Cortical Hubs Form a Module for Multisensory Integration on Top of the Hierarchy of Cortical Networks

Article (PDF Available)inFrontiers in Neuroinformatics 4:1 · March 2010with37 Reads
DOI: 10.3389/neuro.11.001.2010 · Source: PubMed
Sensory stimuli entering the nervous system follow particular paths of processing, typically separated (segregated) from the paths of other modal information. However, sensory perception, awareness and cognition emerge from the combination of information (integration). The corticocortical networks of cats and macaque monkeys display three prominent characteristics: (i) modular organisation (facilitating the segregation), (ii) abundant alternative processing paths and (iii) the presence of highly connected hubs. Here, we study in detail the organisation and potential function of the cortical hubs by graph analysis and information theoretical methods. We find that the cortical hubs form a spatially delocalised, but topologically central module with the capacity to integrate multisensory information in a collaborative manner. With this, we resolve the underlying anatomical substrate that supports the simultaneous capacity of the cortex to segregate and to integrate multisensory information.
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 1
published: 19 March 2010
doi: 10.3389/neuro.11.001.2010
2007; Zhou et al., 2007; Hagmann et al., 2008). While the organisa-
tion of cortical areas into clusters permits the segregated processing
of information of different modality, the large number of connec-
tions involves that sensory information is highly accessible to all
cortical areas, regardless of its modal origin. A detailed analysis of
the corticocortical communication substrate has revealed the central
role of the cortical hubs, by facilitating the communication between
the different sensory modalities (
Zamora-López et al., 2009).
Whether the cortical hubs act as passive transmitters of informa-
tion, or they perform a more active function is a relevant question
that we try to answer in the present paper. We start by summarising
principles of complex network analysis and information theory in
Section “Materials and Methods”. Section “Topological Capacity
of Integration contains a thorough application of graph theo-
retical measures which reveal that the cortical hubs form an addi-
tional module, expressed as a higher hierarchical level. In Section
“Functional Capacity of Integration, we challenge the intuitively
assigned integrative properties of this central module by means of
dynamical and information theoretical measures. On the one hand,
we fi nd that only simultaneous lesion of particular hubs leads to
a dynamical segregation of the sensory modules (visual, auditory,
somatosensory-motor and frontolimbic). On the other hand, the
same hubs form a dynamical cluster after simultaneous excitation of
primary sensory areas, a clear sign of their integrative capacities.
We rst introduce basic concepts of graph theory. A network is
an abstract manner to represent different aspects of a real system,
providing it with a form (topology) which can be mathematically
The mammalian nervous system is responsible for collecting and
processing of information, and for providing adaptive responses
which permit the organism to survive in a permanently changing
environment. Sensory neurones encode environmental information
into electrical signals which propagate in a “bottom-up manner
through different processing stages (
Kandel et al., 2000; Bear et al.,
). Each level provides responses of increasing complexity and at
different time scales, e.g. refl ex arcs, emotional responses and more
elaborate cognitive responses. Information of the same modality (e.g.
visual, auditory, somatosensory, etc.) traverses the body together,
typically separated from the processing paths of other modalities.
This permits that particular regions of the cortex specialise in detect-
ing different features of the sensory stimuli, e.g. orientation, velocity
and colour of the visual input; or frequency and pitch of the audi-
tory stimuli. However, in order to generate a coherent perception of
the reality, the brain needs to combine (integrate) this multisensory
information at some place (
Robertson, 2003) and during some time
Fahle, 1993; Singer and Gray, 1995; Engel and Singer, 2001). For that,
the paths of information need to converge.
It has been argued that the functional capacity of the NS to bal-
ance between segregation (specialisation) and integration might be
facilitated by its structural organisation (
Sporns and Tononi, 2001).
Analysis of the connectivity between regions of the cerebral cortex
in macaque monkeys and cats has revealed the following character-
istics: (i) clustered organisation of the cortical areas (
Scannell and
Young, 1993; Scannell et al., 1995; Hilgetag et al., 2000; Hilgetag
and Kaiser, 2004
) (see Figure 2), (ii) a large density of connections,
and (iii) a broad degree distribution containing highly connected
areas which are referred as hubs (
Zemanová et al., 2006; Sporns et al.,
Cortical hubs form a module for multisensory integration on
top of the hierarchy of cortical networks
Gorka Zamora-López
*, Changsong Zhou
and Jürgen Kurths
Interdisciplinary Center for Dynamics of Complex Systems, University of Potsdam, Potsdam, Germany
Department of Physics, Centre for Nonlinear Studies, Hong Kong Baptist University, Hong Kong, China
The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Hong Kong, China
Transdisciplinary concepts and methods, Potsdam Institute for Climate Impact Research, Potsdam, Germany
Institute of Physics, Humboldt University, Berlin, Germany
Sensory stimuli entering the nervous system follow particular paths of processing, typically
separated (segregated) from the paths of other modal information. However, sensory perception,
awareness and cognition emerge from the combination of information (integration). The
corticocortical networks of cats and macaque monkeys display three prominent characteristics:
(i) modular organisation (facilitating the segregation), (ii) abundant alternative processing paths
and (iii) the presence of highly connected hubs. Here, we study in detail the organisation and
potential function of the cortical hubs by graph analysis and information theoretical methods.
We nd that the cortical hubs form a spatially delocalised, but topologically central module
with the capacity to integrate multisensory information in a collaborative manner. With this,
we resolve the underlying anatomical substrate that supports the simultaneous capacity of the
cortex to segregate and to integrate multisensory information.
Keywords: corticocortical networks, cortical hubs, multisensory integration, segregation, integration
Edited by:
Claus C. Hilgetag, Jacobs University
Bremen, Germany
Reviewed by:
Steven Bressler, Florida Atlantic
University, USA
David Meunier, University of
Cambridge, UK
Gorka Zamora-López, Interdisciplinary
Center for Dynamics of Complex
Systems, University of Potsdam,
Komplex II – Golm (Haus 28) ,
Karl-Liebknecht-Str. 24, D-14476
Potsdam, Germany.
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 2
Zamora-López et al. Cortical module for integration
tractable. A network G (N, L), composed of N nodes interconnected
by L links, is described by an adjacency matrix A with entries A
= 1
when there is a link pointing from node i to node j, and A
= 0
otherwise. The density of G is the fraction between the number
of links L and the total number of links possible:
. In
order to characterise the topological scales of networks, there exist
many statistical descriptors, all measurable from the information
encoded in the adjacency matrix. The output degree
ki A
of a node i is the number of efferent connections that it projects to
other nodes, and its input degree
ki A
, is the number of
the afferent connections it receives. The degree distribution p(k)
is the probability that a randomly chosen node has degree k. One
of the key discoveries that triggered a renewed interest in graph
theory is that the distribution p(k) of many empirical networks
approximately follows a power-law p(k) k
(Newman, 2003),
where γ is the degree exponent. In such scale-free(-like) networks
the majority of nodes possess a small number of neighbours, and
few nodes (the hubs) are highly connected.
Distance and centrality
The distance d
between two nodes i and j is the length of the short-
est path between them, i.e. the minimal number of links crossed
to travel from i to j. If there is a link i j, then d
= 1. If there is
no other choice than going through an intermediate node k such
that i k j, then d
= 2, and so on. When there exists no path
from i to j then d
= . The average pathlength l is the average
distance between all pairs of nodes. The shortest path between two
nodes is usually not unique and there are several alternative shortest
paths. In order to characterise the infl uence of individual nodes
on the fl ow and the spread of information through a network, the
betweenness centrality C
(i), is defi ned as the fraction of all shortest
paths passing through i (
Anthonisse, 1971; Freeman, 1977):
where σ
(i) is the number of shortest paths starting in s, running
through i and fi nishing in t, and σ
is the number of all shortest
paths from s to t.
Matching index
The topological similarity of two nodes can be characterised as the
number of common neighbours they share. In the extreme case,
two nodes are topologically identical if both have the same set of
connections. The neighbourhood of node i is defi ned as the set of
nodes it connects with, Γ(i) = {j : A
= 1}. In graphs without mul-
tiple links the size of the neighbourhood |Γ(i)| equals the degree
of i. The matching index of two nodes i and j is thus the overlap
of their neighbourhoods: MI(i,j) = |Γ(i) Γ(j)|. Defi ned in this
manner MI(i,j) depends on the degrees of i and j, and the values for
different pairs are not comparable. Imagine two nodes with degrees
k(i) = k(j) = 3 which are connected to the same neighbours. As
Γ(i) = Γ(j) their matching is MI(i,j) = 3. Imagine other two nodes
with degrees k(i) = 3 and k(j) = 4. Maximally, they could share
three neighbours and have MI(i,j) = 3 as well, despite i and j
are topologically equivalent but i and j are not. In order to com-
pare the values for different pairs the measure can be normalised by
the number of distinct neighbours of the two nodes, i.e. the union
of the two neighbourhoods |Γ(
i) Γ(j)| as illustrated in Figure 1.
The normalised matching index can be computed as:
MI i j
ki k j A A
in jm
(, )
|() ()|
|() ()|
() ( )
, =
Now, MI(i,j) = 1 only if i and j are connected exactly to the
same nodes, Γ(i) = Γ(j), and MI(i,j) = 0 if they have no common
Reference surrogate networks
Graph theoretical measures help understand the topological organ-
isation of networks. Equally relevant is to uncover the features
which are characteristic to the underlying system and the funda-
mental properties of its development. In this sense, the question
is not whether a graph measure takes a specifi c numerical value,
but whether this value distinguishes the empirical network G
from others of similar characteristics. For that, the formulation
of appropriate null-models is required. A typical such null case is
to generate surrogate networks with the same size N, number of
links L and degree distribution p(k) as in G
. The link switching
method (
Katz and Powell, 1957; Holland and Leinhardt, 1977; Rao
et al., 1996; Kannan et al., 1999; Roberts, 2000
) consists of the fol-
lowing iterative process: starting from G
, at each iteration two
links are chosen at random (i
) and (i
). The links are
rewired as (i
) and (i
) provided that the new links do not
already exist and do not introduce self-loops, i.e. i i. Repeating
the process suffi cient times the resulting surrogate network con-
serves the initial degree distribution but any higher order structure
is destroyed.
The classical textbook illustration of the cerebral cortex as a sur-
face (grey matter) which can be subdivided into functional or
cytoarchitectonic regions is only a limited picture. Additionally,
long-range fi bres link the cortical areas via the white matter forming
FIGURE 1 | Schematic representation of the normalised matching index,
computed as in Eq. 2. For proper comparison between pairs, the measure is
normalised by the number of different neighbours of v and v .
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 3
Zamora-López et al. Cortical module for integration
a complex network which is neither regular nor completely random.
This intricated structure enhances the richness and complexity of
information processing capabilities of the cerebral cortex. In this
paper we focus on the analysis of the cortical connectivity of the
cat because it is, up to date, the most complete and reliable dataset
of this kind.
Corticocortical connectivity of the cat
The dataset of the corticocortical connections within the cortex of
cats was created after an extensive collation of literature reporting
anatomical tract-tracing experiments (
Scannell and Young, 1993;
Scannell et al., 1995
). It consists of a parcellation into 53 cortical
areas and 826 fi bres of axons between them as summarised in
Figure 2. The connections are weighted according to the axonal
density of the projections. After application of data mining methods
Scannell and Young, 1993; Hilgetag and Kaiser, 2004), the network
was found to be organised into four distinguishable clusters which
closely follow functional subdivisions: visual (V), auditory (A),
somatosensory-motor (SM) and frontolimbic (FL).
Surrogate data
In order to perform signifi cance tests of the graph measures, an
ensemble of 1000 surrogate networks has been created following
the link switching method (see Section “Graph Analysis”). All the
resulting networks have the same size N = 53, the same number of
links L = 826 and the same degree distribution as the corticocortical
FIGURE 2 | Weighted adjacency matrix W of the corticocortical connectivity
of the cat comprising of L = 826 directed connections between N = 53 cortical
areas (
Scannell and Young, 1993; Scannell et al., 1995). For visualisation
purposes, the non-existing connections (0) have been replaced by dots. The
network has clustered organisation, refl ecting four functional subdivisions: visual
(V), auditory (A), somatosensory-motor (SM) and frontolimbic (FL).
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 4
Zamora-López et al. Cortical module for integration
network of the cat. To assure that any further internal structure is
destroyed, each surrogate network is the product of 10 × L itera-
tions. In the following, this set will be referred as the rewired ensem-
ble {G
}, and the original corticocortical network of the cat as G
The ensemble average of graph measures applied on the surrogate
set {G
} will be considered as the expected values.
Information theory has been very successful to describe transmis-
sion of information, encoding and channel capacity. At the root
of this success lies the original idea of Shannon to apply concepts
of statistical physics to represent the nature of communication.
Consider a system A with M possible states. That is, a measurement
made on A yields the values a
, with a probability p(a
The average amount of information gained from a measurement
that specifi es one particular value a
is given by the entropy of the
system (
Shannon, 1948; Cover and Thomas, 1991):
HA pa pa
() .=−
() ()
The entropy can be interpreted as the amount of surprise one
should feel upon reading the result of a measurement (
Faser and
Swinney, 1986
). It vanishes when the system has only one accessible
state because the value a is always obtained, i.e. there is no surprise.
H(A) is maximum when all the states are equally likely, i.e. there
are no preferred states.
The statistical dependence between two systems x
and x
is quan-
tifi ed by their mutual information:
Ix x Hx Hx Hxx
12 1 2 12
By defi nition, the joint entropy is H(x
) H(x
) + H(x
). The
equality is only fulfi lled if x
and x
are statistically independent,
hence MI(x
) = 0, and otherwise MI(x
) > 0.
In a series of papers Tononi and Sporns proposed a particular meas-
ure of integration (
Tononi and Sporns, 1994; Tononi et al., 1996,
). Given a system X composed of N subsystems x
, integration
is defi ned as:
() ()=
where H(x
) is the entropy of one subsystem and H(X) = H(x
is the joint entropy of the system considered as a whole. I(X) = 0
only if all x
X are statistically independent of each other, and posi-
tive otherwise. After this defi nition, integration is the extension of
mutual information for more than two systems. In other words, I(X)
measures the internal level of statistical dependence among all the
subsystems x
Linear dynamical systems
The steady-state of a linear system whose N subsystems
x = (x
) are driven by a Gaussian noise ξ = (ξ
is described by
xg Ax
=∑ +ξ
, where g is the coupling strength
and A
is the transpose of the adjacency matrix. Otherwise the
dynamics of x
would be characterised by its own outputs, not
by the inputs it receives. Written in matrix form:
In practical terms the variable x
might be interpreted as the
activity level of the cortical area i (
Kötter and Sommer, 2000; Young
et al., 2000
), or as the mean fi ring rate of the neurones in the area i
Graben et al., 2007). The entropy of such a multivariate Gaussian
system can be analytically calculated out of its covariance matrix
such that
() ( )| ()|=
2log π
, where |·| stands for
the determinant (
Papoulis, 1991; Tononi and Sporns, 1994). The
entropy of an individual Gaussian process is
Hx e
() ( ),=
2log πν
where ν
is the variance of x
, say, the i
diagonal element of the
COV(X) matrix. Replacing H(X) and H(x
) into Eq. 5 and apply-
ing basic algebra, we reduce the integration of such a multivariate
Gaussian system as:
This expression shows that I(X) of the linear system is prop-
erly normalised and is independent of system size N. The covari-
ance matrix can be analytically computed by solving the system
such that
x =⋅=
, and averaging over the states pro-
duced by successive values of ξ one fi nds: COV(X) = x · x
(Q · ξ)·(ξ
· Q
)=Q · Q
Comparing different systems
To compare I(X) of different systems, the matrix A
needs to be
adequately normalised because application of the same coupling
strength g to different networks might set them into different
dynamical states. Hence, they might not be comparable. The lin-
ear System (6) has several poles depending on g. The smallest pole
corresponds to
where λ
is the largest eigenvalue of the
transposed adjacency matrix A
. The solutions only have physical
meaning for g < g
, otherwise the stationarity condition does not
hold. In Figure 3 the poles corresponding to the corticocortical
network of the cat are shown. Notice that at the poles, both entropy
and integration diverge. To make the comparison of the dynamics
of different networks possible, we normalise the adjacency matrices
In this manner, all systems have the smallest
pole at g = 1.
Finally, a proper coupling strength g needs to be chosen. For
that, we have estimated the covariance matrices of the cat cortical
network under different coupling strengths (Figure 4). They are
similar to the correlation patterns arising from more complex
models (
Zemanová et al., 2006; Honey et al., 2007; Zhou et al.,
2006, 2007
). This similarity indicates the validity of the simple
linear System (6) for the exploratory purposes here intended.
All networks considered in Section “Functional Capacity of
Integration are normalised by their fi rst pole and a coupling
strength of g = 0.5 is applied. Unless otherwise stated, the noise
level is set to ξ
= 1.0.
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Zamora-López et al. Cortical module for integration
FIGURE 3 | Parametric study of the linear System (6) using the cortical
network of the cat. (A) Integrability range. When the determinant |1 gÂ| = 0
the system has a pole. Negative values lead to non-physical solutions. (B)
Entropy and (C) Integration diverge around the poles.
FIGURE 4 | Covariance matrix of the cat cortical network as a linear system. The adjacency matrix has been previously normalised by 1/λ
and the noise level
set to ξ
= 1.0. Coupling strengths are: (A) g = 0.52, (B) g = 0.84 and (C) g = 0.92.
In order to characterise the connectional organisation of the nervous
system and to understand its functional implications, the complex
network approach has been applied in the recent years, particu-
larly at the level of the cerebral cortex. This analysis has revealed
several organisation properties, e.g. the clustering of cortical areas
according to their sensory modality (visual, auditory, somatosen-
sory-motor and frontolimbic). Recently, it has been reported that
communication paths between cortical areas in different sensory
modules are not random, but mediated by the hubs of the network
Zamora-López et al., 2009). In this section we present a more
detailed graph analysis aiming to characterise the potential func-
tion of the cortical hubs.
Inter-modal communication
The betweenness centrality C
(ν) quantifi es the relevance of a node
v within the communication paths in a network. As represented
in Figure 5A, we observe that within each of the sensory systems,
few cortical areas possess a large betweenness. With C
(ν) > 500 we
nd: visual areas 20a, 7 and AES; auditory area EPp; somatosensory-
motor areas 6m and 5Al; and frontolimbic areas Ia, Ig, CGp, 35
and 36. On the contrary, only the visual primary cortex (area 17)
and the hippocampus have C
(ν) = 0. In general, we observe that
cortical regions known to perform highly specialised sensory func-
tion have few connections and very low centrality, e.g. primary and
secondary visual or auditory areas, and early somatosensory-motor
areas. These areas typically contain ordered mappings of the sen-
sory stimuli such as retinotopic or tonotopic maps, see Appendix
Scannell et al. (1995).
The centrality of a node usually correlates with its degree,
hence, it is trivial to find out that precisely the hubs have larger
centrality. Drawing any further conclusion requires performing
a proper significance test. For comparison, the average C
of the nodes in all the 1000 rewired networks of the surrogate
ensemble {G
} has been computed. The ascending line in Figure
5B shows the expected dependence of the betweenness centrality
on the degree of the nodes. As a node receives k
(ν) inputs and
projects k
(ν) outputs, the number of shortest paths passing
through v is linearly proportional to k
(ν) in the surrogate
networks. The most prominent observation is that, while C
the low degree areas follow the expected centrality, the centrality
Subsets of elements
The entropy of a subset of systems S X can be obtained by
rst computing COV(X) as indicated above, and then extracting
the covariance submatrix COV(S) out of COV(X) by consider-
ing only the elements x
S. The entropy of the subset is then
() ( ) | ()|=
2log π
, and its integration I(S) is:
() ()
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 6
Zamora-López et al. Cortical module for integration
φ() ,k
is the number of nodes with k(v) k and
is the
number of links between them. Notice that φ(k) is an increasing
function of k. As
is the density of the network, after
the nodes with low degrees are removed the remaining reduced
network contains more links per node. Thus, a plain measure of
φ(k) is not very informative because hubs have a higher intrinsic
chance of being connected to each other. Again, a conclusive inter-
pretation requires the comparison to random networks with the
same degree distribution. The question is then whether φ(k) of
the real network grows faster or slower with k than the expected
k-density φ
(k) out of the surrogate networks {G
}. If φ(k) grows
faster than φ
(k), it means that the hubs are more connected than
expected and form a dense module (a rich-club). On the contrary,
if φ(k) grows slower than φ
(k), the hubs are more independent
of each other than expected.
In Figure 6A the k-density φ
(k) of G
is presented together
with the ensemble average φ
(k). For low degrees, φ
(k) follows
very close the expectation, but for degrees k(v) > 15, φ
(k) starts to
grow faster showing that the hubs of the network form a rich-club.
The largest difference occurs for k = 23, comprising of 11 cortical
hubs from all the four sensory systems (Figure 6B). Compared to
the internal density of the four modules of the network, we fi nd
that the hubs form an even denser module (Table 1).
Topological similarity of cortical hubs
A central assumption in systems neuroscience is that the func-
tion of brain regions are specifi ed by their afferents and efferents
Passingham et al., 2002). Under this assumption, it is to be expected
that cortical areas of similar function, i.e. specialised in the process-
ing of same modal information, should display a similar pattern of
FIGURE 6 | Rich-club organisation. (A) k-density of the corticocortical
network of the cat φ
, compared to the expectation out of the surrogate
ensemble {G
}. The largest difference occurs at k = 23 (vertically dashed line)
giving rise to (B) a rich-club composed of 11 areas.
FIGURE 5 | Centrality of cortical areas. (A) Betweenness of cortical areas
shows that at each sensory system few areas are very central. (B) Comparison
between C
of cortical areas and the expected centrality due to their degree
(brown line). As a consequence of the modular and hierarchical organisation of
the network, low degree areas closely follow the expected centrality but hubs
are signifi cantly more central than expected. Communication paths between
sensory systems are centralised through the hubs.
of the hubs is largely significant. This is an evident consequence
of the modular organisation of the network and the particular
role of the cortical hubs for the inter-modal communication.
Communication paths running between low-degree areas of dif-
ferent modules are usually mediated through the hubs (
López et al., 2009
This signifi cance test permits us to uncover the most likely candi-
dates to be a hub of the network, not only in terms of their number
of links, but considering their contribution for the corticocortical
communications. The hubs found here are potential candidates
to perform high level integration because they have access to the
information of different modalities. However, with the current
results we can only affi rm with certainty that the hubs are useful
for the transmission of information from one modality to another.
Concluding whether they perform any further function or not, it
requires a more careful analysis.
Collective organisation of cortical hubs
A relevant question is now whether the cortical hubs are func-
tionally independent of each other, i.e. each hub has a specialised
function, or they perform some collaborative function. A graph
measure to characterise the relation between the hubs of a net-
work is the rich-club phenomenon. The k-density φ(k), is defi ned
as the internal density of links between the nodes with degree
larger than k:
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 7
Zamora-López et al. Cortical module for integration
projections. In the case of the cortical hubs, it has been shown in
the previous section that they form a tightly connected module.
Whether this module could be regarded as a functional module, at
least from a topological point of view, is the goal of the following
analysis. The matching index MI(v,v) is a graph measure to estimate
the topological similarity of two nodes, by counting the number of
common neighbours of v and v (Section “Graph Analysis”). In order
to compare the values obtained for different pairs, the measure is
normalised such that MI(v,v) = 1 only if all the neighbours of node
v are also all the neighbours of v. See the example in Figure 1.
We have computed the matching index for all pairs of cortical
areas and the result is shown in matrix form, Figure 7A. Visual
inspection reveals the modular organisation of the network. This
is refl ected by the fact that MI(v,v) is typically larger if both v
and v belong to the same anatomical module, than if they belong
to different modules. To highlight this difference, in Figure 7B
the distribution of the matching values is shown: when the areas
belong to the same module (internal matching), or to different
modules (external matching). The external matching has a broad
skewed distribution but peaking near MI = 0.15. The internal
matching displays a more constrained distribution with maximum
at approximately MI = 0.55. In Table 1 the average matching of the
network is compared to the average internal matching for each of
the anatomical modules V, A, SM and FL. The internal averages are
FIGURE 7 | Topological similarity of cortical areas. (A) Pairwise matching
index MI(v,v ) for all areas summarised in matrix form. Self-matching MI(v,v) is
ignored for visualisation. (B) Distribution of the MI values in (A) if the areas v
and v are in the same anatomical module V, A, SM or FL (dashed line), and if
they belong to different modules (solid line). (C) Recomputed distribution of MI
if the areas belong to different modules, but cortical hubs are discarded (solid
line). And distribution of MI(v,v) only if v and v are hubs in the Rich-Club
(dotted line).
Table 1 | Comparison between the anatomical modules and the Rich-Club. Both the internal density of links and the average matching of the areas in each of
the functional modules V, A, SM and FL are larger than the whole network averages. The same happens for the areas in the Rich-Club, with values comparable to,
or larger than those for the anatomical modules.
always larger than the global average despite the broad deviations,
confi rms the expected functional cohesiveness of the modules; not
only in terms of their internal density of connections, but also in
terms of their common connectivity.
As pointed out, the distribution of external matching is skewed
and contains some larger values up to MI 0.6. We nd that most of
these larger values are contributed precisely by the links between the
cortical hubs which lie in different modules. We have recomputed
the distribution of external matching, but ignoring the matching
between the cortical hubs (solid line in Figure 7C). The distribution
decays now faster than in Figure 7B. Finally, the distribution of the
internal matching for the 11 hubs forming the rich-club is displayed
(dotted line of Figure 7C). It appears clearly separated from that of
the distribution of external matching and peaking near MI = 0.55.
Its average is 0.52 ± 0.10, comparable to, or larger than, the internal
matching of the anatomical modules, Table 1. These observations
support the idea that the cortical hubs form a functional module
on their own, as the anatomical modules do.
Hierarchical organisation and integration capacity
The two structural properties of the cortical hubs here presented, (i)
hubs are densely connected with each other and (ii) they are func-
tionally interrelated in terms of their inputs and outputs, extend the
current understanding of cortical networks by uncovering that the
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 8
Zamora-López et al. Cortical module for integration
multisensory hubs form yet another module which lies at a higher
level in the hierarchical organisation. In the complex networks liter-
ature one fi nds two types of hierarchical topologies. The model after
Arenas et al. (2006) considers hierarchies as the agglomeration of
modules, say, small modules join to form larger modules, Figure 8A.
Another type of hierarchy after
Ravasz and Barabási (2003) can be
regarded as a tree-like fractal structure which produces modular
networks with scale-free degree distribution. At each level, there
is a central community connecting to all the modules at the same
level, and to all modules in the hierarchies below. Such centralised
patterns are repeated through different scales, Figure 8B.
The organisation that we uncover here is none of these two, but
it might be regarded as a combination of them. Notice that in the
model by
Arenas et al. (2006), the small communities are randomly
linked to each other such that their union forms a larger commu-
nity. In the present case, the inter-community links are not random,
but centralised. Therefore, the highest hierarchical level is formed
by a partial overlap of the underlying modules. See Figure 8C for
a schematic representation.
The functional implications of the topological fi ndings
described in this section, necessarily arise from intuitive inter-
pretation of the intrinsic relationship between structure and func-
tion in neural systems. To provide a more solid ground to these
intuitive interpretations, in the following section we challenge
them by means of dynamical and information theoretical meas-
ures. We focus in a very simple dynamical model which has the
benefi t of being analytically solvable, although its validity for our
purposes is confi rmed by comparison to the dynamical output
of more complex models, see Section “Information Theory and
The structural organisation described in the previous section
supports the idea that the cortical hubs might be responsible for
combining the multisensory information hence facilitate the emer-
gence of a global (integrated) perception. In this sense, we aim for
a defi nition of integration which characterises the capacity of one
or more nodes to receive information of different character and com-
bine it to produce new useful information. Certainly, this defi nition
involves crucial theoretical problems, e.g. what the character of
information is, or what are the rules under which information is
combined. Nevertheless, within a networked system, the nodes with
a capacity to integrate information should obey certain measurable
conditions. We propose the following:
1) Accessibility to information: A node can perform an integra-
tive function only if it has general access to the information
contained within the system.
2) Sharing of information: Two or more nodes can perform
integrative function in a collaborative manner only if they are
suffi ciently connected with each other.
3) Segregation after selective damage: If a node has an integra-
tive function, its removal should lead to a decrease of the inte-
grative capabilities of the whole system.
From the structural point of view, the hubs listed in Figure
6B obey these three conditions. They are the most central areas
and they are densely connected to each other. Besides, robust-
ness studies (
Kaiser et al., 2007) have shown that intentional
lesion of the highly connected cortical areas largely affect the
communication within the network. In the following, we intro-
duce a framework to characterise the integrative function of the
hubs by means of dynamical systems and information theory.
Additionally, we perform a probabilistic analysis of the compo-
sition of the dynamical core, rather than a deterministic one.
The reason is that even if the corticocortical networks of the
cat is the most complete and reliable dataset of its kind up to
date, it is not free of experimental errors. For example, some of
the real connections might still be absent in the data. We aim
to discriminate those hubs which, grouped together, possess
a larger potential to integrate multisensory information from
those groups which might have lesser capacities. For that, we
FIGURE 8 | Hierarchical organisation of complex networks. (A) Hierarchies
as agglomeration of modules (
Arenas et al., 2006). (B) Centralised and fractal
hierarchical model (
Ravasz and Barabási, 2003). (C) Illustrative representation
of the modular and hierarchical structure found in the corticocortical
connectivity of the cat. The highest hierarchical level is formed by a densely
interconnected overlap of the modules.
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 9
Zamora-López et al. Cortical module for integration
arbitrarily choose all the areas with output degree k
(ν) 20 as
potential members of the integrator module giving rise to a set
of N
= 19 areas:
= {20a, 7, AES, EPp, 6l, 6m, 5Am, 5Al, 5Bm, 5Bl, SSSAi,
SSAo, PFCL, Ia, Ig, CGa, CGp, 35, 36}.
The statistical analysis consists in measuring the integrative
capacities of all the 524,097 combinations of sizes N
= 1 to N
= 19
out of the 19 hubs in S
Integration capacity after sensory stimulation
Consider the linear System (6) with  being the transposed and
normalised adjacency matrix of the cat G
. All areas are driven
by a small Gaussian noise level ξ
= 1.0 and coupled by g = 0.5.
This case might be regarded as the activity of the network in the
resting-state because all x
are driven by noise of small intensity
and there is no sensory input. Now, we intend to illustrate the
joint capacity of a group of areas to integrate information of
different character. Even if it is unclear how to defi ne the character
of information, in the case of cortical networks it is known that
sensory information enters the cortex through specifi c regions
termed as primary sensory areas: primary visual cortex (area
17), primary auditory cortex (area AI) and primary somato-
sensory cortex (areas 1, 2 and 3b). According to
Scannell et al.
(1995) the cortical areas 1, 2 and 3b are subregions of the primary
somatosensory area, named by some authors as SI. Hence, we
simultaneously excite all the primary sensory areas {17, AI, 1, 2,
and 3b} by assigning them a larger noise level ξ
= 10.0) and we
measure the integration I(S) of all the subsets S of hubs out of
. Because of the excited condition, we denote the integration
of the subsets as I
The results depicted in Figure 9A show that I
(S) can largely dif-
fer. For example, among all the subsets of size N
= 10, the integra-
tion of some of them is very small, I
(S) 0.1, while the integration
of others becomes much larger, I
(S) 0.5. These differences permit
us to identify those cortical hubs which, grouped together, become
more statistically dependent among them as a consequence of the
multisensory stimulation. Considering only those subsets whose
(S) lies within the largest 10% (red crosses in Figure 9A) a co-
participation matrix C is constructed such that C
is the number
of times (given in frequency) that two cortical hubs participate
together in one of the maximal sets, Figure 9B. It is observed that
areas {7, AES; EPp; 6m; Ia, Ig, CGp, 35, 36} participate together in
over 75% of all the maximal sets. Visual area 20a and the soma-
tosensory-motor area 6l participate only in 50% of the occasions
with those areas in the core. The remaining areas, {5Am, 5Al, 5Bm,
5Bl, SSSAi, SSSAo and PFCL}, can be discarded as members of the
dynamical core.
FIGURE 9 | Functional segregation and integration. (A) Local
integration I(S) of cortical hubs after stimulation of the primary sensory areas.
(B) Co-participation matrix of cortical hubs within the subsets leading to large
(S) (red dots). (C) Modular integration
of the sensory modules V, A, SM and
FL after simultaneous lesion of cortical hubs. N
is the number of hubs removed.
(D) Co-participation matrix of the hubs within the subsets S which lead to a
larger decrease in the dynamical dependence
of the sensory modules
(marked by red dots).
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 10
Zamora-López et al. Cortical module for integration
Dynamical segregation after multiple lesions
Within a networked system the removal of critical nodes should
lead to a decrease in its integrative capacities. In the following, we
study the impact of targeted lesions of the corticocortical network
of the cat, G
. For all the possible subsets S composed of hubs in
, we perform a lesion to the network by simultaneously remov-
ing the nodes x
S and characterise the consequent functional
segregation of the network G
= G
S as the change in statistical
dependence between the four modules (V, A, SM and FL). Lesion
of areas critical for the integration capacities of the system should
lead to a dynamical segregation of the modules, i.e. a decrease in
their statistical dependence.
Recall that integration I(X) as defi ned in Eq. 7 is an extension
of the mutual information for more than two systems. It repre-
sents the limit case in which the statistical dependence among
all the elements x
in the system X is quantifi ed. To cover differ-
ent scales of organisation we propose to characterise the statisti-
cal dependence between groups of elements. Imagine a partition
P = {S
} into n groups (modules) of the elements x
that X = S
∪…∪ S
. Then, we de ne the modular integration
of the partition P as:
() ().=
Note that when n = N, then I
(X) = I(X).
Considering the partition P
= {V, A, SM, FL} and the cortico-
cortical network of the cat, then
= 0.29
. The modular inte-
gration of each lesioned network G
is computed for the partition
. Notice that (a) the nodes are also removed from the partition
and (b) every G
is adequately normalised by its largest eigenvalue
such that the measured observables are comparable across reali-
sations (see Section “Information Theory and Integration”). The
results in Figure 9C permit us again to discriminate between sub-
sets of hubs whose simultaneous removal lead to a large segrega-
tion of the network, while removal of other subsets has barely no
effect. For example, among all the possible lesions of size N
= 10,
some trigger a large segregation of the modules,
while other lesions do even increase their dynamical dependence:
Selecting only those subsets whose lesion leads to a larger
segregation of the modules, i.e.
lies among 10% of
the minimal modular integration for each size N
(red dots
in Figure 9A), a co-participation matrix C is constructed,
Figure 9D. The entries C
are the number of times (given in
frequency) that two areas participate together in one of the
minimal subsets. A core of cortical areas is found which par-
ticipate together in over 70% of these cases: {7, AES; EPp; Ia,
Ig, CGp, 35, 36}. Somatosensory-motor areas 6m, 5Al and 5Bl
join them in over 50% of the cases.
In summary, both the multiple lesion and the multisensory
excitation analysis performed in this section lead to the identi-
cation of the same cortical hubs as responsible for the integra-
tion of multisensory information in the corticocortical network
of the cat. Moreover, this set largely coincides with the top hier-
archical level found by the graph analysis in Section Topological
Capacity of Integration, corroborating the integrative function
assigned to the hubs by intuitive interpretation of their topologi-
cal characteristics.
In this paper we have analysed the modular and hierarchical organi-
sation of the corticocortical network of the cat and its relationship
to the intrinsic necessities of the brain to simultaneously segregate
and integrate multisensory information. From the topological point
of view, we have extended the current understanding of cortical
organisation with the fi nding that the cortical hubs form a central
module on top of the cortical hierarchy; which is expressed as the
partial overlap of the four anatomical modules (visual, auditory,
somatosensory-motor and frontolimbic). By means of dynamical
and information theoretical measures, we have corroborated its
capacity to integrate multisensory information, i.e. after simultane-
ous excitation of visual, auditory and somatosensory primary areas,
a particular set of hubs becomes statistically dependent forming a
dynamical cluster. Additionally, the simultaneous lesion of these
hubs leads to a largest decrease in the integrative capacities of the
network. Both structural and functional results indicate that visual
areas 7 and AES, auditory area EPp and frontolimbic areas Ia, Ig,
CGp, 35 and 36 are the most likely candidates to form the top
hierarchical module. The participation of somatosensory-motor
areas is less clear, although area 6m is the strongest candidate of
them. Visual area 20a and somatosensory-motor areas 5Al and 5Bl
are also potential candidates.
The modular and hierarchical organisation here detected agrees
with the behaviour observed in dynamical simulations of cortical
networks. The resting state dynamics are typically governed by the
formation of dynamical clusters which closely relate to the anatomi-
cal modules, but the infl uence of the hierarchical organisation is
also expressed. In
Zemanová et al. (2006) and Zhou et al. (2006,
it was shown that the correlation between the dynamical
clusters is mediated by the cortical hubs. In
Honey et al. (2007) the
centrality of the hubs was found to oscillate in time. Simulation
of excitable dynamics on hierarchical networks (
et al., 2008
) has shown that the dynamical behaviour of the corti-
cal network of the cat may be dominated either by the modular
structure or by the hubs, depending on the time scales.
The separation of modal information paths is a relevant charac-
teristic of organisation in the nervous system that permits simul-
taneous (parallel) processing of sensory input and detection of
its features. Cortical regions containing neurones specialised in
similar function, e.g. in processing information of the same sen-
sory modality, lie geographically close to each other (Figure 10A).
However, a coherent perception and the emergence of mental
states such as awareness and consciousness require that infor-
mation is integrated at different levels: the binding of sensory
features into entities, the combination of entities with memo-
ries (personal experiences) into events, etc. While experimental
techniques have led to a deep understanding about the basis of
sensory perception, the nature of integration and the localisation
of brain regions involved in it, is still under the subject of debate.
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 11
Zamora-López et al. Cortical module for integration
As stated by Fuster (2003), simple extrapolation of the principles
of sensory organisation do not lead to the identifi cation of the
substrate for cognition.
Several models have proposed that high-level functions are rep-
resented by distributed, interactive and overlapping networks of
neurones, which transcend any of the traditional subdivisions of
the cortex by structural (cytoarchitecture) or functional criteria
Damasio, 1989; Fuster, 2003, 2006; Tononi, 2004). During the
recent years increasing experimental evidence has confi rmed this
hypothesis and the networked perspective has gained the favour
against the assumption of a single brain region fully responsible
for integration (
Stam and Reijneveld, 2007; Bullmore and Sporns,
2009; Knight, 2009
). The anatomical networked connectivity may
serve as the basis in which localised and distributed functional
networks rapidly emerge and dissolve governed by coordination
dynamics according to the sensory stimulation and the ongoing
activity (
Bressler and Kelso, 2001).
As a further evidence, our results resolve the anatomical organi-
sation substrate that supports the capacity of the cerebral cortex
to simultaneously segregate and integrate information. In the
light of this organisation, it could be envisioned that multisensory
integration emerges from the collaborative function of the cortical
hubs. While early sensory cortical regions perform specialised
processing of the sensory input, the hubs of the network may
work together to combine the multisensory information. A relevant
organisation difference is that the cortical hubs form a module
which is densely connected by axonal paths through the white mat-
ter, but is geographically delocalised (Figure 10B).
The current paper focuses in the corticocortical connectivity
of cats because it is, up to date, the most complete and reliable
dataset of its kind. Hence, it is the most suitable for a detailed
and statistically consistent analysis. The main limitation is that
it comprises of interconnection between cortical areas in only
one cerebral hemisphere. Because of the known inter-hemisfere
differences in many mammals, particularly in humans, it will
be very valuable in the future to acquire the connectivity within
and between both hemispheres in animal and human models.
Based on current literature in which the cortical networks of the
macaque and cat models display similar features, we expect that
the general organisation principles here exposed to be valid in a
wide range of mammals.
An interesting challenge is now to explain the emergence of
this modular and hierarchical organisation in terms of evolution
and development, in particular how the delocalised cluster of
hubs could have evolved if, apparently, areas of similar function
tend to be grouped close to each other. Very likely, the balancing
between short wiring requirements (leading to minimisation of
energy costs) and short processing paths allowing for robustness
and fast responses (
Kaiser and Hilgetag, 2006) plays a major role.
It would also be of relevance to fi nd out whether similar hierarchi-
cal patterns are repeated across smaller scales within the cortex,
i.e. the interconnections between cortical columns and micro-
columns. This would imply an underlying fractal-like complex
architecture which can emerge from simple rules of assembly
during development.
FIGURE 10 | Spatial location of the areas according to their modality: visual (yellow), auditory (red), somatosensory-motor (green) and frontolimbic (blue).
While areas of similar modality tend to lie close to each other (A), the hubs form a topological cluster which is spatially delocalised (B).
Frontiers in Neuroinformatics March 2010 | Volume 4 | Article 1 | 12
Zamora-López et al. Cortical module for integration
Finally, we should remind that current non-invasive techniques
such as EEG, MEG and fMRI reveal only the presence of brain
activity. They permit to identify which brain regions are associated
with certain experimental condition. However, at the current stage
it is very diffi cult, if not impossible, to understand what is exactly
an activated region doing. Is it fi ltering a signal? Is it integrating
information? Is an activation detected only because that particular
region contains memories which are being retrieved and passed to
other regions for processing? In our opinion, it would be highly
interesting to further develop concepts of information theory as
the modular and local capacity of integration here presented which
applied to the time series of regional activity might help understand
the particular function of individual brain regions within a given
experimental task.
We thank Lucia Zemanová, Claus-C. Hilgetag and Werner Sommer
for valuable discussions. Gorka Zamora-López and Jürgen Kurths
are supported by the Deutsche Forschungsgemeinschaft, research
group FOR 868 (contract No. KU 837/23-1) and by the BioSim
network of excellence (contract No. LSHB-CT-2004-005137 and
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Copyright © 2010 Zamora-López, Zhou and
Kurths. This is an open-access article subject
to an exclusive license agreement between
the authors and the Frontiers Research
Foundation, which permits unrestricted
use, distribution, and reproduction in any
medium, provided the original authors and
source are credited.
02 February 2010; published online: 19
March 2010.
Citation: Zamora-López G, Zhou C
and Kurths J (2010) Cortical hubs form
a module for multisensory integration
on top of the hierarchy of cortical net-
works. Front. Neuroinform. 4:1. doi:
Conflict of Interest Statement: The
authors declare that the research was con-
ducted in the absence of any commercial or
nancial relationships that could be con-
strued as a potential confl ict of interest.
Received: 06 April 2009; paper pend-
ing published: 10 June 2009; accepted:
    • "In particular, high-degree structural and functional hubs appear to be central in the PLS-derived network patterns. This result provides further evidence that, by virtue of their high connectivity, hub regions integrate information and facilitate communication among multiple brain regions (Zamora-Lopez et al. 2010; van den Heuvel and Sporns 2011; van den Heuvel et al. 2012; Mišicét al. 2014). As a result, the formation of global network patterns naturally revolves around hub regions, which serve to promote synchronization among distributed areas. "
    [Show abstract] [Hide abstract] ABSTRACT: The dynamics of spontaneous fluctuations in neural activity are shaped by underlying patterns of anatomical connectivity. While numerous studies have demonstrated edge-wise correspondence between structural and functional connections, much less is known about how large-scale coherent functional network patterns emerge from the topology of structural networks. In the present study, we deploy a multivariate statistical technique, partial least squares, to investigate the association between spatially extended structural networks and functional networks. We find multiple statistically robust patterns, reflecting reliable combinations of structural and functional subnetworks that are optimally associated with one another. Importantly, these patterns generally do not show a one-to-one correspondence between structural and functional edges, but are instead distributed and heterogeneous, with many functional relationships arising from nonoverlapping sets of anatomical connections. We also find that structural connections between high-degree hubs are disproportionately represented, suggesting that these connections are particularly important in establishing coherent functional networks. Altogether, these results demonstrate that the network organization of the cerebral cortex supports the emergence of diverse functional network configurations that often diverge from the underlying anatomical substrate.
    Full-text · Article · Apr 2016
    • "Our measure satisfactorily vanishes in both extremal cases: dynamical independence and global synchrony. On the contrary, the 'neural complexity' measure proposed in [2] grows monotonically with coupling strength and becomes infinity when the network is globally synchronised (see Supplementary Material for details). Our measure derives from the one introduced in [39, 40] . "
    [Show abstract] [Hide abstract] ABSTRACT: The major structural ingredients of the brain and neural connectomes have been identified in recent years. These are (i) the arrangement of the networks into modules and (ii) the presence of highly connected regions (hubs) forming so-called rich-clubs. It has been speculated that the combination of these features allows the brain to segregate and integrate information but a de- tailed investigation of their functional implications is missing. Here, we examine how these network properties shape the collective dynamics of the brain. We find that both ingredients are crucial for the brain to host complex dynamical behaviour. Comparing the connectomes of C. elegans, cats, macaques and humans to surrogate networks in which one of the two features is destroyed, the functional complexity of the perturbed networks is always decreased. Moreover, a comparison between simulated and empirically obtained resting-state functional connectivity indicates that the human brain, at rest, is in a dynamical state that reflects the largest complexity the anatomical connectome is able to host. In other words, the brain operates at the limit of the network resources it has at hand. Finally, we introduce a new model of hierarchical networks that successfully combines modular organisation with rich-club forming hubs. Our model hosts more complex dynamics than the hierarchical network models previously defined and widely used as benchmarks.
    Full-text · Article · Feb 2016 · Physica A: Statistical Mechanics and its Applications
    • "On the other hand, it will lead to great damage of the whole networks in most cases due to a key node's failure. It is well known that many mechanisms such as spreading, cascading, and synchronizing are highly affected by a tiny fraction of key nodes [11][12][13][14][15][16]. In recent years, a series of cascading large blackouts have occurred in some countries, which caused huge social economy loss. "
    [Show abstract] [Hide abstract] ABSTRACT: Evaluating the importance of nodes for complex networks is of great significance to the research of survivability and robusticity of networks. This paper proposes an effective ranking method based on degree value and the importance of lines. It can well identify the importance of bridge nodes with lower computational complexity. Firstly, the properties of nodes that are connected to a line are used to compute the importance of the line. Then, the contribution of nodes to the importance of lines is calculated. Finally, degree of nodes and the contribution of nodes to the importance of lines are considered to rank the importance of nodes. Five real networks are used as test data. The experimental results show that our method can effectively evaluate the importance of nodes for complex networks.
    Article · Feb 2016
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