Page 1
Investigations into Restingstate Connectivity
using Independent Component Analysis
FMRIB Technical Report TR05CB1
(A related paper has been accepted for publication in
Philosophical Transactions of the Royal Society,
Special Issue on ’Multimodal neuroimaging of brain connectivity’)
Christian F. Beckmann, Marilena DeLuca, Joseph T. Devlin and Stephen M. Smith
Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK
Corresponding author is Christian F. Beckmann: beckmann@fmrib.ox.ac.uk
Abstract
Inferring restingstate connectivity patterns from functional magnetic resonance imaging (FMRI) data is a challenging
task for any analytical technique. In this paper we review a probabilistic independent component analysis (PICA) approach,
optimised for the analysis of FMRI data (Beckmann and Smith, 2004), and discuss the role which this exploratory technique
can take in scientific investigations into the structure of these effects. We apply PICA to FMRI data acquired at rest in order
to characterise the spatiotemporal structure of such data, and demonstrate that this is an effective and robust tool for the
identification of lowfrequency restingstate patterns from data acquired at various different spatial and temporal resolutions.
We show that these networks exhibit high spatial consistency across subjects and closely resemble discrete cortical functional
networks such as visual cortical areas or sensory motor cortex.
Keywords: Functional Magnetic Resonance Imaging; brain connectivity; Restingstate fluctuations; Independent Com
ponent Analysis;
1 Introduction
FunctionalMagneticResonanceImaging(FMRI)hasbecomeanimportantneuroscientifictoolforprobingneuralmechanisms
in the human brain. Typical FMRI experiments have focused on the acquisition of T2*sensitive MR images during periods
of increased oxygen consumption (due to neuronal response to externally controlled experimental conditions) and contrast
the measured image intensities with recordings obtained at ’rest’. Critically, some important quantitative concepts in FMRI
analysis such as the calculation of percent signal change or the interpretation of deactivation implicitly hinge on a suitable
definition of this baseline/rest signal. The baseline ’restingstate’ of the brain itself, however, is a somewhat ill defined and
poorly understood concept.
Of particular interest in this context are certain lowfrequency fluctuations of the measured cerebral haemodynamics
(around 0.01–0.1Hz) which exhibit complex spatial structure reminiscent of FMRI ’activation maps’ and which can be iden
tified in FMRI data taken both under rest condition and under external stimulation. Recently, some attention has been focused
on the characterisation of these maps and the identification of possible origins of slow variations in the measured blood oxygen
level dependent signal. Various researchers have suggested that these signal variations, temporally correlated across the brain,
are of neuronal origin and correspond to functional restingstate networks (RSNs) which jointly characterise the neuronal
baseline activity of the human brain in the absence of deliberate and/or externally stimulated neuronal activity, and may reflect
functionally distinct networks.
Biswal et al. (1995) first demonstrated the feasibility of using FMRI to detect such spatially distributed networks within
primary motor cortex during restingstate by calculating temporal correlations across the brain with the time course from a
seed voxel whose spatial location was chosen from a prior fingertapping study. The temporal signal from a seed voxel in the
motor cortex was correlated with other motor cortex voxels and uncorrelated with other voxels, with major frequency peaks in
1
Page 2
the resting correlations at around 0.02Hz. Lowe et al. (1998) found similar results using both singleslice low time of repetition
(TR of 130ms) and wholehead volumes with longer TR (2000ms) while Xiong et al. (1999) describe functional connectivity
maps that cover additional nonmotor areas. Based also on findings from PET studies, the existence of a default mode brain
network involving several regions including the posterior cingulate cortex has been proposed (Raichle et al., 2001; Shulman
et al., 1997; Mazoyer et al., 2001). Using simulteneously acquired EEG and FMRI data under rest, Goldman et al. (2002)
have shown that the variation in Alpha rhythm in EEG (812Hz) is correlated with the FMRI measurements. In particular,
the authors report that increased alpha power was correlated with decreased BOLD signal in multiple regions of occipital,
superior temporal, inferior frontal, and cingulate cortex, and with increased signal in the thalamus and insula. These results
have important implications for interpretation of RSNs as they suggest a neuronal cause for these fluctuations.
Alternatively, it has been argued that these effects simply reflect vascular processes unrelated to neuronal function, which
would make RSNs of less interest to neuroscience (though still of potential clinical interest). Physiological noise in the
resting brain and its echotime and field strength dependencies were investigated by Kruger and Glover (2001) who showed
that physiological noise demonstrates a field strength dependency, exceeds the thermal as well as scanner noise at 3T and is
increased in grey matter (see also Woolrich et al. (2001)). Various researchers have investigated the relation between low
frequency fluctuations in the measured BOLD signal and other physiological observations: Obrig et al. (2000) reviewed and
studied lowfrequency variations in oxygenation, cerebral blood flow (CBF) and metabolism and report significant correlations
with similar fluctuations observed by near infrared spectroscopy (NIRS). More recently, Wise et al. (2004) have investigated
the influence of arterial carbon dioxide fluctuations by using the endtidal level of exhaled carbon dioxide as covariate of
interest in a General Linear Model (GLM) analysis. The most significant changes were concentrated in the occipital, parietal
and temporal lobes as well as in the cingulate cortex, and suggest that vascular processes (unrelated to neuronal function) play
a significant role in the generation of such restingstate patterns.
EstimatingthetemporalandspatialcharacteristicsoftheselowfrequencyfluctuationsfromFMRIdatapresentsaformidable
challenge to analytical techniques. In the majority of existing studies, resting patterns are inferred by a correlation analysis
of the voxelwise FMRI recodings against a reference time course obtained from secondary recordings (e.g. from EEG,
NIRS or physiologic measurements like the carbondioxide concentration) or simply by regressing against a single voxel’s
time course from resting data which is believed to be of functional relevance (seedvoxel based correlation analysis). These
techniques fundamentally test very specific hypotheses about the temporal structure of these effects. Recently, however, In
dependent Component Analysis has succesfully been applied to the estimation of certain lowfrequency patterns (Goldman
and Cohen, 2003; Kiviniemi et al., 2003; Greicius et al., 2004). An important benefit of such exploratory techniques over
more hypothesisbased techniques is the ability to identify various types of signal fluctuations by virtue of their spatial and/or
temporal characteristics without the need to specify an explicit temporal model. Such flexibility in data modelling is essential
in cases where the effects of interest are not very well understood and cannot be predicted acurately.
This paper is organised as follows: in section 2 we review a probabilistic approach to Independent Component Analysis
(PICA) specifically optimised for the analysis of FMRI data (Beckmann and Smith, 2004). Section 3 discusses the constraints
of this exploratory data analysis technique when used for the identification of largescale noise fluctuations. In particular,
we demonstrate that optimisation for maximally independent spatial sources does not imply an inability to estimate largely
overlapping spatial maps. We demonstrate the ability of PICA to extract resting fluctuations and apply the technique to FMRI
resting data in order to test a set of important hypotheses about the structure of restingstate connectivity in the human brain.
In particular, we will investigate (i) if and how estimated source processes are driven by less interesting physiological effects
such as the cardiac or respiratory cycle, (ii) the spatial characteristics of estimated maps in terms of locality within grey matter
and (iii) the consistency of maps obtained from multiple subjects.
2 Decomposing FMRI data using ICA
Independent Component Analysis (ICA, Comon (1994); Bell and Sejnowski (1995); McKeown et al. (1998)) is a technique
which decomposes a 2dimensional (time × voxels) data matrix1into a set of time courses and associated spatial maps which
jointly describe the temporal and spatial characteristics of underlying hidden signals (components). A probabilistic ICA model
extends this by assuming that the pdimensional vectors of observations (time series in the case of FMRI data) is generated
from a set of q(< p) statistically independent nonGaussian sources (spatial maps) via a linear and instantaneous ’mixing’
process corrupted by additive Gaussian noise η(t):
xi= Asi+ ηi
(1)
1Here, we only discuss the case of a decomposition into spatially independent source signals; the reason for this will become apparent later.
2
Page 3
Here, xidenotes the individual measurements2at voxel location i, sidenotes the nonGaussian source signals contained in
the data and ηidenotes Gaussian noise3ηi∼ G(0,σ2Σi).
The p × q dimensional mixing matrix A is assumed to be nondegenerate, i.e. of rank q. Solving the blind separation
problem requires finding a linear ’unmixing’ matrix W of dimension q × p such that
? s = Wx
The PICA model is similar to the standard GLM with the difference that, unlike the design matrix in the GLM, the mixing
matrix A is no longer prespecified prior to model fitting but will be estimated from the data. The spatial source signals
correspond to parameter estimate images in the GLM with the additional constraint of being statistically independent of each
other.
is a good approximation to the true source signals s.
2.1 Parameter estimation
Without loss of generality we can assume that the source signals have unit variance. If the noise covariance Σiis known,
we can prewhiten the data and obtain a new representation ¯ xi =¯Asi+ ¯ ηi, where ¯ ηi∼ G(0,σ2I), i.e. where the noise
covariance is isotropic at every voxel location. To simplify notation, we will henceforth assume isotropic noise and drop the
additonal bar.
Noise and signal are uncorrelated, so the data covariance matrix Rx= ?xixt
matrix A can be estimated as the matrix square root of Rx−σ2I: let X be a p×N matrix containing all N different FMRI
time series in its columns and let X = U(NΛ)
i? = AAt+ σ2I, i.e. the unknown mixing
1
2V be the singular value decomposition of X. Then
?AML= Uq(Λq− σ2Iq)
1
2Qt,
(2)
where Uqand Λqcontain the first q Eigenvectors and Eigenvalues. The matrix Q denotes a q × q orthogonal rotation matrix,
i.e. a matrix with QQt= I. This matrix is not directly identifyable from the data covariance matrix since Rxis invariant
under postmultiplication of A by any orthogonal rotation¯Q given that (A¯Q)(A¯Q)t= A¯Q¯QtAt= AAt= Rx− σ2I.
Estimating the mixing matrix A, however, reduces to identifying the square matrix Q after whitening the data with respect
to the noise covariance Σiand projecting the temporally whitened observations onto the space spanned by the q Eigenvectors
of Rxwith largest Eigenvalues. The maximum likelihood estimates of sources and σ are obtained using generalised least
squares:
? sML=?
and
? σ2
Solving the model in the case of an unknown noise covariance can be achieved by iterating estimates of the mixing matrix
and the sources and reestimating the noise covariances from the residuals ? η. The form of Σitypically is constrained by a
et al., 2001), and restrict the structure to autoregressive noise. However, since the exploratory approach allows modelling of
various sources of variability, e.g. temporally consistent physiological noise, as part of the signal in equation 1, the noise
model itself can actually be quite simplistic.
A consequence of the isotropic noise model is that as an initial preprocessing step we will modify the original data time
courses to be normalised to zero mean and unit variance. This preconditions the data under the null hypothesis of no signal:
the data matrix X is identical (up to second order statistics) to a simple set of realisations from a G(0,I) noise process. Any
signal will have to reveal itself via its deviation from Gaussianity.
The maximum likelihood estimators depend on knowledge of the number of underlying sources q. In the noise free case
this quantity can easily be deduced from the rank of the covariance of the observations Rxwhich is of rank q. In the presence
of isotropic noise, however, the covariance matrix will be of full rank where the additional noise has the effect of raising the
Eigenvalues of the covariance matrix by σ2(Roberts and Everson, 2001). Inferring the number of estimable source processes
amounts to testing for sphericity of Eigenspaces beyond a given threshold level (Beckmann and Smith, 2004). Simplistic
criteria like the reconstruction error or predictive likelihood will naturally predict that the accuracy steadily increases with
increased dimensionality. Thus, criteria like retaining 99.9% of the variability result in arbitrary threshold levels (Beckmann
Wx
with
?
W = (?A
p − q
t?A)1?A
λl.
t
ML=
1
p
?
l=q+1
(3)
suitable parameterisation; here we use the common approaches to FMRI noise modelling (Bullmore et al., 1996; Woolrich
2For simplicity we assume demeaned data.
3The covariance of the noise is allowed to be voxel dependent in order to encode the vastly different noise covariance observed within different tissue
types (Woolrich et al., 2001).
3
Page 4
et al., 2001). This problem is intensified by the fact that the data covariance Rxis being estimated by the sample covariance
matrix. In the absence of any source signals, the Eigenspectrum of this sample covariance matrix is not identical to σ2Ip
but instead distributed skewed around the true noise covariance: the Eigenspectrum will depict an apparent difference in the
significance of individual directions within the noise (Everson and Roberts, 2000), even in the absence of signal. In the case
of Gaussian noise, however, this ’skew’ of the Eigenspectrum is of analytic form: the Eigenvalues have a Wishart distribution
and we can adjust the observed Eigenspectrum by the quantiles of the predicted cumulative distribution of Eigenvalues from
Gaussian noise (Johnstone, 2000) , prior to estimating the model order. If we assume that the source distributions p(s) are
Gaussian, the model then reduces to probabilistic PCA (Tipping and Bishop, 1999) and we can use Bayesian model selection
criteria. Within the PICA approach, we use the Laplace approximation to the posterior distribution of the model evidence that
can be calculated efficiently from the adjusted Eigenspectrum (Minka, 2000; Beckmann and Smith, 2004).
In order to complete the estimation of the mixing matrix and the sources, we need to optimise an orthogonal rotation
matrix Q in the space of whitened observations:
? s = Wx = Q˜ x,
Hyv¨ arinen and Oja (1997) have presented an elegant fixed point algorithm that uses approximations to negentropy in
order to optimise for nonGaussian source distributions and give a clear account of the relation between this approach to
statistical independence. In brief, the individual sources are obtained by projecting the data x onto the individual rows of Q,
i.e. the rth source is estimated as
? sr= vt
the following contrast function:
J(sr) ∝ [E{F( ? sr)} − E{F(ν)}],
combines the highorder moments of srin order to estimate the amount of nonGaussianity in the individual sources. From
equation 5, the vectors vt
1997).
(4)
where ˜ x = (Λq− σ2Iq)−1/2Ut
qx denotes the spatially whitened data.
r˜ x,
where vt
rdenotes the rth row of Q. In order to optimise for nonGaussian source estimates, Hyv¨ arinen and Oja (1997) propose
(5)
where ν denotes a standardised Gaussian variable, E denotes the expectation and F is a general nonquadratic function that
rare optimised to maximise J(? sr) using an approximative Newton method (Hyv¨ arinen and Oja,
2.2
After estimating the mixing matrix?A, the source estimates are calculated by projecting each voxel’s time course onto the time
the estimated noise is a linear projection of the true noise and is unconfounded by residual signal. At every voxel location we
have preconditioned the data such that xihas unit standard deviation and the estimate of the noise variance ? σ2
’Zstatistic maps’ zr·by dividing the raw IC maps by the standard error of the residual noise.
In order to assess the Zmaps for ’significantly activated’ voxels, we employ mixture modelling of the probability density
of the Zstatistic spatial maps.
From equation 3 it follows that ? si=?
of one Gaussian and two Gamma distributions, to model background noise and positive and negative BOLD effects (Hartvig
and Jensen, 2000; Beckmann et al., 2003). The mixture is fitted using an expectationmaximisation algorithm Dempster
et al. (1977). In cases where the number of ’active’ voxels is very small, the relative proportions of the Gamma densities
in the overall mixture distribution might be estimated as zero. In this case, a simple transformation to spatial Zscores and
subsequent thresholding is appropriate, i.e. reverting to nullhypothesis testing instead of the otherwise preferable alternative
hypothesis testing. Otherwise we can evaluate the fitted mixture model to calculate the posterior probability of ’activation’ as
the ratio of the probability of intensity value under the ’noise’ Gaussian relative to the sum of probabilities of the value under
the ’activation’ Gamma densities4.
Any threshold level, though arbitrary, directly relates to the loss function we like to associate with the estimation process,
e.g. a threshold level of 0.5 places an equal loss on false positives and false negatives (Hartvig and Jensen, 2000).
Inference
courses contained in the columns of the unmixing matrix?
location will approximately equal the true variance of the noise. We can thus convert the individual spatial IC maps sr·into
W. In the case where the model order q was estimated correctly,
iat each voxel
WAsi+?
Wηi, i.e. the noise term in equation 1 manifests itself as additive Gaussian
noise in the estimated sources. We therefore model the distribution of the spatial intensity values of each Zmap by a mixture
2.3 PICA Algorithm Overview
The individual steps that constitute the Probabilistic Independent Component Analysis are illustrated in figure 1. The de
meaned original data is first normalised to unit variance at each voxel location. If appropriate spatial information is available,
4In this case ’activation’ is to be understood as signal that ’cannot be explained as random correlation coefficient’.
4
Page 5
PICA
map
standard
deviation
of b η
IC
maps
Z stat.
map
prob.
maps
noise
estimate
spatially
whitened
data
voxelwise
prewhitened
data
variance–
normalised
data
original
data
?
prior
infor–
mation
+
Σi
6
Rx

??

?
?
modelorder

?

Mixture Models
PPCA
estimate
unmixing
Figure 1: Schematic illustration of the probabilistic ICA model (Beckmann and Smith, 2004)
thisisencodedintheestimationofthesamplecovariancematrixRx. Individualvoxelweights, e.g. graymattersegmentation,
can be used to calculate a weighted covariance matrix while voxelpair weightings can be used to calculate the withingroup
covariance (Beckmann and Smith, 2004). Probabilistic PCA is used to infer upon the unknown number of sources and results
in an estimate of the noise and a set of spatially whitened observations. We can estimate the noise covariance structure Σifrom
the residuals in order to voxelwise (temporally) prewhiten and renormalise the data and iterate the entire cycle. Estimation
of Σifrom residuals in the case of autocorrelated noise can be achieved as described by Woolrich et al. (2001). In practice,
the output results do not suggest a strong dependency on the form of Σiand preliminary results suggest that it is sufficient to
iterate these steps only once. From the spatially whitened observations, the individual component maps are obtained using a
modified fixed point iteration scheme (FastICA (Hyv¨ arinen and Oja, 1997)) to optimise for non Gaussian source estimates via
maximising the negentropy. These maps are separately transformed to Zscores. In contrast to raw IC estimates which only
encode the estimated signal, these Z score maps depend on the amount of variability explained by the entire decomposition
at each voxel location relative to the residual noise similar to statistical parametric maps from a GLM analysis. This is an
important aspect of the probabilistic ICA model as now these maps also reflect the degree to which the signal explained
within this model fits to the data and, unlike standard ICA, no longer ignores the signal variation which remains unaccounted
for. Finally, Gaussian/Gamma Mixture Models are fitted to the individual Z maps in order to infer voxel locations that are
significantly modulated by the associated time course.
3Estimating overlapping maps using ICA
The choice of optimising for independence between spatial maps could equally well be replaced by optimising for indepen
dence between time courses. Different authors have argued in favour of one or the other technique, where the main objection
appears to revolve around the question of whether orthogonality (i.e. uncorrelatedness) between estimated sources should
be enforced in the temporal or spatial domain (Friston, 1998; Petersen et al., 2000). At a conceptual level, the notion of
orthogonality is overly restrictive in either domain: for temporal modes, the existence of stimulus correlated effects (e.g. mo
tion artefacts or higher order brain function) means that enforced orthogonality necessarily results in a misrepresentation of
underlying temporal signals. Similarly, for spatial modes, (Friston, 1998) has argued that even though different brain function
might be spatially localised, the principle of ’functional integration’ might imply that neuronal processes share a large pro
portion of cortical anatomy. These arguments suggest that independence and implied orthogonality are always suboptimal for
the analysis of data which is as complicated as that obtained from functional MRI experiments.
From a signal detection point of view, however, it is important to consider the extent to which signal ’appears’ in space or
5
Page 6
050100 150200 250
0
time (s)
050100 150200 250
0
time (s)
050 100 150200250
0
time (s)
050 100150 200250
0
time (s)
050 100 150200250
0
time (s)
050100150200250
0
time (s)
(ρ ∼ 0.5)(ρ ∼ 0.27)(ρ ∼ 0.0)(ρ ∼ 0.0)(ρ ∼ 0.47)
(a) ’true’ maps(b) regression maps(c) PCA maps(d) PICA maps(e) thesholded maps
Figure 2: Estimation of largely overlapping signals in the presence of noise: 2 source signals with spatial correlation of
ρ ∼ 0.5 were introduced into Gaussian noise (σ = 3) to form an artificial data set of size 250x10000 (a). In the presence
of noise, the spatial correlation of leastsquares estimates is significantly reduced (b). Estimating principal components from
the data results in a poor representation in the temporal and spatial domain (c). ICA estimates from the same data (d) show
much improved detection power and represent the spatial maps and time courses well. Thresholded maps (e) are again highly
correlated at ρ ∼ 0.47. Note that spatial ICA maps, like PCA maps, are constrained to be orthogonal. This restriction itself,
therefore, does not necessarily imply poor spatial representation of signals even in cases where ’true’ spatial maps are highly
correlated.
time. Within the temporal domain, signal often spans the entire length of an experiment. If the ’true’ temporal characteristics
of different signals are partially correlated (e.g. stimuluscorrelated motion), a decomposition which enforces orthogonality
in the temporal domain will necessarily misrepresent at least one of the time series in order to satisfy the constraint. In the
spatial domain, however, ’signals’ in FMRI are sparse and typically are contained in a small proportion of all voxels. Even for
what in FMRI are considered ’large’ activation clusters or for artefactual sources with large spatial extent (e.g. image ghosts),
only a fraction of intracranial voxels are involved5. In the presence of noise, the majority of voxels in any spatial maps have
random ’background noise’ value and will reduce the observed spatial correlation such that even when ’true’ spatial maps
are significantly overlapping, a decomposition which enforces orthogonality between estimated spatial maps can still give a
relatively accurate representation of the signal.
Formally, consider the case of two source signals s1and s2, represented as column vectors of length N, and (zeromean)
Gaussian noise η1and η2with variance σ2
1and σ2
2. In the presence of noise, the correlation changes from
ρ(s1,s2) =
st
1s2
N?Var(s1)?Var(s2)
5For residual motion artefacts, every voxel is theoretically influenced by an associated motion time series, but only voxels near intensity boundaries are
detectable.
6
Page 7
to
ρ(s1+ η1,s2+ η2) =
st
1s2
N?Var(s1) + σ2
1
?Var(s2) + σ2
2
.
When signals are sparse, Var(s1) and Var(s2) are small and the denominator of ρ(s1+η1,s2+η2) is dominated by the noise
variance. The reduction in correlation between the noisefree and noisy case is a function of the signal amplitude modulation,
the sparseness and the relative noise level.
As an example figure 2(a) shows two partially overlapping spatial ’signals’ each occupying ∼ 17% of the total image
areas together with two artificial time courses. Due to their partial overlap, these source signals are spatially correlated with
a correlation of ρ ∼ 0.5. In the absence of noise these maps can not be estimated accurately by any technique enforcing
orthogonality between estimated spatial maps. In the presence of noise6, however, the spatial correlation between linear
estimates reduces significantly: figure 2(b) shows the spatial maps obtained from performing linear regression of the data
against the ’true’ time series. The spatial maps obtained from a PCA decomposition (c) have ∼ 0 spatial correlation and fail to
identify the ’true’ spatial maps. Also, the temporal characteristics of the signal are not well represented. By comparison, the
estimated spatial maps from an ICA decompostion (d) well represent signal in space and time. Although the spatial sources are
clearly visible, the spatial correlation between the estimated spatial maps is still ∼ 0. This is a consequence of the optimisation
for maximally nonGaussian source projections. Final thresholded ICA maps derived from a Gaussian/Gamma mixture model
on the noisy maps give a reasonably good spatial representation for the original sources: the estimated thresholded maps (e)
have large spatial correlation (ρ ∼ 0.47).
This example demonstrates that the mathematical constraint of orthogonality within the set of spatial maps does not
necessarily imply that large areas of ’activation’ which overlap significantly between maps can no longer be extracted. Instead,
the amount to which this mathematical constraint restricts the estimation of partly overlapping sources is a function of (i)
the overall sparseness of signals and (ii) the signaltonoise ratio. This suggests that in practice the constraints induced by
optimising for independence are less restrictive in the spatial domain than the temporal domain. Though compensating for
partial correlation of ’signal’ by anticorrelating ’noise’ conceptually is also possible in the temporal domain, the significantly
lower number of time points does not typically provide a sufficient number of ’background’ time points that could be utilised
to ensure orthogonality while not altering ’interesting’ portions of the estimated source signals. This property is particular
important for investigating restingstate networks because it means that functionally distinct systems can overlap anatomically
as long as they have sufficiently distinct time courses.
4Experimental Method
In order to characterise the lowfrequency structured noise components in ’resting’ data, we acquired different data sets to
address four specific questions:
1. To compare seedvoxel correlation techniques with PICA, we collected 200 volumes from a single subject under rest
and active finger tapping (30s on/off block design). Data were acquired on a Phillips NT 1.5T MRI system with a
notional 2x2x8mm resolution, a repetition time (TR) of 3s and an echotime (TE) of 40ms.
2. To evaluate the extent to which neural effects can be distinguished from nonneural physiological effects such as aliased
cardiac or respitory cycles, we collected resting data with a high temporal resolution (B0=3T, TR=125ms, TE=30ms,
3.75x3.75mm inplane resolution). The data consists of 2160 slices through a single axial plane chosen to intersect
the sensorimotor cortices bilaterally. In addition, we collected 60 volumes under a 30s on/off bilateral finger tapping
paradigm at a typical TR of 3s. All data were acquired on a VarianSiemens 3T MRI system.
3. To determine whether low frequency resting fluctuations appear within grey matter or are instead driven by contributions
from larger blood vessels, we collected 300 volumes (12 slices) of resting data at 3T with spatial resolution of 2x2x6mm
and TR=3s.
4. Finally, to investigate the spatial consistency of restingstate patterns across subjects, data were collected from nm 10
subjects during rest. For each, 200 volumes of whole head functional data were acquired at 3T with typical FMRI
resolution (3x3x3mm, TR=3.4s, TE=40ms). In addition, a highresolution T1weighted reference scan (1x1x1.5mm
resolution) was also acquired for the purpose of anatomical localisation.
Subjects were lying supine in the MRI scanner and instructed to keep their eyes closed and not to fall asleep during
functional scanning.
6Zeromean Gaussian noise with σ = 3; the maximum signal amplitude modulation is 2.
7
Page 8
0 0.02 0.04 0.06 0.08 0.10.12 0.14 0.16
0
0.5
1
relative power
Frequency (Hz)
????
?:
????
?:
(a) (b)
highest Zscoreseed voxel
R
L
0 0.02 0.04 0.06 0.080.1 0.12 0.14 0.16
0
0.5
1
relative power
Frequency (Hz)
00.02 0.04 0.06 0.080.10.12 0.14 0.16
0
0.5
1
relative power
Frequency (Hz)
(c)
Figure 3: Comparison of seedvoxel based correlation analysis and PICA: for seedvoxel based analysis, an activation data
set is first analysed to identify the location of most significant response to external stimulation (a). The time course of the
coinciding voxel in the resting data is used as a reference time course for a correlation analysis of all other time courses
acquired under rest. The resulting correlation map (b) shows significant resting correlation in similar motor areas as the
activation map but also identifies part of the ipsilateral motor cortex. In addition, other regions outside of these motor areas
were also found including medial and lateral posterior parietal areas and prefrontal regions. In a PICA decomposition of
the resting data (c), similar cortical regions are identified by two (out of 40) separate spatial maps. The multiple regression
framework implicit in a PICA decomposition separates resting correlations in motor areas (left) from other cortical areas. This
separation is induced by the fact that the associated time courses are significantly different: the associated normalised power
spectra show different peak frequencies. All spatial maps were thresholded using mixture modelling (at p > 0.5) and are
shown in radiological convention.
4.1Analysis Methods
The individual data sets were preprocessed before running correlationbased or ICAbased statistical analyses using tools
from the FMRIB Software Library (FSL, www.fmrib.ox.ac.uk/fsl). Time series were first realigned to correct for small head
movements (Jenkinson et al., 2002). Then nonbrain (e.g. scalp and CSF) were removed using an automated brain extraction
tool (Smith, 2002). Finally, the data were spatially smoothed using a Gaussian kernel (5mm). After statistical analysis
(whether correlation or ICAbased), the resulting statistical maps were thresholded using histogram mixture modelling as
described above.
8
Page 9
4.2 Seedvoxel based correlation analysis vs. multivariate PICA regression
Activationseeded correlation analysis is based on the hypothesis that in resting data the lowfrequency temporal fluctuations
are correlated in regions which are functionally associated (Biswal et al., 1995; Lowe et al., 1998). In this approach an
activation dataset (e.g. under a simple motor paradigm) is acquired along with data at rest. The activation data is first analysed
to identify areas which activate significantly. The coordinates of the highest activating voxel are then used to define a seed
voxel in the resting data. A statistical map is generated by calculating the correlation of all time courses in the resting data
against the time course of the seed voxel in order to find a temporally consistent resting network. The applicability of this
technique, however, is limited by the fact that seedvoxel based analysis relies on the time course at the seed voxel location
being a ’good’ representative for the set of correlated voxels under rest. As a consequence, the seedvoxel based approach
is restricted to cases where seed areas can be inferred accurately and robustly from activation studies (like motor area).
Furthermore, the choice of the seed voxel is rather arbitrary (as, indeed, is the exact location of a peak Zstat) and can be
biased by different types of FMRI noise. In particular, the usefulness of such a correlation analysis is severely limited in
cases where the reference time course itself is a mixture of time courses, e.g. different lowfrequency fluctuations, spatially
structured highfrequency signals such as that induced by the N/2 ghost, head motion etc. These problems are analogous to
those that characterise the difference between simple correlation analysis and the GLM for modelbased FMRI analysis: a
multiple regression model can account for temporal effects which coincide at a single voxel location.
Figure 3 illustrates the difference between seedvoxel based correlation analysis and PICA using data from a simple finger
tapping experiment and data acquired under rest (i.e. the first dataset). Modelbased analysis of the activation data produced
plausible motor cortex activation in the contralateral hemisphere (a), although in this case, the peak Zscore was located
in the postcentral gyrus rather than in motor cortex. Using this voxel as the seed time course in a subsequent correlation
based analysis of the resting data (i.e. excluding the motor task blocks) shows significant correlation in similar areas such
as the motor cortex bilaterally and the supplemental motor area (SMA) along the midline (b). On the other hand medial
posterior cortical areas and frontal parts also show significant correlation, despite not being identified as parts of the motor
system engaged in the finger tapping contrast (a). Based on the Laplace approximation of the Bayesian model evidence, the
PICA approach estimates 40 components, including various artefacts such as Nyquist ghosting, headmotion and large blood
vessels. Two of the remaining components (shown in figure 3(c)) jointly cover almost identical postthresholded areas as the
map obtained from seedvoxel based correlation analysis. Within the PICA approach, these areas are separated into different
spatial maps due to the fact that the associated time courses are sufficiently different. (as can be seen by the different power
spectra). The PICA decomposition suggests that the voxels shown in figure 3(b) are part of two different spatial patterns which
appear in the single correlation map by virtue of the fact that the seed voxel has partial correlation with voxels shown in the
two PICAderived maps. The multiple regression analysis underlying a PICA decomposition, by comparison, can separate
these effects and gives a more plausible representation of a motor network.
4.3 Relation between physiological noise and restingstate fluctuations
One question that arises with respect to restingstate networks such as the one shown in figure 3 is whether the findings are
functionally significant, or whether they are simply a consequence of aliased physiological effects such as the cardiac and
respiratory cycles. In order to investigate the frequency characteristics of resting fluctuations we acquired single slice data
covering the motor cortex at low TR (125ms) and at a more typical TR (3s). The high temporal sampling data is necessary
to separate lowfrequency effects from signal fluctuations due to the cardiac or respiratory effects. These occur naturally
at frequencies of 0.31Hz and so can easily become aliased by normal TR sampling to give significant power at the low
frequencies (0.015 to 0.035Hz) typical of restingstate fluctuations. By collecting low TR data such aliasing will be avoided.
This data has about twice as many samples in the temporal domain than voxels across space. In order to reduce computational
load, therefore, we assumed a blockdiagonal form of the data covariance matrix for the initial PCA dimensionality reduction
which is part of the spatial PICA decomposition.
Figure 4 shows PICA estimates obtained from lowTR resting data (left) and analysis results from activation data (self
paced bilateral finger tapping) acquired at a more typical sampling rate of 3s (right). On the lowTR data, the separate com
ponents found include a single cardiaccyclerelated map with peak frequency of ∼1Hz (fig 4(a)), a respirationrelated map
with peak frequency of ∼0.3Hz (fig. 4(b)) as well as a map showing the spatial extent of lower frequency resting fluctuations
(0.020.1Hz, fig 4(c))  in this case largely contained within sensorimotor areas. With high temporal sampling the PICA ap
proach clearly separates simple physiological noise components from resting fluctuations. By comparison, figure 4(df) shows
corresponding PICA maps estimated from data acquired with a more typical TR. Here, the spatial maps of the respiratory and
cardiac fluctuations were identified purely based on their spatial correspondence with maps shown in figure 4(a,b) (spatial
correlation of 0.64 and 0.42 respectively). At this more normal temporal sampling rate, the simple frequency characteristics
of these effects are no longer detectable due to aliasing. The primary activation map, however, relates to activation due to a
30s on/off block design (periodicity of 0.01677) and can be identified easily both in the spatial and frequency domain. This
9
Page 10
0.51 1.5
Frequency (Hz)
2 2.53 3.54
0
0.5
1
relative power
0.020.04 0.06
Frequency (Hz)
0.08 0.1 0.120.140.16
0
0.5
1
relative power
0.1 0.2 0.3 0.4
Frequency (Hz)
0.50.6 0.7 0.80.91
0
0.5
1
relative power
0.02 0.040.06
Frequency (Hz)
0.080.1 0.120.14 0.16
0
0.5
1
relative power
0.10.2 0.3 0.4
Frequency (Hz)
0.5 0.60.70.80.91
0
0.5
1
relative power
0.02 0.040.06
Frequency (Hz)
0.08 0.1 0.120.140.16
0
0.5
1
relative power
low TR (125ms)typical TR (3s)
(a)
RL
(d)
(b) (e)
(c)(f)
Figure4: Investigatingtherelationshipbetweenphysiologicalnoiseandlowfrequencyfluctuationsinthespatialandtemporal
domain: The different components estimated from the lowTR data (left) show a clear separation of physiological artefacts
induced by the cardiac cycle (a) and the respiratory cycle (b) from lowfrequency fluctuations (c) both in the spatial maps and
the corresponding power spectra. At higher TR the temporal signature of the cardiac and respiratory cycles become aliased
and no longer identifyable in the frequency domain. The spatial maps (d,e), however, show a high degree of correspondence
with maps (a) and (b) (spatial correlation of 0.64 and 0.42, respectively), suggesting that the PICA approach is able to separate
relatively uninteresting physiological noise from other effects such as restingstate maps even in cases where the physiological
noise fluctuations become aliased in the temporal domain.
(a)
R
(b)
L
0 0.020.040.06
Frequency (Hz)
0.08 0.1 0.120.140.16
0
0.5
1
relative power
Figure 5:
resolution in the xy plane suggests that the restingstate fluctuations are well localised in greymatter (a). Furthermore, they
appear to be spatially different from ’blood vessel networks’ (BVNs) which mainly show larger blood vessels and surrounding
tissue (b).
Investigating the spatial structure of restingstate fluctuation: PICA analysis of EPI data acquired at 2x2 mm
suggests that even at higher TR PICAderived spatial maps separate cardiac and respiratory effects from other effects such as
activation maps or lowfrequency restingstate fluctuations.
10
Page 11
4.4Spatial characteristics of restingstate fluctuations
The functional relevance of lowfrequency patterns depends on the spatial locality in greymatter. At typical spatial FMRI
resolution, the estimated lowfrequency patterns indeed appear to be ’grey matter networks’. Figure 5(a) shows example
spatial maps found using PICA on the data with higher inplane spatial resolution (2x2mm; third data set). The significant
voxels do generally lie within grey matter and include little or no white matter. In almost all cases a PICA decomposition also
generates spatial maps depicting ’blood vessel networks’ (BVNs). These have a similar power spectrum with peak frequencies
of around 0.2Hz but mainly show larger blood vessels and surrounding tissue (fig. 5(b)).
4.5 Consistency of restingstate fluctuations across subjects
Our initial analysis suggests that lowfrequency resting patterns in FMRI are not only predominantly contained within grey
matter, but also appear to be localised within discrete areas of functional significance. In order to investigate this further, we
perform an exploratory group analysis for data from 10 subjects obtained under rest (fourth data set).
Data was first motion corrected and coregistered using affine linear registration (Jenkinson and Smith, 2001) into a com
mon space defined by the midtransformation of all 10 transformation matrices which take the individual lowresolution data
sets to the space of the MNI template. This resulted in 10 new EPI data sets which all experienced the same average amount
of displacement due to coregistration and which were kept at the original EPI resolution. The individual data sets were then
spatially smoothed by a Gaussian kernel with FWHM 7mm and preprocessed by performing voxelwise variance normalisa
tion and demeaning as described in section 2. The PCA Eigenbasis, however, was calculated from the mean data covariance
matrix, i.e. from the covariance matrix of the spatially concatenated data matrix of size (time × (voxels × subject)). All tem
poral Eigenvectors showed dominant lowfrequency content, the initial data reduction stage therefore effectively amounts to a
temporal lowpass filtering of the original data by projecting each of the 10 data sets onto the 30 dominant Eigenvectors. The
10 individual (dimensionalityreduced) data sets were then temporally concatenated to form a data matrix of size 300×58032.
Using the Laplace approximation to the Bayesian evidence for model order selection, the ICA decomposition estimated 23
spatiotemporal processes. The resulting spatial maps were thresholded using the Gaussian/Gamma alternative hypothesis
testing approach. Note that this methodology differs from the GroupICA methodology introduced by Calhoun et al. (2001)
in that the individual data is not projected onto an individual subspace but instead initial data reduction is performed by
projecting each data set onto a common PCA Eigenbasis.
Figure 6 shows example sagittal, coronal and axial slices for 8 spatial patterns (out of 23), overlayed onto the mean
subjects’ highresolution structural image (1x1x1.5mm) aligned to the MNI template (all coordinates are in mm from the
anterior commissure). The final thresholded maps can be classified as follows:
• (a) Medial visual cortical areas: These include primary visual areas located in the calcarine sulcus bilaterally as
well as medial, but not lateral, extrastriate regions such as the lingual gyrus. In addition, activation was seen in the
inferior divison of precuneous cortex and in the lateral geniculate nucleus of the thalamus, the primary ’relaystation’
linking visual input to primary visual cortex. Indeed, previous DWI (Diffusion weighted imaging) studies have shown
that this region of thalamus connects to the occipital lobe with high probability (Behrens et al. (2003), the thalamic
connectivity atlas derived from DWI is available at http://www.fmrib.ox.ac.uk/connect/). Although each of these areas
(including thalamus) fall within the vascular territory of the posterior cerebral artery, the pattern of results is unlikely
to be due to simple temporal patterns of blood supply for two reasons. First, lateral occipitotemporal regions are also
supplied by the posterior cerebral artery and these do not exhibit the same resting time course. In fact, one region of
the middle temporal gyrus (MT, blue) demonstrated a deactivation at rest. Second, the blood supply to the thalamus is
also driven by contributions from other arteries via the circle of Willis, and thus would be unlikely to exhibit the same
temporal pattern of blood flow as the posterior cerebral artery alone. Instead, these activations may correspond to a set
of connected regions primarily composed of the primary visual system.
• (b) Lateral visual cortical areas: These included the occipital pole extending laterally towards the occipitotemporal
junction, encompassing nonprimary regions of visual cortex. In addition, activation was seen more dorsally in superior
parietal regions. This set of regions is frequently found to be coactivated in functional studies of visual attention or
visuospatial attention. Deactivation is found in posterior cingulate cortex (Brodmann’s area 30), a region which has
been found to coactivate in studies of orientation and navigation in largescale spaces (Maguire, 2001) and in a more
recent study has been found to deactivate in a delayedmatchtosample task under sleep deprivation (Habeck et al.,
2004).
• (c) Auditory system: Activation in this component encompassed primary and secondary auditory cortices, including
Heschl’s gyrus, planum polare and planum temporale, the lateral superior temporal gyrus, and posterior insular cor
tex (Rivier and Clarke, 1997; Rademacher et al., 2001). Additional activation was observed in the anterior cingulate
11
Page 12
(a)
x=17y=73z=12
RL
(b)
x=13 y=61 z=6
RL
(c)
x=3y=17 z=1.5
RL
(d)
x=1 y=21 z=51
RL
(e)
x=4 y=29z=33
RL
(f)
x=5y=6 z=27
RL
(g)
x=45 y=42z=47
RL
(h)
x=45y=42 z=47
RL
Figure 6:
withlowfrequencyrestingpatternsestimatedfromagroupof10subjects. Allimageshavebeencoregisteredintothespaceof
the MNI template. The coordinates refer to mm distances from the anterior commissure and images are shown in radiological
convention.
Different PICAestimated resting patterns: saggital, coronal and axial views of different spatial maps associated
cortex, anterior supramarginal gyrus, and thalamus. Although these regions are primarily supplied by the middle cere
bral artery (MCA), like previous RSNs, this appears to be confined to functionally related areas rather than encompass
the entire frontoparietal area supplied by the MCA.
• (d) Sensorimotor system: These included activation in pre and postcentral gyri extending from the superior bank of
the Sylvian fissure to the medial wall of the interhemispheric fissure and included the supplemental motor area (SMA).
This pattern of activation corresponds closely to that seen in bimanual motor tasks. Similar patterns have been identified
in previous RSN studies (Biswal et al., 1995).
• (e) Visuospatial system: Activation was observed in the posterior parietal cortex at the occipitoparietal junction,
along the midline in the precuneus and posterior cingulate cortex, and in the frontal pole. Within this spatial map,
deactivation was mainly found in preSMA. These regions are the same as the physiological baseline areas proposed
by Gusnard and Raichle (2001). The authors hypothesise that activity within the posterior cingulate cortex and adjacent
precuneus is associated with the representation of the world around us. Similarly, previous studies have demonstrated
that lesions affecting the lateral posterior parietal areas lead to severe deficits in spatial attention (Posner et al., 1984;
Mesulam, 1981), while disrupting the input to the region prevents patients from benefiting from spatial cues (Alivisatos
and Milner, 1989; Koski et al., 1998; Petrides and Pandya, 2002). Similar findings in macaques show that neuronal re
12
Page 13
sponses in a corresponding region (area 7a) are suppressed when stimuli appear at a cued spatial location (Constantinidis
and Steinmetz, 2001). Taken together, these findings suggest that the posterior parietal cortex is engaged in orienting
to salient visuospatial cues. Interestingly, the only region to show deactivation was the preSMA, a region consistently
implicated in internally (i.e. memorydriven), rather than externally cued, tasks (Rushworth et al., 2004). Overall then,
this pattern of findings is consistent with findings by Gusnard and Raichle (2001) that activation in this component may
reflect a system of cortical regions engaged in attending to visuospatial information. A similar spatial map has been
identified using both seedvoxel based correlation analysis and PICA (Greicius et al., 2003, 2004) and has been shown
to have reduced activity in the posterior cingulate cortex in Alzheimer’s disease.
• (f) Executive Control: Areas of activation include superior and middle prefrontal cortices, anterior cingulate and
paracingulate gyri, and ventrolateral prefrontal cortex. In addition, there was subcortical activation in a region of the
thalamus which connects to prefrontal cortex with high probability (Behrens et al., 2003; JohansenBerg et al., 2004).
These areas have been hypothesised to provide bias signals to other areas of the brain in order to implement cognitive
control (Miller and Cohen, 2001).
• (g),(h) Dorsal visual stream: Unlike all of the previous components, these two components showed primarily later
alized activations corresponding roughly to the dorsal visual stream. For instance, (g) shows activation in right lateral
occipital complex, right inferior parietal cortex, bilateral intraparietal sulcus, and right middle and superior frontal gyri.
The complementary pattern is seen in the left hemisphere in (h), including the bilateral intraparietal activation. In fact,
this is the only area to show a bilateral response in these two components and activation in the region overlaps in the
two components, demonstrating that PICA can be used to reveal separate neural systems that contain spatial overlap
(i.e. functional integration, cf. Friston (2002)).
5 Discussion
Various researchers have demonstrated that an ICA decomposition can be used to identify patterns of activation, image arte
facts and physiologicallygenerated components including RSNs (De Luca et al., 2002a,b; Kiviniemi et al., 2003; Goldman
and Cohen, 2003; Beckmann and Smith, 2004; DeLuca et al., 2004; Greicius et al., 2004). Here we extend the scope of
previous investigation into the use of ICA in FMRI, investigating a variety of important aspects relating to the applicability of
ICA to restingstate studies. We have demonstrated that an ICA approach can identify a variety of fluctuations (even in cases
where these signals coincide at a particular voxel’s location) and that ICA is able to estmate even largely overlapping spatial
processes. Furthermore, using high and lowTR data, we have provided evidence that ICAderived spatial maps of RSNs are
unaffected by respiratory/cardiac fluctuations even though at normal TR the temporal structure of the latter becomes aliased
into a frequency range which overlaps that of restingstate fluctuations. Our results suggest that the resting patterns, which
qualitatively resemble FMRI activation maps, are largely contained within grey matter and have a different spatial character
istic than ICA maps of major blood vessels. Finally, using data from 10 subjects, we have shown that restingstate patterns
are spatially consistent across subjects, clearly identifying networks of functional significance including areas such as visual,
sensory or motor cortex as being reproducibly found across subjects.
The above results do not necessarily imply that these spatial patterns are of neuronal origin; they might simply relate
to changes in local physiology such as fluctuations linked to local cytoarchitecture and/or local vasculature, which would
make RSNs of less interest to neuroscience. As an example, Wise et al. (2004) have demonstrated that large cortical areas
of the occipital, parietal and temporal lobes exhibit fluctuations which covary significantly with the endital level of exhaled
carbon dioxide. Further studies are require to characterise the extent to which these nonneuronal processes relate to the ICA
findings. The maps generated by the ICA group analysis separate these large areas into smaller networks, suggesting that,
while there might be a common underlying lowfrequency signal induced by vascular processes due to the arterial carbon
dioxide fluctuations, these networks have characteristic additional signal fluctuations which can be detected by ICA.
Regardless of their underlying cause, however, RSNs are a major source of structured nonmodelled noise in FMRI, and
as such deserve to be better understood. Not only do they contribute significantly to the residual variance (lowering sensitivity
to true activation), but because they often correlate temporally with experimental paradigm timings, can cause positive or
negative bias in the estimated activation (i.e, cause false positive or false negatives).
A limiting factor to the interpretability of PICAderived maps clearly stems from the fact that the FMRI BOLD signal is an
indirect measure of neuronal activity. The spatial sensitivity and specificity from using ICA on resting FMRI data, however,
is relatively high, which could be utilised for more advanced approaches, e.g. joint temporal and spatial exploratory data
decompositions such as those introduced by Mart´ ınezMontes et al. (2004), which simultaneously explain data from imaging
modalities with high temporal (EEG) and high spatial resolution (FMRI).
13
Page 14
6Acknowledgements
The authors wish to thank Heidi JohansenBerg and Tim Behrens for access to DWIderived thalamic connectivity data. The
authors gratefully acknowledge the financial support from the UK EPSRC, MRC and GlaxoSmithKline.
References
Alivisatos, B. and Milner, B. (1989). Effects of frontal or temporal lobectomy on the use of advance information in a choice
reaction task. Neuropsychologia, 27:495–503.
Beckmann, C., Noble, J., and Smith, S. (2001). Investigating the intrinsic dimensionality of FMRI data for ICA. In Seventh
Int. Conf. on Functional Mapping of the Human Brain.
Beckmann, C.andSmith, S.(2004). Probabilisticindependentcomponentanalysisforfunctionalmagneticresonanceimaging.
IEEE Trans. on Medical Imaging, 23(2):137–152.
Beckmann, C., Woolrich, M., and Smith, S. (2003). Gaussian / Gamma mixture modelling of ICA/GLM spatial maps. In
Ninth Int. Conf. on Functional Mapping of the Human Brain.
Behrens, T., JohansenBerg, H., Woolrich, M., Smith, S., WheelerKingshott, C., Boulby, P., Barker, G., Sillery, E., Sheehan,
K., Ciccarelli, O., Thompson, A., Brady, J., and Matthews, P. (2003). Noninvasive mapping of connections between human
thalamus and cortex using diffusion imaging. Nature Neuroscience, 6(7):750–757.
Bell, A. andSejnowski, T.(1995). Aninformationmaximisationapproachto blindseparation andblinddeconvolution. Neural
Computation, 7(6):1129–1159.
Biswal, B., Yetkin, F., V.M., H., and Hyde, J. (1995). Functional connectivity in the motor cortex of resting human brain using
echoplanar MRI. Magnetic Resonance in Medicine, 34:537–541.
Bullmore, E., Brammer, M., Williams, S., RabeHesketh, S., Janot, N., David, A., Mellers, J., Howard, R., and Sham,
P. (1996). Statistical methods of estimation and inference for functional MR image analysis. Magnetic Resonance in
Medicine, 35(2):261–277.
Calhoun, V., Adali, T., Pearlson, G., and Pekar, J. (2001). A method for making group inferences from functional MRI data
using independent component analysis. Human Brain Mapping, 14(3):140–151.
Comon, P. (1994). Independent component analysis – a new concept? Signal Processing, 36:287–314.
Constantinidis, C. and Steinmetz, M. (2001). Neuronal responses in area 7a to multiple stimulus displays: Ii. responses are
suppressed at the cued location. Cereb Cortex, 11(7):592–597.
De Luca, M., Beckmann, C., Behrens, T., Clare, S., Matthews, P., De Stefano, N., Woolrich, M., and Smith, S. (2002a).
Low frequency signals in FMRI  ”resting state networks” and the ”intensity normalisation problem”. In Proc. Int. Soc. of
Magnetic Resonance in Medicine.
De Luca, M., Beckmann, C., Clare, S., Behrens, T., De Stefano, N., Matthews, P., Woolrich, M., and Smith, S. (2002b).
Further investigations into ”resting state networks” and the ”intensity normalisation problem”. In Eighth Int. Conf. on
Functional Mapping of the Human Brain.
DeLuca, M., Beckmann, C., Clare, S., Matthews, P., De Stefano, N., and Smith, S. (2004). Investigations of resting state
networks in FMRI. in preparation.
Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm
(with discussion). Journal of the Royal Statistical Society Series B, 39:1–38.
Everson, R. and Roberts, S. (2000). Inferring the eigenvalues of covariance matrices from limited, noisy data. IEEE Transac
tions on Signal Processing, 48(7):2083–2091.
Friston, K. (1998). Modes or models: A critique on independent component analysis for fMRI. Trends in Cognitive Sciences,
2(10):373–5.
Friston, K. (2002). Functional integration and inference in the brain. Prog. Neurobiol., 68(2):113–143.
14
Page 15
Goldman, R. and Cohen, M. (2003). Tomographic distribution of resting alpha rhythm sources revealed by independent
component analysis. In Ninth Int. Conf. on Functional Mapping of the Human Brain.
Goldman, R., Stern, J., Engel, J., and M, C. (2002). Simultaneous EEG and fMRI of the alpha rhythm. NeuroReport,
18:2487–92.
Greicius, M.D., Krasnow, B., Reiss, A.L., and Menon, V. (2003). Functinal connectivity in the resting brain: A network
analysis of the default mode hypothesis. PNAS, 100(1):253–258.
Greicius, M.D., Srivastava, G., Reiss, A.L., and Menon, V. (2004). Defaultmode network activity distinguishes alzheimer’s
disease from healthy aging: Evidence from functional MRI. PNAS, 101(13):4637–4642.
Gusnard, D. and Raichle, M. (2001). Searching for a baseline: Functional imaging and the resting human brain. Nature
Review, Neuroscience, 2:685–92.
Habeck, C., Rakitin, B., Moeller, J., Scarmeas, N., Zarahn, E., Brown, T., and Stern, Y. (2004). An eventrelated fmri study
of the neurobehavioral impact of sleep deprivation on performance of a delayedmatchtosample task. Cognitive Brain
Research, 18:306–321.
Hartvig, N. and Jensen, J. (2000). Spatial mixture modelling of fMRI data. Human Brain Mapping, 11(4):233–248.
Hyv¨ arinen, A. and Oja, E. (1997). A fast fixedpoint algorithm for independent component analysis. Neural Computation,
9(7):1483–1492.
Jenkinson, M., Bannister, P., Brady, J., and Smith, S. (2002). Improved optimisation for the robust and accurate linear
registration and motion correction of brain images. NeuroImage, 17(2):825–841.
Jenkinson, M. and Smith, S. (2001). A global optimisation method for robust affine registration of brain images. Medical
Image Analysis, 5(2):143–156.
JohansenBerg, H., Behrens, T., Sillery, E., Ciccarelli, O., Thompson, A., S.M., S., and Matthews, P. (2004). Functional
anatomical validation and individual variation of diffusion tractographybased segmentation of the human thalamus. Cereb
Cortex, in print.
Johnstone, I. (2000). On the distribution of the largest principal component. Technical report, Department of Statistics,
Stanford University.
Kiviniemi, V., Kantola, J.H., Jauhiainen, J., Hyv¨ arinen, A., and Tervonen, O. (2003). Independent component analysis of
nondetermistic fMRI signal sources. NeuroImage, 19(2):253–260.
Koski, L., Paus, T., and Petrides, M. (1998). Directed attention after unilateral frontal excisions in humans. Neuropsychologia,
36:1363–1371.
Kr¨ uger, G. and Glover, G.H. (2001). Physiological noise in oxygenationsensitive magnetic resonance imaging. Magnetic
Resonance in Medicine, 46:631–637.
Lowe, M., Mock, B. J., and Sorensen,J.A. (1998). Functional connectivity in single and multislice echoplanar imaging using
restingstate fluctuations. NeuroImage, 7(2):119–132.
Maguire, E. (2001). The retrosplenial contribution to human navigation: a review of lesion and neuroimaging findings. Scand.
J. Psychol., 42(3):225–238.
Mart´ ınezMontes, E., Vald´ esSosa, P., Miwakeichi, F., Goldman, R., and Cohen, M. (2004). Concurrent eeg/fmri analysis by
multiway partial least squares. NeuroImage, 22(3):1023–1034.
Mazoyer, B., Zago, L., Bricogne, S., Etard, O., Houde, O., Crivello, F., Joliot, M., Petit, L., and TzourioMazoyer, N. (2001).
Cortical networks for working memory and executive functions sustain the cnscious resting state in man. Brain Research
Bullettin, 54(3):287–98.
McKeown, M.J., Makeig, S., Brown, G. G., Jung, T. P., Kindermann, S. S., Bell, A. J., and Sejnowski, T. J. (1998). Analysis
of fMRI data by blind separation into independent spatial components. Human Brain Mapping, 6(3):160–88.
Mesulam, M.M. (1981). A cortical network for directed attention and unilateral neglect. Annals of Neurology, 10:309–325.
15
Page 16
Miller, E. and Cohen, J. (2001). An integrative theory of prefrontal cortex function. Annual Review of Neuroscience, 24:167–
202.
Minka, T. (2000). Automatic choice of dimensionality for PCA. Technical Report 514, MIT Media Lab.
Obrig, H., Neufang, M., Wenzel, R., Kohl, M., Steinbrink, J., Einhaupl, K., and Villringer, A. (2000). Spontaneous low
frequency oscillations of cerebral hemodynamics and metabolism in human adults. NeuroImage, 12(6):623–639.
Petersen, K., Hansen, L., Kolenda, T., Rostrup, E., and Strother, S. (2000). On the independent components of functional
neuroimages. In Second Int. Symp. on Independent Component Analysis and Blind Signal Separation, 615–620.
Petrides, M. and Pandya, D. (2002). Association pathways of the prefrontal cortex and functional observations. In Stuss, D.
and Knight, R., editors, Principles of Frontal Lobe Function, pages 31–50. Oxford University Press.
Posner, M.I., Walker, J.A., Friedrich, F.J., and Rafal, R.D. (1984). Effects of parietal injury on covert orienting of attention.
Journal of Neuroscience, 4:1863–1874.
Rademacher, J., Morosan, P., Schormann, T., Schleicher, A., Werner, C., Freund, H.J., and Zilles, K. (2001). Probabilistic
Mapping and Volume Measurement of Human Primary Auditory Cortex. NeuroImage, 13(4):669–683.
Raichle, M., MacLeod, A., Snyder, A., Powers, W., and Gusnard, D. (2001). A default mode of brain function. PNAS,
98(2)676–682.
Rivier, F.andClarke, S.(1997). Cytochromeoxidase, acetylcholinesterase, andnadphdiaphorasestaininginhumansupratem
poral and insular cortex: Evidence for multiple auditory areas. NeuroImage, 6(4):288–304.
Roberts, S.andEverson, R., editors(2001). IndependentComponentAnalysis: PrinciplesandPractice. CambridgeUniversity
Press.
Rushworth, M., Walton, M., Kennerley, S., and Bannerman, D. (2004). Action sets and decisions in the medial frontal cortex.
Trends Cogn. Sci., 8(9):410–417.
Shulman, G., Fiez, J., Corbetta, M., Buckner, R., Miezin, F. M., Raichle, M., and Petersen, S. (1997). Common blood flow
changes across visual task: Ii. decreases in cerebral cortex. Journal of Cognitive Neuroscience, 9(5):648–63.
Smith, S.M. (2002). Fast robust automated brain extraction. Human Brain Mapping, 17(3):143–155.
Tipping, M. and Bishop, C. (1999). Mixtures of probabilistic principal component analyzers. Neural Computation, 11(2):443–
482.
Wise, R., Ide, K., Poulin, M.J., and Tracey, I. (2004). Resting fluctuations in arterial carbon dioxide induce significant low
frequency variations in bold signal. NeuroImage, 21(4):1652–1664.
Woolrich, M., Ripley, B.D., Brady, M., and Smith, S.M. (2001). Temporal autocorrelation in univariate linear modelling of
FMRI data. NeuroImage, 14(6):1370–1386.
Xiong, J., Parsons, L.M., Gao, J.H., and Fox, P.T. (1999). Interregional connectivity to primary motor cortex revealed using
MRI resting state images. Human Brain Mapping, 8(23):151–156.
16