# Brain Functional Connectivity

## Brain Functional Connectivity in resting state fMRI

Luca Ferrarini

Baldur van Lew

Julien Milles

Supported by the Gisela Thier Foundation (L. Ferrarini)

### Background

This project started officially on January the 1^{st}, 2008. Goal of the project is to investigate brain functional connectivity at rest in healthy individuals and in patients affected by particular brain disorders, such as depression or Alzheimer disease. Particular emphasis in the initial phases of the project has been given to the brain functional organization of healthy subjects; resting state functional MRI have been acquired, and subsequently analyzed within a complex network theoretical framework.

The first step in the analysis is to decide the scale at which a given 4-dimensional fMRI volume needs to be investigated. A common option in literature is to use a pre-defined anatomical atlas (such as the set the Anatomical Automatic Labeling, or AAL): the time courses of all voxels are first averaged together, providing a mean time-course for the given structure. Subsequently, pairs of time-courses are correlated with each other. Different mathematical tools can be used to this goal, such time (partial) correlation, coherence analysis in the Fourier domain, or (as more often is the case) simultaneous frequency/space analysis via correlation of wavelet coefficients. Repeating the analysis for all the possible pairs of structures leads to a symmetric matrix of correlation coefficients. Similarly, one could choose to perform the analysis at voxel level: conceptually, nothing changes.

The next step is to decide which correlations are significant for the analysis and which not. Again, at least two possible approaches are available. If one’s goal is to represent each subject with a complex network representation of its functional connectivity, then the simplest method is to threshold the correlation matrix: any correlation coefficient higher than a given threshold is considered significant, and a connecting link is drawn between the two nodes representing the corresponding paired structures. Alternatively, one might aim at a global complex network representing statistically an entire population. In this case, for any given pair of structures, the entire set of correlation coefficients across subjects can be tested statistically for the null hypothesis that it’s correlation is zero. If the hypothesis is rejected, then a link is drawn between the two structures. When two populations are available (e.g., healthy subjects and patients), both approaches are still valid: in one case one would end up with several networks (one per individual), while in the other only two networks representing the two populations. It is worth noticing that if statistical tests are needed upon network’s properties between populations, then only the first approach is reasonable, since it provides two sets of values for a given network’s property, which can then be compared statistically.

Regardless how a complex network has been obtained, one then wants to assess several topological properties which characterize the network. The most important properties we have investigated so far are: degree distribution, clustering coefficients, characteristic path, global efficiency, local efficiency, cost efficiency, and modularity. Some of these properties are essential to characterize the topology of a given network, and can be used to prove the small-worldness property of brain functional connectivity at rest.

Finally, once the topological properties have been extracted, one can proceed with a statistical analysis of their distribution within a population or between groups.

### Preliminary Results

Since we started this project in January 2008, we have come across some interesting results. In particular, we have:

1. Introduced a new definition of modularity of complex networks, and applied it to the brain functional connectivity of healthy subjects;

2. Thoroughly investigated changes in local, global, and cost efficiency in healthy subjects, at atlas level;

3. Thoroughly investigated the small-world properties of brain functional connectivity in healthy subjects at voxel level, simultaneously developing parallel code to be run on graphic processing units (GPU)

Apart from our main line of research, we have also been involved with groups adopting a different approach to the analysis of fMRI data: the probabilistic Independent Component Analysis (pICA). These collaborations led to other publications in the field of depression and drug research.

### Status

The project is ongoing. Currently, we are investigating the degree distribution of several healthy subjects at voxel level, in order o finally established whether a scale-free organization is present or not. At the same time, we are developing advanced statistical tools to build subject-based networks in which each correlation coefficient is tested for its significance, rather than simply being thresholded. Finally, we are investigating (at atlas level) how several topological properties change in subject with mild cognitive impairment, and subjects with major depression. The analysis at voxel level pushes us to develop parallel implementation of the algorithms needed to assess most of the topological properties. Developments is being carried on for GPUs systems, using CUDA and OpenCL.

### Gallery

Fig. 1: Pipeline for generating a complex network representing brain functional connectivity (at atlas scale)

Fig 2: Consistency of topological properties across frequency bands

Fig 3: A new definition of modularity. Given two nodes (e.g. A and B) the modular index of their associated cluster (A, B, C, and D) is calculated using an auxiliary node H and an unbiased definition of clustering coefficient (see Ferrarini et al., HBM 2009)

Fig 4: (top row) The new definition of modularity highlights a hierarchical organization in brain functional connectivity at rest (green histogram) as compared to random networks (red historgram). (bottom row) Previous definition of modularity could not as well discriminate between random networks and brain functional connectivity at rest. (click on the image to increase resolution)

### Contact

For further information, please contact:

Dr. JR Milles, PhD

Division of Image Processing

Department of Radiology, 1-C2S

Leiden University Medical Center

P.O. Box 9600

2300 RC Leiden

The Netherlands

Tel. +31 (0)71 526 5342

Fax. +31 (0)71 526 6801

mailto: J.R.Milles@lumc.nl

### Publications

#### Journal/Conference Papers

- Ferrarini L., Veer I.M., Baerends E., van Tol M.J., Renken R.J., van der Wee N.J.A., Veltman D., Aleman A., Zitman F.G., Penninx B.W.J.H., van Buchem M.A., Reiber J.H.C., Rombouts S.A.R.B., Milles J.,
*"Hierarchical functional modularity in the resting-state human brain"*, Human Brain Mapping 30(7) July 2009.

#### Conference abstracts

- L. Ferrarini, I. Veer, E. Baerends, M-J. van Tol, N.J.A. van der Wee, M.A. van Buchem, J.H.C. Reiber, S.A.R.B. Rombouts, and J. Milles,
*"Consistency of Global and Local E±ciency across Frequency Bands in MR Functional Connectivity"*, Human Brain Mapping Conference – HBM 2009. San Francisco - California (U.S.A.) - I.M. Veer, C.F. Beckmann, E. Baerends, M-J. van Tol, L. Ferrarini, J. Milles, D.J. Veltman, A. Aleman, M.A. van Buchem, N.J. van der Wee, and S.A.R.B. Rombouts,
*"Reduced functional connectivity in major depression: a whole brain study of multiple resting-state networks"*, Human Brain Mapping Conference - HBM 2009. San Francisco - California (U.S.A.) - E. Baerends, R. Zoethout, C.F. Beckmann, I.M. Veer, T. van Osch, J. Milles, L. Ferrarini, J. Gross, R. Post, M.A. van Buchem, J. van Gerven, and S.A.R.B. Rombouts,
*"Morphine and ethanol alter functional connectivity of**the brain at rest"*, Human Brain Mapping Conference - HBM 2009. San Francisco - California (U.S.A.)