A tutorial in connectome analysis: Topological and spatial features of brain networks

Resting-state functional connectivity in late-life depression: higher global connectivity and more long distance connections

Functional magnetic resonance imaging recordings in the resting-state (RS) from the human brain are characterized by spontaneous low-frequency fluctuations in the blood oxygenation level dependent signal that reveal functional connectivity (FC) via their spatial synchronicity. This RS study applied network analysis to compare FC between late-life depression (LLD) patients and control subjects. Raw cross-correlation matrices (CM) for LLD were characterized by higher FC. We analyzed the small-world (SW) and modular organization of these networks consisting of 110 nodes each as well as the connectivity patterns of individual nodes of the basal ganglia. Topological network measures showed no significant differences between groups. The composition of top hubs was similar between LLD and control subjects, however in the LLD group posterior medial-parietal regions were more highly connected compared to controls. In LLD, a number of brain regions showed connections with more distant neighbors leading to an increase of the average Euclidean distance between connected regions compared to controls. In addition, right caudate nucleus connectivity was more diffuse in LLD. In summary, LLD was associated with overall increased FC strength and changes in the average distance between connected nodes, but did not lead to global changes in SW or modular organization.

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble.

Modeling the connectome of a simple spinal cord

In this paper we develop a computational model of the anatomy of a spinal cord. We address a long-standing ambition of neuroscience to understand the structure–function problem by modeling the complete spinal cord connectome map in the 2-day old hatchling Xenopus tadpole. Our approach to modeling neuronal connectivity is based on developmental processes of axon growth. A simple mathematical model of axon growth allows us to reconstruct a biologically realistic connectome of the tadpole spinal cord based on neurobiological data. In our model we distribute neuron cell bodies and dendrites on both sides of the body based on experimental measurements. If growing axons cross the dendrite of another neuron, they make a synaptic contact with a defined probability. The total neuronal network contains ∼1,500 neurons of six cell-types with a total of ∼120,000 connections. The anatomical model contains random components so each repetition of the connectome reconstruction procedure generates a different neuronal network, though all share consistent features such as distributions of cell bodies, dendrites, and axon lengths. Our study reveals a complex structure for the connectome with many interesting specific features including contrasting distributions of connection length distributions. The connectome also shows some similarities to connectivity graphs for other animals such as the global neuronal network of C. elegans. In addition to the interesting intrinsic properties of the connectome, we expect the ability to grow and analyze a biologically realistic spinal cord connectome will provide valuable insights into the properties of the real neuronal networks underlying simple behavior.

Hierarchical information-based clustering for connectivity-based cortex parcellation

One of the most promising avenues for compiling connectivity data originates from the notion that individual brain regions maintain individual connectivity profiles; the functional repertoire of a cortical area (“the functional fingerprint”) is closely related to its anatomical connections (“the connectional fingerprint”) and, hence, a segregated cortical area may be characterized by a highly coherent connectivity pattern. Diffusion tractography can be used to identify borders between such cortical areas. Each cortical area is defined based upon a unique probabilistic tractogram and such a tractogram is representative of a group of tractograms, thereby forming the cortical area. The underlying methodology is called connectivity-based cortex parcellation and requires clustering or grouping of similar diffusion tractograms. Despite the relative success of this technique in producing anatomically sensible results, existing clustering techniques in the context of connectivity-based parcellation typically depend on several non-trivial assumptions. In this paper, we embody an unsupervised hierarchical information-based framework to clustering probabilistic tractograms that avoids many drawbacks offered by previous methods. Cortex parcellation of the inferior frontal gyrus together with the precentral gyrus demonstrates a proof of concept of the proposed method: The automatic parcellation reveals cortical subunits consistent with cytoarchitectonic maps and previous studies including connectivity-based parcellation. Further insight into the hierarchically modular architecture of cortical subunits is given by revealing coarser cortical structures that differentiate between primary as well as premotoric areas and those associated with pre-frontal areas.

Impaired structural motor connectome in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a severe neurodegenerative disease selectively affecting upper and lower motor neurons. Patients with ALS suffer from progressive paralysis and eventually die on average after three years. The underlying neurobiology of upper motor neuron degeneration and its effects on the complex network of the brain are, however, largely unknown. Here, we examined the effects of ALS on the structural brain network topology in 35 patients with ALS and 19 healthy controls. Using diffusion tensor imaging (DTI), the brain network was reconstructed for each individual participant. The connectivity of this reconstructed brain network was compared between patients and controls using complexity theory without - a priori selected - regions of interest. Patients with ALS showed an impaired sub-network of regions with reduced white matter connectivity (p = 0.0108, permutation testing). This impaired sub-network was strongly centered around primary motor regions (bilateral precentral gyrus and right paracentral lobule), including secondary motor regions (bilateral caudal middle frontal gyrus and pallidum) as well as high-order hub regions (right posterior cingulate and precuneus). In addition, we found a significant reduction in overall efficiency (p = 0.0095) and clustering (p = 0.0415). From our findings, we conclude that upper motor neuron degeneration in ALS affects both primary motor connections as well as secondary motor connections, together composing an impaired sub-network. The degenerative process in ALS was found to be widespread, but interlinked and targeted to the motor connectome.

Integrating temporal and spatial scales: human structural network motifs across age and region of interest size

Human brain networks can be characterized at different temporal or spatial scales given by the age of the subject or the spatial resolution of the neuroimaging method. Integration of data across scales can only be successful if the combined networks show a similar architecture. One way to compare networks is to look at spatial features, based on fiber length, and topological features of individual nodes where outlier nodes form single node motifs whose frequency yields a fingerprint of the network. Here, we observe how characteristic single node motifs change over age (12–23 years) and network size (414, 813, and 1615 nodes) for diffusion tensor imaging structural connectivity in healthy human subjects. First, we find the number and diversity of motifs in a network to be strongly correlated. Second, comparing different scales, the number and diversity of motifs varied across the temporal (subject age) and spatial (network resolution) scale: certain motifs might only occur at one spatial scale or for a certain age range. Third, regions of interest which show one motif at a lower resolution may show a range of motifs at a higher resolution which may or may not include the original motif at the lower resolution. Therefore, both the type and localization of motifs differ for different spatial resolutions. Our results also indicate that spatial resolution has a higher effect on topological measures whereas spatial measures, based on fiber lengths, remain more comparable between resolutions. Therefore, spatial resolution is crucial when comparing characteristic node fingerprints given by topological and spatial network features. As node motifs are based on topological and spatial properties of brain connectivity networks, these conclusions are also relevant to other studies using connectome analysis.

Evolution and development of brain networks: from Caenorhabditis elegans to Homo sapiens

Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes involving a limited amount of tasks and modalities to complex functional and behavioral processing integrating different kinds of information from highly specialized tissue. However, studies in a range of species suggest that fundamental similarities, in spatial and topological features as well as in developmental mechanisms for network formation, are retained across evolution. 'Small-world' topology and highly connected regions (hubs) are prevalent across the evolutionary scale, ensuring efficient processing and resilience to internal (e.g. lesions) and external (e.g. environment) changes. Furthermore, in most species, even the establishment of hubs, long-range connections linking distant components, and a modular organization, relies on similar mechanisms. In conclusion, evolutionary divergence leads to greater complexity while following essential developmental constraints.