In order to better understand the high complexity of the brain, the detailed study of its individual components clearly seems insufficient. The backbone of complexity in the nervous system is composed of the large scale architectural characteristics of the neuronal network. Newly, by the advent of MR tractography, its investigation is accessible. We report on two important network characteristics that were already guessed from functional investigations and animal ex vivo studies, but never directly addressed in the human subject, ie the small world and hierarchical architecture of the human long-range brain axonal network

Gigandet, X

Hagmann, P.

Kurant, M.

Meuli, R.

Thiran, J.P.

Thiran, P.

van Wedeen, V.

In order to better understand the high complexity of the brain, the detailed study of its individual components clearly seems insufficient. The backbone of complexity in the nervous system is composed of the large scale architectural characteristics of the neuronal network. Newly, by the advent of MR tractography, its investigation is accessible. We report on two important network characteristics that were already guessed from functional investigations and animal ex vivo studies, but never directly addressed in the human subject, ie the small world and hierarchical architecture of the human long-range brain axonal network.LTS

Gigandet, X.

Wedeen, V.

Thiran, J.

Infoscience - École polytechnique fédérale de Lausanne

Imaging the brain neuronal network with diffusion MRI: a way to understand its global architecture  P. Hagmann1,2, M. Kurant3, X. Gigandet2, P. Thiran3, V. Wedeen4, R. Meuli1, J-P. Thiran2 1Department of Radiology, University Hospital, Lausanne, Switzerland, 2Signal Processing Institute, Ecole Polytechnique Fédérale, Lausanne, Switzerland, 3Laboratory for computer Communications and Applications, Ecole Polytechnique Fédérale, Lausanne, Switzerland, 4MGH Martinos Center for Biomedical Imaging, Harvard Medical School, Charlestown, MA, United States Introduction Biological neuronal networks, and in particular the human brain, are remarkable natural systems capable of complicated patterns of behavior. To understand the emergence of higher level brain functions, the individual study of its components clearly seems insufficient. It is necessary to consider global properties of such complex systems. The backbone of complexity in the nervous system is composed by the large scale architectural characteristics of the neuronal network. We propose to study these properties by using DSI tractography. After having proposed a procedure to image the human long-range brain axonal network, we report on its small world and hierarchical architecture.  Material and Methods We perform a whole brain study of a healthy volunteer on an Achieva 3T Philips scanner. We use a diffusion weighted single shot EPI sequence with the following timing parameters: TR/TE/Delta/delta  = 3000/100/47.6/35 ms and b-max = 12000 mm2/s. Q-space is sampled and the data reconstructed according to a standard DSI scheme [1]. The acquisition block was made of 32 slices of a 128x128 matrix with a spatial resolution of 2x2x3 mm3. DSI tractography is performed as described in [2] by initiating fibers uniformly over the whole brain. As opposed to the classical procedure of tract selection using manually chosen ROIs, in the present experiment we choose the ROIs differently. We place a 3D grid over the brain image. This corresponds to covering the brain with lots of small ROIs of size 8x8x8 mm3 in study 1 and 4x4x4 mm3 in study 2. Furthermore we identify the brain Gray Matter (GM) by using a T1w based segmentation algorithm and actually consider as ROIs only the boxes that contain GM. We construct a graph where the vertices represent the set of ROIs defined above. A weighted edge between two vertices is drawn if there is at least one fiber that has its origin and termination in the pair of different ROIs. The edge weight corresponds to the connection density between ROIs: it is the ratio number of fibers / (their average length * cortical surface in the ROI). This graph represents the brain long-range axonal connectivity between small cortical areas, in study 1 made of 748 and in study 2 of 4522 cortex positions. Now, we construct an unweighted version of this graph by setting an arbitrary threshold on the weight of edges, and keeping only the strongest connections, whose weight exceeded this threshold; the resulting graph is denoted by Gbrain. This allows us to apply standard tools to study the large scale properties of the system. First, we test if the graph Gbrain is a small world, which is an important property of many complex networks [3]. The small-world feature of a graph is assessed from two metrics: average path length L, and clustering coefficient C. L is the average number of hops between two randomly chosen nodes, and C captures the extent to which the network is clustered. As a reference point we take a random graph Grand with the same number of vertices and edges as Gbrain, but where the edges are thrown randomly. The graph Gbrain can be declared a small world, if Lbrain/Lrand≈1 and Cbrain/Crand>>1. Second we want to investigate the potential hierarchy of the data. We use hierarchical clustering, which is a way to investigate grouping in a data set, simultaneously over a variety of scales, by creating a cluster tree [4]. For the current application we simply define the distance d(i,j) as the length of the shortest path between nodes i and j. d(R,S) is the distance between two sets of vertices (1). The algorithm groups then successively the nodes by increasing distance. Results By varying the size of ROI we have constructed brain graphs Gbrain of different sizes. In Tab. A, we present the average path length L and the clustering coefficient C obtained for the graphs with 748 and 4522 nodes. For both graph sizes, the average path length Lbrain of the brain is comparable with the average path length Lrand of its random graph equivalent, whereas the clustering coefficient is higher for the brain. More importantly, with increasing refinement of the measures (and hence the number of nodes), the ratio Cbrain/Crand increases significantly, enhancing the small world characteristic. The application of the hierarchical clustering algorithm results in a structure that can be nicely summarized by a dendrogram in Fig.B. If we read it from top to bottom, we first notice that there are two main clusters. They are separated by a large linkage distance and clearly correspond to the left and right hemispheres. Considering the right hemisphere first, we notice next that a separation occurs between fronto-temporal and parieto-occipital cortices, which means that, in terms of White Matter (WM) axonal connectivity, fronto-temporal as well as parieto-occipital intra-connectivity is intense as compared to the looser fronto-parietal, fronto-occipital or temporo-parieto-occipital links (Fig C). Further decomposition of the lobes occurs into functionally significant areas. Similar decomposition occurs on the left hemisphere. Discussion The current approach distinguishes [5] itself from the standard tractography as it aims to study the global connective relationships between neuronal components and not the precise trajectories of specific links in 3D Euclidean space. Accordingly we combine conceptual models of neuronal networks with new brain measurement tools. The modeling part uses techniques provided by the fast growing field of complex networks, whereas the brain measurement tools are based on diffusion MRI, which is a unique technique that captures human brain connectivity at large scales and non invasively. Although there is a large resolution discrepancy between the true neuronal network (~1010 edges) and the imaged network (105 edges), it nevertheless provides us with exquisite information on the "coarse grain" topology of the network and may asymptotically reflect its real microscopic organization. As such our network imaging procedure is not very different from other imaging modalities, where resolution limitation amounts to average out the architecture. Our findings on the small world network organization of the human brain are further supported by various works on evolution theory [6] and confirm some basic evolutionary principles, such as minimal wiring length for maximal bandwidth. Furthermore, based on post-mortem tracing, studies in rat and macaque monkey brain regions reconstructed axonal connectivity graphs and found similar small world topologies for these brain parts, which again confirm our findings [7]. The identified groupings of cortical regions roughly agree with Brodmann’s cytoarchitectonics and functional cortical subdivisions. At a certain "resolution" we segregate cortical lobes or lobes aggregates, whereas at another level of finer "resolution" sub-lobar entities of functional significance appear. We can recognize a segregation into visual, auditory, motoric and somato-sensory as well as associative prefrontal and parietal areas. Generally speaking, these results confirm experiments made on local brain regions of macaque monkey and cat that showed a highly structured connectivity among brain areas [7] and seem to be an essential feature for multisensorial integration and higher brain function. References [1] Wedeen V, Hagmann P et al (2005) Magn. Res. Med. [2] Hagmann P, et al. Proc. Intl. Soc. Mag. Reson. Med (2004) 623. [3] Watts DJ, Strogatz SH Nature (1998) 393; 440-2. [4] Kaufman L, Rousseeuw PJ. Finding groups in data: an introduction to cluster analysis (1990) Wiley. [5] Hagmann P (2005) PhD thesis, EPFL [6] S. Laughlin, T. Sejnowski (2003) Science 301;1870-4. [7] Hilgetag CC, Kaiser M, Neuroinformatics (2004) 2;353-60. Acknowledgments This work was supported by the Swiss National Science Foundation grant number 3235B0-102868.  (1) 1( , ) ( , )∈ ∈= ∑∑R SR SR S i jd d i j  A) Vertex number Average degree Lbrain Lrand Cbrain Crand 748 51.5 2.34 1.96 0.031 0.0079 4522 25.3 3.33 2.89 0.011 0.00068 B)  C)              D)  Hierarchical clustering subdivides the right hemisphere into temporal, parieto-occipital and fronto-prefrontal areas (Fig C). Lower levels of decomposition seen in Fig D compatible with functionally relevant areas.  

Imaging the brain neuronal network with diffusion MRI: a way to understand its global architecture

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Imaging the Brain Neuronal Network with Diffusion MRI: A Way to Understand Its Global Architecture

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Imaging the Brain Neuronal Network with Diffusion MRI: A Way to Understand Its Global Architecture

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