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This chapter considers the relationship between ongoing electroencephalographic (EEG) activity as recorded in event-related paradigms and trial averages time locked to some class of experimental events, known as eventrelated potentials (ERPs). It first discusses the concept of the ERP as averaging potentials generated by spatially coherent activity within a number of cortical EEG source areas as well as nonbrain sources typically treated as data artifacts. Event-related potential image (ERP-image) plotting is used to visualize variability in EEG dynamics across trials associated with events of interest using an example data set. The concept and use of independent component analysis (ICA) is then introduced to undo the effects of source signal mixing at scalp electrodes and to identify EEG sources contributing to the averaged ERP. After presenting some basic time-frequency measures useful for studying trial-to-trial variability, the chapter takes another look at trial-to-trial variability, now focusing on the contributions of selected independent component processes to the recorded scalp signals.
ERPs and partial phase resetting. The right panel shows an ERPimage plot visualizing the responses in over 400 single trials of a bilateral occipital independent component (IC) process following presentation of a letter at the central fixation point of a subject participating in a working memory task. The bilateral component (IC6, sixth by variance expressed in the data) produces a response largely resembling a one-cycle sinusoid at 9 Hz. The mean ERP trace (below the ERP image) plots its mean time course, time locked to stimulus onset. The ERSP trace (below that) shows that the mean level of 9-Hz energy in the data, during this period, is 15 dB or more higher than in the pre-stimulus (or ensuing) period. The ITC trace (below that) confirms that during this ERP feature the phase of the entire 9-Hz activity in the trials is highly consistent (ITC approaching 1). The blue backgrounds show p < .01 probability limits, demonstrating that all three measures are highly significantly different from baseline in this period. The panel on the left shows a quite different set of over 100 data trials for a medial (or medial bilateral) occipital IC process in the five-box task of Fig. 3.1 in which stimuli were presented above and left of a central fixation cross, while the subject retained fixation. The large amount of alpha band activity produced by this IC process under these circumstances likely reflects 'alpha flooding' of relevant visual cortex when visual attention is forced by the task to remain elsewhere in the visual field (Worden et al., 2000).
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ERP Features and EEG Dynamics: An ICA Perspective
Scott Makeig and Julie Onton
smakeig@ucsd.edu
julie@sccn.ucsd.edu
Swartz Center for Computational Neuroscience
Institute for Neural Computation
University of California San Diego
La Jolla, California, USA
An invited chapter for:
S. Luck & E. Kappenman (2009). Oxford Handbook of Event-Related Potential Components.
New York, Oxford University Press
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Prefatory remarks
Following the advent of averaging computers in the early 1960s, event-related potential (ERP)
averaging became the first functional brain imaging method to open a window into human brain
processing of first sensory and then cognitive events, and the first to demonstrate statistically
reliable differences in this processing depending on the contextual significance of these events
or their unexpected absence. Yet the same response averaging methods, now easily performed on
any personal computer, may have encouraged the separation of electrophysiological brain
research into two camps. For nearly half a century now, researchers mainly in psychology
departments have recorded human scalp electroencephalographic (EEG) data and studied the
features of human average ERPs time-locked to events and behavior, while researchers mainly in
physiology departments measured averaged event-related changes in the number of spikes
emitted by single neurons in animals, captured from high-pass filtered local field potential (LFP)
recordings from microelectrodes. Since the spatial scales of these phenomena are so different,
these two groups have had little to say to one another. In fact, relationships between these quite
different average brain response measures can be learned only by studying the spatiotemporal
complexities of the whole EEG and LFP signals from which they are respectively extracted, and
by understanding not only their average behavior, but the complexities of their moment-to-
moment dynamics as well.
Many open questions remain about the nature and variability of these
electrophysiological signals, including the functional relationships of their dynamics to behavior
and experience. This investigation is now beginning, with much more remaining to be
discovered about the distributed macroscopic electromagnetic brain dynamics that allow our
brains to support us to optimize our behavior and brain activity to meet the challenge of each
moment. From this point of view, key open questions for those interested in understanding the
nature and origins of average scalp ERPs are how to identify the brain sources of EEG and ERP
dynamics, their locations, and their dynamic inter-relationships. To adequately address these
questions, new analysis methods are required and are becoming available.
Our research over the past dozen years has convinced us, and an increasing number of
other researchers, that using independent component analysis (ICA) to find spatial filters for
information sources in scalp-recorded EEG (and other) data, combined in particular with trial-
by-trial visualization and time/frequency analysis methods, are a powerful approach to
identifying the complex spatiotemporal dynamics that underlie both ERP averages and the
continually unfolding and varying brain field potential phenomena they index. In essence, ICA is
a method for training or learning spatial filters that, when applied to data collected from many
scalp locations, each focus on one source of information in the data. Characterizing the
information content of data rather than its variance (the goal of previous signal processing
methods) is a powerful new approach to analysis of complex signals that is becoming ever more
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important for data mining of all sorts. Applied to EEG data, ICA tackles ‘head on’ the major
confounding factor that has limited the development of EEG-based brain imaging methods,
namely the broad spread of EEG source potentials through the brain, skull, and scalp and the
mixing of these signals at each scalp electrode.
I. EEG sources and source projections
In this chapter, we consider the relationship between ongoing EEG activity as recorded in event-
related paradigms, and trial averages time locked to some class of experimental events, known as
event-related potentials (ERPs). We first discuss the concept of the ERP as averaging potentials
generated by spatially coherent activity within a number of cortical EEG source areas as well as
non-brain sources typically treated as data artifacts. We use “ERP-image” plotting to visualize
variability in EEG dynamics across trials associated with events of interest using an example
data set. We then introduce the concept and use of independent component analysis (ICA) to
undo the effects of source signal mixing at scalp electrodes and to identify EEG sources
contributing to the averaged ERP. We note that “independent components” are brain or non-
brain processes more or less active throughout the dataset, and thus represent a quite different
use of the term “component” in the title and elsewhere in this volume. After introducing some
basic time/frequency measures useful for studying trial-to-trial variability, we take another look
at trial-to-trial variability, now focusing on the contributions of selected independent component
processes to the recorded scalp signals. We hope the chapter will help the reader interested in
event-related EEG analysis to think carefully about trial-to-trial EEG stability and variability.
The latter we suggest largely reflects not “ERP noise” but instead the brain’s carefully
constructed response to the highly individual, complex, and context-defined “challenges” posed
by unfolding events.
What is an EEG source?
A fundamental fact about electrophysiological signals recorded at any spatial scale is that they
reflect and index emergent partial coherence (in both time and space) of electrophysiological
events occurring at smaller scales. Brain electrophysiological signals recorded by relatively large
and/or distant electrodes can be viewed as phenomena emerging from the possibly one
quadrillion synaptic events that occur in the human brain each second. These events, in turn,
arise within the still more vast complexity of brain molecular and sub-molecular dynamics. The
synchronies and near-synchronies, in time and space, of synaptic and non-synaptic neural field
dynamics precipitate not only neural spikes, but also other intracellular and extra-cellular field
phenomena – both those measurable only at near field (e.g., within the range of a neural arbor),
and those recorded only at far field (in particular, as electrically far from the brain as the human
scalp). The emergence of spatiotemporal field synchrony or near-synchrony across an area of
cortex is conceptually akin to the emergence of a galaxy in the plasma of space. Both are
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spontaneously emergent dynamic phenomena large enough to be detected and measured at a
distance – via EEG electrodes and powerful telescopes, respectively.
The emergence of synchronous or near-synchronous local field activity across some
portion of the cortical mantle requires that cells in the synchronized cortical area be physically
coupled in some manner. A basic fact of cortical connectivity is that cortico-cortical connections
between cells are highly weighted toward local (e.g., shorter than 0.5-mm) connections,
particularly those coupling nearby inhibitory cells whose fast gap-junction connections support
the spread of near-synchronous field dynamics through local cortical areas (Murre and Sturdy,
1995; Stettler et al., 2002). Also important for sustaining rhythmic EEG activity are
thalamocortical connections that are predominantly (though not exclusively) organized in a
radial, one-to-one manner (Frost and Caviness, 1980). EEG is therefore likely to arise as
emergent mesoscopic patterns (Freeman, 2000) of local field synchrony or near-synchrony in
compact thalamocortical networks. Potentials arising from vertical field gradients associated
with pyramidal cells arrayed orthogonal to the cortical surface produce the local field potentials
recorded on the cortical surface (Luck, 2005; Nunez, 2005). Synchronous (or near-synchronous)
field activity across a cortical patch produces the far-field potentials that are conveyed by volume
conduction to scalp electrodes. Both scalp and direct cortical recordings agree that in nearly all
cognitive states, such locally coherent field activities arise within many parts of human cortex,
often with distinctive dynamic signatures in different areas. Direct observations in animals report
that cortical EEG signals are indeed associated with sub-centimeter sized cortical patches whose
spatial patterns resemble ‘phase cones’ (like ‘pond ripples,’ (Freeman and Barrie, 2000)) or
repeatedly spreading ‘avalanche’ events (Beggs and Plenz, 2003), though more adequate multi-
resolution recording and modeling are needed to better define their spatiotemporal geometry and
dynamics.
In this chapter, we will use the term EEG source to mean a compact cortical patch (or
occasionally, connected patches) within which temporally coherent (or partially-coherent) local
field activity emerges, thereby producing a far-field potential contributing appreciably to the
EEG signals recorded on the scalp. While non-cortical brain sources may contribute to the
recorded EEG (as for example, auditory brain stem potentials), their contributions are typically
small compared to cortical potentials and we will therefore assume for this chapter that
resolvable EEG signals of interest are of cortical origin. We will use the phrase source activity to
refer to the varying far-field potential arising within an EEG source area and volume-conducted
to the scalp electrodes. Recorded EEG signals are then, in this view, the sum of EEG source
activities, contributions of non-brain sources such as scalp muscle, eye movement, and cardiac
artifacts, plus (ideally small) electrode and environmental noise.
Note that the activity contributed by a cortical source to the recorded EEG typically does
not comprise all the local field activity within the cortical source domain, since potentials
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recorded with small cortical electrodes at different points in a cortical source domain may only
be weakly coherent with the far-field activity that is partially coherent across the domain and is
therefore not projected to the scalp electrodes. That is, only the portion of the local field activity
in a source domain that is synchronous across the domain will contribute appreciably to the net
source potentials recorded by scalp electrodes. Thus, cortical electrophysiology is by its nature
multiscale, its properties differ depending on the size of the recording electrodes and their
distance from the source areas in ways that are currently far from adequately observed or
modeled. Scalp EEG recordings predominantly capture the sum of locally coherent source
activities within a number of cortical source domains, plus non-brain artifact signals.
Roles of EEG source activities
The primary function of our brain is to organize and control our behavior 'in the moment' so as to
optimize its outcome. For many neurobiologists, field potential recordings have been considered
of possible interest at best only as passive, indirect, and quite poor statistical indices of changes
in neural spike rates, their primary measure of interest. In fact, however, the variations in
electrical potential recorded by EEG or LFP electrodes better reflect variations in concurrent
dendritic synaptic input to neurons, input that may or may not provoke action potentials. Action
potential generation is provoked by receipt of sufficient dendritic input within a brief (several-
millisecond) time window. The emergence of synchronized local field potentials across a cortical
area may therefore reflect changes in occurrence of joint spiking events across groups of
associated neurons in that area. Some recent experimental results also suggest that local field
potentials may also actively affect spike timing and degree of synchrony between neurons within
a partially-synchronized source domain, biasing their joint spike timing towards (or away from)
concentration into brief, potent volleys (Voronin et al., 1999; Francis et al., 2003; Radman et al.,
2006). By this means, small statistical adjustments in joint spike timing of neurons with common
axonal targets effected by spatially synchronized local field potentials might be associated with
large changes in effective neural communication, and thence with behavior and behavioral
outcome (Fries et al., 2007).
According to recent reports, the timing and phase of extracellular fields may also enhance
or weaken the effects of concurrent input on future cell and areal responsivity, by affecting the
amount of long-term synaptic potentiation (LTP) produced by that input (Dan and Poo, 2004).
Thus, locally synchronous (or near-synchronous) field activity arising within compact cortical
source areas may not only weakly index neural dynamics on spatial scales larger than a single
neuron, but may also play a more direct and active role in organizing the distributed brain
dynamics that support experience, behavior, and changes in psychophysiological state. The
spatiotemporal dynamics of cortical field synchrony, and their relationship to neural spike timing
have still been relatively little studied (Logothetis et al., 2001; Bollimunta et al., 2008) and,
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contrary to standard presumption, there is likely much more to be discovered about relationships
between extra-cellular fields and intracellular potentials in living brains.
Spatial source variability
The concept that an EEG source represents the emergence of synchronous field activity across a
cortical patch is undoubtedly a simplification of the actual more complex, multi-scale dynamics
that produce near-synchronous activity within an EEG source domain. Although the concept that
EEG is produced by synchronous field activity in small cortical domains is supported
qualitatively by fMRI results that are generally dominated by roughly cm-scale or smaller
pockets of enhanced activity, and by a few reports of direct field potential grid recordings
(Bullock, 1983; Freeman and Barrie, 2000), when cortical activity in animals is viewed at a
smaller (sub-mm) scale using optical imaging, smaller-scale moving waves of electromagnetic
activity are observed (Arieli et al., 1995). However, simple calculation of the phase difference
between the edges and the center of a ‘pond ripple’ pattern at EEG frequencies, based on the
estimated (cm2-scale) domain sizes and observed traveling wave velocities (1-2 m/s), suggests
that the spatial wavelength of the radiating ‘ripples’ is considerably larger than the size of the
domain, meaning that the topographic scalp projection of a cortical ‘phase cone’ is close to that
of totally synchronous activity across the patch, as in our simplified EEG source model1.
However, larger-scale travelling or meandering waves at slow (1-3 Hz) delta or infraslow
(<1 Hz) EEG frequencies have also been observed in epilepsy, sleep, and migraine (Massimini et
al., 2004), and (near 12-Hz) sleep spindles may also ‘wander’ over cortex in concert with
spatially varying activity in coupled regions of the thalamic reticular nucleus (Rulkov et al.,
2004). Sufficiently detailed recordings from high-density, multi-resolution arrays are not yet
available to allow models of the relationship between these moving activity patterns and
apparently stable EEG source dynamics in waking life.
Temporal source variability
A hallmark of EEG is that its temporal dynamics are highly non-stationary and exhibit
continuous changes on all time scales (Linkenkaer-Hansen et al., 2001). Changing EEG
dynamics index changes in and between local synchronies that are driven or affected by a variety
of mechanisms including sensory information as well as broadly projecting brainstem-based
arousal or ‘value’ systems identified by their central neurotransmitters dopamine,
acetylcholine, serotonin, neurepinephrine, etc. These ‘neuromodulatory’ systems based in
brainstem areas project to widespread cortical areas and are very likely an important source of
temporal variability in the spatiotemporal coherence that produces far-field signals recorded at
the scalp, variability that gives flexibility and individuality to our distributed brain responses so
as to respond most appropriately to the particular challenge of the moment. Ranganath and
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Rainer (Ranganath and Rainer, 2003) have reviewed what is known and still unknown about
these systems and their interactions with cortical field potentials.
Volume conduction and source mixing
Experimental neurobiology suggests that the spontaneous emergence of partial coherence of
complex rhythmic temporal patterns of local field activity across compact cortical ‘phase cone’
or ‘avalanche’ domains a few mm or larger in diameter produce the scalp EEG and therefore
ERP signals. The differences between distinct parts of neurons within the partially-synchronized
and nearly-aligned pyramidal cell domain sum coherently both in local recordings and as
measured at any distance after passing by volume conduction through intervening conductive
media including cortical grey and white matter, cerebral-spinal fluid (CSF), skull, and skin
(Akalin-Acar and Gencer, 2004; Gencer and Akalin-Acar, 2005). The very broad cortical source
field patterns (each generally resembling the double-lobed pattern iron filings take when placed
around a bar magnet) are attenuated by the partial resistance of these media, and their
propagation patterns are spatially distorted at tissue boundaries where conductance changes. The
broadly projecting, spatially distorted, and severely attenuated signals are then summed within
conductive EEG electrodes attached to the scalp (Nunez, 1977)2.
Forward and inverse modeling
A first question for EEG/ERP researchers, therefore, is or should be how to separate the recorded
EEG activities recorded at all the scalp channels into a set of activities originating within
different spatial source domains. Finding the appropriate spatial filters is, unfortunately,
technically difficult, and were any arbitrary 3-D arrangement of source configurations
physiologically possible, any number of them could be found that would produce the same scalp
potentials (Grave de Peralta-Menendez and Gonzalez-Andino, 1998). A biophysical solution to
this so-called inverse problem must begin with construction of a forward head model specifying
(1) where in the brain the electromagnetic sources may be expected to appear, and (2) in which
orientations, and (3) how their electromagnetic fields propagate through the subject’s head to the
recording electrodes (Akalin-Acar and Gencer, 2004). Fortunately, the well-grounded
assumption that the brain EEG sources are cortical source patches whose field patterns are
oriented near-perpendicular to the local cortical surface allows more physiologically plausible
estimates since these assumptions allow a fair MR image-derived model of the shape, location,
and local orientation of subject cortex (Fischl et al., 2004). Constructing individualized cortical
models for EEG analysis requires extensive computation and expensive MR head images, and
thus the process is still rarely carried out for routine EEG/ERP experiments. While adequate
head models are needed to develop EEG into a 3-D functional brain imaging modality, different
analysis goals may require various degrees of anatomic accuracy, and use of standard head
models may suffice for many analysis purposes.
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Given an accurate forward head model, the inverse problem is still underdetermined if
multiple sources contribute to the observed scalp potential distribution whose sources are to be
determined. In contrast, the solution is much simpler, and its answer better determined, if the
scalp maps whose source projections they sum are simple maps representing the activity of only
one source. Both EEG and MEG researchers have long attempted to consider scalp maps of
amplitude peaks in average ERPs to be simple maps. That is, they attempt to use ERP averaging,
a purely temporal filtering method, as a means of, in effect, spatial filtering, attempting to
eliminate from each channel the projections of EEG sources not directly affected by the time-
locking events.
In many cases, taking the difference between two average ERPs time-locked to related
sets of experimental events may further restrict the number of strongly contributing brain source
areas. Unfortunately, trial averaging or differencing is rarely completely effective for this
purpose, since meaningful sensory (as well as purely cognitive) events rapidly perturb the
statistics of many cortical EEG source areas as well as subcortical areas (Halgren et al., 1998;
Schroeder et al., 1998). Therefore, except for very early sensory brainstem and cortical
potentials, ERP maps sum activities that arise, typically, in many source domains. This means
that scalp maps of ERP or ERP difference-wave peaks are only rarely simple maps representing
potentials projected to the scalp from a single source. To optimally estimate the source
distribution responsible for EEG or ERP data, it is desirable to find a better way to isolate simple
maps representing the projection of single sources contributing to the data, a subject we will
return to in Section III.
II. ERP trial averaging and trial variability
Figure 3.1A shows a single-subject ERP for all 238 scalp channels averaged over 500 data
epochs time-locked to onsets (a latency 0) of an infrequently presented visual target disc in a
visuospatial selective attention task (Makeig et al., 1999b; Makeig et al., 1999a; Makeig et al.,
2002; Makeig et al., 2004b). ERP traces for all 238 channels are overlaid on the same plot axis.
Interpolated scalp maps show the ERP scalp distribution at four indicated latencies. The bottom
panel shows the ERP average of the same 500 epochs, but now time-locked to the subject’s
button press in each trial. In both panels, the data were averaged after removing artifacts
produced by eye movements, eye blinks, electrocardiographic (ECG) activity, and
electromyographic (EMG) from scalp and neck muscles using independent component analysis
(ICA), as explained in Section III3,4. The late positive complex (LPC or ‘P300’) feature of this
averaged response to the infrequent attended visual targets is attenuated by the highpass filtering
above 1 Hz applied to the data; it is most evident in the motor response-locked data average (Fig.
3.1B). We will use these data through this chapter to explore relations between the average ERPs
as shown in this figure and the single EEG data epochs that were averaged to produce them.
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Figure 3.1. ERP traces from
each of 238 scalp channels
averaged over 500 EEG
epochs in a single subject,
time locked to (A) continually
anticipated but infrequently
presented visual target stimuli
in a visuospatial selective
attention task, and (B)
immediately following
speeded subject button
presses cued by target
presentation4 Solid lines
cutting vertically through the
ERP channel trace bundles
lead to cartoon heads
showing the interpolated
scalp potential distribution at
the moment indicated.
The trial-averaging model
Over the past near half-century, the predominant method for reducing the complexity of event-
related EEG data collected in sensory and cognitive paradigms is to form event-related potential
(ERP) averages of trial records time-locked to sets of experimental events assumed by the
experimenter to generate the same or essentially similar brain responses. To gain a realistic
understanding of the features of ERP trial averages and their relationship to the underlying brain
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dynamics, it is important to understand both the strengths and limitations of ERP averaging. The
physiological model underlying ERP averaging is that cortical processing of sensory (or other)
event information follows a fixed spatiotemporal sequence of source activities, and that this
processing produces a fixed sequence of deviations in scalp potentials whose distribution reflects
the locations of their cortical generators. However, these traces of the cortical processing
sequence are obscured in single response epochs by typically much larger ongoing EEG
activities generated in many brain areas, as well as artifacts generated in non-brain structures.
Crucially, these ongoing activities are assumed to be unaffected by the time-locking events of
interest.
Thus, in the ERP averaging model, EEG epochs are assumed to sum (1) a temporally
consistent event-related activity sequence (“the evoked response”), plus (2) event-unrelated
ongoing or spontaneous EEG activities (not contributing to the ERP). Under these circumstances,
averaging a sufficient number of event-locked epochs subtracts, cancels, or spatially filters out
the unrelated brain activities, leaving a single average response epoch dominated by the
consistent event-related activity sequence, recorded on the scalp as the flowing ERP field
‘movie.’ The amplitudes of EEG (or other non-brain) activities unaffected by the time-locking
events that remain in the average will be approximately 1/N1/2 of the amplitude of those activities
in the single trials, where N is the number of epochs averaged. Thus, achieving a faithful
representation of the actual (and typically relatively small) evoked response sequence usually
requires averaging a relatively large number of event-related epochs known or assumed to
contain the same time-locked ERP sequence.
To understand how ERP averaging leads to a reduction in event-unrelated EEG activity,
we first need to define the phase of an EEG source signal. The simplest sense of the term might
be the sign or polarity of the recorded potential at a given time point, either positive or negative
in relation to some baseline potential (typically established by averaging the potentials recorded
in some period of the recording assumed to be unaffected by the events of interest). A more
specific meaning for the ‘phase’ of a signal at some time point and frequency is as the phase of a
best-fitting brief, tapered sinusoid at the given frequency centered on that time point. Thus the
phase of an EEG source or scalp signal, at any given time point and frequency, is defined by the
relation of its value at that time point to its values in an enclosing window of time points. Note
that at a given time point a signal has a different phase at each frequency. Also, since EEG
signals are relatively smooth, EEG phase differences between neighboring time points cannot
vary freely but must change smoothly.5
ERP averaging can remove the contributions of those source activities unrelated to the
time-locking events by means of phase cancellation, which works as follows. If a given source
signal is unaffected by the time-locking events, and if the timing of the experimental events is
not based on the ongoing EEG signals, their phase at each latency and frequency will differ
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randomly across trials. Mathematically, the sum of random-phase signals at a given frequency
tends to become smaller and smaller (at that frequency) as the number of summed trials
increases. We can see this most easily by considering the signs of the signals (+ or -) instead of
their phases. If the signs of a set of signal epoch values at a given latency are random, then in the
average of those epochs the positive-phase and negative-phase values in different epochs will
partially cancel each other, and the magnitude of the average epoch at that latency will be
smaller than the average of the same values were they all of the same sign.
Similarly, if at a given analysis frequency (say for example 9 Hz), the single-trial EEG
signals have a random phase distribution when measured in a time window centered at some
latency (say, 200 ms following the time-locking event), then the vectors that can be used to
represent their amplitudes and phases at that frequency will be more or less evenly distributed
around the phase circle, and the expected length of the vector average of these vectors will
become smaller as the number of trial vectors averaged increases, provided that the exact timing
of experimental events cannot be predicted by the brain. On average, the length of the average
phase vector will decrease as the square root of the number of trials averaged. In this way, trial
averaging filters out all features of the data that are not wholly or at least partially phase-locked
to the time-locking events at any frequency and latency.
It is important to understand how event-related phase-locking and time-locking differ.
For example, imagine a set of EEG trial epochs, time-locked to a particular type of event, that
each contain a burst of 10-Hz alpha band activity centered 500 ms after the time-locking event.
Further, imagine that these alpha bursts, while undeniably time-locked to the experimental events
of interest, may exhibit any phase at 500 ms (ascending, descending, etc.). These bursts,
therefore, are not phase-locked to the events. An ERP average of enough such epochs would
therefore contain little trace of 10-Hz activity at 500 ms, even thought this is a striking feature of
the single-trial data. This is because trial averaging filters out all activity that is not both time-
locked and phase-locked to the time-locking event (see discussion of time- and phase-locking
below). Thus, scalp ERPs do not capture all of the consistent event-related dynamics in the
averaged EEG epochs, but only those dynamic processes that affect the phase distribution of
their signals at some analysis frequencies and trial latencies. We will consider this question
again in Section IV (see also Chapter 2, this volume).
However, if a given brain source contributes a fixed activity sequence to a given scalp
channel signal in every trial, at each analysis frequency and epoch latency the phase of its
contributions to the scalp signals will be consistent across trials, and the ERP average at that
scalp channel will contain all of that source’s activity sequence, without diminution. If the phase
of its single-trial activity at a given frequency and latency is variable and only weakly consistent,
relative to a true random phase process, then the source will contribute only weakly to the scalp
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ERP. If the source activity has truly random phase at the given frequency and latency, then its
ERP contribution will be minimal and further decreasing as more trials are averaged.
If all the EEG sources that project to a scalp channel have fixed evoked activity
sequences, then their collective contribution to the channel in each trial will be the sum of all
their source activities, and the average ERP at that channel will be the average of the summed
source activities at each trial latency. Thus source mixing that occurs at the scalp electrode could
decrease (or increase) the apparent ERP magnitude through the same process of phase
cancellation. But again, only those signals that are phase-locked to the time-locking events from
trial to trial will be retained in the average. And conversely, for activity at a given frequency and
latency to be removed from the signal by averaging, only the signal phase in the single trials
need be random.
Limitations of event-related averaging
The mean of any distribution is simply one statistical measure of the distribution – a statistic that,
if provided apart from other statistics, may be informative and/or misleading. For example,
telling a New Guinean unacquainted with Americans that the average adult American height is
5’6” (1.68 m) might give him or her an adequate concept of the distribution of American adult
heights – assuming the shapes and the widths of the (near-normal) height distributions in the two
cultures are not dissimilar. However, sending Martian scientists the arithmetically equally correct
information that the average human is half male and half female might well engender quite
incorrect ideas about human biology and society. The problem here is that human sexual
physiology has not one but two quite distinct modes (female and male), information that is not
captured in or conveyed by the average. Thus, the average of a distribution may or may not in
itself provide or suggest a useful and realistic model of the underlying distribution or its features.
This may be even more problematic for time series averages that sum disparate activities of
many distinct brain and non-brain sources whose detailed features are of primary interest,
including their spatial and temporal trial-to-trial variability.
Spatial variability of event-related activity
Note how the scalp topographies of the ERPs in both panels of Figure 3.1 differ slightly before
and after the button press. If ERP spatial variations were generated within or directly under the
scalp itself, such changes would reflect potential changes occurring directly below the most
strongly affected electrodes. Such an interpretation, while having naïve appeal, is however
contrary to the anatomic and biophysical facts about volume-conducted cortical field potentials
that actually produce scalp EEG signals, as summarized above. The very broad ‘point-spread’
pattern of potentials propagating out by volume conduction from each cortical source area means
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that each source contributes to some extent to the signals recorded at nearly all of the scalp
electrodes, and contributes appreciably to many of them.
Further, if each source area is spatially fixed (or nearly so), by itself it cannot produce a
moving topographic pattern of field activity on the scalp it can only produce proportional and
simultaneous changes across all the electrodes in its projection pattern. Therefore, changes in the
scalp map of average ERP data (as in Fig. 3.1) must reflect sums of time-varying potentials
projected in the broad and highly-overlapping scalp patterns from several spatially-fixed EEG
source activities, each contributing to the ERP in spatially and temporally overlapping time
windows. This view is compatible with fMRI results showing that cortical activations and
deactivations mainly occur within compact cortical domains – though direct high-resolution,
multi-scale observations of electrocortical activity that could constitute ‘ground truth’ evidence
for this assumption are not yet available.
Two main points here are, first, that basic biophysical knowledge is not consistent with
an interpretation of ERP potentials as exclusively (or even principally) reflecting activity
generated directly below each electrode, a fact it is easy to lose sight of when focusing on the
details of single-channel ERP or EEG waveforms. Second, although when animated, changes in
high-density ERP time series appear to flow across the scalp, features of most ERPs recorded in
cognitive experiments are much more likely produced by sums of time-varying activities of
relatively small, spatially-fixed cortical generator domains, each with a broad ‘point-spread’
pattern of projection to the scalp surface. Looking ahead a bit: Although the exact size
distribution of these domains is not yet known, fairly precise indications of their centers can be
obtained by methods that spatially filter the scalp EEG data to focus on single sources (see
Section III).
ERPs as spatial filters?
Early ERP analysis attempted to deal with the difficulty in interpretation posed by volume
conduction and scalp mixing by assuming that event-related averaging provides sufficient spatial
filtering of the many source signals reaching the scalp electrodes so that activity from only one
affected source area contributes to each ERP amplitude peak. That is, some early ERP
researchers hoped that the sequence of peaks comprising ERP waveforms would each spatially
filter out all activities not generated in a single cortical area.
However, subsequent research clearly suggested that soon after sensory signals arrive in
cortex following meaningful events, multiple EEG sources begin to contribute to ERP averages.
It has now been shown that in animals coordination of activities between early visual areas
(Grinvald et al., 1994) and between primary visual and auditory cortex (Foxe and Schroeder,
2005) begins as early as 30 ms after stimulus onsets, and invasive recordings from epileptic
14
patients for clinical purposes show that by at most 150 ms after presentation of meaningful visual
stimuli, the phase statistics of local field processes are altered in many parts of the brain, both
cortical and subcortical (Klopp et al., 2000). Thus, the somewhat different scalp distributions in
the single-channel ERP scalp field maps of Fig. 3.1 in fact represent differently weighted
mixtures of mean event-related activities, time-locked to subject button presses, from several to
ma ny cortical sources having broad and strongly overlapping scalp projections. Also, direct
cortical recordings from both animals and humans show that, through activity cycles through
thalamocortical and other network connections involving significant delays, single cortical areas
often produce multi-peaked complexes instead of single response peaks in response to single
stimulus presentation events (Swadlow and Gusev, 2000), adding to the spatial overlapping of
source activities in ERP waveforms.
Thus, response averaging is not an efficient method for spatial filtering of event-related
EEG data since it typically does not produce a sequence of simple maps each reflecting the
projection to the scalp of a single cortical source. Computing the ERP ‘difference wave’ at each
scalp channel between ERPs in two contrasting conditions may more effectively isolate
condition differences in the activity of a single generator or set of generators, although in general
the effectiveness of this approach cannot be guaranteed. Finding more effective methods for
spatial filtering of EEG data into EEG source activities is therefore of urgent importance to
human electrophysiology research.
Temporal variability of event-related activity
Another problem with modeling event-related EEG dynamics based on ERP averages alone is
that ERP averaging collapses and thus conceals both the orderly (event-, task-, or context-
related) as well as the disorderly (event-, task-, and context-unrelated) trial-to-trial variability in
the recorded EEG scalp and source signals – giving no way for the user to determine the relative
proportions or types of these two classes of signal variations that are present in the single trials.
A model of brain activity built solely on an ERP average of scalp activity in event-related epochs
must fail to include many aspects of the brain processes that produce it. If the single-trial EEG
epochs each sum activity and time-varying activities from multiple spatial sources whose
dynamics are tightly linked to multiple task or context-related factors, focusing solely on their
average may discourage study of their orderly trial-to-trial variations.
Averaging itself simplifies not only the spatial pattern, but also the temporal patterns of
the signals averaged, retaining only that portion of the signals (typically, a small portion) that are
both time-locked and phase-locked to the time-locking signals (as explained above and in
Chapter 2, this volume). Far too often trial-to-trial variability of EEG signals is simply dismissed
by researchers (either explicitly or implicitly), as representing irrelevant brain ‘noise’ without
sufficient consideration or evidence for this assumption. To consider this point more carefully,
15
let us examine some aspects of the trial-to-trial temporal variability in scalp EEG activity before
and after target presentations in the selective visual attention task session for which Fig. 3.1
showed the ERP averages.
A first step towards understanding trial-by-trial variability in EEG epochs time-locked to
some class of time-locking events is to find useful ways to visualize their variability. Jung and
Makeig have developed a method of sorting the order of single trials by some criterion and then
plotting them as horizontal color-coded lines in a rectangular image they called the ERP image
(Makeig et al., 1999b; Jung et al., 2001). In ERP-image plots, single-trial traces drawn as
horizontal colored lines, with color (instead of vertical placement) encoding potential. The
colored lines can be fused into a rectangular image and smoothed, if desired, with a vertical
moving average to bring out trends. Crucially, the order in which the trials are sorted (bottom to
top) need not follow the actual time order of the trials, but can be based on any other criterion.
Unlike, the average ERP, which is fixed, the ERP images resulting from different trial sorting
orders can differ dramatically from each other, each bringing out one or more aspects of trial-to-
trial variability in the data.
Panel A of Figure 3.2 uses this method to visualize nearly 500 single trials time locked to
visual target stimulus presentations at a scalp site near the vertex (Cz) – the same stimulus-
locked trials averaged to form the ERP shown in Fig. 3.1A, with the (vertical) order of trials here
sorted in their original time order. For easier visualization of event-related patterns across trials,
in each panel of Fig. 3.2 we have smoothed the single-trial data (vertically) with a 20-trial
moving window. The solid vertical line in panel A marks the onset of the visual target, the
vertical dashed line the subject’s median button press latency. The average ERP (shown below
the panel) appears to have only a small and temporally diffuse late positive complex (LPC or, for
historical reasons, “P300”) feature, here peaking near 400 ms after stimulus onset.
Panel B shows the same data trials, but here sorted by the latency of the subject’s button
press (dashed trace), again smoothing with a 20-trial moving average. We now see that in most
trials a (much more distinct) LPC follows the subject’s button press by about 120 ms, with LPC
amplitude smaller in long-RT trials (near the top of the ERP-image panel). This panel shows
which features of the post-stimulus E RP are primarily time-locked to the stimulus onset itself
(e.g., the negative (blue) pre-response N2 peak), and which to the subject behavioral response
(the following LPC and two sparser ensuing positive wave fronts). The trial-to-trial latency
variability of the LPC cannot be labeled as irrelevant trial-to-trial ‘noise,’ and cannot be deduced
from the stimulus-locked trial average (blue trace below panels A and B) in which trial-to-trial
variability time-locked to the button press rather than the stimulus onset is temporally “smeared
out.”
16
Figure 3.2. Six ERP-image plots of nearly 500 visual target response epochs (same data as in
Fig. 3.1) at a scalp electrode near the vertex (referred to right mastoid). In each panel, trial
potentials are sorted (from bottom to top) in the order indicated, then smoothed (vertically) with
a 20-trial moving window, and finally color-coded (see color bar on lower right). In left panels
(A-C), the trials are aligned to the moment of stimulus onset in each trial. In right panels (D-F ),
17
they are aligned to the moment of the subject button-press response. The trace below each image
shows the ERP average of the trials. Stimulus-locked ERP peaks N2 and LPC (late positive
complex) are labeled in A. The trial sorting criteria are indicated in each ERP-image panel.
Horizontal arrows show the value (C) and phase (E,F) sorting windows. The ERP images
illustrate the wide variety of trial-to-trial differences in the data.
Panel C shows again the same trials, here sorted instead b y me an potential in the N2
response ERP latency window indicated by the dashed lines. We see that only in about the
bottom half of the trials is the mean potential in this window actually negative. But these include
about a (bottom) third of the trials in which the negativity is relatively large, thereby
“outweighing” the contributions of the trials in which the single-trial value is positive, thus
producing a negative peak in the average ERP (again shown below the ERP-image panel).
The curving post-RT positive (red-orange) wave fronts in the ERP-image plot in panel B
reveal that the evoked LPC can be more accurately represented by an ERP average of the same
data epochs time-aligned to the subject button press rather than to stimulus onset – as in panel D.
In particular, the average motor response-aligned ERP (below panel D) better reflects the abrupt
onset, slope, and duration of the post-motor LPC in the single trials than the stimulus-aligned
ERP (below panel A). As in panel B, panel D shows that the post-button press positivity is
generally stronger in (lowermost) trials with short button press latencies, and is weak or even
absent in (uppermost) trials with long response latencies. Also, the slightly curving (red)
response column in panel D suggests that the time locking of the LPC peak to the button press is
only relatively constant, the LPC appearing slightly wider and centered slightly later in shortest-
latency trials, relative to other trials.
These scalp data, measuring the potential difference between an “active” electrode near
the vertex (Cz) and a “reference” electrode on the right mastoid (see cartoon head above panel
A), actually sum broadly spreading projections of field activities projecting by volume
conduction from several to many cortical sources. The mean power spectrum for these trials
(above panel A) contains a strong alpha-band peak at 10 Hz. Panel E shows the same response-
aligned trials as in D, now sorted according to the best-fitting 10-Hz phase in the indicated three-
cycle (300-ms) wide trial sorting window centered on the LPC. In this ERP-image view of the
data, the central positive (red) LPC peak of the activity in the single trials forms a red curving
wave front near the center of the sorting window. The peak latency difference (from bottommost
to topmost trials in the image), clearly visible in panel E, is hidden in panel D using a different
trial-sorting order.
Panel F shows again the same response-aligned trial data, but now sorted by alpha phase
in the pre-response (but post-stimulus) period between the dotted lines. Here, we see that
18
ongoing alpha activity that is random phase before the button press (as reflected in the perfectly
diagonal positive and negative wave fronts in the sorting window), but the ensuing LPC
positivity peaking in this view about 120 ms after the button press is nearly vertical in this view,
and therefore appears to be independent of the phase of the the preceding alpha band activity
(which might well have a different set of sources than those generating the LPC). Note that the
LPC positivity is again wider than the tighter peak obtained in the alpha-sorted view of the same
data in panel E, though panels (D- F) all visualize aspects of the same data and have the same
motor response-locked ERP.
What conclusions can we draw from these six quite different ways of plotting the same
data? Note that each panel highlights a different way of separating the ERP trial average into a
set of single-trial activities, followed by moving-average smoothing to bring out trial-to-trial
trends in the trial-sorted data images. Each panel represents, in a way, a decomposition of the
single-trial data highlighting some foreground features and smoothing other types of trial-to-trial
variability to form a kind of background “noise” (as it were). Which of these decompositions in
this sense if any of them is the most physiologically realistic or ‘correct’ decomposition?
Arithmetically, there is no difference between them; in each case the same trial data, aligned as
in panels A-C or D-F, have the same ERP average, no matter how the trials are sorted – just as 5
pennies are equally the sum of 3+1+1 or 1+3+1 coin subsets.
The standard model underlying ERP analysis is that the EEG data essentially sum, (1)
contributions to the ERP occurring in each trial, and (2) other (undefined) variable activities
unaffected by the time-locking events and therefore not contributing to the ERP. Is t h is standard
(“ERP + background”) decomposition of the single-trial signals more physiologically “realistic,”
in any sense, than the different implied “decompositions” of the data into the quite different
features that are highlighted (plus those obscured) in these six quite different ERP-image panels?
In particular do any of these views parse the data into physiologically distinct source
contributions?
From these ERP-image representations of the data, we can at least see some ways in
which an average ERP of the trials is simply one statistical measure of them, a measure that does
not reveal their orderly (though complex) temporal variations or multiple spatial sources. In each
trial, the subject performed the same task – attempting to produce quick button press responses to
target stimuli while withholding responses to non-targets. Panel B clarifies at least one aspect of
trial-to-trial EEG variability directly related to subject behavior (e.g., their manual response
latency). What other trial-to-trial differences, either in stimulus features (here, in target location),
and/or in the trial context (here, the history of preceding stimuli and manual responses) may have
altered the nature of the ‘challenge’ posed to the subject’s brain and thus affected aspects of
trial-to-trial EEG variations? Neither the ERP averages nor these six ERP-image panels answer
these questions. There are many other possible decompositions into putative underlying EEG
19
source activities that examination of its trial average ERP cannot rule in or out as reflecting
physiologically valid distinctions among spatial sources and their event-related temporal
patterns.
At the least, these panels illustrate the fact that trial-to-trial variations in EEG data are not
simply “EEG noise.” Rather, they include several types of orderly trial-to-trial variability linked
to several EEG source and/or behavioral and task parameters. Panels C-F, in particular, pose an
interesting question. Is the LPC activity at this channel, time-aligned to the subject button presses
dominated by positive-phase alpha activity (as panel E suggests) or by a broader fixed-latency,
central LP C peak (as in panel F)? Or perhaps, by both types of activity arising in different
cortical domains and both projecting to the vertex to differing relative extents in different trials?
Figure 3.3. ERP-image plots separating the
ERP image in panel A, in which the trials are
sorted by mean potential between the two
dashed lines surrounding the post-response ERP
peak, into the sum of (B) an ERP-image of the
best-fitting (non-negative) mean-ERP
contribution to each trial, and (C) the remaining
unexplained portion of each trial. As in Fig. 3.2,
the mean of the single-trial data in each panel is
shown below the panel. The ERP has been
largely (though not completely) removed from
the lower panel data. This decomposition is
compatible with the assumption that the single-
trial data sum a single ERP response of variable
amplitude (B) plus unrelated EEG activity (C).
However, many EEG sources may make
separate contributions to the data and to the
ERP average. Regression of the whole average
ERP trace on the single data trials does not take
into account the spatiotemporal variability of
the independent sources of trial-to-trial
variation, for example the partial sorting by
value remaining within the sorting window and
near 300 ms. (Vertical smoothing window width
20 trials).
A simple ERP model of the trial-to-trial variability in EEG data represents the non-ERP
portion of the data as summing contributions of brain source activities that are unaffected by the
20
time-locking events. In an extreme version of this model, the amplitude of the ERP might be
assumed to be identical in every trial, with any trial differences reflecting additional task-
irrelevant EEG (or non-brain artifact) activity. But Figure 3.2 suggests that such a strict version
of the model is unlikely to adequately capture the trial-to-trial variability in the event-related
dynamics in these trials.
Panel A of Figure 3.3 shows the same trial data as in Fig. 3.2, but now sorted by mean
potential in the indicated post-response LP C data window. Panels B and C visualize an ERP-
based decomposition of the data in panel A, all three panels using the same trial sorting order
(sorting by LPC amplitude). Panel B shows the estimated contribution of the mean ERP to each
trial, as determined by finding the best least-square fit of the mean ERP to each single-trial epoch
but not allowing negative ERP trial weights in the few lowest trials. Panel C shows the
remaining (non-ERP) data for each trial. Thus, the sum of the values in panels B and C are the
whole-trial data as shown in panel A. At least two latency windows in Panel C (90-150 ms and
200-300 ms) exhibit systematic differences from a random trial distribution, indicating trial-to-
trial variability of potentials in those windows is partially independent of the overall amount of
ERP-like activity in the trial. But is this attempted decomposition of the single-channel data (in
panel A) into ERP and non-ERP data portions (in panels B and C) a physiologically valid
separation between completely motor response-locked (ERP) and motor response-independent
(non-ERP) cortical source processes in the data?
How can we begin to find answers to this question? To model the nature of the highly
variable signals occurring during these recorded data epochs, ideally we should first find a way
to separate the whole scalp EEG data into a set of functionally and physiologically distinct
source activities.
III. Separating EEG sources using Independent Component Analysis (ICA)
In 1995 the first author and colleagues at Salk Institute (La Jolla, CA) performed the first
decomposition of multi-channel EEG data into its maximally independent components (Makeig,
1996) using a then-new and elegant ‘infomax’ algorithm (Bell and Sejnowski, 1995) that
followed insights, a few years earlier, that weighted sums of independent source signals should
be separable ‘blindly’ into the individual source signals without advance knowledge of the nature
of the source processes, as had been thought necessary (Jutten and Herault, 1991; Comon, 1994).
The prototypical example of this problem is the ‘cocktail party problem’ in which an array of
microphones records mixtures of the voices of several people talking at once at a cocktail party.
Individually, the recordings sound like indecipherable ‘cocktail party noise.’ The blind source
separation problem is to determine how to combine the recorded signals so as to separate out
each speaker’s voice, “blind” to any knowledge of the nature or properties of individual sources.
21
At root, the insight allowing the solution to this problem is that the individual speakers’
voices are the only sources of independent information in the recorded data. By adapting
randomly weighted sums of the recorded signals in such a way as to make the weighted-sum
signals more and more temporally independent of each other, the unmixing process must finally
arrive at producing the individual voice signals. In signal processing terms, the joint microphone
data is separated into its maximally independent signal components, which must be the original
voice sources since they are the only possible independent sources in the recorded mixtures.
When the process proceeds without relying on any knowledge of the qualities of the
individual source signals, the unmixing process is called blind source separation. Using temporal
independence to separate the source signals is a form of blind source separation called
independent component analysis (ICA). Intuitively, two time series are maximally independent
when their waveforms are maximally distinct from each other. More technically, independent
time series have no mutual information, meaning that knowing the value of one process at a
given time gives no information at all (even partial or probabilistic) about the concurrent value of
the other process.
Reading about the ICA solution to the cocktail problem in the influential paper of Bell
and Sejnowski before its publication in 1995, the first author suspected that the same approach
should be applicable to EEG data. The results of the first EEG decomposition (Makeig, 1996)
were highly promising, and subsequent work over the next dozen years or more has confirmed
the ability of ICA to identify both temporally and functionally independent source signals in
multi-channel EEG or other electrophysiological data. ICA in effect creates a set of spatial
filters. Each independent component (IC) filter cancels out the contributions of all but one of the
distinct source signals that contribute to the multi-channel data. ICA can be thought of as a
method of data information-driven spatial filtering or beamforming (Iyer et al., 1990) that learns
spatial filters that each focus on a distinct physical source of EEG signals – separating out
distinct brain generator processes as well as different non-brain (artifact) signals.
More formally, a linear decomposition of a (channels by time points) signal matrix is its
representation as any weighted sum of component signal matrices of the same size (the same
numbers of channels and time points). Figure 3.4 schematically visualizes the simple matrix
algebraic formulation of the linear signal decomposition used in ICA. The scalp data channel
signals are formed into a matrix (top center). ICA decomposition finds an unmixing matrix (W)
which, when multiplied by the data matrix, decomposes the data (downwards pointing arrow)
into a matrix of independent component (IC) signals, called the IC activations (lower right), of
the same size as the input scalp data. Multiplying the IC activations matrix by the inverse of the
unmixing matrix W (lower middle) reconstitutes or back-projects the original scalp data channels
(upwards pointing arrow).
22
Figure 3.4. Schematic flowchart for Independent Component Analysis (ICA) data decomposition
and back-projection. ICA applied to a matrix of EEG scalp data (upper middle) finds an
‘unmixing’ matrix of weights (W, upper left) that, when multiplied by the (channels by time
points) Scalp data matrix, gives a matrix of independent component (IC) activities or activations
(lower right). This is the process of ICA decomposition (downward arrow) of the data into
maximally temporally independent processes, each with its distinct time series and scalp map.
The process of back-projection (upward arrow) recaptures the original scalp data by multiplying
the IC activations matrix (lower right) by the matrix of independent component (IC) scalp maps
(lower center) whose columns give the relative projection weights from each component to each
scalp channel. The IC scalp map or ‘mixing’ matrix (W-1, lower center) is the inverse of the
‘mixing matrix’ (W, upper left). In simple matrix algebra form, if the indicated scalp data matrix
is X and the component activations matrix U, then algebraically WX = U and X = W-1U. Here,
W is a matrix of spatial filters learned by ICA from the EEG scalp data that, when applied to the
data finds the activity projections of the underlying EEG source processes, and the IC
activations (lower right). This general schematic holds for all “complete” linear decomposition
methods returning as many components as there are data channels.
The inverse of the unmixing matrix, W-1, is the component mixing matrix (lower center)
whose columns give the relative strengths and polarities of the projections of one component
source signal to each of the scalp channels. In the figure, the values in the columns of the mixing
23
matrix are color coded and interpolated onto cartoon heads to visualize the topographic
projection patterns or scalp maps associated with each of the sources.
The component scalp maps found by ICA decomposition are not constrained to have any
particular relationship to each other (unlike in PCA decomposition). They may be highly (though
not perfectly) correlated. They may also have any (simple or complex) spatial pattern, although
in practice scalp maps for components truly accounting for a distinct source process
(contributing independent temporal information to the data) must reflect the relative projections
of the source process to the individual scalp channels. Thus, a source comprised of spatially
coherent local field activity across a cortical patch must have a scalp map that matches that of a
single tiny battery (dipole) placed in “the electrical center of mass” (as it were) of the source
patch and called its equivalent dipole (Scherg, 1990). However, IC scalp maps may, again have
any form, depending on the pattern of the source projection to the scalp electrodes, and on the
degree of dominance of a (maximally) independent component by a single signal source.
What is an independent component?
Before going further, we must first discuss a basic terminological confound. ICA (like PCA and
other linear decompositions) uses the term component’ to mean something quite different than
its use elsewhere in this volume (including its title), i.e. as a contraction of the term “ERP
component feature” – some identifiable feature in an ERP waveform (typically associated with a
single peak). By broader definition, an ERP component may be any functionally distinct feature
or portion of an ERP waveform, i.e. a feature with a functionally distinct relationship to
experimental parameters, and/or an ERP feature generated in a particular brain region (see
Chapter 1, this volume).
In this chapter, however, we will use the term component process (or component for
short) to mean some portion of an entire multi-channel recorded data set separated from the
remaining recorded data by linear decomposition. To minimize confusion, we will substitute a
terminological equivalent, ‘ERP peak’ or ‘ERP peak feature,’ for the more usual term ‘ERP
component.’ Thus again, in this chapter components will not refer to ERP peaks or other features
but to EEG source processes, each accounting for some portion of the continuous EEG activity
(at all time points) forming a multi-channel data set. Each data set component naturally then also
accounts for some portion (large, small, or negligible) of any ERP average of epochs drawn from
the data set.
As shown in Fig. 3.4, an independent component (process) of an EEG data set (or IC for
short) comprises both a fixed scalp map and a time series that gives its relative amplitude (or
“activation”) and polarity (positive or negative) at each time point. The scalp map shows the
relative weights or projection strengths (and polarities) of the projection from the component
24
process to each electrode location. The component activation time series gives the relative
amplitude and polarity of the component’s activity at each time point. Because we define an
EEG source as being spatially stable, a component scalp map remains constant over time. The
back-projection of each component process to each scalp channel is the product of the
component activation time series with the scalp map weight for that channel. The IC back-
projection to all the channels is the portion or component of the scalp data (at all channels)
contributed by the component process. The original channel signals are the sums of the back-
projected activities of all the independent components. That is, the scalp data are the collection
of all the summed back-projections of all the independent components to all the channels.
In simple matrix algebra form, if the scalp data matrix is X and the component activations
matrix U, then algebraically WX = U, where W is the unmixing matrix of spatial filters learned
by I C A decomposition of the EEG scalp data. This equation simply says that applying spatial
filters W to the data X ( b y simple matrix multiplication) gives the activation time courses of the
independent component processes. The converse process that reconstitutes the data from the
components is, algebraically, X = W
-1U where W-1 (the matrix inverse of W) is the component
mixing matrix. These same equations can be used to represent any linear decomposition method,
though other methods may use different names for the matrices.
Independent components of EEG data
It is important to understand that each scalp EEG recording channel is itself in effect a spatially
filtered measure of the varying scalp potential field, recording only the time-varying potential
difference between two scalp electrodes, the so-called “active” electrode and one or more
“reference” electrodes at which brain and non-brain signals are potentially just as “active as
the so-called “active” electrode. ICA attempts to replace these scalp channel electrode-difference
filters with IC filters using other linear electrode combinations chosen so as to pass individual
EEG source signals while rejecting all other sources. The degree of source fidelity ICA can
achieve depends on the number of data channels versus the number of active sources – as well as
on the length and quality of the data.
Before considering in detail the assumptions underlying ICA and giving heuristic
guidelines for how to apply it, let us first show model examples of independent EEG components
or ICs. ICs of EEG data can be roughly separated into three types: ICs accounting for brain and
non-brain (artifact) processes, respectively, and small ICs whose maps and activities appear
noisy and are poorly if at all replicated from session to session. This last category can be
considered a ‘noisy’ part of the EEG signals that ICA is not able to resolve into components
dominated by a single source (although not every small IC fits this description). Between these
three IC categories, there may be ICs in ‘grey areas’ whose assignment to one of these three
25
categories is difficult. Here, let us first consider ICs clearly accounting for activity from
particular non-brain (artifact) sources.
Independent non-brain component processes: Noise or signals?
ICA characteristically separates several important classes of non-brain EEG artifact activity from
the rest of the EEG signal into separate sources including eye blinks, eye movement potentials,
electromyographic (EMG) and electrocardiographic (ECG) signals, line noise, and single-
channel noise (Jung et al., 2000b; Jung et al., 2000a). This important benefit of ICA
decomposition of EEG data was apparent from the first attempt to apply it (Makeig, 1996). ICA
has thus found initial use in many EEG laboratories simply as a method for removing eye blinks
and other artifacts from data. For data sets heavily contaminated by eye blinks or other artifacts,
for instance data collected from young children, the ability to analyze brain activity in data trials
including eye movement artifacts can mean the difference between analyzing and rejecting the
subject data altogether.
Unlike regression-based methods for artifact removal, ICA artifact separation allows
artifact subtraction (often called artifact ‘correction’) without requiring a separate (‘pure’)
reference channel for each signal. In practice, regression methods risk eliminating brain signals
that also project to the (impure) reference channel (e.g., frontal brain sources also project to an
‘electrooculographic (EOG) channel’ near the eyes). Figure 3.5 shows scalp maps, spectra, and
ERP-image plots (above their trial-average ERPs) for four typical independent artifact source
components separated by ICA from the visual selective attention task session considered in
earlier figures. The highly distinct activity features separated from the data by ICA make the
qualitative implications of temporal independence clear. The recovered component waveforms
are the most temporally distinct portions of the recorded data. Separation by ICA of non-brain
source processes allow detailed analysis of the separated source process time courses. Note, for
example, that the subject refrained from blinking for over a second following target stimulus
presentations (Fig. 3.5A).
When, as here, the electrode montage includes both head and neck sites, scalp maps of
head muscle components exhibit a characteristic polarity reversal at the insertion point of the
muscle into the skull, with the direction of the dipole following the direction of the muscle fibers.
Note the scalp map associated with an EMG component signal (Fig. 3.5B). Note also the abrupt
changes in EMG activity level in the component ERP-image plot near trials 180, 300, and 370
(lower left), a common occurrence for scalp muscle activity recorded during experiments in
which the subject is sitting comfortably while attempting to minimize head and eye movements.
These marked changes in activity level of this muscle were likely neither willfully controlled nor
noted by the subject. By so clearly separating non-brain processes contributing to EEG data, ICA
26
allows these activities to be analyzed as concurrently recorded biological (or other) signals
instead of simply being rejected as non-brain “artifacts.”
Figure 3.5. Typical
component properties
of four non-brain
independent
component processes
accounting
respectively for eye
blinks, lateral eye
movements, left post-
auricular
electromyographic
(EMG) activity, and
electrocardiographic
(ECG) activity, from
the 238-channel EEG
recording studied in
Figures 3.2 and 3.3.
Upper panels show
the interpolated
component scalp
map, activity ERP
image, average ERP
(below ERP image),
and mean power
spectrum. Lower
panel shows the
maximally
independent activities
of the four processes
during a five-second period. Note the characteristic activity elements, also seen in the ERP-
image representations.
27
Spatially stereotyped versus non-stereotyped artifacts
It is important, however, to understand the distinction between spatially stereotyped non-brain
signal sources, such as eye blinks and scalp muscle activities that always project with the same
topographic pattern to the scalp channels, and non-stereotyped non-brain signal phenomena that
have varying spatial scalp projections. Consider, for example, the case of an unruly subject who
vigorously scratches his or her scalp for a second or two during the EEG recording. This quickly
produces a series of some hundreds of EEG data points (i.e., EEG scalp maps) whose
topographic patterns do not match each other nor appear elsewhere in the data. The one-time-
only appearance of each of these scalp maps is in effect temporally independent of all other data
sources, possibly hugely increasing the number of ‘temporally independent’ sources ICA needs
to separate into a finite number of component activities. Further, during this period the changes
in electrode contact with the skin may alter the spatial pattern with which the other brain and
non-brain signal sources project to the electrode array, violating the ICA assumption that these
spatial projection patterns are stable throughout the data.
Thus, including a stretch of data dominated by this or other spatially non-stereotyped
(SNS) artifact in the data given to ICA for decomposition can only limit the success of the
decomposition at identifying physiologically distinct EEG source processes. Such SNS periods
may be identified by eye while scrolling through the data, by use of simple heuristics (Delorme
et al., 2007a), by similar observations of a preliminary ICA decomposition of the whole data, or
even automatically during ICA training by computing the probability of each data point fitting
the current ICA model and rejecting highly improbable data points from further training.
Cases intermediate between spatially stereotyped and non-stereotyped artifacts are
phenomena with spatially stereotyped but non-stationary scalp patterns, for example slow blinks
(Onton and Makeig, 2006), ballistocardiographic (BCG) cardiac artifacts recorded within a high-
field magnetic resonance scanner (Debener et al., 2008), and slow waves in sleep (Massimini et
al., 2004). In such cases, ICA typically finds a small set of maximally independent components
that each captures one or more time periods of the repeating activity pattern, thereby separating it
from other source activities.
Independent brain component processes
Using ICA solely to remove non-brain source processes, while valuable, does not exploit the
power of ICA to separate the activities of individual brain sources that contribute to the scalp
data. Some might ask that since no part of the brain acts wholly independently from the rest of
the brain, how can ICA decomposition extract physiologically meaningful component signals?
The answer to this question is that ICA finds the maximally independent components for a data
set, even if traces of dependence remain between them. This dependence might be transient – for
28
example the occasional strong similarity of occasional evoked activity in otherwise maximally
independent left and right lateral occipital processes produced by central visual stimulus
presentation (Makeig et al., 2002). Or the dependence might be limited, for example only
reflected in weakly coherent, low amplitude, high frequency activity.
Even in cases in which two ICs have remnant mutual dependence, i.e. when their joint
activities could be said to form "a dependent two-dimensional subspace" of the data, ICA should
still separate the activity of this subspace from the activities of other, single independent
component processes. For example, a moving scalp artifact produced by slow eye blinks might
be separated into two or more independent components, each accounting for one phase of the
moving blink potential. In this case, the spatiotemporally overlapping component activities
would differ from one another, not allowing their parsing as a single IC. Though not completely
independent of each other, the time courses of the partially dependent ICs might still be
independent of any other IC time course in the data and sufficiently different from each other to
require more than one IC (Meinecke et al., 2002).
Figure 3.6. Equivalent
dipoles for six maximally
independent brain source
components. Near each IC
index (ranked in order of
variance contributed to the
scalp data), the residual
variance (r.v.) of the
equivalent dipole model
across the 238-channel
component scalp map is
indicated, based on fitting
the measured 3-D
electrode locations to an
individualized three-shell
boundary element method
(BEM) head model. All the
residual variances are low
(< 6%), indicating that the
component maps are
compatible with an origin
in a single (or, IC8, in dual
bilateral cortical patches). The equivalent dipoles (center) are likely situated somewhat closer to
the cortical surface than the locations of the equivalent model dipoles. The five-second activation
periods shown in the lower panel give representative (not concurrent) examples of bursts of
29
frontal midline (IC21) theta (and higher frequency) activity, and posterior (IC3, IC4) alpha
source activities for three of the components.
Again, the computed IC single equivalent dipole locations cannot represent the spatial
distribution of the cortical generator domains. Instead, they represent the computed positions (in
the BEM head model) of vanishingly small oriented dipoles whose scalp projection patterns
match most closely the actual IC component maps (across all electrodes). In general, an
equivalent dipole for a cortical patch source is typically deeper in the brain than the cortical
patch itself (Scherg, 1990). Recent advances in distributed inverse source localization methods
suggest that it may soon prove possible to estimate, using subject MR images, the patch (or
patches) of subject cortex that most likely constitute each IC source domain. Such a goal is likely
not reachable by the alternate strategy of first computing an ERP average and then finding
inverse source distributions of one or more ERP scalp maps, since the ERP scalp map at any
point in time is typically a weighted mixture of contributions from several cortical source areas.
ICA assumptions
As illustrated in Figures 3.5 and 3.6 (above), ICA decomposition has proven to be highly
successful for studying EEG data – Why? An important part of the answer must be that there is
an approximate fit, at least, between ICA assumptions and the physiological nature of EEG
sources themselves (Makeig et al., 2004a; Onton and Makeig, 2006; Onton et al., 2006).
Basically, ICA “blindly” separates the scalp data given it into component processes whose
spatial and temporal properties are not known in advance, based on the following five
assumptions:
(1) That the component source locations (and thereby their topographic projection patterns to
the scalp sensors) are fixed throughout the data.
(2) That the projected component source activities are summed linearly at the sensors.
(3) That there are no differential delays involved in projecting the source signals to the
different sensors.
(4) That the probability distributions of the individual component source activity values are
not precisely Gaussian.
(5) That the component source activity waveforms are (maximally) temporally independent
of one another.
The last (‘independence’) assumption (5) can be translated informally as saying that the
component source activity time patterns are maximally distinct from one another, an assumption
partially supported by intracranial recordings from neighboring areas (Destexhe et al., 1999).
More technically, a set of signals are temporally independent, in the sense used for ICA, if
knowing the activity (µV) values of any subset of the signals at a given time point gives no clue
about the activity values of any subset of remaining sources at the same time point. Thus each
30
component source signal is, in a particular sense, an independent source of information in the
data, contributing a temporal pattern not in any way determinable from the values (at the same
time point) of the other component source signals.
The spread of information-based signal processing into nearly every signal processing
application area in the last decade (Jutten and Karhunen, 2004) derives primarily from the basic
interest of investigators in all research areas in identifying the sources of information that
contribute to their multi-dimensional data. However, the value of ICA for decomposing any
signal is determined by the degree to which the ICA assumptions fit the manner in which the
data are actually generated and recorded. For EEG signals, the assumptions of simple summation
at the electrodes (2) and lack of differential delay (3) are met precisely. The non-Gaussian
distribution assumption (4) is plausible for EEG sources generated by nonlinear cortical
dynamics as well as for non-brain artifact sources including cardiac signals, line noise, muscle
signals, eye blinks and eye movements, etc. that are not themselves sums of smaller uncorrelated
signals.
As mentioned earlier, the ICA spatial source stationarity assumption (1) is consistent with
indirect evidence from fMRI and other brain imaging methods, and the independence assumption
(5) is consistent with the very sparse long-range cortico-cortical coupling and the predominantly
radial thalamocortical connectivity profile. However, both these assumptions have limitations. In
particular, optical dye recordings in animals of local field potentials at the millimeter and smaller
scale reveal moving wave patterns (Arieli et al., 1995), and comparison of ICA solutions across a
group of subjects participating in the same task suggests that the spatially stable EEG sources
separated from the data by ICA depend in part on the task the subject is performing (Onton,
2005). Thus, further research is needed on methods of identifying spatial lability in EEG source
data (Anemuller et al., 2003) and for identifying changes in the spatial distribution of the sources
as subject task, strategy, or preoccupation changes (Lee, 2000). However, given a hypothetical
switch between two sites of EEG signal generation as the subject alternately performs two tasks,
ICA should in theory return two components each showing the task-related activity only during
one performance condition.
Dual-dipole IC processes
From the viewpoint of ICA decomposition, an EEG source is nothing more than an independent
time course of information in the data, whatever its scalp projection pattern. The scalp
projections (and hence, scalp maps) of ICA components are thus constrained only b y t h e
projection patterns of the actual physical sources of the data. Cortical (or other) source signals
arising in separate cortical patches may be partially or wholly synchronized if the separate
patches are physically linked by dense white matter tracts (such as corpus callosum), or are
identically stimulated. In this case, ICA decomposition will (rightly) return a component
31
summing the scalp projections of the two (physical) source patches. For example, a single IC
typically accounts for eye blink artifacts from the two eyes, whose synchronized small upward
movements during the blink induce electrical activity accounted for by an equivalent dipole
located in each eye.
Similarly, ICA may return one or more brain components whose scalp maps sum the
projections of two equivalent dipoles, usually with bilaterally near symmetrical locations and
scalp projections, compatible with patches connected by corpus callosum. Theoretically, cortical
activities on either end of any dense white matter tract might synchronize and their activities be
combined into a single IC, though to us this has not yet been conclusively demonstrated. It
makes no sense to say that ICA fails to separate “sources” in this case, unless one for example
(re)defines the term “EEG source” to mean activity in a single cortical patch. However, in
practice the number of dual-dipolar” ICs is relatively small (except for most ICs accounting for
eye movements, thankfully).
ICA ambiguity
Discussions of the polarity and amplitude ambiguity inherent in IC activations in some early ICA
papers have been confusing to some readers. In fact, this ambiguity is present only when the IC
activations and IC scalp maps are considered separately. We might say that the sign and scaling
of the (back-projected) component in the data is split (arbitrarily) between its activation and
scalp map. Since -1 × -1 = 1, inverting the signs of both an IC activation and its scalp map will
not change their product, or the back-projection of the IC into the original data, which will retain
its original polarity. These ambiguities should be kept in mind when examining or comparing IC
activations or scalp maps.
However, the µV scaling of the back-projected IC scalp activity is precisely the product
of the scalp map values with the activation time series. Thus, ICA decomposition does not lose
this information, as is sometimes mistakenly suggested. Also, while IC potentials at the cortical
surface are also proportional to the IC activation, accurate source location and electrical head
models are needed to determine the actual IC strength on or in the cortex, since this depends on
the resistance between scalp and cortex, which in turn varies across heads and source locations.
Note that, ICA does not itself sort the components into any fixed order. Thus,
decompositions of similar data, even data from the first and second halves of the same recording
session, are not guaranteed to return ICs in the same order. ICs from different data sets need to
be compared with each other using one or more measures of their time courses and/or scalp
maps, for example their power spectra and equivalent dipole locations.
32
Number of data channels
How many data channels should be used for ICA filtering to be successful? The most
computationally efficient and robust ICA methods, such as infomax ICA, neither increase nor
decrease the dimensionality of the data they find the same number of components as there are
data channels and are therefore called “complete” decomposition methods6. How many
independent sources contribute to EEG data? It is highly likely that there are always more (brain
and non-brain) sources with distinct (e.g., near-independent) time courses and unique scalp maps
than any possible number of recording channels, since synchronized cortical field activity likely
occurs, at least transiently, at more than one spatial scale, and to some extent uncorrelated noise
is generated at each of the electrodes. Most such source activities will be small to negligible, but
their presence guarantees that the number of degrees of freedom of the recorded data will never
be less than the number of data channels.
Data contributions from numbers of sources beyond the number of available component
degrees of freedom (i.e., beyond the number of data channels) will be mixed into some or all of
the resulting components, thereby adding a kind of ‘noise’ to the results of the decomposition.
The noise inherent to ICA decomposition of EEG data is evidenced by the indeterminate scalp
maps of the very smallest ICs in a high-dimensional data decomposition, ICs that may not prove
stable under repeated decomposition and whose scalp maps are often far from ‘dipolar’ (i.e.,
resembling the projection of a single dipolar source). Because of the need for ICA to ‘mix’ all of
the EEG sources into the available number of components, decomposing data with a larger
number of (clean signal) channels may be preferable when there are enough data to decompose
them (see following). But decomposing a smaller number of channels will likely prove beneficial
as well.
Data requirements
Successful ICA decomposition requires an adequate amount of data. We may say,
metaphorically, that the independence of many source signals cannot be “expressed” in brief
mixtures of them. To “express” their independence (or less metaphorically, for an ICA algorithm
to recognize it), a considerable amount of data is typically required. Thus, successful ICA
decomposition typically profits from being applied to a large amount of data, typically the entire
collection of continuous data or extracted and then concatenated single trials from an event-
related EEG/ERP task session. The most frequent mistake researchers make in attempting to
apply ICA to their data is to attempt to apply ICA decomposition to too few data points. For data
with large numbers of channels (64 or more), we suggest it is optimal to decompose a number of
time points at least 20 or more times the number of channels squared. This is only a heuristic
standard, not a strict minimum, and using this much data does not in itself guarantee an optimal
decomposition. For very dense scalp arrays, this standard could require an unreasonable amount
33
of data. For example, to decompose 256-channel data 20 × 2562 time points at 256 points/sec
would require over 80 minutes of recording time and occupy nearly 1.5 GB, though by this same
standard for 64-channel data a 22-minute recording occupying about 0.35 GB would suffice.
We are not as sure about the influence of sampling rate on ICA decomposition. Doubling
the sampling rate during a recording period shortened by half might not produce as effective a
decomposition, since the higher frequencies captured in the data acquired with a higher sampling
rate would be small, relative to lower frequency activity, and might have lower source-signal-to-
noise ratio. See Onton & Makeig (Onton and Makeig, 2006) for further discussion.
Optimally the data should be from a period in which the subject is predominantly in the
same state (for example, awake and attentive), and performing the same type of task or tasks.
Although standard ICA methods are theoretically able to separate data into sources that are
principally active at different periods in the data set, a promising newer mode of ICA
decomposition allows learning multiple sets of independent components wherein each time point
is associated with only one decomposition (Palmer, 2008).
Since most ICA decompositions do not use relationships among time points to perform
the source separation (infomax ICA actually re-shuffles the order of the time points in each
training step), it makes no difference whether the data are from contiguous time periods or from
separate data epochs. For example, Makeig et al. (2002) reported a 31-channel decomposition of
data only from the N1 response-peak period following presentations of visual stimuli. This was
possible because of the large number of such stimuli (2,500) viewed by each subject, and the
relatively small number of channels recorded (31).
Finally, it should be noted that ICA is reference free, since a n y re -referencing of the data
that preserves its dimensionality does not change its information content or its sources. After re-
referencing, the IC scalp maps will change but IC activation dynamics and equivalent model
dipole locations should not change except as a result of normal statistical variability, which is
typically small for ICs with highly ‘dipolar’ scalp maps.
ICA versus PCA
Another well-known method of linear decomposition of multi-channel data, principal component
analysis (PCA), transforms multi-channel data into a sum of uncorrelated principal components
so named because they each, in sequence, account for the most possible (or ‘principal’) variance
in the remaining uncorrelated (or orthogonal) portion of the signal data not accounted for by the
preceding principal components. By contrast, independent components (ICs) produced by ICA
have no natural order though it is common to sort them by descending variance of the (back-
projected) scalp data they each account for. Again, for either PCA or ICA the whole scalp data
34
are the sum of the individual component contributions. The simple system of Fig. 3.4 thus
applies to PCA as well, though for PCA, W-1 is called the eigenvector matrix and W is its
inverse. Also, in PCA both the eigenvector matrix and the activations or factor weights matrices
are normalized, and an intervening diagonal matrix E, the eigenvalues matrix, is used to hold the
relative scaling of the components (i.e., X = W
-1EU), while the columns of the mixing matrix as
well as the rows of the activations matrices are each normalized (to have unity root-mean-square
values).
The important difference between ICA and PCA is in their quite different goals or
objectives. We may say that PCA attempts to lump together maximum signal variance from
however many sources into as few principal components as possible, whereas ICA attempts to
split the signal into its separate information sources, regardless of their variance. This makes
PCA useful for compressing the number of dimensions in the data while preserving as much as
possible of the data variance. However, elimination of low-variance PCs for the purpose of
dimension reduction most likely deletes portions of nearly all the source activities, not just the
smaller ones. When data length is not long enough to successfully decompose all available
channels, another possibility is to perform ICA decomposition of data from some channel subset.
The relative value of these two approaches (principal subspace versus channel subspace) is
difficult to evaluate in advance.
The ‘maximum successive variance’ objective of PCA also forces both the principal
component activities and the scalp projections (scalp maps) to be mutually uncorrelated
(orthogonal). Since the scalp projections of brain (and non-brain) sources are rarely themselves
orthogonal, this property forces all but the first very few principal component scalp maps to
resemble checkerboards that cannot reasonably represent the activity of single EEG sources. In
general, principal component maps do not resemble the projection of a single EEG source unless
one source (often, eye blinks) or two sources with near-orthogonal maps (for example, lateral
and vertical eye movements) dominate the signal variance.
For this reason, some ERP researchers advocate the use of post-PCA component rotation
methods developed for earlier factor analysis approaches, such as Varimax or Promax (Dien et
al., 2005). These may help focus the scalp maps of the very first components to emphasize a few
large source activities (such as eye blink artifacts and lateral eye movements), but both
simulations and actual decompositions show their power to accomplish this for many brain and
non-brain sources pales in comparison to ICA methods when properly applied to sufficient data
(Makeig et al., 1999b; Makeig et al., 2002).
Independence among source waveforms, however, is a much stronger assumption than
the simple absence of correlations between source pair signals. Substituting the stronger
assumption of independence between component activities instead of requiring them only to be
35
uncorrelated allows ICA to return independent components (ICs) having any (non-identical)
scalp maps. Every IC scalp map is then free to represent the projection of a single brain or non-
brain signal source, whereas PCA component maps are constrained to be uncorrelated and
therefore most have a “checkerboard” appearance not compatible with a single cortical (or other)
source projection.
Theoretically, exact independence is such a strict requirement that it can never be
established for EEG signals with finite length. ICA algorithms, therefore, may at best produce
components with maximal independence by ensuring that components continually approach
independence as the ICA algorithm iteratively applied to the data. The degree of IC
independence achieved may differ for different data sets and also for different ICA algorithms
applied to the same dataset. Our discussion of the nature of brain EEG sources (Section I)
implies that the more independent the recovered IC activities, the more dipolar (or occasionally,
bilateral dual-dipolar) the IC scalp maps of brain components, a trend supported by recent tests
(Delorme, unpublished data).
Independent component contributions to single trials and ERPs
By definition and design, independent component processes contribute nearly independent
temporal variability to sets of single-trial epochs. Each IC represents an independent EEG
process whose continuous activity variations in the single trials are available for inspection and
analysis. In particular, brain-based ICs with near-dipolar scalp maps may each be presumed to
index the near-synchronous field activity arising in a single patch of cortical neuropile (or
occasionally, simultaneously in two bilaterally symmetric and likely tightly-coupled cortical
patches). Examining the trial-to-trial variability in the IC activities relative to a set of time-
locking events may allow a more detailed understanding of event-related brain dynamics than
examination of raw scalp channel data themselves, since the effects of source (and artifact)
mixing by volume conduction have been removed or strongly reduced by ICA.
As an example of this, Figure 3.7 shows ERP-image plots of the activities of six independent
components in the same response-locked single-trial data as earlier figures. In each ERP image,
IC activity is scaled (in µV) as in it projects to the near-vertex (Cz) electrode. Locations of the
equivalent IC dipoles are shown in the central panel. Trials are ordered exactly as in Fig. 3.3, by
the amplitude of the LPC peak 120 ms after the button press (0 ms) at the vertex. Note the quite
high degree of overlap of the ‘dipolar’ scalp maps of these midline components that contribute
temporally independent contributions to the recorded EEG signals.
36
Figure 3.7. ERP images for six midline and one bilateral brain independent components (ICs) in
the same session as earlier figures (compare Fig. 3.6), with trials sorted in the same order as
Fig. 3.3, and scaled as they contribute to the near-vertex channel signal imaged in Fig. 3.3.
There, the trials were sorted by the amplitude of the LPC peak centered 120 ms after the button
press (at latency 0 ms) at the near-vertex channel shown on the head cartoon (middle right
panel). The sum of the signals projected by these six component processes is shown in the same
panel (note difference in color scale). The summed contributions of the other 232 non-artifact
components to the same channel are shown in the lower right panel. The channel ERP-image
plot (Fig. 3.3A) is thus the sum of the two ERP-image panels with grey backgrounds at the right
of this figure. Separately, the contributions to the ERP of each of the other components summed
in the lower right panel are smaller than those of the six components whose contributions are
shown in the other panels.
37
The sum of the signals projected by these six component processes is shown in the
middle right (grey) panel. Note that the trial order used here, which sorts the trials by ERP
amplitude at the selected channel (as in Fig. 3.3B), only partially sorts the post-response
amplitude of each IC activation. This is shown by the uneven gradations of the post-motor
response positivity in the component ERP-image panels and in the sum of their contributions at
the same near-vertex channel (middle right panel). This implies that contributions to the activity
fitting the mean ERP template in Fig. 3.3B sum varying spatial combinations of these and other
brain source processes in the different trials.
Note also in Fig. 3.7 the different peak latencies of the LPC peak for ICs 2, 6, and 15 (top
row). The trial ordering selected in Fig. 3.3 based on the amplitude of the average ERP ignores
these single trial and component process differences. It sorts trials according to the amplitude of
the average summed contributions of these and other independent sources, rather than on the
varying amplitudes and latencies of the individual source processes.
The summed and similarly smoothed (smaller) contributions of all the other 232 non-
artifact components to the same channel in the single trials are shown in the lower right (grey)
panel. The channel ERP image in Fig. 3.3A is thus the sum of the two right (grey) panels, as well
as the sum of the two ERP-image panels Fig. 3.3 B and C. Neither of the ‘remainder’ ERP
images (Fig. 3.3C or Fig. 3.7 lower right) suggest a satisfactory modeling of the LPC as
summing just two factors i.e. neither the ‘six-ICs’ model imaged in Fig. 3.7 (lower right) nor
the ‘invariant-ERP’ model in Fig. 3.3 (B and C). Using the ICA model, however, we may
examine, for example, whether the particular trial-to-trial differences in the LPC window of each
identified IC may indicate that its response varies with some dimension of the varying trial
context (e.g., each trial’s particular cognitive and behavioral demands and demand history).
Figure 3.8 shows that a portion of the I C trial-to-trial variability highlighted in Fig. 3.7 is
indeed linked in orderly ways to behavioral trial differences. It shows ERP-image plots for the
same six independent components (ICs) as in Fig. 3.7, again scaled as they contribute to the
central scalp channel (center right) but here sorted by subject reaction time and then smoothed
with a wider (50-trial) moving window to more clearly visualize trends. Note that the wider
averaging window reduces the overall amplitude of the imaged data through phase cancellation
of trial-to-trial I C variability in neighboring trials (compare the color µV scale limits here with
those in Fig. 3.7).
38
Figure 3.8. ERP images for the same six independent components (ICs) as in Fig. 3.7, again
scaled as they contribute to the central scalp channel (center right cartoon head) but here sorted
by subject reaction time and then smoothed with a broader (50-trial) moving window (note color
scales). The middle right panel shows the summed contribution of the six ICs to the whole
channel signal, with again (lower right) the difference between the whole signals and the sum of
these six source contributions. This view reveals that a portion of the trial variability evidenced
in Fig. 3.7 is tightly linked to differences in subject reaction time. For anterior sources ICs 2 and
8, the negativity preceding the button press is time-locked to stimulus onsets, while the
subsequent LPC is mainly time-locked to the subject button press. For central midline sources
IC15 and IC6, the negativity onset and offset are time-locked to the stimulus and button press
respectively. Posterior sources IC3 and IC4 appear to exhibit partial phase resetting of their
alpha activities by stimulus presentations. The single scalp channel signal sums all these (and
other) event-related source dynamics.
39
The middle right panel shows the summed contribution of the six ICs to the whole
channel signal, and the lower right panel, again the remainder of the whole channel signals they
do not account for. This view reveals that a portion of the trial variability evidenced in Fig. 3.7 is
tightly linked to differences in subject reaction time. For anterior sources ICs 2 and 8, the
negativity preceding the button press is time-locked to stimulus onsets, while the subsequent
LPC is mainly time-locked to the subject button press. For central midline sources IC15 and IC6,
the negativity onset and offset are time-locked to the stimulus and button press respectively.
Posterior sources IC3 and IC4 appear to exhibit partial phase resetting of their alpha activities
following stimulus presentations (see Section IV). The single scalp channel data and ERP sum
all these (and doubtless other) event-related source process contributions.
It may be worth the reader’s effort to examine again carefully the trial variability in
different dimensions visualized for scalp channel data in Figs. 3.2 and 3.3, and for IC data in
Figs. 3.7 and 3.8.
Independent component clustering
To compare, group, or further average ERPs across subjects and/or sessions, channel data are
typically identified by the labeled (Cz, Pz, etc.) or measured (x,y,z) channel positions on the
scalp. Though equating of equivalent scalp locations across sessions and subjects is adequate for
many purposes, it ignores the variety of individual cortical configuration differences, particularly
in the positions and orientations of cortical sulci, that may orient anatomically equivalent EEG
source projections toward different scalp areas in different subjects. In this case, functionally
equivalent sources may have quite different scalp maps, and therefore electrodes at analogous
locations will record different weighted mixtures of source activities. Thus, for example, signals
from ‘my Cz’ and your Cz’ may not be equivalent, even if our brains have equivalent cortical
areas that function identically. This produces unavoidable and rarely considered variability in
scalp recordings that are compared or averaged across subjects.
Since under favorable circumstances ICA can separate scalp-recorded signals into the
volume-conducted activities of maximally independent brain sources, it may be more accurate to
group, compare, and characterize functionally equivalent clusters of ICs across subjects and/or
sessions. Finding these IC equivalence classes is the challenge of IC clustering across subjects
and/or sessions. IC clusters may be selected on the basis of their equivalent dipole locations,
ERPs, and/or other measures.7
Figure 3.9 shows a sample application of IC clustering to a grand mean ERP averaging
data from 12 subjects who participated in a visual attention-shift experiment. Throughout the
experiment, subjects made speeded manual choice responses to indicate in which dimension
(shape or color) the lateral target stimulus (presented at 0 ms) differed from a simultaneously
40
presented neutral background stimulus. In the 12 subjects’ ICA-decomposed data, we identified
22 clusters of similarly located and similarly reacting ICs by comparing equivalent dipole
locations, mean power spectra and event-related spectral perturbations (ERSPs, see Section IV)
in three stimulus conditions. Figure 3.9 focuses on a grand-mean ERP time locked to stimulus
presentation (at latency 0 s) in one condition. The central panel shows IC equivalent dipole
locations for four of 22 identified IC clusters.
Figure 3.9. Equivalent
model dipole locations,
mean scalp maps, and
cluster projection
envelopes of four (of
22) independent
component cluster
contributions to a
visual stimulus ERP
(grand mean over 12
subjects) in a visual
attention-shift
experiment. ERP
envelopes show only
the most positive and
most negative channel
values at each response
latency. Here, the
envelope (see text) of
the grand-average
back-projection of the
indicated IC cluster is
color-filled. The outer
black traces are the
envelope of the whole grand-mean ERP after removing contributions of component clusters and
outlier components accounting for eye, muscle, and other non-brain artifacts. The bottom two
panels show clusters accounting for most of the P1 peak in the grand-mean ERP. The upper two
panels indicate the portions of the grand-mean ERP accounted for by a central posterior cluster
(blue, with maximal contribution to the peak labeled P2) and a midline cluster (red, with
maximal contribution to the later peak labeled P3).
41
The black traces in the four top and bottom plot panels show the envelope of the grand
mean ERP (i.e., its maximum and minimum channel values at each latency). The four top and
bottom panels show the cluster-mean scalp maps and the boundaries of the colored regions, the
envelopes of those portions of the grand-mean ERP accounted for by each of the four clusters.8
Envelope plotting allows the ERP contributions of one or more ICs or IC clusters to be visually
compared with the envelope of the whole scalp ERP.
The lower panels show two lateral occipital IC clusters (see the green and purple IC
dipoles) that accounted for nearly all the bilateral positive peak near 110 ms in the ERP, plus a
later sustained “ridge-like” feature. The upper two panels show the portions of the grand mean
ERP accounted for by a central posterior cluster (blue) whose maximum ERP contribution was t o
the positive peak near 220 ms, and a midline cluster (red) that contributed maximally to a later
positive peak near 350 ms.
Note that although the model dipoles are represented, for visual convenience, as small
balls, the actual uncertainty in their individual locations is rather larger, as are the distributions of
cortical territory across which synchronized local field activity (in our model) produce the far-
field potentials recorded by the scalp electrodes. Sources of dipole location error in Fig. 3.9
include possible differences in recorded electrode positions relative to each other and the scalp,
errors in co-registering the electrodes to the head model, and differences in head shape, and
possible differences in head tissue conductivity parameters. Although the equivalent model
dipole locations shown in the middle panel are relatively tightly grouped, their spread may also
reflect differences in the locations of functionally equivalent cortical areas across subjects, since
similarities between activity measures were also considered in assigning components to clusters.
IC clustering is required to compare ICA decompositions from more than one subject or
session. It can be used to understand the locations and dynamics of independent component
processes contributing to average ERPs as well as to the unaveraged single trials. IC clustering
provides an involved but under favorable circumstances, we believe a more adequate answer to
the inverse problem of estimating the distributed sources of ERP scalp maps and the relationship
of the source dynamics to experimental events and conditions. In particular, IC clustering gives a
more adequate solution than simply attempting to model the distributed cortical sources of ERP
scalp maps themselves. IC clustering also allows testing for differences within and/or between
subject groups reflected in the presence or absence of ICs in one or more clusters and/or on
details of the clustered IC locations or activities.
IV. Time/frequency analysis of event-related EEG data
42
Time-locked but not phase-locked: Event-related spectral perturbations (ERSPs)
To understand the relationship of ERP features to the event-related dynamics of the entire EEG
signals from which they are derived, it is convenient to use time/frequency analysis that models
the single-trial data as summing an ever-changing collection of sinusoidal bursts across a wide
frequency range. Note that producing this representation of the data does not mean that the EEG
is necessarily composed of such bursts, or that the burst shape or window employed in the
analysis is necessarily a physiologically accurate template. Rather, as Joseph Fourier first
showed for heat flows along a copper tube, frequency analysis, and later non-stationary
time/frequency analysis, can be used to represent any temporal activity pattern, not limited to
those portions of the recorded signals that do indeed resemble single time/frequency basis
elements, e.g. symmetric and smoothly tapered bursts at a single frequency. However, the
frequent appearance of periodicities at multiple frequencies is a clear and remarkable feature of
EEG records and this property of the signals show quite clear and spatially distinct changes
accompany changes in arousal and attention, making time/frequency analysis clearly useful for
EEG analysis.
Rather than averaging the recorded (‘time-domain’) event-related data epochs directly,
one may average their time/frequency transforms (see also Chapter 2, this volume). Averaging
time/frequency power or log power values in a regular grid of time/frequency windows gives an
event-related spectrogram that is nearly always dominated by relatively large low-frequency
activities. Normalizing the result, therefore, by subtracting the mean log power spectrum within
some defined ‘baseline’ period (pre-stimulus or otherwise, as relevant to the analysis) allows a
color-coded time/frequency image of mean log spectral differences we call the event-related
spectral perturbation (ERSP) image (Makeig, 1993). Basing the ERSP on changes in log power
implicitly assumes a multiplicative model by which EEG spectral changes represent the
multiplication or division of the baseline power at each frequency in each latency window
relative to the time-locking events.
Determining either the amplitude or the phase of activity at a particular time/frequency
point involves matching the data in a window surrounding the given time point to the oscillatory
basis element (typically a tapered sinusoidal burst or ‘wavelet’). To measure low frequencies,
this window must be relatively long, limiting the frequency range considered for short data
epochs. Also, event-related changes in spectral power may last longer than significant features in
the ERP. For these reasons, our own typical time/frequency analyses use epochs including at
least 1 s before the time-locking event and continuing to 2 s or more following it, allowing a
frequency decomposition based on a three-cycle tapered sinusoidal wavelet down to 3 Hz.
The mean ERSP of a set of event-related data epochs can index event-related dynamics
that leave no trace at all in the ERP average of the same epochs, as first shown for alpha band
43
activity by Pfurtscheller and Aranibar (Pfurtscheller and Aranibar, 1977). Thus the ERSP
transform of the average ERP for a set of data epochs, while of possible interest to compute, may
bear little or no resemblance to the average ERSP for the same collection of epochs. For one,
significant ERSP features may long outlast the reliable ERP features. For example, Figure 3.10
(top panel) shows a mean event-related spectral perturbation (ERSP) time/frequency image for a
left-frontal independent component (IC2) time-locked to button presses following target stimuli
(from the same session as Fig. 3.1-3.8). Regions of non-significant difference from baseline
(here p < .001, uncorrected for multiple comparison) are masked with light green. The ERSP
image reveals that mean alpha band power just below 10 Hz increases weakly following the
button press, while mean low-beta activity (15-20 Hz) in two frequency ranges increases most
markedly after 400 ms. Activity at the 6-Hz baseline spectral peak (see top left side-facing blue
baseline spectrum) does not change, though activity below 5 Hz increases weakly around the
button press, and then decreases beginning 200 ms after the button press.
Spectral power in the average ERP is often referred to as the spectrum of activity evoked
by events, while changes in spectral power appearing in the ERSP are dubbed changes induced
by events. However, this terminological distinction should not suggest that the two are
necessarily physiologically distinct. To see this, we need to consider changes in phase statistics
associated with experimental events.
Phase-locking across trials: inter-trial coherence (ITC)
The ERSP disregards completely the consistency or inconsistency of the phase of the activity at
each frequency and latency in a set of event-related epochs. Inter-trial coherence (ITC), or more
precisely, inter-trial phase coherence, introduced as ‘phase-locking factor’ by Tallon-Baudry et
al. (Tallon-Baudry et al., 1996), measures the degree of consistency, across trials, of the phase of
the best-fitting time/frequency basis element at each latency/frequency point. Phase consistency
is measured on a scale from 0 (no consistency, phase across trials is random and uniform around
the phase circle) to 1 (phase perfectly consistent across trials). The ITC for any finite set of
randomly-selected data epochs will typically not be 0. Therefore, it is important to compute a
baseline threshold for the appearance of significantly non-random phase coherence. An ITC
reliability threshold for a set of trial data can be found using either parametric or non-parametric
statistical methods (Mardia, 1972; Delorme and Makeig, 2004).
It is important to note that the ITC and ERSP images for a given set of event-locked data
epochs may have few or even no common features. For example, in Fig. 3.10 the post-motor
response increases in alpha and then in beta-band power in the frontal midline IC spectrum are
not mirrored by significant changes in ITC at the same latencies and frequencies.
44
Figure 3.10. Event-related
time/frequency analysis of the
set of independent component
trials shown in Fig. 3.7 and 3.8
(upper left). Mean event-
related spectral perturbation
(ERSP, top) and inter-trial
coherence (ITC, bottom)
time/frequency images for a
leftward-pointing mid-frontal
independent component (IC2)
time-locked to button presses
following target stimuli.
Regions of non-significant
difference from baseline (p< .001, uncorrected) are masked with light green. The top (ERSP)
image reveals that mean alpha band power at 10 Hz increases weakly following the button press.
On average, low-beta activity (15-20 Hz) activities first decrease slightly, then increase after 400
ms. Activity at the baseline spectral peak (6 Hz, see top left baseline spectrum plot) does not
change, though activity below 5 Hz is maximal at the button press. The bottom (ITC) image
shows that 4-Hz activity becomes partially but significantly phase-locked around the button
press, meaning the portion of the component ERP (lower trace) near 4 Hz is statistically
significant (compare the ERP trace below), as are its weak 10-Hz “scalloping” between -50 and
200 ms. Component activation units (‘act.’) are proportional to scalp µV. The statistically
significant changes in mean spectral power in the beta band, shown in the upper panel, are not
associated with significant ERP features and therefore represent changes in component activity
time-aligned but not phase-aligned to the button presses.
However, there is an intimate relationship between the ITC and the ERP. I n particular,
the occurrence of a significant ERP peak or other feature requires significant ITC (see Section
II). In this sense, a significant ERP value at any time point reflects and requires significant ITC
values at one or more frequencies at that time point (except in odd, improbable cases). Note also
that the ITC for any frequency may be significant even at latencies at which the mean potential
ERP value is 0. For example, if the 0 value in the ERP occurs during the zero crossing of an
alpha oscillation in each trial, then the ITC at that alpha frequency might be highly significant,
although the ERP at that time point might have a value of 0. The ITC may also be significant, at
a particular latency, at more than one frequency. If so, this will be reflected in the shape of the
ERP waveform surrounding the latency in question.
45
For example, in the ITC image in Figure 3.10 (lower panel), activity near 4 Hz becomes
partially but significantly phase-locked around the button press event (0 ms), meaning the
portion of the component ERP (bottom trace) at 4 Hz is statistically significant. As well, ITC
becomes (barely) significant at 10 Hz, a fact reflected in the weak 10-Hz ‘scalloping’ in the ERP
waveform between -200 and +300 ms. No other ITC frequencies, and therefore no other ERP
frequencies, are significantly different from chance. The statistically significant ERSP changes in
mean spectral power in the beta and low-gamma bands, shown in the upper panel, are not
associated with significant ITC features and therefore represent component activity that is phase
inconsistent, i.e. not phase-aligned (or phase-coherent) across trials, and so does not contribute
significantly to the trial-average ERP.
ERPs and partial phase resetting
The relatively low peak ITC values in Fig. 3.10 (~0.4) are not unusual for longer-latency ERP
features. An alternate model, first proposed for selected event-related data as early as 1974 by
Sayers (Sayers et al., 1974), is known as the phase-resetting or partial phase-resetting model.
Phase resetting refers to a phenomenon seen both in mathematical models and in biological
systems in which the phase of an ongoing periodicity (e.g., the cardiac or circadian cycle) is reset
to a fixed value relative to the delivered perturbing stimulus. For example, brief exposure to
strong light delivered to a dark-adapted rat (or human) at almost any phase of the wake-sleep
cycle, will tend to reset the cycle to a fixed phase value (Winfree, 1980; Czeisler et al., 1986;
Honma et al., 1987; Tass, 1999). At the frequency of the ongoing, spontaneous rhythm, an ITC
measure time-locked to comparable events delivered at random time points throughout the
session will become significant as the phase of the rhythm in some or most of the trials is reset to
a fixed value. If the phase of the rhythmic activity then tends to continue to advance in a regular
manner from its initial reset value, the ITC time-locked to the events of interest will remain
significant for some number of cycles until, across trials, natural variability randomly separates
the advancing phase values.
The term ‘phase resetting’ has been applied to EEG dynamics in a less formal sense,
since in most cases there is no constant, ongoing rhythm for experimental events to perturb.
Rather, in many cases the signal contains only intermittent bursts of alpha or other frequency
spindles of various lengths. The term ‘phase resetting’, therefore, can be formally applied in
some statistical sense to mean that the phase statistics (as measured, for example, by the ITC) are
transiently perturbed following events of interest. If, whenever rhythmic activity at a given
frequency is present, its phase distribution following the time-locking events becomes non-
uniform, ITC will increase and may tend to remain significant for as long as the rhythmic
activity is present.
46
Figure 3.11. ERPs
and partial phase
resetting. The right
panel shows an ERP-
image plot visualizing
the responses in over
400 single trials of a
bilateral occipital
independent
component (IC)
process following
presentation of a letter
at the central fixation
point of a subject
participating in a
working memory task.
The bilateral
component (IC6, sixth
by variance expressed in the data) produces a response largely resembling a one-cycle sinusoid
at 9 Hz. The mean ERP trace (below the ERP image) plots its mean time course, time locked to
stimulus onset. The ERSP trace (below that) shows that the mean level of 9-Hz energy in the
data, during this period, is 15 dB or more higher than in the pre-stimulus (or ensuing) period.
The ITC trace (below that) confirms that during this ERP feature the phase of the entire 9-Hz
activity in the trials is highly consistent (ITC approaching 1). The blue backgrounds show p <
.01 probability limits, demonstrating that all three measures are highly significantly different
from baseline in this period. The panel on the left shows a quite different set of over 100 data
trials for a medial (or medial bilateral) occipital IC process in the five-box task of Fig. 3.1 in
which stimuli were presented above and left of a central fixation cross, while the subject retained
fixation. The large amount of alpha band activity produced by this IC process under these
circumstances likely reflects ‘alpha flooding’ of relevant visual cortex when visual attention is
forced by the task to remain elsewhere in the visual field (Worden et al., 2000).
Figure 3.11 shows ERP-image plots for two sets of visual-stimulus locked trial data from
two ICs captured in different subjects under rather different task conditions. In panel 3.11A
(left), the stimulus is a briefly-flashed disk presented at a central, visually unattended target
square located above a central fixation cross during a visual selective attention task. The IC
shown here has a bilateral equivalent dipole model in or near primary visual cortex, and produces
abundant alpha-band activity (see power spectrum), likely reflecting the ‘alpha flooding’ of
visual cortical areas sensitive to the foveal fixation region when the subject places his or her
47
visual attention elsewhere in the visual field (Worden et al., 2000). This alpha activity appears to
be ‘partially phase-reset’ (ITC ~ 0.4) for nearly 500 ms (5 alpha cycles) following stimulus
presentation. In the ERP image, trials are sorted by alpha phase in a three-cycle window ending
50 ms after stimulus onset. The possibility of ‘partial phase resetting’ is suggested by the
bending and then near-vertical alignment of the positive and negative wave fronts beginning near
100 ms in the ERP image, when the ITC becomes significant.
Note that the visual evidence presented by this ERP-image, including the finding of a
significant ITC (lower ITC trace), are not in themselves sufficient evidence to prove that these
data truly fit a ‘phase resetting’ model (for more discussion, see Chapter 2, this volume). Nor do
they necessarily rule out a ‘true-ERP’ model for the data, e.g. a model in which the same ERP
(upper ERP trace) resembling an alpha burst is simply added to ongoing alpha and other EEG
activity in every trial (as in Fig. 3.3), and that the ongoing alpha activity is in turn reduced in
amplitude just enough to make total mean alpha power at each latency constant, as observed here
(middle ERSP trace). However, keep in mind that these data are the result of spatial filtering by
ICA of a single independent source, very likely focused on a single source area (or closely
spaced medial bilateral areas), given the highly ‘dipolar’ from of the IC scalp map. It thus seems
to us physiologically implausible that, following these visual events, this same cortical source
area produces ongoing random-phase alpha activity plus a fixed but wholly unrelated alpha-burst
ERP. Several groups have recently proposed measures to further test phase resetting models on
data such as these (Mazaheri and Jensen, 2006; Hanslmayr et al., 2007; Martinez-Montes et al.,
2008). Ultimately, the issue will likely be settled by fitting concurrent scalp and intracranial EEG
recordings to generative models of cortical field dynamics, a process begun by groups studying
human brain responses during cortical recording (Wang et al., 2005).
In panel 3.11B (right), on the other hand, the time-locking stimulus is a letter presented at
fixation in a letter working memory task. The spectrum of the bilateral lateral-occipital IC (inset)
has only a weak alpha band peak, and no sign of prolonged alpha-band phase resetting following
the highly stereotyped (ITC > 0.8) component IC stimulus-evoked response (which contributes
strongly to the P1-N1-P2 features of the full scalp ERP, not shown). At the frequency best fitting
the ERP complex (9 Hz), mean single-trial amplitude during the ERP is nearly 6 times (over 15
dB) higher than the mean amplitude of activity at the same frequency in the pre-stimulus
baseline. Phase-sorting the single trials at 9 Hz in a window ending 50 ms after stimulus onset
(as in A) shows that the phase of the weak alpha activity present in single trials during the
baseline period has no obvious effect on the latencies of the subsequent evoked-response activity
in the same trials. For this IC stimulus response, therefore, a ‘partial phase-resetting model’
seems unnatural and a ‘true ERP’ model adequate. However, even here one may ask whether, for
example, the frequency peak of the ERP (9 Hz) may not also be a peak of the spontaneous
(baseline) spectrum of this cortical area.
48
Many authors have attempted to draw a hard distinction between evoked and induced
event-related activities, defining evoked activity as being activity completely time-locked and
phase-locked to the stimulus (ITC = 1) and thereby composing the ERP, while the remainder of
the single-trial activity, having no phase locking to the time-locking events (ITC = 0) is defined
as induced (Galambos, 1992). While this distinction may be useful for some purposes, drawing
this terminological distinction does not mean this decomposition of the EEG signal into evoked
(ERP) activity plus induced (other EEG) activity has a n y natural physiological basis. Think of a
stack of five pennies Again, does this stack ‘really’ sum two groups of two and three, or of
groups of four and one? In fact, the stack of pennies retains no trace of how it was constructed
and thus cannot be said to be any more ‘really’ 3+2 than 4+1, no matter how it was originally
constructed. The same applies to the model of event-related EEG data illustrated in Fig. 3.3:
EEG data = ERP + Other, a model that, as ICA decomposition and Figs. 3.7 and 3.8 suggest,
disregards the varying single-trial contributions of spatially separable data information sources,
some clearly linked to trial-by-trial behavioral differences.
Figs. 3.7 and 3.8 suggest that scalp ERPs sum channel activity arising from different
mixtures of spatial source processes in different trials. But how should we think of the average
response of a single IC? Assuming that an IC activation does index locally-synchronous or near-
synchronous field activity of a single patch of cortex, can the IC activity producing the IC
ERPactivity (strictly time-locked to the set of evoking events) be physiologically distinct
from other (non phase-locked) EEG activity originating at the same moments in presumably the
same cortical patch?
Linear summation in cortex, even of direct sensory input and ongoing cortical dynamics, appears
physiologically implausible without strong nonlinear interactions. Fiser and colleagues (Fiser et
al., 2004) have noted that even at prototypical sensory cortex the input layer of primary visual
cortex (in ferrets), only a few percent of the synapses deliver information directly from the eyes
via the lateral geniculate nucleus (LGN). In accord with this fact, they report that “at all ages
including the mature animal, correlations in spontaneous neural firing [during natural vision]
were only slightly modified by visual stimulation, irrespective of the sensory input. These results
suggest that in both the developing and mature visual cortex, sensory evoked neural activity
represents the modulation and triggering of ongoing circuit dynamics by input signals, rather
than directly reflecting the structure of the input signal itself” (Fiser et al., 2004). If this is the
case even for V1, it should not be less so for cortical areas that are not primary sensory areas.
Clearly, deeper understanding of the EEG dynamic changes associated with sensory and other
events will require more detailed observation and modeling of brain dynamics at multiple spatial
scales. In terms of EEG research, more detailed observations and modeling are needed of trial-
by-trial differences in oscillatory activity and its relationship to its transformation by
experimental events.
49
Event-related coherence
Cognitive events – moments at which we apperceive the significance of some sensory event and
mentally ‘grasp’ its immediate consequences for our attention and behavioral planning must
involve and/or produce complex and distributed changes in EEG dynamics. Furthermore, some
mechanism of information transfer between brain regions must exist that is dynamically
dependent both on the nature of the stimulus and its relation to subject expectations and
intentions. A possible mechanism for this transfer may be indexed by transient temporal coupling
between pairs of sources relative to experimental events. One measure of this coupling is event-
related coherence (ERC) (Delorme and Makeig, 2003).
The preponderance of coherence of all sorts observed between pairs of scalp channel
signals is accounted for by ICA as deriving from common IC projections to both scalp channels.
A change in amplitude of a single IC, relative to other ICs that project to the same channel pair,
may produce a change in their measured (zero-lag) scalp channel coherence without any actual
coherence changes occurring at the cortical source level. By maximally reducing the effects of
volume conduction on the data, ICA decomposition allows a more principled study of transient
or intermittent coherence between IC source activities.
Recently, we used ICA decomposition of target response data from the same five-box
task used here for illustrative purposes to show that brief and weakly spatially coherent theta
wave complexes arise in frontal midline, somatomotor, and parietal cortex in many subjects
following significant events (Makeig et al., 2004b), often beginning in frontal polar cortex
(Delorme et al., 2007b). But how can the activities of ‘independent’ components be
(occasionally) phase coherent? As described previously, ICA decomposition actually derives
maximally independent components this allows the discovered IC activity patterns to exhibit
occasional transient dependence – for example, in the five-box data at one frequency in at most a
fifth of the trials. In this and related cases, we found the partial coherences to have non-zero
phase lags, and to remain when each component ERP was (artificially) regressed out of each
single trial activity and coherence was computed only on the remainder. Event-related coherence
is another measure that cannot be deduced from ERP waveforms alone, and cannot be
confidently interpreted when computed for pairs of scalp-channel signals. ICA preserves only
those coherences that represent transient coupling of the frequency-domain activities of two EEG
sources with a fixed latency difference.
A ‘close up’ example of similar ‘phase reorganization’ in human brain was recently
provided by the study by Wang and colleagues of event-related local field activity in multi-
channel ‘thumbtack’ electrodes pushed through a small piece of intact cortex in anterior
cingulate before its clinically required removal in a brain operation (Wang et al., 2005). They
reported that theta band activity was generated in superficial layers of anterior cingulate cortex
50
(ACC) both before and after presentations of a variety of task-relevant stimuli, while after
presentations phase-locking between ACC and other brain areas increased transiently.
V. Meeting the Challenge of the Moment
For us to survive and thrive, at each moment our brain must integrate its awareness of its present
situation and environment, including existing plans for action and/or inaction, with its emerging
sensory experience and mnemonic associations. It must optimally engage or revise its attentional
distribution, action plans, and physiological body state in a way adequate to meet the challenge
of the moment.
This volume summarizes the results of nearly fifty years of scientific experience in
studying the shapes and sizes of average event-related potential (ERP) responses of scalp EEG
signals to sensory or other events, responses that depend in large part on the significance of the
events to the subject and on the context in which they occur. EEG is the oldest and most non-
invasive functional brain imaging modality; it is also the least expensive and most highly
portable. The continuing promise of EEG brain imaging is that the highly labile dynamics of
EEG scalp fields, signaling changes in local field synchrony within and between cortical areas,
can provide detailed indices of changes in human attentional, intentional, and affective state,
both post hoc and even, to an increasing extent, online, with potentially important applications to
basic scientific research, to clinical and workplace monitoring, and to other fields of human
interest and endeavor.
In this chapter, we have discussed the origins in local cortical synchrony of both EEG
signals and ERP waveforms derived from them. We have defined the concept of an EEG source,
based on both EEG analysis and physiological evidence, and have demonstrated the utility of
independent component analysis (ICA) for separating multi-channel EEG recordings into a set of
temporally and functionally independent brain and non-brain source processes. Finally, we have
shown a simple example of using ICA decomposition to study the sources that contribute to (as
well as those that contaminate) ERPs, and their activities in the single-trial EEG data. We have
given examples of using ERP-image plotting to visualize the dependence of EEG responses in
single trials on behavioral, EEG, or other parameters, have introduced time/frequency analysis in
the form of inter-trial coherence (ITC) to show that the activity captured in average ERPs reflects
trial-to-trial phase consistency, and have introduced the concept that some ERP features may
reflect reorganization (or perturbation) of the exact timing or phase statistics of ongoing activity
in the same cortical areas, as long suggested by investigators familiar with dynamic modeling
methods used in engineering.
We believe the increasingly urgent challenge for the field of ERP and more general EEG
research is to discover the brain source dynamics that produce the characteristic features of
51
evoked responses and to model the trial-by-trial (and condition-by-condition) differences in EEG
(and ERP) dynamics associated with the large variety of events that unfold continually in our
daily lives, within an ever-evolving situational context – events that pose a wide variety of
challenges to which our brains respond effectively.
We believe this to be an exciting time to study human electrophysiology, an era in which
non-invasive EEG recording is moving toward fulfilling its promise of becoming a true
functional brain imaging modality. Current knowledge and understanding of EEG dynamics is
likely to advance steadily as new analysis tools developed for this purpose become more widely
applied. One result should be a deeper and fuller understanding of the nature and significance of
ERP features9.
52
Endnotes
1For example, at 20 Hz and traveling at 1 m/s, a radiating ‘pond ripple’ would reach the edge of a
1-cm source domain in 5 ms, one tenth of a 20-Hz cycle. Therefore, there would only be a 2π/10
= 36 degree phase lag between the center and the edge of the patch, and the spatiotemporal
pattern of potentials at scalp electrodes would be highly correlated with the pattern produced by
completely synchronous 20-Hz activity across the same 1-cm domain.
2Though less commonly appreciated, intracranial electrodes also record volume-conducted
signals from distant sources along with local field activity produced just under the electrode
(Lee, 2005).
3 These EEG data were collected synchronously from 250 scalp plus four infra-ocular and two
electrocardiographic (ECG) electrodes with an active reference (Biosemi, Amsterdam) at a
sampling rate of 256 Hz and 24-bit A/D resolution. Onsets and offsets of target discs, as well
subject button presses, were recorded in a simultaneously acquired event channel. The recording
montage covered most of the skull, forehead, and lateral face surface, omitting chin and fleshy
cheek areas. Locations of the electrodes relative to skull landmarks for each subject were
recorded (Polhemus, Inc.). Electrodes with grossly abnormal activity patterns were removed
from the data, leaving 238 channels. After re-referencing to digitally linked mastoids, the data
were digitally filtered to emphasize frequencies above 1 Hz. Data periods containing broadly
distributed, high-amplitude muscle noise and other irregular artifacts were identified by tests for
high kurtosis or low-probability activity and removed from analysis. Occurrence of eye blink,
other eye movement, or isolated muscle noise artifact was not a criterion for rejection.
Remaining data time points were then concatenated and submitted to decomposition by extended
infomax ICA using the binica function available in the EEGLAB toolbox
(http://sccn.ucsd.edu/eeglab). Decompositions used extended-mode infomax ICA (Makeig et al.,
1997) with default training parameters. Extended infomax was used to allow recovery of any
components with sub-gaussian activity distributions, including 60-Hz line noise contamination.
ICA components clearly and predominantly accounting for eye movement, muscle, cardiac,
single-channel, or other artifactual activity were removed from the ERP data. Both the target
stimulus-locked and motor response-locked epochs analyzed in the figures were referred to a
mean baseline in a 500-ms period before target stimulus onsets.
4Data figures in this chapter were produced using software tools from the freely available
EEGLAB Matlab software environment (sccn.ucsd.edu/eeglab/). The single-subject 256-channel
data set from which we derived most of the figures was recorded and first studied by Delorme et
al. (Delorme et al., 2007b) and is available for download in raw and in EEGLAB formats from
the EEGLAB web site (above).
53
5In particular, the phase of a digitally recorded signal cannot be defined above its Nyquist
frequency (half of its sampling rate) and is ambiguous at its Nyquist frequency.
6Methods that find more components are available, but require narrower source assumptions and
more computation time.
7EEGLAB includes Matlab-based tools for applying, evaluating, and exploring component
clustering.
8Data used for the IC cluster figure were collected by Klaus Gramann at the University of
Munich from 12 subjects performing a visual feature discrimination task. The
electroencephalogram (EEG) was recorded continuously at a sampling rate of 500 Hz using 64
Ag/AgCl electrodes mounted on an elastic cap. EEG signals were amplified using a 0.1–100-Hz
bandpass filter and filtered off-line using a 1–40-Hz bandpass. All electrodes were recorded
referenced to Cz and then re-referenced off-line to linked mastoids. Average ERPs in an 800-ms
epoch were computed relative to a 200-ms pre-stimulus baseline. ICA decomposition used
extended infomax. ICs were clustered across subjects using EEGLAB clustering functions based
on their respective dynamics under three target stimulus-difference conditions (whether or not
the target had a different color, different shape, or both than the accompanying standard stimuli).
Only ICs whose equivalent dipole projection to the scalp had a residual variance from the IC
scalp map below 15% and an equivalent dipole location within the brain volume were considered
for clustering. These ICs were separated into 22 clusters based on their equivalent dipole
locations, event-related spectral perturbations (ERSPs) and inter-trial coherences (ITCs) in the
500 ms following target onsets.
9Thanks to Arnaud Delorme and David Groppe for helpful discussions, and to our many
colleagues from the Swartz Center for Computational Neurosciences, UCSD and Computational
Neurobiology Laboratory, Salk Institute for their invaluable support, insight, and companionship
on our long and continuing quest to better understand human event-related brain dynamics.
54
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... The evaluation of the EEG signals requires feature detection, feature extraction and removal of artefacts. Thus, ICA can be thought of as a method for data-driven spatial filtering or beamforming that learns spatial filters, where each focuses on a distinct physical source of EEG signals-separating out cognitive processes as well as different non-cognitive (artefact) signals [29]. Independent Component Analysis (ICA) or rather Blind Source Separation (BSS) was applied to determine items. ...
... To restore the source signals from the mixed signals, a minimum of the same number of observations as sources (quadratic case) are required. Undetermined systems need other algorithms [29]. In the interest of simplification, there are underlying source signals x i (t) which are functions of some original source signals s i (t) see 1 and 2. The observed signals, which are the amplitudes of the recorded signals at time point t. ...
... The unmixing process finally produces the individual signals. Intuitively, two-time series are most independent when their waveforms are maximally distinct from each other [29]. Technically, independent time series have no mutual information, meaning that knowing the value of one process at a given time does not give even partial or probabilistic information about the concurrent value of the other process. ...
... Hopfinger & West, 2006). We exploited the extensively used tool, independent component analysis (ICA), for eye movement artefact removal (Makeig & Onton, 2012), extending it here to OKN, testing with electroencephalography (EEG) whether the neural processing of these cues and targets during OKS with or without OKN movements was completely different from that occurring in previous studies and to each other or whether they were characterised by a similar pattern. ...
... Independent component analysis (ICA) is used extensively to remove the artefacts in the signal that arise from movement of the eyes (Delorme et al., 2007;Delorme & Makeig, 2004;Makeig et al., 1996;Makeig & Onton, 2012;Nikolaev et al., 2016) and is used for example in studies of neural processing during eye movements (Chen et al., 2017). ICA is a heuristic algorithm which presents the user with an array of candidate components, from which the user selects one or some to remove from the signal. ...
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... In this work, we focus on adapting how brain activity is typically visualized as a topographic map. For example, brain activity recorded through Electroencephalography (EEG) measurements [28] is represented as a top view of the head with a superimposed topographic map of neural activity [29]. Adapting this approach to be applicable to DNNs can help to visualize and understand their internal processes more intuitively, too. ...
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... Several advances in the study of source brain activity (Onton et al., 2006;Makeig and Onton, 2011;Akalin Acar et al., 2013;Bigdely-Shamlo et al., 2013) allow separate weightedcombinations of mean event-related activities arising from several to many cortical sources that are mixed on scalp ERPs channels. Therefore, the aim of the present study was to investigate potential mechanisms, from a source-resolved ERP perspective, that could explain how practicing long-term physical and mental exercise can benefit neural processing during the execution of an attention switching task. ...
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The main objective of this Research Topic was to gather studies that shed more light on the benefits of physical exercise in the neurophysiological system, from childhood to old age and from the field of health to sports or professional performance. For example, we consider important those studies that deepen into the epigenetic mechanisms involved in the aging process and their modulation through physical exercise, improving prevention and treatment therapies, and those that contributes to better understand how physical activity improves brain functions (e.g., increased hippocampal), or what effect cognitive loads cause in variables such as heart rate variability or brain waves. We also consider it particularly interesting to show studies that can reflect how physical exercise can be a good preventive strategy to avoid or counteract neurodegenerative diseases, such as Alzheimer, and consequently, increase the time and quality of life. Thus, some of the topics of interest for this Research Topic are studies that contemplate the latest advances on neurophysiological and epigenetic effects of physical exercise on the aging, or beneficial effects of the practice of physical activity and sport on anti-aging and neuroprotective mechanisms. Equally relevant aspects to consider are the effects of physical exercise to prevent neurodegenerative diseases, the relationship between physical exercise practice and improvement of brain functions, the effects of cognitive loads at the neurophysiological level, or the neurophysiological system behavior related to sports or professional performance.
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Background Tinnitus is an auditory condition with no effective treatments. Seven of the 25 most widely used treatment are sound based therapies, but no methods to select an appropriate one have been established. Method Therefore, this investigation aimed to establish a method to select an appropriate acoustic therapy by finding comparable psycho-neurological effects. For that purpose, 71 Mexican volunteers (60 tinnitus sufferers and 11 controls) followed one of five two-month treatments that aimed to (1) diminish the level of attention towards tinnitus via neuro-modulation, (2) habituate to tinnitus by retraining or (3) to relieve distress (binaural beats and music). From the treatment outcomes, six features were defined: (1) hearing loss, (2) anxiety level, (3) stress level, (4) overall amount of neural electrical response to acoustic therapy, (5) EEG channel wherefrom the maximum neural response was obtained, and (6) assigned group. Then, a cluster analysis based on the k-means method was undertaken. Results As a result, a strong structure (silhouette measure = 0.798) of six clusters showed that tinnitus sufferers who reported diminution of stress and anxiety, and no side effects, mainly proceeded from neuro-modulation treatments. Furthermore, most of tinnitus sufferers who reported increase of anxiety mainly proceeded from tinnitus retraining and binaural beats. Finally, tinnitus sufferers who only reported anxiety diminution mainly proceeded from tinnitus retraining and music therapy. Conclusion Taken together, these findings are a guideline to select an appropriate therapy according to clinical history and psycho-neurological effects, what has not been proposed until now.