Identification of large-scale networks in the brain using fMRI
Introduction
During the past decade, investigation of cerebral activity has put more and more emphasis on the analysis of the interactions within large-scale networks of brain areas (Horwitz et al., 1999, Varela et al., 2001). It is now widely accepted that direct, indirect and stimulus-locked interactions between spatially remote brain regions can be measured by the correlation of their fMRI time series. This correlation has been called functional connectivity (Friston, 1994).
While activation analysis allows to search for regions specifically activated during a task as compared to another, functional connectivity makes it possible to explore which networks of regions are strongly interacting for a given condition, without reference to any control condition. The seminal work of Biswal et al. (1995) has introduced (functional) connectivity maps to explore the network connected with a seed region located in the primary motor cortex on resting-state data sets. A connectivity map is a three-dimensional volume whose value at each voxel is the correlation between the time series of this voxel and that of the seed region. A suitable threshold applied to the map allows to identify the network of brain regions functionally connected to the seed. It was suggested that such a network includes mostly those regions with strong anatomical connections to the seed, either direct or indirect (Xiong et al., 1999). This technique was applied on resting-state data sets for a variety of other non-motor seed regions, located in visual (Lowe et al., 1998), language (Cordes et al., 2000) and cingulate (Greicius et al., 2003) cortices, as well as subcortical regions (Stein et al., 2000). By contrast, only few studies have investigated correlation maps for subjects steadily performing a given task (Lowe et al., 2000, Greicius et al., 2003), although many techniques concentrated on comparing patterns of connectivity between tasks (McIntosh and Gonzalez-Lima, 1994, Friston et al., 1997).
Although connectivity maps have proved to be a powerful tool, the technique is not fully satisfactory. The exploration of brain functional networks relies heavily on the choice of the seed region, which allows to get insight only into the network associated with this particular seed. In addition, for seed regions picked at random, connectivity maps do not reveal meaningful cortical areas. They are rather restricted to a few voxels close to the seed region or dominated by noise, and comprise regions located in the ventricles, blood vessels or the outline of the brain. To our knowledge, no method has been proposed yet to overcome these issues.
Other approaches for identifying large-scale patterns of functional connectivity exist that do not rely on a seed region. These include principal components analysis (Friston et al., 1993), independent components analysis (McKeown et al., 1998) and fuzzy clustering (Baumgartner et al., 1998). These techniques were initially developed in the general context of multivariate statistics, and they optimize certain mathematical criteria, respectively: spatial decorrelation, spatial independence and intracluster homogeneity. Unfortunately, there is no clear and systematic relationship between these criteria and functional connectivity within large-scale networks of brain regions.
In this paper, we propose a new method to identify the salient large-scale networks of the human brain in an exploratory and systematic way. Our approach is based on the main acknowledged features of large-scale neural networks. According to Varela et al. (2001), neural assemblies are defined as distributed local networks transiently linked by (large-scale) reciprocal dynamic connections. In the same paper, a local network is defined as a large patch (∼1 cm) of neural tissue that synchronizes its activity through the local cytoarchitecture. This definition has its roots deep back to the concept of Hebbian cell assemblies (Hebb, 1949), which are groups of entities (neurons) that act together in a coherent fashion. The same paper also defines large-scale dynamic connections as interactions based on large fiber pathways among regions that are far apart in the brain (>1 cm).
In fMRI, dynamic connections, either local or large-scale, are thought to be reflected by high temporal correlation values (Horwitz et al., 1999). The voxels belonging to a local network (region) should therefore exhibit highly correlated time series (Zang et al., 2004). Large-scale interactions moreover imply that the time series of each region in the network exhibits strong correlation with the time series of another distant region in the network. Such strong correlations between time series may however also be related to the spatially structured noise in fMRI (Cordes et al., 2002). The spatial correlations of the noise must therefore be taken into account when dealing with the practical identification of the network.
The large-scale network identification (LSNI) method proposed in this paper consists of three steps described in Theory. Firstly, the cortex is divided into disjoint and temporally homogeneous regions (Finding homogeneous brain regions). Secondly, a procedure for estimating the spatial correlations of the noise is described (Robust estimation of the spatial correlation in the noise). Thirdly, the large-scale functional connections are identified as outlier correlations between distant regions that would not occur by chance in the distribution of noise correlations (Identification of large-scale networks). On synthetic data sets, we assess that the false-positive rate of the method is controlled, and we investigate the ability of our method to identify large-scale networks with various numbers of regions and various signal-to-noise ratios (Application to synthetic data sets). We give a description of the networks on real motor data sets with a block-designed paradigm (Application to real data sets). We finally discuss the relevance and limitations of the LSNI method, as well as its potential applications (Discussion).
Section snippets
Finding homogeneous brain regions
The first feature of a large-scale functional network is that each region of the network should be homogeneous, i.e. composed of voxels whose time series share some similarity. We therefore aim to segment the brain cortex into a set of disjoint regions, each being a set of voxels connected with respect to 26-connexity, and such that the resulting regions are functionally homogeneous according to a certain criterion. This is achieved by means of a competitive region growing algorithm, which is
Synthetic data sets
All simulations used the partition of the gray matter into brain regions, namely that obtained on real data sets for subject 1 (see Data analysis). Time series with the same parameters as those of the real data sets (i.e. T = 128, TR = 2.33 s) were simulated in these regions with the following two different sampling procedures.
For the first simulation (S1), synthetic data sets met the null hypothesis of a spatially stationary noise with no large-scale interactions. The time series were composed
Real data sets
Four right-handed male healthy volunteers (age: 25 to 27 years) participated in an fMRI study of motor sequence learning. The protocol was approved by the local ethic committee. One functional run was analyzed for each subject. In this run, subjects were alternating a control task and a motor sequence task, following a conventional 30-s-long block-designed paradigm. The control task consisted of looking at a fixation cross displayed on a screen. The motor sequence task consisted of pressing the
Discussion
The LSNI method proposed in this paper consists of three steps: definition of homogeneous regions, estimation of the correlation in the noise and identification of large-scale networks. These steps were designed under the following hypotheses regarding the statistical properties of the noise:
- (1)
The noise is predominant, i.e. the time series in most brain regions are only noise. We proved on fully synthetic data sets that it was possible to achieve a sensitive detection of a network with 30% of the
Conclusion
In this paper, we have proposed a method for large-scale network identification (LSNI) in fMRI on the basis of two main spatial features, namely the local temporal homogeneity of the regions and the existence of strong large-scale interactions. To achieve this identification, the spatial structure of the noise was robustly estimated. A simulation study demonstrated that the procedure correctly controlled the false-positive rate, and was indeed able to identify functional networks involving up
Acknowledgments
The authors are thankful to Roberto Toro and Jean Daunizeau for helpful comments.
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