# Contribution of Exploratory Methods to the Investigation  of Extended Large-Scale Brain Networks in Functional MRI: Methodologies, Results, and Challenges

Authors: V. Perlbarg; G. Marrelec
Journal: International Journal of Biomedical Imaging
 (2008)

---

## Abstract

A large-scale brain network can be defined as a set of segregated and integrated
regions, that is, distant regions that share strong anatomical connections
and functional interactions. Data-driven investigation of such networks has
recently received a great deal of attention in blood-oxygen-level-dependent
(BOLD) functional magnetic resonance imaging (fMRI). We here review the
rationale for such an investigation, the methods used, the results obtained,
and also discuss some issues that have to be faced for an efficient exploration.


---

## Body

## 1. Introduction

Blood-oxygen-level-dependent (BOLD) functional magnetic
resonance imaging (fMRI) is an imaging technique that makes it possible to
dynamically and noninvasively track metabolic and hemodynamic changes in the
brain [1, 2]. The
early developments of BOLD fMRI data analysis have mostly relied on a method
called general linear model (GLM), whose objective is to pinpoint the differential
involvement of certain regions during various tasks [3–5].
Voxel clusters that exhibited such a behavior are declared “activated” and
gathered into a so-called activation map that provides the output of the GLM
approach; each map represents all regions that are significantly correlated
with the stimulus time course. GLM-based methods have been extensively used in
order to extract regions in a wide variety of conditions (see, e.g., [6] for a review of activation
studies related to the premotor cortex).The GLM,
however, does not properly render the brain's intricate organization, which is
believed to be based on two major principles: segregation and integration [7, 8]. According to these
two principles, functional tasks are performed by specific collections of brain
regions, also called networks, that are anatomically connected and can engage
in complex interactions [9–11]. Even though the BOLD contrast is only remotely related
to neuronal activity, it was first hypothesized, and then evidenced, that this
imaging modality is able to reflect, at least to some extent, the strong
constraints imposed on the brain by segregation and integration. This
realization came from the investigation of the (misleadingly called) “rest”
condition. First, studies showed that brain regions could still be correlated
at rest, hinting for the existence of functional brain networks that could still
be present and imaged even when no task was explicitly required from the
subject [12, 13].
Network investigation also started with a closer examination of the
“baseline,” that is, the signal measured when a subject is in the “rest” condition
of a protocol, between two task conditions [14]. This approach was justified from the fact that, from an
energetic perspective, the brain uses a significant part of the body's energy,
independently of the presence or absence of a “task” [15, 16]. As methods of
increasing complexity were developed and validated, the objective of many
methodological developments shifted from GLM-related procedures to methods that
were able to extract networks from BOLD fMRI data.This paper is
an attempt to review the latest advances in investigation of extended
large-scale networks in fMRI from a methodological perspective, as well as the
networks that have been found using these methods. This new methodology, if
confirmed, has very deep implications in terms of methods that should be
developed, and we discuss some of the issues that such methods will have to
deal with in order to provide reliable and useful results.


## 2. Large-Scale Networks as a Consequence of Brain Organization

An extended large-scale functional brain network may
be defined as a (potentially large) number of segregated regions (potentially
spread over the whole brain) that interact in order to execute a coherent task.
While Bressler and Tognoli [17] mostly consider
“high-level brain functions of which cognition is comprised,” it is important
to emphasize the fact that about any function that the brain is able to process
is likely to have a network representation (see, e.g., Section 4 for a
description of some low-level brain functions, such as vision and audition
processing).Large-scale
networks share many important features. First, they are widely distributed over
the brain. As a consequence of the segregation principle, it is hypothesized
that they can be broken down into small brain regions, coined “nodes” by Mesulam [18], “units” by Marrelec et al.
[19], and “local cortical area
networks” by Bressler and Tognoli [17], each
region being characterized by a consistent functional behavior. Such nodes can
readily be identified in subcortical structures, which are often gathered into
nuclei [20]. As to the cortex,
despite cytoarchitectonic features (embodied, e.g., by the
work of   Brodmann [21] and his eponymous regions)
that vary across its surface, its parcellation based on structural criteria
alone remains globally a challenge. Nonetheless, local brain areas are also
strongly characterized by their function [17]. For instance, primary sensory regions (e.g., visual) have
been localized in a quite reproducible manner; within these regions, areas
responding more specifically to certain types of inputs have been successfully
identified (e.g., vertical versus horizontal lines in the primary visual
cortex [22]). Still, even though
various levels of specialization can usually be observed, there is a general
agreement that most regions cannot be unambiguously associated with one
specific function (see, e.g., [23] for Broca's area) and, in general, a region will exhibit a
certain level of “multifunctionality” [17]: its contribution will not be limited to one task but will
be allowed to vary within a given range of functions that it is able to
implement.As a
consequence of the integration principle, large-scale networks are also
characterized by potentially distant regions with strong (anatomical)
connections and (functional) interactions. Whether top-down or bottom-up,
serial or parallel, connections and interactions are quintessential of
networks [18, 24, 25].
Anatomically, interregional connectivity is suspected to be rather sparse [26–30]. Even though most connections originating from one
region are thought to re-enter the same region, axons are known to connect
regions that are far apart from each other, for example, homologue regions [e.g., [31–33]]. Functionally, these
connections have translations at all levels, from electrophysiology [34–38]
to measures of the electromagnetic field [39] and of the BOLD signal [12, 13].Whether coined
“new phrenology” [40] or
considered as being “beyond phrenology” [25], such an approach leads to a model of brain functions in
which most functional tasks are subserved by functional brain networks, that is,
collections of specialized regions that collaborate in order to generate a
coherent behavior [11, 36]. In support of this approach, several networks
have already been described and documented. Luria [10] refers to three blocks: one that “regulates the energy level
and tone of the cortex,” another one that is strongly implicated in
information processing, and a last one that is involved in higher, complex
tasks, such as “the formation of intentions and programs for behavior.” Mesulam [18] proposed two distinct
subdivisions of the brain. First, based on the co-occurrence of functions with
similar features, the brain can be divided into five major “subtypes”:
primary sensory-motor, unimodal association, heteromodal association,
paralimbic, and limbic. There are also at least five large-scale networks, each
dealing with a specific cognitive function: spatial awareness, language,
explicit memory/emotion, face-object recognition, and working memory-executive
function. These networks are not isolated from one another, but interact in
very complex fashion, for example, through “transmodal” areas.


## 3. fMRI Investigation of Large-Scale Networks

Relying on the assumption that BOLD fMRI is indeed
able to image brain networks (see, e.g., [15] for a review of the neurophysiological substrate of
neuroimaging), two categories of methods may be identified for such studies:
approaches that make use of prior cognitive information and fully exploratory
methods.


### 3.1. Using Neurocognitive Information

Correlational methods were historically the first ones
to be applied to investigate large-scale networks in fMRI data analysis, in the
form of functional connectivity studies and functional connectivity maps [12, 41–47]. Starting
from a voxel or region—the so-called “seed” voxel/region—one extracts all
voxels whose time courses are significantly correlated with that of the seed.
Measures other than temporal correlation have also been used, such as coherence
and partial coherence [48, 49]. Selection of the seed region is a key issue in studies of functional
connectivity. First, a brain region is selected according to its function
(e.g., cortical representation for hand movement, [47]). The corresponding seed is then
obtained from either prior anatomical knowledge or functional manipulation.
Anatomically, common approaches consist of using coordinates in a standardized
space (Talairach or MNI) [44], or
having an expert delineate the region on anatomical images [48]. Functionally, the seed can be obtained
from an activation map, provided that the region of interest can be
characterized by its implication in a specific task (e.g., the primary motor
cortex in a simple movement) [41, 45, 47].As opposed to
effective connectivity—where Gonçlaves and Hall [50] showed that results of SEM analyses may vary depending on
the choice of the seed voxel—robustness of functional connectivity maps with
regard to the selection of the seed region and its spatial extent have barely
been examined yet. Vincent et al. [51] showed
that, for the visual or the somatomotor network, the resulting functional
connectivity map was robust to the choice of the starting seed region. Many
other parameters (e.g., design, size of each region) may have an influence on
the outcome of the analysis, potentially leading to different spatial
structures or correlation values between structures. Full exploration of a
whole network (i.e., with many regions) would imply the recourse to several
successive computations of functional connectivity maps, each map being used to
select a region significantly correlated as seed voxel for the next step—a
procedure that is lengthy, complex, and whose convergence is not assured. Wang and Xia [52] have recently proposed a method
to perform this exploration in only one step.


### 3.2. Blind Exploration

The goal of fully exploratory methods is to provide
data-driven approaches of large-scale network detection in which no prior
cognitive information is required for the methods to proceed. A number of such
procedures have been proposed, most of them relying more or less closely on
either of the two key features of large-scale networks, namely integration and
segregation.The vast
majority of approaches proceed as follows. Based on a similarity measure, they
gather voxels irrespective of their anatomical proximity (and, hence, of
segregation) into separate classes that are strongly similar to each other and
dissimilar from one another. For each class, the output is a map representative
of the class and an associated time course. All methods have one or several
parameters whose tuning affects the number of classes. Since each class tends
to gather voxels that are strongly correlated, it is often univocally
identified with a large-scale network. Blind approaches include methods based
on eigenvalue decomposition, such as principal component analysis (PCA) [53–55], correlation
clustering [56], Kendall's
coefficient of concordance [57, 58], K-means [59, 60], fuzzy clustering
methods [54, 56], self-organizing map algorithms [61], Kohonen clustering neural
network and fuzzy C-means [62],
hierarchical clustering [60, 63],
integration and information-theoretic quantities [64, 65], and spatial
independent component analysis (sICA) [66]. While most methods provide maps that are exclusive (a
voxel can only belong to one map), a few (e.g., fuzzy clustering or ICA)
provide an index of the plausibility for a voxel to belong to each of the
different classes. Most methods also provide local criteria, calling for
stepwise analyses, at the exception of PCA and ICA that use global measures
and, consequently, are able to perform classification in one step.Most approaches
mentioned in the previous paragraph have only been used a limited number of
time in fMRI data analysis so far. This can probably be accounted for by the
complexity of their algorithms, which is commensurate with the difficulty of
the task at hand. Outstandingly, sICA has been used quite a lot recently, with
results that are rather promising. Regardless of its popularity, though, the
network interpretation of the results obtained needs to be proved beyond simple
criteria (these include, e.g., that voxels located close to each other or in
homologue regions tend to belong to the same class). For instance, for
PCA, Friston and Büchel [67] mention that the
interpretation of the eigenimages in biological terms might be dubious, since
they could be rotated in the data space and still be a solution to the problem
(but see [68]). By contrast,
components obtained through ICA can be more easily related to known
physiological noises or functional processes [66, 69]. The methodological reasons for this success
are, however, still not clear, and many explanations are plausible: the
relevance of the assumption of spatial independence, the adequacy of the
underlying mixing model, the efficiency of the global criterion/one-step
discrimination approach, or some interesting feature of the
information-theoretic optimization algorithm. In any case, the fact that its
application simplifies the results to a maximum and produces a very limited
number of widespread networks, making interpretation easier, clearly plays in
its favor (compare, e.g., with [70, 71], or [72]). Its sensitivity, which
is much higher than that of clustering methods, might also explain its success.
Nevertheless, it must still be kept in mind that the assumptions underlying ICA
(perfect synchrony within a network and spatial independence between networks)
impose an extreme and unrealistic case of integration. While the simplification
of several time courses into one is performed only once for ICA, the stepwise
procedures implemented by other methods essentially go through the same
approximation at each step, leading to an error that is probably far larger.Unlike the
numerous approaches to functional integration, few methods have specifically
sought to extract segregated regions. Some methods decrease the complexity of
the data by using predefined regions (e.g., according to the Tzourio-Mazoyer et al. [81] template). Approaches
using predefinite regions do not check that all voxels within a region exhibit
homogeneous bahaviors; they merely assume that it is the case. Average signals
are then extracted from each region, on which any integration-based approach,
such as hierarchical clustering [71, 72], can be applied. Intuitively, many
clustering methods mentioned previously (e.g., K-means, hierarchical
clustering, or information-theoretic measures) could easily be applied for the
purpose of detecting segregated regions by incorporating a constraint of
contiguity between voxels that could be merged. Among these, only the
information-theoretic approach explicitly takes both within- and
between-classes measures of similarity into account. Specifically, they optimize
a so-called functional clustering index (FCI) that keeps a balance between
region homogeneity (strong segregation) and sparseness of inter-regional
interactions (low integration) [64, 65]—the latter constraint being hard to justify
from a network perspective. As to other clustering methods, as noted by Goutte et al. [60] in accordance to Huygens'
formula, maximizing a measure of the internal coherence of a class (associated
with segregation) is often equivalent to minimizing the same measure of
coherence but computed between classes (that could be associated with
integration). As such, the behavior of such methods with regard to networks
would again lead to questioning.A tentative
approach to consider simultaneously segregation and integration has been
conducted by the large scale
network identification (LSNI) method by Bellec et al. [80]. LSNI first clusters neighboring voxels
into small regions using a region-growing algorithm [82] and then selects regions that
exhibit a significant correlation with other distant regions. Such a procedure
allows to define brain functional regions and networks in a purely data-driven
way. While the sensitivity of the algorithm proposed was rather low, it had the
great advantage to explicitly define and address the two principles of
functional segregation and integration. So far, this method seems adapted for
individual analyses; its extension to group studies seems limited due to the
subject-dependent definition of regions.


### 4. Typology of Networks Extracted with fMRI

During the last decade, several brain systems have
been studied in fMRI using functional connectivity-related approaches. These
studies have revealed integrated systems, including primary systems and
associative networks. Exploratory approaches have also allowed to extract
several functional networks at once. Even if all brain areas are not included
in a network, these networks involve many areas and constitute a possible
functional parcellation of the brain.The motor
network was the first network studied through functional connectivity
analyses. Biswal et al. [12] reported
correlations in low-frequency resting-state fluctuations between left and right
motor areas using single-slice fast-sampled acquisitions. This result was later
reproduced with multislice acquisitions where an extended motor network was
shown to correlate with a region in the primary motor cortex [44, 47]. Lowe et al. [44] showed that other functional networks
could be detected using other seed regions, namely the visual network with a
seed around the calcarine fissure and a limbic network with a seed in the
amygdala. An auditory and a language systems were later extracted in the same
way [41, 43]. Other
networks were also studied using the seed-region functional connectivity
approach, such as the default-mode network [83–86], the attentional
networks [42, 83, 87], and memory networks [46, 88].More
recently, a larger number of functional networks were revealed using
exploratory methods based on ICA [76–78]. Even if the number of
extracted networks varied, their spatial organizations were reproducible across
studies. For instance, all three studies just mentioned found functional
networks involving the same systems that were sometimes split into different
parts (e.g., left/right, rostral/caudal). Using group ICA studies of
resting-state datasets [76–78], which were the most reproducible, we selected
seven functional networks: a motor/sensorimotor system, a visual system, an
auditory system, a default-mode network, a dorsal attentional network, a
ventral attentional network, and an executive control network. Van de ven et al. [75] systematically studied the
reproducibility of ICA results on individual datasets and the results using
hierarchical clustering [63] and
self-organizing map algorithm (SOM) [61] were presented on an individual level. The results from
studies that provided a systematic description of all networks found are
reported in Table 1.
In Figure 1 and Table 2, we also reported results from a study on a
population of 20 healthy subjects acquired at rest, where networks were
extracted using spatial ICA and a hierarchical clustering approach similar to that of Esposito et al. [79].Table 1
Literature
summary of the different networks found in network investigation of fMRI data.
Methods—HC: hierarchical clustering, SOM: self-organizing map algorithm, ICA:
independent component analysis. Networks—M/SM: motor/sensorimotor, V: visual,
A: auditory, DM: default mode, dAtt: dorsal attentional, vAtt: ventral
attentional, EC: executive control. Networks found are denoted by “X.” (*) In
addition to primary cortices (sensorimotor, visual, and auditory), the clusters
shown by Cordes et al. [63] were essentially
bilateral single regions (thalami, fusiform gyri, and frontal gyri) which were
parts of different networks of reference. (†) Except for
the sensorimotor system, the networks identified by
Peltier et al. [61] were not properly labeled; the
spatial organizations of the maps shown seemed similar to the attentional
networks. (‡) The results
presented by Calhoun et al. [73] were partial, mentioning the
extraction of other networks that they did not show neither comment; another
study on similar datasets showed that the sensorimotor and the dorsal
attentional networks might be detected too [74].
TaskReferenceMethodNetworkM/SMVADMdAttvAttECAt rest[61]HCXXXX(*)X(*)[63]SOMX(†)(†)[73]ICAXXXX[75]ICAXXXXXX[76]ICAXXXXXXX[77]ICAXXXXXBlocked visual[78]ICAX(‡)XXX(‡)[79]ICAXXXBlocked motor[80]LSNIXXXTable 2
Example of extended large-scale networks extracted in fMRI at rest. Peak foci corresponding to the six networks identified using spatial ICA and a hierarchical clustering
approach similar to that of [79] on a group of 20 healthy subjects
acquired at rest—M/SM: motor/sensorimotor, V: visual, DM: default mode, dAtt: dorsal attentional, vAtt: ventral attentional, EC: executive control.Table 2
Continued.Figure 1
Example of extended large-scale
networks extracted in fMRI at rest. The six networks were identified using
spatial ICA and a hierarchical clustering approach similar to that of [79] on a group of 20 healthy
subjects acquired at rest. Networks—M/SM: motor/sensorimotor, V: visual, DM:
default mode, dAtt: dorsal attentional, vAtt: ventral attentional, EC:
executive control. The auditory network was not found as a separate network but
some temporal regions of the primary auditory cortex are overlapped by other
networks (in particular the M/SM network and the two attentional networks). The
union of all networks does not add up to comprise the entire brain; for
instance, some parts of the frontal cortex do not belong to any reported networks.
By contrast, some brain regions simultaneously belong to several networks (in
black).The
sensorimotor system involves at least the pre- and postcentral gyri (including
the primary motor cortex and supplementary motor area). The visual system
involves both medial striate and extrastriate regions (calcarine sulcus and
lingual gyrus), as well as lateral occipital regions (nonprimary visual
regions); these two visual networks (primary and associative) were identified
separately by the three group-ICA studies. The auditory system involves
principally lateral superior temporal gyri, the Heschl's gyrus and insular
cortex. The so-called default-mode network involves the anterior and posterior
cingulate cortices, the medial prefrontal cortex and lateral parietal
regions [15, 89–91]. The dorsal attentional network involves lateral
prefrontal and dorsal partietal cortex; these regions are involved in
visio-spatial control [42, 92, 93]. The ventral attentional network involves inferior
occipito-parietal regions and inferior lateral prefrontal regions; these regions
are principally involved in new item recognition [42, 94]. Last, the executive
control network involves superior and middle prefrontal cortices, ventrolateral
prefrontal cortex and anterior cingulate gyrus [95].Other studies have
applied these exploratory approaches to extract integrated functional networks
from fMRI datasets acquired during external stimulation [73, 79, 80]. The results
of these three studies are also compiled in Table 1. These results showed that
the detection  of the functional networks not directly related to the
stimulation were less sensitive than that without
external stimulation.


## 3.1. Using Neurocognitive Information

Correlational methods were historically the first ones
to be applied to investigate large-scale networks in fMRI data analysis, in the
form of functional connectivity studies and functional connectivity maps [12, 41–47]. Starting
from a voxel or region—the so-called “seed” voxel/region—one extracts all
voxels whose time courses are significantly correlated with that of the seed.
Measures other than temporal correlation have also been used, such as coherence
and partial coherence [48, 49]. Selection of the seed region is a key issue in studies of functional
connectivity. First, a brain region is selected according to its function
(e.g., cortical representation for hand movement, [47]). The corresponding seed is then
obtained from either prior anatomical knowledge or functional manipulation.
Anatomically, common approaches consist of using coordinates in a standardized
space (Talairach or MNI) [44], or
having an expert delineate the region on anatomical images [48]. Functionally, the seed can be obtained
from an activation map, provided that the region of interest can be
characterized by its implication in a specific task (e.g., the primary motor
cortex in a simple movement) [41, 45, 47].As opposed to
effective connectivity—where Gonçlaves and Hall [50] showed that results of SEM analyses may vary depending on
the choice of the seed voxel—robustness of functional connectivity maps with
regard to the selection of the seed region and its spatial extent have barely
been examined yet. Vincent et al. [51] showed
that, for the visual or the somatomotor network, the resulting functional
connectivity map was robust to the choice of the starting seed region. Many
other parameters (e.g., design, size of each region) may have an influence on
the outcome of the analysis, potentially leading to different spatial
structures or correlation values between structures. Full exploration of a
whole network (i.e., with many regions) would imply the recourse to several
successive computations of functional connectivity maps, each map being used to
select a region significantly correlated as seed voxel for the next step—a
procedure that is lengthy, complex, and whose convergence is not assured. Wang and Xia [52] have recently proposed a method
to perform this exploration in only one step.


## 3.2. Blind Exploration

The goal of fully exploratory methods is to provide
data-driven approaches of large-scale network detection in which no prior
cognitive information is required for the methods to proceed. A number of such
procedures have been proposed, most of them relying more or less closely on
either of the two key features of large-scale networks, namely integration and
segregation.The vast
majority of approaches proceed as follows. Based on a similarity measure, they
gather voxels irrespective of their anatomical proximity (and, hence, of
segregation) into separate classes that are strongly similar to each other and
dissimilar from one another. For each class, the output is a map representative
of the class and an associated time course. All methods have one or several
parameters whose tuning affects the number of classes. Since each class tends
to gather voxels that are strongly correlated, it is often univocally
identified with a large-scale network. Blind approaches include methods based
on eigenvalue decomposition, such as principal component analysis (PCA) [53–55], correlation
clustering [56], Kendall's
coefficient of concordance [57, 58], K-means [59, 60], fuzzy clustering
methods [54, 56], self-organizing map algorithms [61], Kohonen clustering neural
network and fuzzy C-means [62],
hierarchical clustering [60, 63],
integration and information-theoretic quantities [64, 65], and spatial
independent component analysis (sICA) [66]. While most methods provide maps that are exclusive (a
voxel can only belong to one map), a few (e.g., fuzzy clustering or ICA)
provide an index of the plausibility for a voxel to belong to each of the
different classes. Most methods also provide local criteria, calling for
stepwise analyses, at the exception of PCA and ICA that use global measures
and, consequently, are able to perform classification in one step.Most approaches
mentioned in the previous paragraph have only been used a limited number of
time in fMRI data analysis so far. This can probably be accounted for by the
complexity of their algorithms, which is commensurate with the difficulty of
the task at hand. Outstandingly, sICA has been used quite a lot recently, with
results that are rather promising. Regardless of its popularity, though, the
network interpretation of the results obtained needs to be proved beyond simple
criteria (these include, e.g., that voxels located close to each other or in
homologue regions tend to belong to the same class). For instance, for
PCA, Friston and Büchel [67] mention that the
interpretation of the eigenimages in biological terms might be dubious, since
they could be rotated in the data space and still be a solution to the problem
(but see [68]). By contrast,
components obtained through ICA can be more easily related to known
physiological noises or functional processes [66, 69]. The methodological reasons for this success
are, however, still not clear, and many explanations are plausible: the
relevance of the assumption of spatial independence, the adequacy of the
underlying mixing model, the efficiency of the global criterion/one-step
discrimination approach, or some interesting feature of the
information-theoretic optimization algorithm. In any case, the fact that its
application simplifies the results to a maximum and produces a very limited
number of widespread networks, making interpretation easier, clearly plays in
its favor (compare, e.g., with [70, 71], or [72]). Its sensitivity, which
is much higher than that of clustering methods, might also explain its success.
Nevertheless, it must still be kept in mind that the assumptions underlying ICA
(perfect synchrony within a network and spatial independence between networks)
impose an extreme and unrealistic case of integration. While the simplification
of several time courses into one is performed only once for ICA, the stepwise
procedures implemented by other methods essentially go through the same
approximation at each step, leading to an error that is probably far larger.Unlike the
numerous approaches to functional integration, few methods have specifically
sought to extract segregated regions. Some methods decrease the complexity of
the data by using predefined regions (e.g., according to the Tzourio-Mazoyer et al. [81] template). Approaches
using predefinite regions do not check that all voxels within a region exhibit
homogeneous bahaviors; they merely assume that it is the case. Average signals
are then extracted from each region, on which any integration-based approach,
such as hierarchical clustering [71, 72], can be applied. Intuitively, many
clustering methods mentioned previously (e.g., K-means, hierarchical
clustering, or information-theoretic measures) could easily be applied for the
purpose of detecting segregated regions by incorporating a constraint of
contiguity between voxels that could be merged. Among these, only the
information-theoretic approach explicitly takes both within- and
between-classes measures of similarity into account. Specifically, they optimize
a so-called functional clustering index (FCI) that keeps a balance between
region homogeneity (strong segregation) and sparseness of inter-regional
interactions (low integration) [64, 65]—the latter constraint being hard to justify
from a network perspective. As to other clustering methods, as noted by Goutte et al. [60] in accordance to Huygens'
formula, maximizing a measure of the internal coherence of a class (associated
with segregation) is often equivalent to minimizing the same measure of
coherence but computed between classes (that could be associated with
integration). As such, the behavior of such methods with regard to networks
would again lead to questioning.A tentative
approach to consider simultaneously segregation and integration has been
conducted by the large scale
network identification (LSNI) method by Bellec et al. [80]. LSNI first clusters neighboring voxels
into small regions using a region-growing algorithm [82] and then selects regions that
exhibit a significant correlation with other distant regions. Such a procedure
allows to define brain functional regions and networks in a purely data-driven
way. While the sensitivity of the algorithm proposed was rather low, it had the
great advantage to explicitly define and address the two principles of
functional segregation and integration. So far, this method seems adapted for
individual analyses; its extension to group studies seems limited due to the
subject-dependent definition of regions.


## 4. Typology of Networks Extracted with fMRI

During the last decade, several brain systems have
been studied in fMRI using functional connectivity-related approaches. These
studies have revealed integrated systems, including primary systems and
associative networks. Exploratory approaches have also allowed to extract
several functional networks at once. Even if all brain areas are not included
in a network, these networks involve many areas and constitute a possible
functional parcellation of the brain.The motor
network was the first network studied through functional connectivity
analyses. Biswal et al. [12] reported
correlations in low-frequency resting-state fluctuations between left and right
motor areas using single-slice fast-sampled acquisitions. This result was later
reproduced with multislice acquisitions where an extended motor network was
shown to correlate with a region in the primary motor cortex [44, 47]. Lowe et al. [44] showed that other functional networks
could be detected using other seed regions, namely the visual network with a
seed around the calcarine fissure and a limbic network with a seed in the
amygdala. An auditory and a language systems were later extracted in the same
way [41, 43]. Other
networks were also studied using the seed-region functional connectivity
approach, such as the default-mode network [83–86], the attentional
networks [42, 83, 87], and memory networks [46, 88].More
recently, a larger number of functional networks were revealed using
exploratory methods based on ICA [76–78]. Even if the number of
extracted networks varied, their spatial organizations were reproducible across
studies. For instance, all three studies just mentioned found functional
networks involving the same systems that were sometimes split into different
parts (e.g., left/right, rostral/caudal). Using group ICA studies of
resting-state datasets [76–78], which were the most reproducible, we selected
seven functional networks: a motor/sensorimotor system, a visual system, an
auditory system, a default-mode network, a dorsal attentional network, a
ventral attentional network, and an executive control network. Van de ven et al. [75] systematically studied the
reproducibility of ICA results on individual datasets and the results using
hierarchical clustering [63] and
self-organizing map algorithm (SOM) [61] were presented on an individual level. The results from
studies that provided a systematic description of all networks found are
reported in Table 1.
In Figure 1 and Table 2, we also reported results from a study on a
population of 20 healthy subjects acquired at rest, where networks were
extracted using spatial ICA and a hierarchical clustering approach similar to that of Esposito et al. [79].Table 1
Literature
summary of the different networks found in network investigation of fMRI data.
Methods—HC: hierarchical clustering, SOM: self-organizing map algorithm, ICA:
independent component analysis. Networks—M/SM: motor/sensorimotor, V: visual,
A: auditory, DM: default mode, dAtt: dorsal attentional, vAtt: ventral
attentional, EC: executive control. Networks found are denoted by “X.” (*) In
addition to primary cortices (sensorimotor, visual, and auditory), the clusters
shown by Cordes et al. [63] were essentially
bilateral single regions (thalami, fusiform gyri, and frontal gyri) which were
parts of different networks of reference. (†) Except for
the sensorimotor system, the networks identified by
Peltier et al. [61] were not properly labeled; the
spatial organizations of the maps shown seemed similar to the attentional
networks. (‡) The results
presented by Calhoun et al. [73] were partial, mentioning the
extraction of other networks that they did not show neither comment; another
study on similar datasets showed that the sensorimotor and the dorsal
attentional networks might be detected too [74].
TaskReferenceMethodNetworkM/SMVADMdAttvAttECAt rest[61]HCXXXX(*)X(*)[63]SOMX(†)(†)[73]ICAXXXX[75]ICAXXXXXX[76]ICAXXXXXXX[77]ICAXXXXXBlocked visual[78]ICAX(‡)XXX(‡)[79]ICAXXXBlocked motor[80]LSNIXXXTable 2
Example of extended large-scale networks extracted in fMRI at rest. Peak foci corresponding to the six networks identified using spatial ICA and a hierarchical clustering
approach similar to that of [79] on a group of 20 healthy subjects
acquired at rest—M/SM: motor/sensorimotor, V: visual, DM: default mode, dAtt: dorsal attentional, vAtt: ventral attentional, EC: executive control.Table 2
Continued.Figure 1
Example of extended large-scale
networks extracted in fMRI at rest. The six networks were identified using
spatial ICA and a hierarchical clustering approach similar to that of [79] on a group of 20 healthy
subjects acquired at rest. Networks—M/SM: motor/sensorimotor, V: visual, DM:
default mode, dAtt: dorsal attentional, vAtt: ventral attentional, EC:
executive control. The auditory network was not found as a separate network but
some temporal regions of the primary auditory cortex are overlapped by other
networks (in particular the M/SM network and the two attentional networks). The
union of all networks does not add up to comprise the entire brain; for
instance, some parts of the frontal cortex do not belong to any reported networks.
By contrast, some brain regions simultaneously belong to several networks (in
black).The
sensorimotor system involves at least the pre- and postcentral gyri (including
the primary motor cortex and supplementary motor area). The visual system
involves both medial striate and extrastriate regions (calcarine sulcus and
lingual gyrus), as well as lateral occipital regions (nonprimary visual
regions); these two visual networks (primary and associative) were identified
separately by the three group-ICA studies. The auditory system involves
principally lateral superior temporal gyri, the Heschl's gyrus and insular
cortex. The so-called default-mode network involves the anterior and posterior
cingulate cortices, the medial prefrontal cortex and lateral parietal
regions [15, 89–91]. The dorsal attentional network involves lateral
prefrontal and dorsal partietal cortex; these regions are involved in
visio-spatial control [42, 92, 93]. The ventral attentional network involves inferior
occipito-parietal regions and inferior lateral prefrontal regions; these regions
are principally involved in new item recognition [42, 94]. Last, the executive
control network involves superior and middle prefrontal cortices, ventrolateral
prefrontal cortex and anterior cingulate gyrus [95].Other studies have
applied these exploratory approaches to extract integrated functional networks
from fMRI datasets acquired during external stimulation [73, 79, 80]. The results
of these three studies are also compiled in Table 1. These results showed that
the detection  of the functional networks not directly related to the
stimulation were less sensitive than that without
external stimulation.


## 5. Future Issues

Tracking the presence of extended large-scale networks
in BOLD fMRI data raises many issues. We have here focused on some aspects
related to the neurocognitive aspects of networks, their identifiability by
fMRI, and the methodological questions raised by network analyses.


### 5.1. Neurocognitive Aspects

The major issue to be faced is arguably the very
definition of an extended large-scale brain network. Indeed, even though the
brain is far from being fully connected, any region is eventually connected to
any other regions if one takes polysynaptic connections into account.
Obviously, stating that the brain can be considered as one network is by no way
satisfying, no more than it is to say that each macrocolumn forms a networks by
itself. The strongly hierarchical nature of the brain's anatomical and
structural organization induces similar characteristics at all levels. As the
brain can be decomposed in networks, each network can in turn be further
partitioned into subnetworks, subnetworks into subsubnetworks, and so on.
Furthermore, even though there probably is a (potentially loose) relationship
between anatomical and functional organizations, it is still unknown how
functional integration and segregation are coded in anatomical terms. For the
exact same structural organization, it has been shown that networks can be
observed to break down as one discriminates different sets of functional tasks
or behaviors with increasing precision. For instance, the visual system can be
decomposed into a ventral and a dorsal stream [22]. These two subnetworks, albeit interacting, have very distinct
functions [42, 92, 96]. Similarly, the motor system can be further
separated into a cerebello-cortical and a basal-cortical loop with different
patterns of involvement [97, 98]. The difficulty to define a network does not
yield for primary networks only. For instance, it has been argued that the
fronto-parietal network could be further partitioned into two subnetworks
subserving attention and working memory, respectively, [99], while the working memory network
itself could be further broken down in two, with one subnetwork mediating
attentional selection and another one rather underlying language functions [100]. Networks are not exclusive from
each other either. Mesulam [18] refers
to transmodal nodes that connect various neurocognitive networks. For instance,
activation of some fronto-parietal regions is observed during different
cognitive tasks [101]; are these
regions transmodal or part of a subnetwork that has a specific function?
Similarly, the insular cortex is typically a multimodal association area that
is not specifically activated by auditory stimuli. However, as reported in
Section 4, recent papers have consistently classified it as belonging to a
so-called auditory system. As evidenced by Figure 1, there are also some
overlapping between networks, and voxels can be simultaneously classified as
belonging to different networks. What is the function of such regions? Could
this overlapping between networks be related to synchronization through distinct
frequency-bands [35]—if such
a phenomenon is indeed visible through fMRI BOLD imaging? Regarding the
influence of a task on a network, an issue that has not received much attention
yet, studies have shown that networks could indeed be influenced by the
processing of a task, either during the task [86] or even after it [102]. It is hence not unrealistic to suspect that processing of a
task might also modify the very structure of some networks.Another cogent
question is the relationship between networks as detected by fMRI data analyses
and those mentioned in the literature. Networks extracted from fMRI are the
consequence of the optimization of a mathematical criterion whose link to
neuroscience is, at the very least, not obvious. While some results have been
rather successfully related to the neurocognitive literature (e.g., attentional
network), other results are more complex to interpret. Some networks extracted
seem to share commonalities with some of the subtypes
described by Mesulam [18] (e.g., the motor network; cf.
Section 2), while others seem to be rather
related to  Mesulam [18]'s neurocognitive networks
(e.g., the attentional network). Besides, the union of all reported networks
(e.g., by sICA) does not include the whole brain. Some brain regions are then
excluded from the functional networks organization of the brain. Why so?
Globally, the criterion used for network extraction might make the methods
sensitive to some functions or types of connections. For instance, top-down and
bottom-up influences have distinct features [25, 34, 36–38].
Can they be detected equally well by existing methods?Apart from
these difficulties, there has also been evidence of variability across healthy
subjects [80, 103] that
could be explained by many factors, such as development and/or age [104, 105], and, in general, all
forms of plasticity [106, 107]. Pathologies, for example, stroke [108, 109] or tumors [110–113], render the issue
even more complex. Some studies have shown that certain pathologies can have
network-specific effects: behavioral deficits in spatial neglects for the
fronto-parietal network [114];
epilepsy [115] and Alzheimer's
disease [116] for the
default-mode network. Nonetheless, these results must be used with caution, for
it is not clear yet whether they truly reflect a change in neuronal properties
or, as, for example, in grade II glioma, a mere modification of the metabolic
and vascular properties of the surrounding tissues.


### 5.2. BOLD fMRI Imaging

Use of BOLD fMRI as a way to investigate large-scale
networks relies on three successive assumptions, namely, that information
exchanges between neurons is related to synchronies, synchronies to the BOLD
contrast, and the BOLD contrast to the fMRI data effectively measured.Synchronies are
the blueprint of communication between regions [17, 39, 117–120] and, as such, should be strongly related to large-scale networks.
A challenging issue is to determine the exact relationship between the spatial
distribution and interaction pattern of regions within a large-scale network on
the one hand and, on the other hand, the spatial and frequential distribution
of oscillations.Another issue
is the connection between neuronal activity/synchrony and the appearance of a
BOLD signal. While much still needs to be unraveled as to the connection
between neuronal synchronies and the BOLD signal, it now seems more and more
accepted that a sustained change in neuronal activity is likely to entail a
relative change in the BOLD level [121–124], even
though the exact relationship is expected to be rather complex [125].Still, the BOLD
signal is only a fraction of the total signal that is acquired in fMRI, a
signal that is not exempt from many kinds of artifacts [126–128]. In
particular, some physiological processes (e.g., cardiac, respiratory, or
movement-related) induce spurious effects that contaminate the BOLD signal in
the whole brain [129, 130].
Such artifacts are predominant in certain regions of the brain, such as the
basal arteries for cardiac activity or the interfaces between cerebrospinal
fluid pools and brain tissus for breathing and head movements. This
origin-dependent predilection implies a spatial structure of the noise. Some
network detection algorithms may hence recognize voxels influenced by the same
spatially structured artifact as meeting the requirement for strong temporal
coherence and, hence, assign them to a common structure. This feature has been
successfully used by ICA techniques to provide efficient noise separation and
removal techniques [66, 131, 132]. Yet, the issue arises when
structures induced by noise are wrongly interpreted as functional networks;
their detection and removal is hence of very high importance. The fundamental
question, while examining spatial structures with a similar temporal behavior,
is “do we measure neurally induced signal or consequences of physiological
processes [133]?” Even though our understanding of
the potential artifacts that can contaminate the BOLD fMRI signal improves, the
consequences of many potential sources of structured noise have barely been
mentioned, let alone investigated. For instance, it is believed that some
mechanisms related to the regulation of blood flow (e.g., through the level of
CO2 in the blood) could induce
coherent changes in BOLD signal throughout the brain—giving birth to an
effect likely to be identified as a functional network. In fact, such an effect
has been used to explain the presence of the default-mode network in fMRI [134, 135]. Now, whether these regions
are wrongfully classified as belonging to a common functional network because
their voxels are corrupted by the same artifact, or whether they are actually
regions that drive the physiological response is a matter that remains to be
solved.


### 5.3. Data Analysis

Many questions remain open regarding what
methodologies to apply to extract functional networks. We here quickly discuss
issues related to the choice of a model, the redundancy of fMRI signals, the
necessity to provide both individual and group analyses, the importance of
result representation, and the validation of fMRI results with other
modalities.Procedures used
to investigate networks are usually based on mathematical methods that have
been discovered independently of the field of fMRI data analysis. Their
behavior is hence not guided by cognitive but mathematical considerations.
While it can be accepted that most methods are general enough to be applied to
a wide variety of problems, they still require a careful assessment of how best
to adapt them to the issue at hand. We believe that the major point to cope
with here is “how do methods code for segregation and integration? Does it make
sense?” A relevant approach could be to try to derive out consistence
requirements from cognitive consideration of what an “ideal” method should be
able to do: quantify integration between voxels, regions, or networks using the
same principled measure (such as the multiple correlation coefficient [136] or integration [7, 137]);
differentiate between direct and indirect information exchanges (such as
partial correlation [19, 72, 138–141]);
discriminate causality from simple co-occurrence (such as Granger causality [138, 142–144]).
Some methods are able to deal with one aspect of the problem, but none has been
proposed to answer all these questions simultaneously.Besides,
investigation of large-scale networks face a very interesting problem, namely
that of determining the spatial precision under which data should be considered
as segregated and over which they should be said to be integrated. While it is
obvious that neighboring voxels share a great deal of information, methods that
model and summarize the behavior of a whole network with one single time course
clearly oversimplify the problem and discard a lot of cogent information. Bellec et al. [80] proposed a statistical model
that provides a critical distance that separates segregation and integration.
Voxel clustering is another attempt to deal with that issue. However, the
parameters that characterize the clustering coarseness are set a priori, when
they should be determined by the intrinsic properties of the data and allowed
to vary across the brain (e.g., between subcortical and cortical structures,
which have distinct characteristic spatial extents). This step allows one also
to reduce the dimensionality of the data. At least for this reason, it is a
crucial step, because network investigation requires multivariate analyses that
are computationally very demanding (the computational burden roughly
exponentialy increase with the number of regions).In
neurocomputing, models investigating issues very similar to that of large-scale
networks have already been developed [145–148]. However, most
methods developed so far for effective connectivity, such as structural
equation modeling (SEM) [149–152], dynamical causal modeling
(DCM) [153–155], or generative models—including neural mass models [145, 156] and large-scale
neural models [147, 157–159]—, have been of little use to the
investigation of extended large-scale networks, since their intrinsic
complexity prevent them from modeling systems with that many degrees of
freedom (but see, [160]).Methods
originating from graph and/or network theories might prove more adapted to such
problems [161–163],
since they provide global quantification of structures that, besides from being
ubiquitous [164, 165],
are not unlike some models of brain networks. Using such methods, brain
networks have been shown to exhibit small-world [70, 166–170] and scale-free [171, 172] features. The
fact that networks simultaneously exhibit both properties has strong
structural [104, 173] and
functional [174, 175] implications.Being able to
devise methods that can deal with both individual and group analyses is also an
important issue. At the individual level, it is essential to assess the
significance of the different networks [80, 85, 176]. With procedures of increasing
complexity, nonparametric resampling procedures [177], mostly used in the context of
the GLM so far [178], might be
appealing [179]. At the group level, one seeks to determine invariant networks across
subjects. This has been done by either considering a model for the group [76] or solving the problem at an
individual level and then performing clustering [79]. Validation of such methods have
to be developed; a first step in this direction has been proposed by Calhoun et al. [180].Once results
have been produced, representing the results becomes a key issue. Consider for
instance functional connectivity as measured by marginal correlation. Though
computationally tractable on a large-scale network ofN units, even for N large, such a
method generates N(N−1)/2 correlation
coefficients (e.g., 4950 for as few as 100 voxels/regions; 19900 for 200; 499 500 for 1000). Simply representing these on a graph as is commonly done [72, 140, 181]
would prove impossible to read, let alone to interpret. Procedures that
summarize the information have to be proposed; these can rely on PCA/MDS [71, 79, 182];
they could also use other representational techniques [183, 184].Last, but not
least, an essential point to validate and better understand the large-scale
network approach in fMRI is the comparison with results form other imaging
modalities or areas of neuroscience, such as electrophysiology [34–38], electroencephalography (EEG) or
magnetoencephalography (MEG) [39, 125, 185, 186], and diffusion
tensor imaging (DTI) [187–190]. To be able to efficiently
compare results from different imaging modalities, it is essential to better
understand how each modality images the activity of large-scale brain networks.
In this perspective, providing a unified generative and/or statistical model
for several of these modalities would be of the utmost importance, granting
access to multimodal in vivo imaging of the brain in action.


## 5.1. Neurocognitive Aspects

The major issue to be faced is arguably the very
definition of an extended large-scale brain network. Indeed, even though the
brain is far from being fully connected, any region is eventually connected to
any other regions if one takes polysynaptic connections into account.
Obviously, stating that the brain can be considered as one network is by no way
satisfying, no more than it is to say that each macrocolumn forms a networks by
itself. The strongly hierarchical nature of the brain's anatomical and
structural organization induces similar characteristics at all levels. As the
brain can be decomposed in networks, each network can in turn be further
partitioned into subnetworks, subnetworks into subsubnetworks, and so on.
Furthermore, even though there probably is a (potentially loose) relationship
between anatomical and functional organizations, it is still unknown how
functional integration and segregation are coded in anatomical terms. For the
exact same structural organization, it has been shown that networks can be
observed to break down as one discriminates different sets of functional tasks
or behaviors with increasing precision. For instance, the visual system can be
decomposed into a ventral and a dorsal stream [22]. These two subnetworks, albeit interacting, have very distinct
functions [42, 92, 96]. Similarly, the motor system can be further
separated into a cerebello-cortical and a basal-cortical loop with different
patterns of involvement [97, 98]. The difficulty to define a network does not
yield for primary networks only. For instance, it has been argued that the
fronto-parietal network could be further partitioned into two subnetworks
subserving attention and working memory, respectively, [99], while the working memory network
itself could be further broken down in two, with one subnetwork mediating
attentional selection and another one rather underlying language functions [100]. Networks are not exclusive from
each other either. Mesulam [18] refers
to transmodal nodes that connect various neurocognitive networks. For instance,
activation of some fronto-parietal regions is observed during different
cognitive tasks [101]; are these
regions transmodal or part of a subnetwork that has a specific function?
Similarly, the insular cortex is typically a multimodal association area that
is not specifically activated by auditory stimuli. However, as reported in
Section 4, recent papers have consistently classified it as belonging to a
so-called auditory system. As evidenced by Figure 1, there are also some
overlapping between networks, and voxels can be simultaneously classified as
belonging to different networks. What is the function of such regions? Could
this overlapping between networks be related to synchronization through distinct
frequency-bands [35]—if such
a phenomenon is indeed visible through fMRI BOLD imaging? Regarding the
influence of a task on a network, an issue that has not received much attention
yet, studies have shown that networks could indeed be influenced by the
processing of a task, either during the task [86] or even after it [102]. It is hence not unrealistic to suspect that processing of a
task might also modify the very structure of some networks.Another cogent
question is the relationship between networks as detected by fMRI data analyses
and those mentioned in the literature. Networks extracted from fMRI are the
consequence of the optimization of a mathematical criterion whose link to
neuroscience is, at the very least, not obvious. While some results have been
rather successfully related to the neurocognitive literature (e.g., attentional
network), other results are more complex to interpret. Some networks extracted
seem to share commonalities with some of the subtypes
described by Mesulam [18] (e.g., the motor network; cf.
Section 2), while others seem to be rather
related to  Mesulam [18]'s neurocognitive networks
(e.g., the attentional network). Besides, the union of all reported networks
(e.g., by sICA) does not include the whole brain. Some brain regions are then
excluded from the functional networks organization of the brain. Why so?
Globally, the criterion used for network extraction might make the methods
sensitive to some functions or types of connections. For instance, top-down and
bottom-up influences have distinct features [25, 34, 36–38].
Can they be detected equally well by existing methods?Apart from
these difficulties, there has also been evidence of variability across healthy
subjects [80, 103] that
could be explained by many factors, such as development and/or age [104, 105], and, in general, all
forms of plasticity [106, 107]. Pathologies, for example, stroke [108, 109] or tumors [110–113], render the issue
even more complex. Some studies have shown that certain pathologies can have
network-specific effects: behavioral deficits in spatial neglects for the
fronto-parietal network [114];
epilepsy [115] and Alzheimer's
disease [116] for the
default-mode network. Nonetheless, these results must be used with caution, for
it is not clear yet whether they truly reflect a change in neuronal properties
or, as, for example, in grade II glioma, a mere modification of the metabolic
and vascular properties of the surrounding tissues.


## 5.2. BOLD fMRI Imaging

Use of BOLD fMRI as a way to investigate large-scale
networks relies on three successive assumptions, namely, that information
exchanges between neurons is related to synchronies, synchronies to the BOLD
contrast, and the BOLD contrast to the fMRI data effectively measured.Synchronies are
the blueprint of communication between regions [17, 39, 117–120] and, as such, should be strongly related to large-scale networks.
A challenging issue is to determine the exact relationship between the spatial
distribution and interaction pattern of regions within a large-scale network on
the one hand and, on the other hand, the spatial and frequential distribution
of oscillations.Another issue
is the connection between neuronal activity/synchrony and the appearance of a
BOLD signal. While much still needs to be unraveled as to the connection
between neuronal synchronies and the BOLD signal, it now seems more and more
accepted that a sustained change in neuronal activity is likely to entail a
relative change in the BOLD level [121–124], even
though the exact relationship is expected to be rather complex [125].Still, the BOLD
signal is only a fraction of the total signal that is acquired in fMRI, a
signal that is not exempt from many kinds of artifacts [126–128]. In
particular, some physiological processes (e.g., cardiac, respiratory, or
movement-related) induce spurious effects that contaminate the BOLD signal in
the whole brain [129, 130].
Such artifacts are predominant in certain regions of the brain, such as the
basal arteries for cardiac activity or the interfaces between cerebrospinal
fluid pools and brain tissus for breathing and head movements. This
origin-dependent predilection implies a spatial structure of the noise. Some
network detection algorithms may hence recognize voxels influenced by the same
spatially structured artifact as meeting the requirement for strong temporal
coherence and, hence, assign them to a common structure. This feature has been
successfully used by ICA techniques to provide efficient noise separation and
removal techniques [66, 131, 132]. Yet, the issue arises when
structures induced by noise are wrongly interpreted as functional networks;
their detection and removal is hence of very high importance. The fundamental
question, while examining spatial structures with a similar temporal behavior,
is “do we measure neurally induced signal or consequences of physiological
processes [133]?” Even though our understanding of
the potential artifacts that can contaminate the BOLD fMRI signal improves, the
consequences of many potential sources of structured noise have barely been
mentioned, let alone investigated. For instance, it is believed that some
mechanisms related to the regulation of blood flow (e.g., through the level of
CO2 in the blood) could induce
coherent changes in BOLD signal throughout the brain—giving birth to an
effect likely to be identified as a functional network. In fact, such an effect
has been used to explain the presence of the default-mode network in fMRI [134, 135]. Now, whether these regions
are wrongfully classified as belonging to a common functional network because
their voxels are corrupted by the same artifact, or whether they are actually
regions that drive the physiological response is a matter that remains to be
solved.


## 5.3. Data Analysis

Many questions remain open regarding what
methodologies to apply to extract functional networks. We here quickly discuss
issues related to the choice of a model, the redundancy of fMRI signals, the
necessity to provide both individual and group analyses, the importance of
result representation, and the validation of fMRI results with other
modalities.Procedures used
to investigate networks are usually based on mathematical methods that have
been discovered independently of the field of fMRI data analysis. Their
behavior is hence not guided by cognitive but mathematical considerations.
While it can be accepted that most methods are general enough to be applied to
a wide variety of problems, they still require a careful assessment of how best
to adapt them to the issue at hand. We believe that the major point to cope
with here is “how do methods code for segregation and integration? Does it make
sense?” A relevant approach could be to try to derive out consistence
requirements from cognitive consideration of what an “ideal” method should be
able to do: quantify integration between voxels, regions, or networks using the
same principled measure (such as the multiple correlation coefficient [136] or integration [7, 137]);
differentiate between direct and indirect information exchanges (such as
partial correlation [19, 72, 138–141]);
discriminate causality from simple co-occurrence (such as Granger causality [138, 142–144]).
Some methods are able to deal with one aspect of the problem, but none has been
proposed to answer all these questions simultaneously.Besides,
investigation of large-scale networks face a very interesting problem, namely
that of determining the spatial precision under which data should be considered
as segregated and over which they should be said to be integrated. While it is
obvious that neighboring voxels share a great deal of information, methods that
model and summarize the behavior of a whole network with one single time course
clearly oversimplify the problem and discard a lot of cogent information. Bellec et al. [80] proposed a statistical model
that provides a critical distance that separates segregation and integration.
Voxel clustering is another attempt to deal with that issue. However, the
parameters that characterize the clustering coarseness are set a priori, when
they should be determined by the intrinsic properties of the data and allowed
to vary across the brain (e.g., between subcortical and cortical structures,
which have distinct characteristic spatial extents). This step allows one also
to reduce the dimensionality of the data. At least for this reason, it is a
crucial step, because network investigation requires multivariate analyses that
are computationally very demanding (the computational burden roughly
exponentialy increase with the number of regions).In
neurocomputing, models investigating issues very similar to that of large-scale
networks have already been developed [145–148]. However, most
methods developed so far for effective connectivity, such as structural
equation modeling (SEM) [149–152], dynamical causal modeling
(DCM) [153–155], or generative models—including neural mass models [145, 156] and large-scale
neural models [147, 157–159]—, have been of little use to the
investigation of extended large-scale networks, since their intrinsic
complexity prevent them from modeling systems with that many degrees of
freedom (but see, [160]).Methods
originating from graph and/or network theories might prove more adapted to such
problems [161–163],
since they provide global quantification of structures that, besides from being
ubiquitous [164, 165],
are not unlike some models of brain networks. Using such methods, brain
networks have been shown to exhibit small-world [70, 166–170] and scale-free [171, 172] features. The
fact that networks simultaneously exhibit both properties has strong
structural [104, 173] and
functional [174, 175] implications.Being able to
devise methods that can deal with both individual and group analyses is also an
important issue. At the individual level, it is essential to assess the
significance of the different networks [80, 85, 176]. With procedures of increasing
complexity, nonparametric resampling procedures [177], mostly used in the context of
the GLM so far [178], might be
appealing [179]. At the group level, one seeks to determine invariant networks across
subjects. This has been done by either considering a model for the group [76] or solving the problem at an
individual level and then performing clustering [79]. Validation of such methods have
to be developed; a first step in this direction has been proposed by Calhoun et al. [180].Once results
have been produced, representing the results becomes a key issue. Consider for
instance functional connectivity as measured by marginal correlation. Though
computationally tractable on a large-scale network ofN units, even for N large, such a
method generates N(N−1)/2 correlation
coefficients (e.g., 4950 for as few as 100 voxels/regions; 19900 for 200; 499 500 for 1000). Simply representing these on a graph as is commonly done [72, 140, 181]
would prove impossible to read, let alone to interpret. Procedures that
summarize the information have to be proposed; these can rely on PCA/MDS [71, 79, 182];
they could also use other representational techniques [183, 184].Last, but not
least, an essential point to validate and better understand the large-scale
network approach in fMRI is the comparison with results form other imaging
modalities or areas of neuroscience, such as electrophysiology [34–38], electroencephalography (EEG) or
magnetoencephalography (MEG) [39, 125, 185, 186], and diffusion
tensor imaging (DTI) [187–190]. To be able to efficiently
compare results from different imaging modalities, it is essential to better
understand how each modality images the activity of large-scale brain networks.
In this perspective, providing a unified generative and/or statistical model
for several of these modalities would be of the utmost importance, granting
access to multimodal in vivo imaging of the brain in action.



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*Source: 218519-2008-05-08.xml*