Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

http://brainimaging.waisman.wisc.edu/~chung/neuro.processing/literature/rubinov.2010.NI.network.pdf

Complex network measures of brain connectivity: uses and interpretations.

Information processing in the cerebral cortex involves interactions among distributed areas. Anatomical connectivity suggests that certain areas form local hierarchical relations such as within the visual system. Other connectivity patterns, particularly among association areas, suggest the presence of large-scale circuits without clear hierarchical relations. In this study the organization of networks in the human cerebrum was explored using resting-state functional connectivity MRI. Data from 1,000 subjects were registered using surface-based alignment. A clustering approach was employed to identify and replicate networks of functionally coupled regions across the cerebral cortex. The results revealed local networks confined to sensory and motor cortices as well as distributed networks of association regions. Within the sensory and motor cortices, functional connectivity followed topographic representations across adjacent areas. In association cortex, the connectivity patterns often showed abrupt transitions between network boundaries. Focused analyses were performed to better understand properties of network connectivity. A canonical sensory-motor pathway involving primary visual area, putative middle temporal area complex (MT+), lateral intraparietal area, and frontal eye field was analyzed to explore how interactions might arise within and between networks. Results showed that adjacent regions of the MT+ complex demonstrate differential connectivity consistent with a hierarchical pathway that spans networks. The functional connectivity of parietal and prefrontal association cortices was next explored. Distinct connectivity profiles of neighboring regions suggest they participate in distributed networks that, while showing evidence for interactions, are embedded within largely parallel, interdigitated circuits. We conclude by discussing the organization of these large-scale cerebral networks in relation to monkey anatomy and their potential evolutionary expansion in humans to support cognition.

The organization of the human cerebral cortex estimated by intrinsic functional connectivity

Structurally segregated and functionally specialized regions of the human cerebral cortex are interconnected by a dense network of cortico-cortical axonal pathways. By using diffusion spectrum imaging, we noninvasively mapped these pathways within and across cortical hemispheres in individual human participants. An analysis of the resulting large-scale structural brain networks reveals a structural core within posterior medial and parietal cerebral cortex, as well as several distinct temporal and frontal modules. Brain regions within the structural core share high degree, strength, and betweenness centrality, and they constitute connector hubs that link all major structural modules. The structural core contains brain regions that form the posterior components of the human default network. Looking both within and outside of core regions, we observed a substantial correspondence between structural connectivity and resting-state functional connectivity measured in the same participants. The spatial and topological centrality of the core within cortex suggests an important role in functional integration.

/pdf/mapping-the-structural-core-of-human-cerebral-cortex-20wm5mmkq9.pdf

Mapping the Structural Core of Human Cerebral Cortex

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogs to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

Despite the advent of diffusion magnetic resonance imaging and tractography algorithms, the accurate mapping of complex fiber kiss-crossings areas of the brain remains out of reach. In this study, we present a statistical DSI-based tractography algorithm which explores all possible paths in the brain white matter. We also introduce a cortex connectivity graph whose weighted edges correspond to the connection likelihood. The tests performed on the centrum semi-ovale have shown that a simple thresholding applied to the edges of this graph allows us to image the connectivity of any part of the brain to the desired level of complexity.

/pdf/statistical-dsi-brain-tractography-a-way-to-handle-the-kiss-o48m0b3kko.pdf

Statistical DSI brain tractography: a way to handle the kiss-cross uncertainty

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Segmentation step 32.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.1 Feature selection . . . . . . . . . . . . . . . . . . . . . 42.1.2 Re-scaling methods . . . . . . . . . . . . . . . . . . . . 72.2 Segmentation algorithms . . . . . . . . . . . . . . . . . . . . . 92.2.1 State-of-the-art . . . . . . . . . . . . . . . . . . . . . . 92.2.2 The GHMRF algorithm . . . . . . . . . . . . . . . . . 112.3 Summary of segmentation step settings . . . . . . . . . . . . . 132.3.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Initialization . . . . . . . . . . . . . . . . . . . . . . . . 142.3.3 Segmentation algorithm . . . . . . . . . . . . . . . . . 143 Classiﬁcation step 173.1 Region-based feature extraction . . . . . . . . . . . . . . . . . 183.2 Feature selection . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.1 Cross-validation . . . . . . . . . . . . . . . . . . . . . . 203.2.2 Feature selection by sequential generation . . . . . . . 203.3 Classiﬁers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.1 State-of-the-art . . . . . . . . . . . . . . . . . . . . . . 213.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 223.3.3 Classiﬁers used in the study . . . . . . . . . . . . . . . 234 Validation Methods 294.1 Qualitative evaluation images . . . . . . . . . . . . . . . . . . 294.2 Quantitative evaluation tools . . . . . . . . . . . . . . . . . . . 31ii

Satellite Image Segmentation and

The exploration of the human connectome, a term denoting the global structural connectivity of the brain, is accessible to MRI at millimeter and centimeter scales. In this paper, we propose a methodology to map the connectome by constructing normalized whole-brain structural connection matrices derived from diffusion spectrum MRI tractography. Using a template-based approach, we propose a robust method that allows a) the selection of identical cortical regions of interest in different subjects with identification of the associated fiber tracts, b) a straightforward construction and interpretation of anatomically organized whole-brain connection matrices, and c) a statistical inter-subject comparison of brain connectivity.

Xavier Gigandet

Papers

Statistical DSI brain tractography: a way to handle the kiss-cross uncertainty

Satellite Image Segmentation and

Diffusion MR Image Segmentation: Towards Global Brain Connectivity Analysis