Wireless Sensor Network, 2010, 2, 208-217
doi:10.4236/wsn.2010.23028 Published Online March 2010 (http://www.scirp.org/journal/wsn)
Copyright © 2010 SciRes. WSN
Modeling of Circuits within Networks by fMRI
G. de Marco, A. le Pellec
Université Paris X, Laboratoire du contrôle moteur et d’analyse du mouvement, Paris, France
E-mail: demarco.giovanni@gmail.com
Received November 24, 2009; revised December 19, 2009; accepted January 8, 2010
In this review, the authors describe the most recent functional imaging approaches used to explore and iden-
tify circuits within networks and model spatially and anatomically interconnected regions. After defining the
concept of functional and effective connectivity, the authors describe various methods of identification and
modeling of circuits within networks. The description of specific circuits in networks should allow a more
realistic definition of dynamic functioning of the central nervous system which underlies various brain functions.
Keywords: fMRI, CNS, Modeling, Network, Effective Connectivity
1. Introduction
Imaging can be used to locate the brain areas involved in
various forms of motor behavior, attention, vision or
emotion, self-awareness and awareness of others, but
brain network modeling probably remains the greatest
challenge in the field of imaging data analysis [1].
Neuroimaging first allowed researchers to describe the
cortical and subcortical activity of regionally segregated
functional regions during a variety of experimental or
cognitive tasks. More recently, functional integration
studies have described how these functionally special-
ized areas, i.e., areas whose activity is temporally modi-
fied, interact within a highly distributed neural network.
By using functional magnetic resonance imaging (fMRI),
which has become the method most commonly used to
investigate human brain functions and define neural
populations as distributed local networks transiently,
linked by large-scale reciprocal dynamic connections [2].
After defining the concept of functional and effective
connectivity, various approaches to the identification and
modeling of circuits into networks will be presented in
order to more realistically define the dynamics of the
central nervous system which underlies various cerebral
functions. A distinction should be made between meth-
ods that only consider correlations and ignore issues of
causality and influence and methods that attempt to de-
scribe or draw inferences concerning the direction of
influence between regions. Methodological approaches
to the study of connectivity using fMRI data may be
broadly divided into those that are more data-driven and
attempt to map connectivity in the whole brain and those
that use prior knowledge or hypotheses-driven, limited to
a restricted set of regions [3]. These two categories of
analysis are described, as indicated below, as functional
connectivity and effective connectivity, respectively
[4-6]. Techniques in the first group that consider only
correlations between regions include mapping using
seed-voxel correlations. Techniques in the second group
use more elaborate models and additional assumptions
applied to calculate correlations or covariances to ad-
dress questions about directional influences and include
mapping based on structural equation modeling (SEM),
multivariate autoregressive (MAR) modeling, dynamic
causal modeling (DCM).
2. Functional and Effective Connectivity
The dichotomy between local and large-scale networks
serves as a neural basis for the key assumption that brain
functional architecture abides by two principles: func-
tional segregation and functional integration [2,3,7]. A
large-scale brain network can be defined as a set of seg-
regated and integrated regions that share strong ana-
tomical connections and functional interactions. Whether
top-down or bottom-up, connections and interactions are
quintessential aspects of networks [8,9]. Cognitive and
sensorimotor processes depend on complex dynamics of
temporally and spatially segregated brain activities.
While the segregation principle states that some func-
tional processes specifically engage well-localized and
specialized brain regions, it is now thought that brain
functions are most likely to emerge through integration
of information flows across widely distributed regions
[2,10,11]. According to this approach, it is not only iso-
lated brain areas that are presumed to process informa-
G. de Marco ET AL.209
tion but rather a large-scale network, i.e. a set of brain
regions interacting in a coherent and dynamic way.
Hence, according to the functional integration concept,
cortical areas and therefore functions are integrated
within specific dynamic networks.
This concept supposes the existence of a dynamic in-
teraction between interconnected, active areas and that
the brain areas are expressed as networks within inte-
grated systems. In such a system, localized areas are in-
cluded in networks which become dynamic according to
the cognitive task. Brain areas underlie several functions
and can belong successively to several different func-
tional networks. In other words, a given brain area does
not have a single function; its resources can be exploited
in several different cognitive strategies. The principle of
functional integration which is also known in the field of
electrophysiology was used to analyze the event poten-
tials obtained from multielectrode recordings [12]. Thus,
based on the functional integration principle, the rela-
tionships between several brain areas may be examined.
Effective connectivity, closer to the intuitive notion of
a connection, can be defined as the influence that one
neural system exerts over another, either at a synaptic
level (synaptic efficacy) or a cortical level [13,14]. This
approach emphasizes that determining effective connec-
tivity requires a causal model of the interactions between
the elements of the neural system of interest. In electro-
physiology, there is a close relationship between effec-
tive connectivity and synaptic efficacy [15]. Effective
connectivity can be estimated from linear models to test
whether a theoretical model seeking to explain a network
of relationships can actually fit the relationships esti-
mated from the observed data. In the case of fMRI, the
theoretical model is an anatomically constrained model
and the data are interregional covariances of activity
Consequently, effective connectivity represents the
dynamic influence that cortical and subcortical regions
exert on each other via a putative network of interde-
pendent areas [5,12]. This approach might be based on
linear time-invariant models that relate the time-course
of experimentally controlled manipulations to BOLD
signals in a voxel-specific fashion. Although various
statistical models have been proposed [17], these stan-
dard models treat the voxels throughout the brain as iso-
lated black boxes, whose input-output functions are
characterized by BOLD responses evoked by various
experimental conditions [18]. fMRI provides simultane-
ous recordings of activity throughout the brain evoked by
cognitive and sensorimotor challenges, but at the ex-
pense of ignoring temporal information, i.e., the history
of the experimental task (input) or physiologic variable
(signal). This is important, as interactions within the
brain, whether over short or long distances, take time and
are not instantaneous which is implicit within regression
models. Furthermore, the instantaneous state of any brain
system that conforms to a dynamic system will depend
on the history of its input.
3. Data-Driven Approaches
The first category of methods includes seed-voxel corre-
lations, Granger causality derived autoregressive models
[19], fuzzy clustering which assumes that brain voxels
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