFT), which is used to calculate the Fourier series for a discrete (digital) signal. The signal is first broken up into smaller pieces (epochs), and the FFT is calculated by assuming that the epoch repeats itself over and over. Because the signal will not necessarily start and stop at the same voltage, the repeated epochs would not necessarily create a continuous signal. In order to avoid this discontinuity, the signal is “windowed” – multiplied by a function which minimally impacts most of the epoch but rapidly tapers the edges to a value of 0. This avoids discontinuities. Some examples of commonly used window functions are Hamming and Hann windows. Discussion of specific properties of windows is beyond the scope of this chapter and not relevant for most uses of qEEG; however, it can be relevant when interested in very low frequencies.
Technical aspects of the FFT that can be relevant are the limitations on frequency resolution and maximum frequency. If the digital signal has a temporal resolution of Δt (time in seconds between adjacent points in the signal), the maximum frequency in the FFT, F max (in Hz), is
.This is directly related to the Nyquist sampling theorem. If the length of the epoch used to calculate the FFT is T (in seconds), then the frequency resolution, Δf (resolution in Hz between adjacent points in the Fourier series), is
.Thus, if a digital EEG signal was recorded with a temporal resolution of 200 Hz (i.e., Δt is 0.005 s), then F max is 100 Hz. If the FFT is calculated for 2 s epochs (i.e., T is 1 s), then the frequency resolution of the Fourier series is 0.5 Hz. Longer epochs will provide better frequency resolution but at the expense of diluting out rapid or short-lived changes in the frequency content of the signal.
Power
As mentioned above the Fourier series consists of both an amplitude and a phase for each frequency. For most routine qEEG calculations, the phase is ignored. The amplitude squared (r 2) of the Fourier series is referred to as the power (units of V 2/Hz). A plot of power versus frequency is the power spectrum (Fig. 5). The power within a given frequency band refers to the area under the power spectrum curve for that frequency range; the relative power is the ratio of the power within a frequency band to the total power. Plots of power with a given EEG frequency band versus time can show the variability of power in that band; more commonly the relative power is used. A decline in relative alpha variability (ratio of alpha frequency power to total power) has been used to detect delayed cerebral ischemia in patients with subarachnoid hemorrhage [15, 16]. Power in a broader frequency band (3.5–20.7 Hz) can also be used to detect changes in cerebral perfusion pressure in patients with strokes [17].
