Tognoli: spectral peaks and spectral background in EEG
1.
2.
3.
4. e.g. bimanual coordination
social coordination
multimodal binding… etc
e.g. imitation task
0-3 peaks
1 or 2 typical
0-5 peaks
3 or 4 typical
5.
6. Largest window for spectral analysis: the run (here 28.5 sec)
Largest window for spectral analysis: the trial (here 6 sec)
STEADY-STATE,e.g.
multimodalbinding
STRUCTUREDTASKe.g.
imitationtask
a plateau
an “event”
a quasi-stationary
brain state
A predetermined temporal
window (here centered at the grip)
a “homogenous”
behavioral state
a quasi-stationary
brain state
24. Sustained rhythms like alpha in drowsy subjects are
often with poor task specificity.
They are not necessary to perform the task
They may have good inter and intra-individual consistency
They don’t tell us a lot about the task
… yet they are quite systematically modulated by the task
Transients (dead zone of electro-physiologists) may be
key to the behavioral or cognitive state under
investigation. Especially, coordinated brain state are
typically brief.
For some time, we have discussed about the spectral peaks, focusing especially on the 10Hz band. The question today is “what makes up the floor of the EEG spectrum?”. Is it meaningful brain activity or some background noise?
To understand the floor, let us start looking at the peaks once more . I will first ask a (seemingly) unrelated question:
“why do we see more peaks in structured behavioral tasks?”
If we compare the rhythmic activities observed during steady states and during structured (“ecologically valid”) behavioral tasks, we notice that there is a greater variety of peaks in the latter, both intra- and inter-individually.
Both sorts of task draw from a rich repertoire of brain oscillations in the 10Hz band.
Spectra are obtained from various temporal scales. In steady-state paradigms that are heavily used in the lab, windows may be fit to “runs” (1.; often used to obtain a high resolution spectral portray). Here the task involved coordination of finger movements with a series of stimuli that decrease in frequency in a succession of 5 plateaus. Other windows are (2) those fit to a plateau, (3) to an event (sensory or motor) and ultimately (4) to a quasi-stationary brain state. Note that Fourier techniques loose usefulness at the shortest time scales (3 and 4) because of the duration~resolution trade-off (see next slide).
On the bottom is a structured behavioral task (an imitation paradigm). The sequence of behavioral/cognitive states is reported. The windowing may focus on the entire trial (1), a predetermined window that is used to focus time on a certain behavioral state (2, or arbitrary sliding windows employed to obtain power dynamics). If information is available, it would be possible to segment homogenous behavioral states (3. e.g. duration of the finger touching the manipulandum). The shortest window would again be a quasi-stationary brain state. The task at the bottom recruits a wide diversity of mental/behavioral/cognitive processes, whereas the one at the top intentionally limits them.
Remember the time-frequency trade-off in Fourier Analysis. If one wants a fine information in time, the uncertainty in frequency will be large (i.e. the bin size will be large, 1st figure), and if one wants a fine information in frequency, the temporal scales will be large (2nd figure).
Practically, if one wants to see a difference of 0.1 Hz between two oscillations, he needs 10 seconds of data sampled at 1KHz. Let us assume that we look at the alpha band. To discriminate between a peak at 11.6 and another peak at 11.7Hz, one needs to look at the signal for 10 seconds (during which this particular pair of oscillations will have all the time of the world to vanish, reemerge, vanish again and be replaced multitudinous time by a varieties of other patterns, O(10^2)).
Or in other words, the crude spectral resolution at the shortest time scale makes Fourier and related methods unsuitable to capture highly non-stationary EEG signal.
Coming back to the question “why more peaks in structured behavioral tasks?”. These tasks impose demand on more processes than steady-state paradigms. But the key difference is the length of time during which the system is observed: observing the brain for less time, and one sees more peaks. If you vote in a democracy counting 500 persons, your vote will impact more than if your country is 5 million persons wide. That is the same here. At shorter time scales, patterns have greater probability to affect the end result, the average spectrum.
Now, let us examine the relationship between oscillatory activities represented at the instantaneous time-scale and those at the level of windowed spectral analysis [exercise for students]. This is 3.25 sec of data. If we look at a quasi-stationary brain patterns, it may look like this (first colored pattern). Its topographical map (time domain) would include a frontal right component in orange and a left posterior component in blue. Both are uncoupled, with orange being faster. Their spectra would reveal two poles. If we start a cumulative spectrum (building up the content of the window from the microstates), it would look like this (draw- bottom). Then pattern 2 (antiphase, pink/yellow…), then antiphase (green, orange, tangential source), and then the last one (blue and orange again, same as 1st)… As we follow the build-up of the spectrum in this 3 second window, we will see that some of those patterns will sign as peaks, others will be diluted. Whether a particular brain activity is represented or not as a peak depends on three parameters: amplitude, duration and recurrence in the window of spectral analysis. The patterns that do not stand-out form the floor of the EEG spectrum.
Let us look at this subject. On the top plot are the filtered oscillations, middle is the envelope (analogous to instantaneous power) and on the bottom is the cumulative power (incremental mean of the envelope). Note that there is a brief episode of coupling at the beginning (pink, light green), then a blink (that unduly permeated the filter because blinks are not symmetrical waveforms). Then there will be this lasting pattern (blue, yellow), typical of the rest state followed by two of its mates in the other hemisphere (pink). Then a small pattern antiphase (orange-green)… etc
Please note the scaling factor in (1) amplitude and (2) duration between rest and active patterns. For any task-related pattern to stand out in this brain, it ought to be very robust. Most brief, rare and small activities will be overwhelmed by this massive and time-lingering alpha peak as seen on the cumulative distribution.
Now, let us see this in a wakeful subject. Some subjects present a fast turnover of their brain patterns like this one. All activities are short, usually of small amplitude and great diversity (in the old time, this was called a “desynchronized EEG”). Because of this diversity, for any one brain pattern to stand out is going to be difficult. These brains are typically associated with that sort of spectra <click>, no peaks. When passing from the instantaneous time scale to that of the Fourier analysis, all activities have merged together in an indistinct “soup”.
And then, this is what makes the electro-physiologist happy. There is one robust task-related activity like this xi (dark green), which is sustained at the instantaneous time scale and signs in the spectrum <click>. Please note that pattern turnover is intermediary between the slow alternation of the first example and the fast alternation of the second example.
If I summarize, a spectrum may or may not express a particular microstate depending on (1) the resting activities and (2) the competition from other active states.
We hypothesize that this factor greatly contributes to inter-individual variability (why, e.g. a rhythm is found in some subject and not in others). Consequently, better inter-individual consistency may be found at the shorter time scales, the one that electrophysiologists avoid.
(Please remember that inter-individual comparison of magnitude is “meaningless” in EEG (spectral power spans 2 orders of magnitude) without effect on behavioral/cognitive performance.)
spatially discontinuous maxima?
At the instantaneous time scale, distributed scalp topographies stem from 4 basic types of brain patterns: single sources antiphase, and coupled sources inphase, antiphase, and out of phase. As we argued (Tognoli, Kelso, in press), there is a bias for single sources (their effect is sustained over time, in contrast to brief synchrony). However, we should expect some spurious antiphase patterns to survive averaging. Those are typically large in amplitude and sustained in duration.
We do not see a reasonable proportion of spurious antiphase:
When we manage to isolate the spectral peaks properly and proceed to a topographical mapping, we always observe localized activity like the 2 maps on top.
However, if we were mapping the power of an EEG composed with this sort of activity for instance (tangential source, spurious antiphase, bottom left), then we should see maps with two distinct local maxima like this hypothetical map on the bottom right. We never see those maps when we work at the long time scale of Fourier analysis. What are the implications?
It implies that at least some cumulative power maps result from the reorganization of instantaneous spatial patterns, i.e. more than one type of instantaneous pattern contributes to the average spectrum.
Accordingly, let us look in the other direction, how the average spectrum relates to the microstates.
When we look at patterns that exhibit a phase aggregate in the area that peaks, we do not see the same pattern over and over again. This phase aggregate will handshake with a diversity of others…. Anterior, posterior, left, right, all around.
If the system is observed for a sufficient time, The cumulant will appear above the source (intersection domain). This is a good news, it means that inverse problem is less severe at the longer time scale of average spectra. But the spatio-spectral organization will not yield any useful information to understand coordinated brain areas (networks).
A cartoon illustration of the hypothesis: average peaks arise from one area being especially active during the task at that particular frequency, and pairing with many other areas that will “regularize” its topography to a single local maximum.
Let us consider the different time scales: if the brain is observed during an infinite period of time (or 40 minutes…), one can only see the rest state.
If the temporal window is adjusted to the duration of a task, one may see some task related, sustained components,
But this is only for the shortest time scales (those avoided by electrophysiologists) that one may see the transients.
Those time scales are avoided on the rationale that estimates have low reliability, temporal stability.
Transient (defined as brief period of brain dynamics as opposed to “sustained”) are not noise…
To make use of these shorter time scales, the important point is the dynamics. The patterns are interpreted in their relation with behavioral events. They become consistent with proper behavioral context.
In conclusion, the spectral floor is made up with functional processes that did not live long/strong/often enough to become a peak at the time scale under consideration. Some of those transients are presumably important for the task. They may emerge at different time-scale. Manipulating the time scales intelligently shall reveal both transient local and coordinated brain activity. It may require to abandon “spectral windows” and work with instantaneous methods.
To target the microstates in an efficient manner, dependent variables (behavior, physiology…etc) should be sampled along the continuous EEG dynamics and used to find the functional significance of transient brain events: brain~behavior.
