An example compressed spectral array (CSA). Panels, top to bottom: left parietal average signal, left temporal average signal, right temporal average signal, right parietal average signal, relative asymmetry index. Inset: region CSA corresponding to the onset of a seizure as shown in the native EEG segment. This CSA is an example of regular flame pattern of seizures. Please see Sect. 5 and Table 4.1 for further details
Displays Derived from Spectrograms
Asymmetry trends use comparisons in power between homologous electrodes in the right and left hemispheres to highlight power asymmetries between the hemispheres. The comparison can be made based on absolute or relative power. This may be helpful to identify lateralized or focal seizures. Asymmetry spectrograms are shown in subsequent sections as the fifth panel in the case examples discussed in section “Case Vignettes with Example Spectrogram Patterns”. In our case examples, red represents greater power in the right hemisphere and blue represents greater power in the left hemisphere (though in other systems, this color scheme may be reversed).
Methods for Monitoring Burst Suppression
Monitoring burst suppression in ICU patients is another area in which qEEG can be informative. Pharmacologically induced burst suppression is often used in the treatment of refractory status epilepticus. In these cases EEG monitoring is important to ensure that medications can be appropriately titrated in real time to ensure appropriate levels of burst suppression while avoiding over- and under-dosing. It is also helpful to have such monitoring capabilities in patients with pathologically generated burst suppression patterns, such as after severe hypoxic-ischemic injury, to assess for trends in this background pattern for prognostication.
Burst suppression can be quantified using the burst suppression ratio (BSR), defined as the percentage of time within an epoch spent in suppression , or as the burst suppression probability (BSP), defined as the instantaneous probability that the EEG is in the suppressed state [15, 16]. Under steady-state conditions, the BSR and BSP agree closely. However, the BSP algorithm is better suited for tracking the depth of burst suppression under dynamic conditions. An example of tracking the BSP in a patient with status epilepticus is shown in Fig. 4.2.
Burst suppression probability (BSP)). (a) EEG signal compressed over 75 min. (b) Ticker plot representing each burst. (c) BSP increases over time as the periods of suppression become more frequent as the recording progresses
Automated Seizure Detection
One of the ultimate goals of qEEG is to offer the potential for automated detection of clinically significant events such as seizures and ischemia. Ictal patterns are highly variable and thus make the development of such detectors difficult. Features that have been used to develop seizure detectors include amplitude, frequency, rhythmicity, and degree of asymmetry . Most of these algorithms have been designed for identification of classic seizure patterns in the setting of the epilepsy monitoring unit. However, seizures in ICU patients typically have different characteristics than those of the EMU population and thus are not as reliably detected with standard seizure detection algorithms . Pitfalls in qEEG analysis include the high degree of false-positive detections due to common ICU artifacts in addition to false negatives from very brief, low amplitude of slowly evolving seizures. Because seizures occurring in critically ill patients frequently exhibit patterns of rhythmicity and evolution that are slower than those seen in epileptic patients, existing detection programs may be relatively insensitive to certain types of ICU ictal patterns . Another challenge is that many ICU seizures tend to wax and wane with subtle onset and termination rather than the abrupt ictal onset and cessation patterns of seizures typically seen in the EMU.
Automated Detection of Other Epileptiform Patterns
Recently one group has developed software, called NeuroTrend, that attempts to detect patterns in the long-term scalp EEGs in the ICU using the standardized EEG terminology . Persyst Corp. has also recently developed an algorithm for identifying periodic discharges, available in version P13 of its software. Details from the algorithms from both NeuroTrend and Persyst Corp. are unpublished and proprietary. Rigorous external validation studies remain to be performed.
Fundamentals of Spectrograms
Motivation for Spectral Analysis
It is often natural to describe oscillatory signals like the EEG in the frequency domain. Indeed, this is reflected in the convention of describing clinical EEG recordings in terms of activity within frequency bands (e.g., delta, theta, alpha, and beta). In this section we briefly review key concepts from the mathematical analysis of frequency domain or spectral characteristics of signals. This overview will help the reader to better understand common features of spectrograms encountered in the ICU setting, reviewed in section “Interpretation of Spectrograms.”
Spectral Decomposition: Fourier Transforms and the “FFT”
The basic problem of spectral estimation theory is: given a finite segment of a signal, estimate how the total power in the signal is distributed over a range of frequencies. The emphasis on estimation is because the EEG, like many other biological signals, is best regarded as composed of signal and noise. The noise must be suppressed in some way to obtain a clear view of the underlying spectral EEG characteristics that are of interest.
Before one can understand how to analyze stochastic signals like the EEG, one first needs to understand the principles underlying the more basic theory of spectral decomposition, which we will review now. Figure 4.3 shows the decomposition of a fairly complex 9-s long single-channel EEG signal into a series of sinusoids of varying phases and amplitudes. The black curve in Fig. 4.3a shows the original signal, consisting initially of a low-amplitude “baseline” period and an epileptiform discharge around t = 4 s, followed by a larger amplitude oscillating pattern at approximately 2 Hz that decays in amplitude while slowing in frequency to approximately 1 Hz by the end of the figure window.
Spectral decomposition. (a) Original signal (black) with superimposed approximation signal (red) composed of sine and cosine “components” making up the original signal. (b) Frequency decomposition—nine components which make up the largest contribution of the approximation. (c) Amplitude spectrum showing the distribution of frequencies contributing to the signal with higher amplitudes contributing more to the reconstructed signal
The overlaid red curve is an approximation to the black curve, obtained by adding together a series of 50 sine and cosine waves or “components,” with frequencies ranging from 0 to 35 Hz spaced evenly at intervals of approximately 0.7 Hz. The nine components which make the largest contribution to the approximation, i.e., the components with the largest amplitudes, sorted by frequency, are displayed in Fig. 4.3b.
For the most part, the sum of these sinusoidal components faithfully represents the original black signal. Careful scrutiny reveals that the approximation succeeds by a delicate series of constructive and destructive interferences of peaks and troughs. This remarkable balancing act is accomplished automatically by a mathematical formula known as the discrete Fourier series. In the examples shown in Figs. 4.3 and 4.4, the formula used is called the discrete Fourier transform, or DFT.
Effect of signal “sharpness” on spectral components. (a) Bell-shaped “slow wave” with its frequency decomposition and amplitude spectrum. As with Fig. 4.3, the original signal (black) and approximation signal (red) are superimposed. Non-sharp morphology results in a narrow amplitude spectrum. (b) Narrow “spike-shaped” curve with the same functions plotted as in (a). This sharp morphology requires a broader range of sinusoids to approximate its signal
The amplitude spectrum for a signal is obtained by taking the geometric mean of the amplitudes of the sine-cosine pair for each frequency and plotting these amplitudes as a function of frequency, as shown in Fig. 4.3c.
For the most part, the red approximation or “reconstruction” is faithful to the original black signal. However, in places, the reconstruction is not accurate. These failures are instructive. Note particularly the epileptiform discharge or “spike” that occurs at approximately t = 4 s. Here, the reconstruction is smoother than the original signal. It fails to reproduce the abrupt rise in voltage and subsequent abrupt decrease that constitute the spike. This is because in this reconstruction we deliberately excluded sinusoids above 35 Hz from the reconstruction. The true bandwidth of the signal is evidently greater than 35 Hz. That is, higher frequency components are required in the Fourier sum to capture the more abrupt transitions or “sharper turns” that make up an epileptiform discharge. In this case, had we included components for all frequencies up to the Nyquist sampling rate (in this case, approximately 100 Hz), the reconstruction would have been essentially perfect.
Signal Sharpening Manifests as Amplitude Spectrum Broadening
We further illustrate the important relationship between “sharpness” and the presence of higher frequency components in the amplitude spectrum in Fig. 4.4. In Fig. 4.4a, we show a bell-shaped curve, reminiscent of an EEG “slow wave,” together with the components in a frequency decomposition and the corresponding amplitude spectrum. As in the previous figure, there is an underlying black curve and an overlaid red curve which approximates the black curve as a sum of sinusoids with amplitudes calculated by the formula for the DFT. We see that, for a waveform with a blunted or non-sharp morphology, the amplitude spectrum is relatively narrow. By contrast, Fig. 4.4b shows a narrow, spikelike, bell-shaped curve, reminiscent of an epileptiform discharge. We see that a broader range of sinusoids extending to a much higher range of frequencies is required to faithfully represent a spikelike transient . We will see that this observation, that signal “sharpness” manifests in the frequency domain as a broadening of the amplitude spectrum, is fundamental in interpreting spectrograms in ICU EEG monitoring.
From Spectra to Spectrograms
Though we have seen that it is possible to decompose complex signals into simple sinusoidal components, there is something unnatural about this decomposition for signals like the one shown in Fig. 4.3. In particular, the signal appears to change character over course of the 9 s shown. It would be more natural to break signals like this into smaller segments or windows, over which the signal characteristics are approximately constant. In statistical jargon, we desire to break the signal into segments that are statistically stationary.
Figure 4.5 shows an example of another signal that shows marked nonstationarity. This example shows a 3-min-long single-channel EEG signal. Figure 4.5b is the raw signal containing a seizure that begins around t = 20 s and ends around t = 120 s. The panels in Fig. 4.5a show the power spectrum (essentially, the amplitude spectrum squared, except for some smoothing—see next below) calculated from three different windows centered at t = 20, 60, and 130 s. The spectra within these three windows differ markedly, reflecting the evolution of signal characteristics that typify seizure activity.
Nonstationarity of a 3-min EEG signal containing a seizure. (a) Power spectra calculated at three different time windows of the recording (t = 20, 60, 130 s). (b) Raw EEG signal compressed over a 3-min interval, with box insets corresponding to the time windows plotted in (a). (c) Spectrogram of EEG signal from (b) using two sliding windows, box insets correspond to the time windows plotted in (a)
Figure 4.5c shows the result of repeatedly calculating the spectrum of signals in 2-s windows, using a “sliding window” to obtain a new spectrum every 0.1 s. These spectra collectively form an image , or time-frequency spectrogram, formed by representing the power spectrum on a colormap. In this example, the power is shown in decibel (log) units, according to convention. This display convention allows simultaneous visualization of the signal power over a wide range of frequencies in one image, despite the fact that in human EEG the power at different physiologically relevant frequencies can vary by an order of magnitude or more. Representing this EEG signal as a spectrogram clearly brings out the salient dynamical features of the seizure, namely, an increase in the dominant frequency of oscillatory activity and a sharpening of the signal contour, followed by slowing down as the seizure ends. These features are not visible in the raw signal at this scale, though they are clearly evident when examining the signal within a more conventional 10-s window used for clinical review of EEG data. By contrast, these dynamics are clearly evident in the spectrogram despite the “large” 3-min window. The ability of spectrograms to display salient features of the EEG at a zoomed out or “compressed” scale is a major reason that spectrograms are useful in ICU EEG. Further examples at more compressed scales (2 h) will be discussed in subsequent sections.
Understanding Spectrograms: Cardinal Patterns from Synthetic Signals
The principles of spectral analysis described above are exploited to interpret patterns that occur commonly in spectrograms from cEEG recordings in the ICU setting. We illustrate these patterns using synthetic data in Fig. 4.5, before turning to real examples. Figure 4.6a shows a simple signal, a “monotonous” or unchanging low-amplitude sinusoid of 2 Hz. The corresponding spectrogram has a single peak at 2 Hz within every time window that manifests in the spectrogram as a red line at 2 Hz. This signal is reminiscent of the common ICU EEG pattern of “delta slowing” seen in patients with encephalopathy. Figure 4.6b shows a sinusoidal signal with a frequency that begins at 2 Hz, then increases following a linear ramp to 5 Hz while increasing also in amplitude, and then drops abruptly back to 2 Hz. The evolving portion of this pattern is manifest in the spectrogram as an upsloping line. This example is reminiscent of the classic pattern of evolution characteristic of many epileptic seizures and typifies what we will refer to in a subsequent section as a “flame”-type seizure.
Four simulated EEG patterns converted to CSAs. (a) Sinusoidal signal at 2 Hz without variation, reminiscent of “delta slowing.” CSA shows a red line, representing a consistent peak at 2 Hz. (b) Sinusoidal signal with linear ramp from 2 to 5 Hz followed by an abrupt termination, modeling an evolving seizure. CSA shows a rise in the power of frequencies up to 5 Hz corresponding to the linear ramp seen in the sinusoidal signal and a return back to 2 Hz. (c) Synthetic model of periodic sharp discharges at 1 Hz. CSA shows a high-power band at 1 Hz with a broadening of the spectrogram reflecting the sharpness of the discharges as described in Fig. 4.4. (d) Synthetic model of extreme sawtooth pattern, which best exemplifies the broadband-monotonous pattern described in Table 4.1
Figure 4.6c shows a more complex synthetic signal , consisting of a series of sharp discharges of randomly varying amplitudes, occurring in a regular or periodic fashion at 1 Hz. The spectrogram in this case shows high power not only at 1 Hz, reflecting the periodicity of the repeating pattern, but also a broadening of the spectrum up to approximately 5 Hz and beyond. This broadband character of the spectrogram reflects the fact that the morphology of the discharges is sharp and thus has a broad amplitude or power spectrum, as discussed previously in connection with Fig. 4.4b. Figure 4.6d shows another more extreme example, a sawtooth wave.
In both Fig. 4.6c, d, the pattern can be characterized as broadband monotonous, referring to the repetitive periodic nature combined with the relatively broadband of high power due to the sharpness of the underlying discharges. As will be seen in the real examples below, the broadband-monotonous pattern typifies the spectrogram when the underlying EEG is in a state of either periodic epileptiform discharges or certain closely related states of status epilepticus.
Technical Considerations: Trade-Offs in Spectral Estimation
Our discussion regarding spectral estimation has glossed over many important technical details that are critical in certain applications of spectral estimation. We touch briefly on two important fundamental issues that affect the quality of spectrograms.
Trade-Off Between Temporal and Spectral Resolution
Consider again the example of a seizure and its spectrogram shown in Fig. 4.5. In that example we chose to make the window size 2 s. This choice in turn dictated a limit to the level of detail with which we were able to resolve temporal features in the EEG, so that the spectrogram has a certain degree of blurring or smoothness across time. If we attempt to obtain higher temporal resolution by making the analysis windows progressively smaller, we would at the same time see that we progressively lose the ability to distinguish detail in the frequency domain. This is because decreasing the signal segment length (keeping the sampling rate constant) reduces the number of frequency components and increases the spacing between components in the DFT. In effect, nearby peaks in the spectrum become single peaks, in the same way that creating a histogram using wide bins can smooth together and obscure peaks in a distribution that has multiple modes.
This consideration highlights a fundamental trade-off that exists between the maximal spectral resolution (the level of detail with which we can calculate the spectrum, i.e., the spacing between frequency components) and the maximal temporal resolution (the smallest window over which we can perform spectral analysis on a signal). The mathematical reasons behind the trade-off between temporal and spectral resolution are in fact identical to those that describe the well-known “Heisenberg uncertainty principle ,” which describes the inverse relationship between the precision with which one can simultaneously measure the position and velocity of a particle.
Trade-Off Between Bias and Varia nce
A second fundamental trade-off arises from the fact that the EEG, like many other naturally occurring signals, is best regarded as stochastic, containing an underlying signal of interest that is corrupted by noise. Consequently, the spectrum and hence the spectrogram need to be estimated. This fact gives rise to a trade-off between bias and variance.
The bias-variance trade-off in spectral estimation is illustrated in Fig. 4.7. In Fig. 4.7a, we show a sample of a stochastic signal generated by a model with a known power spectrum, shown as a red curve in Fig. 4.7b–e. This spectrum has two peaks, at approximately 11 and 14 Hz. Let us assume that we have already chosen a window size for our spectral estimates, based on either the maximum window length over which the signal can be considered to be statistically stationary or the desired level of temporal resolution. In this case we have chosen a window size of 15 s.
The bias-variance trade-off. (a) A stochastic signal generated by a model with a known power spectrum (red curves, b–e). (b–e) Test of varying time windows used for estimating the discrete Fourier transform. Short time windows (b) result in noisy estimations, while broad windows (e) smooth the data so much as to make peaks indistinguishable
Given the chosen window length, a common but suboptimal way to obtain a spectral “estimate” from this finite-length signal is simply to calculate the discrete Fourier transform, usually using a fast algorithm known as the “fast Fourier transform” (FFT), and to then take the squared amplitude of the result as an estimate of the power spectrum. The result is shown as the blue line in Fig. 4.7b. The spectrum appears very noisy. This is not surprising when one considers that what we have done amounts to “estimating” a quantity using only a single sample. Estimates obtained in this way are sometimes called “periodograms.” (We have passed over the fact that, technically, to calculate the periodogram , one usually multiplies the signal by a windowing function or “data taper” before computing the FFT to reduce an effect known as spectral leakage. All spectral estimates shown in this chapter have been computed with appropriate data tapers.)
Under the right conditions in a laboratory, it might be possible to obtain numerous repeated sample segments of the same signal. Given enough repeated samples, we could obtain an accurate estimate of the underlying true spectrum by averaging periodograms. However, in ICU EEG monitoring, we of course do not have the luxury of holding the patient’s state constant to obtain repeated samples. We are thus forced to resort to methods of reducing the variance of the spectral estimates, i.e., of making the spectrogram smoother. Figure 4.7c–e show progressively more aggressive smoothing of the original signal. Smoothing necessarily blurs together fine spectral details, as evidenced by the fact that beyond a certain point the spectral peaks in this example become indistinguishable (Fig. 4.7e).
We operationally define the spectral resolution of the estimated power spectrum as the minimum distinguishable difference between two narrow peaks that can be distinguished in the estimated spectrum. Judging by eye, the approximate spectral resolution in Fig. 4.7c–e is <1 Hz, 2 Hz, and 5 Hz, respectively. The optimal trade-off between variance reduction (smoothness) and spectral resolution in this example appears to be most closely achieved in Fig. 4.6d. Note that the spectral resolution is thus usually lower than the maximal spectral resolution discussed in the preceding subjection. The maximal spectral resolution depended on the window width rather than on statistical considerations.
The most appropriate degree of spectral smoothing clearly depends on the spectral characteristics and intrinsic smoothness of the underlying processes which generate the signal and thus varies depending on the application. In clinical ICU EEG monitoring, a spectral resolution of approximately 0.75 Hz is usually adequate and allows for sufficient spectral smoothing to obtain high-quality spectral estimates. This is the resolution used for the spectrogram in Fig. 4.5 and in the examples shown later.
Numerous approaches to spectral smoothing have been proposed. Common methods include averaging spectra from consecutive neighboring windows (“weighted overlapping segment averaging ,” WOSA) or replacing the amplitudes in a “noisy” spectrum obtained from an appropriately computed discrete Fourier transform by locally weighted averages of neighboring values. Various window functions or “kernels” can be used for this “kernel smoothing” method. The current state of the art, however, is the method called multitaper spectral estimation algorithm (MTSA), which involves averaging together the amplitude spectra of multiple discrete Fourier-transformed segments that have been pre-multiplied by a specific series of windowing functions or “tapers,” known as the discrete prolate spheroidal sequences (DPSS). While the technical details of MTSA are beyond the score of this chapter, it suffices for our purposes to know that MTSA is the solution to a mathematically well-defined optimization problem, designed to achieve a balance between spectral resolution (bias) and the variance of spectral estimates. Surprisingly, though it was invented in the early 1980s, MTSA is not yet in wide use. In fact spectral estimation routines implemented in many commercial products produce relatively poor-quality spectrograms, very often simply “computing the FFT” [18–20].
As with all smoothing methods, MTSA has adjustable parameters that allow one to decide precisely how to balance the bias against variance. In the remaining figures shown in this chapter, spectrograms are computed with a moving window length of 4 s, with overlapping windows shifting by 0.1 s, and a spectral resolution of 0.75 Hz.
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Interpretation of Spectrograms
We now turn from theory to the interpretation of ICU EEG recordings. While there is no single pattern on a spectrogram that is invariably associated with seizures or other abnormal periodic patterns, many events of interest fall into a small number of recognizable patterns. In this section we briefly review some of the most common spectral patterns associated with pathological ICU EEG events. In the next section, we review a series of actual cases to gain experience with spectrogram interpretation.
The most easily recognizable seizures present with an abrupt increase in power across a range of frequencies that stands out clearly from the surrounding background. Given the red and white color typically used to indicate high power on a color density spectrogram and the shape of these events in the spectrogram, these abrupt changes resemble small flames (e.g., Fig. 4.1). We refer to this pattern as regular flame, to distinguish it from the less clear-cut pattern of choppy flame (see below).
Cyclic seizures are also often easy to recognize as a series of repeating regular flame events (e.g., Figs. 4.1, 4.8, and 4.9). Once a cyclic seizure has been verified by review of the raw EEG, further seizures can often easily be identified by review of the spectrogram alone. It may even be possible for inexperienced users at the bedside, such as nurses or residents, to detect recurrent seizures in these cases.
Cyclic seizures (Case 1). This example is typical of the regular flame morphology. For Figs. 4.8–4.23, the 2-h CSA panels are displayed as follows (from top): left lateral, left central, right central, right lateral, and hemisphere asymmetry (a.k.a. relative asymmetry). For the top four panels, high power is in red and low power in deep blue. The hemisphere asymmetry panel assesses where spectral power of the right > left hemisphere (red), left > right hemisphere (blue), or both are equal (white)
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