Aspects of psychophysiological data analysis: EEG coherency and fMRI
connectivity mapping
Peter C.M. Molenaar & Kathleen M. Gates
The Pennsylvania State University
1. Introduction
The field of cognitive and affective neuroscience has flourished in the past
decades. The increased use of brain imaging techniques, in particular the
mapping of functional connections between brain regions based on
electroencephalographic (EEG) and functional magnetic resonance (fMRI)
registrations (cf. Friston et al., 2008), contributed significantly to this
development. Brain imaging has been very instrumental in identifying cortical
regions associated with emotional states, showing for instance that approachrelated positive emotions and withdrawal-related negative emotions are
correlated with distinct patterns of asymmetrical activity of prefrontal regions (cf.
Fox, 2008, for a comprehensive review of these and many other findings). EEG
and fMRI studies also have been essential in uncovering the neural bases of
emotional development, in particular the development of processing emotion in
the face (cf. Nelson, de Haan, & Thomas, 2006; de Haan & Matheson, 2009).
In what follows we present an overview of various aspects of
psychophysiological data analysis which are important in applied brain imaging,
in particular the estimation of coherency and connectivity maps based on,
respectively, multivariate EEG and fMRI time series. Coherency and connectivity
maps constitute the state of the art in functional brain imaging. The presentation
will be heuristic and general, focusing on relevant statistical models and their
interpretation. Illustrative findings are offered as examples. However, the focus
remains on methods and the reader interested in developmental affective
neuroscience theory is referred to the excellent monograph by Nelson, de Haan,
& Thomas (2006) as well as the edited volume by de Haan & Matheson (2009).
Where relevant, insight is given to issues specifically related to research with
children or standard aspects of experimental psychophysiogical designs. Even
with these limitations it will be impossible to cover all important aspects within the
confines of a single chapter. Therefore ample references to the published
literature will be given where the reader can find more complete coverage.
2. Analysis of multi-lead EEG
EEG registrations obtained with multi-lead montages are standard in
psychophysiological research. Often the aim is two-fold. One, researchers wish
to derive topographic maps displaying the dynamic interaction of the activity of
different neocortical areas. Two, researchers seek to identify the neural sources
underlying this activity. This section outlines the use of topographic coherency
maps and modeling approaches to multi-lead EEG that serve both these aims.
As mentioned briefly in the introduction asymmetry has been linked to
emotional regulation. Asymmetry appears to influence development of emotion
regulation and tendencies. For instance, in terms of absolute activity, increased
levels of right frontal activity has consistently been associated with withdrawal
and negative affect at both the trait (Fox, 1994; Tomarken, Davidson, &
Henriques, 1990) and state levels (Allen, Harmon-Jones, & Cavender, 2001).
Moreover, asymmetry may be influenced by life experiences. Childhood
maltreatment has been linked to greater left hemisphere coherence in adolescent
females (Miskovic, Schmidt, Georgiades, Boyle, & Macmillan, 2010) and children
(Teicher, et al., 1997).
Prior to discussing these approaches, two aspects of the initial analysis of
EEG time series require brief mentioning because they have given rise to
longstanding discussion in the published literature. The first aspect is the choice
of the reference electrode. The second aspect concerns correction for ocular
motion artifacts.
Reference electrode EEG is a measure of quasi-static electric activity of the
brain. An arbitrary constant can be added to the electric potential field without
changing the measured electric activity. Consequently, only differences in
potential can be measured, independent of the arbitrary constant (cf. Geselowitz,
1998). The EEG potential differences at each lead are defined with respect to a
reference electrode which ideally should be neutral. Various references have
been used, such as tip of the nose (e.g., Essl & Rappelsberger, 1998), ear (e.g.,
Thatcher et al., 2001), linked mastoids (e.g., Gevins & Smith, 2000), and average
(e.g., Nunez et al., 2001). None of these references will be entirely neutral,
although this does not affect source localization under noiseless conditions. The
reference which perhaps best approaches neutrality is the so-called infinity
reference (Yao, 2001; Yao et al., 2005). The infinity reference depends upon the
head model, electrode montage, and the neural source distribution model (Yao,
2001); it has been shown to outperform alternative choices of reference electrode
in spectral analysis of multi-lead EEG (Yao et al., 2005).
Ocular motion artifacts The front of the eye (cornea) is positively charged
with respect to the back (retina), thus constituting a dipolar configuration.
Rotation of this dipole due to eye motion will induce electric field changes that
are picked up by EEG registrations. This defines the ocular motion artifact in
EEG. In addition, eye blinks generate related motion artifacts. Conversely,
electro-oculographic (EOG) electrodes positioned close to the eyes will not only
register EOG activity but also pick up EEG activity. These “cross-over” signals
are the main reason why correction of ocular motion artifacts is difficult.
Various methods have been used to correct for ocular motion artifacts. Early
methods include linear regression analysis in the time domain (Gratton et al.,
1983), regression in the frequency domain (Kenemans et al., 1991) and
equivalent dipole modeling (Elbert et al., 1985; Berg & Scherg, 1991). See Croft
& Barry (2000) for an authoritative review of these methods. Recently, methods
based on component analysis (e.g., Jung et al., 2000) as well as dynamic
systems modeling and adaptive filtering (e.g., Haas et al., 2003; Shooshtari et al.,
2006) have been applied. Recent comparative studies of some of these methods
are reported in Wallstrom et al. (2004) and Kierkels et al. (2006). Both studies
report suboptimal results obtained with independent component analysis
approaches to remove ocular motion artifacts. Kierkels et al. (2003) indicate that
multiple regression approaches yield good performance in case only two EOG
electrodes are used. Hoffmann & Falkenstein (2008) report good performance of
independent component analysis when used to remove eye blink artifacts.
EEG coherency maps Topographic EEG coherency maps have been a
prominent tool to assess functional associations between the activities of
different brain regions. Coherency is essentially a correlation measure in the
frequency domain. High levels of coherence suggest increased neuronal
coupling across spatially separate regions. Oftentimes, coherence within a region
or hemisphere is compared to that of its lateral counterpart to assess the degree
of asymmetry. Increased levels of hemispheric cohesion indicate greater
disorganization (Miskovic et al, 2010).
Let yk(t) denote the EEG measured at the k-th electrode (lead) in a montage
of K electrodes positioned across the scalp. It is assumed that the analogue EEG
signal at each lead k=1,2,…,K has been sampled at T+1 equidistant time points
t=0,1,…,T, spanning a time interval of 1 second.
The first step in determining the topographic coherency map is to apply the
discrete Fourier transform (DFT) to the EEG obtained at each lead k=1,2,…,K.
This yields yk(n), where n = n/(T+1), n=0,1,…,T, denotes the frequency. Notice
that yk(n) is complex-valued: yk(n) = yk(n) exp[j k(n)], where j = -1
denotes the imaginary unit. yk(n) is the absolute value of yk(n) and k(n) is
the phase of yk(n). An important property of the DFT is that, under certain
regularity conditions, yk(n) and yk(m) for different frequencies n and m are
asymptotically independent random variables.
The next step is to determine the coherency Ckm(n) = cor[yk(n), ym(n)]
between each pair of leads k,m  {1,2,…,K} at each frequency n. Notice again
that Ckm(n) is complex-valued: Ckm(n) =  Ckm(n) exp[j km(n)]. The absolute
value  Ckm(n) is called the coherence between leads k and m at frequency n;
km(n) is called the phase angle between leads k and m at frequency n.
Brillinger (2001) presents an in-depth discussion of the sampling theory of
coherency estimators.
A different topographic EEG coherence map is defined for each different
frequency (see, e.g., Nunez et al., 1999, for interesting examples). As outlined in
Miller and Long (2008), one of the most easily recognized electrical patterns
seen in the brain, the alpha wave, has a frequency band of 8 to 12 Hz in adults.
Evidence suggests that the alpha wave is spontaneously occurring and has an
inverse relationship with brain activation. However, in children and infants, the
dominant wave is 6 to 9 Hz. Preliminary evidence suggests that inferences of the
alpha wave for infants may be opposite that of adults (Bell, 2002). In addition, at
each frequency a topographic EEG phase angle map can be constructed,
although these are seldom reported in the published literature. We will discuss
topographic EEG phase angle maps below.
Caveats High values of EEG coherence often are interpreted as evidence for
functional connectivity of the brain regions concerned. Unfortunately, this
interpretation may be invalid due to the presence of two confounding factors:
volume conduction and the influence of a common reference (cf. Nunez et al.,
1999). Both confounding factors can give rise to spuriously high coherence
values even in the absence of any cortical interaction. The best way to correct for
these confounding effects is to estimate topographic EEG coherence maps
based on equivalent dipole modeling, to be discussed below (Grasman et al.,
2004). This, however, requires the use of montages containing a large number of
leads (cf. Huizenga et al., 2002).
Several approximate solutions to correct for the confounding effects of
volume conduction and common reference have been proposed if only a small
number of leads is available (K < 32). An excellent overview of these
approximate solutions is presented in Schlögl & Supp (2006), using vectorvalued autoregressive (VAR) time series models to estimate coherencies
Ckm(n). VAR models will be discussed below. A computer program
implementing several of these approximate solutions can be obtained from the
present first author.
Modeling topographic coherency maps The effective functional
connectivity underlying topographic coherency maps is best manifested by
means of equivalent dipole modeling. Figure 1, taken from Grasman et al.
(2004), presents an illustrative result obtained in a successful application of this
approach to MEG data. If applied to model topographic EEG maps, equivalent
dipole modeling serves the combined purposes of reliably estimating the
underlying functional connectivity while correcting for the confounding influences
due to volume conduction and common reference.
If the number of leads is small (K < 32), Nunez’ EEG wave model (Nunez &
Srinivasan, 2006) constitutes an excellent alternate approach to estimate the
effective functional connectivity underlying topographic EEG coherency maps.
The EEG wave model can be interpreted as a complex-valued factor model in
the frequency domain. Its application requires the use of a special rotation
technique which is described in Molenaar (1987). The EEG wave model is
simultaneously fitted to both the topographic EEG coherence maps and phase
angle maps. Based on results obtained in an empirical application of the EEG
wave model, Molenaar (1993) concludes that the estimated functional
connectivity is mainly determined by the topographic phase angle maps.
3. Analysis of fMRI time series
Functional magnetic resonance imaging (fMRI) is an increasingly popular
method to investigate brain activity in response to mental tasks. An excellent
introduction for social scientists to the physical and biophysical principles
underlying magnetic resonance signal generation in the brain is given in Huettel
et al. (2004). Buxton (2002) and Kuperman (2000) give more technical
introductions.
During a typical experimental fMRI run, each subject’s functional activity in
the brain is measured repeatedly over the course of several minutes. Since
scientists seek to identify which areas of the brain increase in activity during a
task, data are acquired for numerous points in the brain, ultimately yielding
multivariate fMRI time series data of very large dimension. Consequently, the
spatial resolution of fMRI scans can be very high – much higher that the spatial
resolution of EEG/MEG. In contrast, the temporal resolution of fMRI is rather low
(in seconds), about a thousand times lower than the temporal resolution of
EEG/MEG (in milliseconds).
FMRI time series require special preprocessing due to the way in which scans
are obtained and in order to correct for head movement and other artifacts. After
this preprocessing step, basically two approaches to the analysis of fMRI time
series are possible: univariate or multivariate approaches. Univariate approaches
typically test for the significance of activity changes (with respect to some
appropriate baseline condition) in each of the measured brain regions. Because
in whole brain scans the number of measured brain regions can be very large (>
104), special statistical decision procedures are required. Sarty (2007) presents
an excellent discussion of preprocessing and univariate modeling and testing of
fMRI time series. Lazar’s (2008) monograph is highly recommended for its
discussion of statistical aspects, and in general as clear introduction to analysis
of fMRI time series. Friston et al. (2008) presents convenient reviews of more
advanced topics.
In this section we focus on the construction of connectivity maps based on
fMRI time series data, which is a multivariate approach. Such connectivity maps
are the fMRI analogue of EEG coherency maps discussed in the previous
setting. They are considered to describe the effective functional relationships
among brain regions during the execution of mental tasks and have thus given
insight into brain processes across the lifespan. For instance, developmental
changes in processes relating to narrative processing have been investigated
using effective connectivity maps of fMRI data (Karunanayaka, et al., 2007).
The standard approach to obtain connectivity maps is to fit path models to
fMRI time series by means of structural equation modeling (cf. Sarty, 2007;
Friston et al., 2008; McIntosh & Gonzalez-Lima,1994). This requires that the
number of brain regions under consideration is drastically reduced to a small
number of so-called regions of interest (ROI). Several inductive techniques to
accomplish this reduction are described in Sarty (2007), Lazar (2008) and Friston
et al. (2008). Alternatively, ROIs can be selected based on a confirmatory
approach using prior knowledge.
The standard approach, however, only considers contemporaneous
interactions between ROIs. By neglecting the temporal auto- and crosscorrelations characterizing multivariate fMRI time series, biased estimates of
contemporaneous relations occur (Gates, Molenaar, Hillary, Ram, & Rovine,
2010). Therefore Kim et al. (2007) propose a combination of structural equation
modeling and vector autoregression (VAR) modeling to fit path models. This
approach constitutes a special case of the dynamic factor modeling approach
introduced in Molenaar (1985). Kim et al. (2007) present an empirical application
of their approach which shows that it is more powerful than the standard
approach in that it recovers more significant interactions between ROIs. Figure 2,
taken from Kim et al. (2007), presents illustrative results obtained in their
application.
Granger causality based on VAR mapping The key step in the approach
proposed by Kim et al. (2007) is the use of vector autoregressions (VAR) to
model fMRI time series. The dynamic connections among ROIs recovered by
means of VAR modeling may or may not be genuine causal interactions. An
interaction is causal if it is directed, that is, if the cause affects the effect but the
reverse is not the case. Moreover, the activity of the cause has to precede in time
the resultant activity of the effect. Because VAR modeling of fMRI time series
recovers dynamic interactions between ROIs, it is the perfect tool to detect such
directed time-lagged interactions between ROIs causing activity in other ROIs,
and has been used thus far has been used to investigate processes relating to
motor activity (Abler et al., 2006), language networks in children (Wilke, Lidzba, &
Krageloh-Mann, 2009), and visual spatial attention (Bressler, Tang, Sylvester,
Shulman, & Corbetta, 2008).
To identify the presence of genuine causal interactions between ROIs, an
approach suggested by Granger (1969) can be applied. In what follows we will
present an outline of this approach, based on Goebel et al. (2003). Let x(t)
denote the fMRI time series associated with ROIs which are expected to cause
acitivity in other ROIs. Let y(t) denote the fMRI time series associated with the
ROIs, the activity of which is expected to be caused by x(t). Moreover, let q(t)
denote the combined time series consisting of x(t) and y(t): q(t) = [x(t), y(t)]. Then
VARs are fitted to x(t), y(t) and q(t). For instance, the VAR fitted to x(t) can be
represented as (similar representations pertain to y(t) and q(t)):
x(t) = A1x(t-1) + A2x(t-2) + … + Apx(t-p) + ex(t).
The Ai, i=1,2,..,p, are square matrices of regression coefficients; ex(t) denotes
residual process noise.
The test for Granger causality involves comparisons between the variances of
the residual process noises in the VARs for x(t), y(t) and q(t). Notice that in the
VAR for q(t), the component series x(t) is explained by lagged instances of both
x(t) and y(t). Similarly, in the VAR for q(t) the component series y(t) is explained
by lagged instances of both y(t) and x(t). Now suppose that in the VAR for x(t)
the variance of the residual process noise is larger than the variance of the
residual process noise of x(t) in the VAR for q(t). Then this implies that y(t) is a
Granger cause for x(t). That is, the dynamic interaction between the ROIs
associated with x(t) and y(t) is directed from y(t) (the cause) to x(t) (the effect).
The reader is referred to Goebel et al. (2003) for further details concerning the
tests of residual process noise variances.
4. Conclusion
The availability of sophisticated noninvasive brain imaging techniques
enables the construction of multidimensional maps displaying the functional
interconnections among the activities of brain areas during the execution of
cognitive tasks. In this chapter we focused on EEG coherency maps and fMRI
connectivity maps as prime examples of these powerful tools of cognitive
neuroscience, explaining important data-analytic aspects of their application and
presenting some illustrations.
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Figure 1. (a) Coherence between sensors with distances greater than 9 cm. (b)
Coherence between sensors predicted by the three-dipole model. (c) Threedipole model – the arrows connecting sources indicate the coherence (averaged
across frequencies) between the source activity.
Figure 2. Unified longitudinal and contemporaneous path model. Six brain
regions with 13 designed longitudinal paths (dashed lines) and 7
contemporaneous paths (solid lines) are described. The longitudinal connections
are to one region at the current time (t) from other regions as well as itself at the
past time (t-1). LPDC = lateral prefrontal cortex, Brodmann area (BA) 8; MedFG
= medial frontal gyrus, BA 8; APC = anterior parietal cortex, BA 7; THAL =
thalamus; PPC = posterior parietal cortex, BA 40; CEREB = cerebellum