The role of symmetry in neural networks and their Laplacian spectra

Human and animal nervous systems constitute complexly wired networks that form the infrastructure for neural processing and integration of information. The organization of these neural networks can be analyzed using the so-called Laplacian spectrum, providing a mathematical tool to produce systems-level network fingerprints. In this article, we examine a characteristic central peak in the spectrum of neural networks, including anatomical brain network maps of the mouse, cat and macaque, as well as anatomical and functional network maps of human brain connectivity. We link the occurrence of this central peak to the level of symmetry in neural networks, an intriguing aspect of network organization resulting from network elements that exhibit similar wiring patterns. Specifically, we propose a measure to capture the global level of symmetry of a network and show that, for both empirical networks and network models, the height of the main peak in the Laplacian spectrum is strongly related to node symmetry in the underlying network. Moreover, examination of spectra of duplication-based model networks shows that neural spectra are best approximated using a trade-off between duplication and diversification. Taken together, our results facilitate a better understanding of neural network spectra and the importance of symmetry in neural networks

Early human brain development:insights into macroscale connectome wiring

BACKGROUND: Early brain development is closely dictated by distinct neurobiological principles. Here, we aimed to map early trajectories of structural brain wiring in the neonatal brain. METHODS: We investigated structural connectome development in 44 newborns, including 23 preterm infants and 21 full-term neonates scanned between 29 and 45 postmenstrual weeks. Diffusion-weighted imaging data were combined with cortical segmentations derived from T2 data to construct neonatal connectome maps. RESULTS: Projection fibers interconnecting primary cortices and deep gray matter structures were noted to mature faster than connections between higher-order association cortices (fractional anisotropy (FA) F = 58.9, p < 0.001, radial diffusivity (RD) F = 28.8, p < 0.001). Neonatal FA-values resembled adult FA-values more than RD, while RD approximated the adult brain faster (F = 358.4, p < 0.001). Maturational trajectories of RD in neonatal white matter pathways revealed substantial overlap with what is known about the sequence of subcortical white matter myelination from histopathological mappings as recorded by early neuroanatomists (mean RD 68 regions r = 0.45, p = 0.008). CONCLUSION: Employing postnatal neuroimaging we reveal that early maturational trajectories of white matter pathways display discriminative developmental features of the neonatal brain network. These findings provide valuable insight into the early stages of structural connectome development

Connectome-Based Patterns of First-Episode Medication-Naïve Patients With Schizophrenia

Emerging evidence indicates that a disruption in brain network organization may play an important role in the pathophysiology of schizophrenia. The neuroimaging fingerprint reflecting the pathophysiology of first-episode schizophrenia remains to be identified. Here, we aimed at characterizing the connectome organization of first-episode medication-naïve patients with schizophrenia. A cross-sectional structural and functional neuroimaging study using two independent samples (principal dataset including 42 medication-naïve, previously untreated patients and 48 healthy controls; replication dataset including 39 first-episode patients [10 untreated patients] and 66 healthy controls) was performed. Brain network architecture was assessed by means of white matter fiber integrity measures derived from diffusion-weighted imaging (DWI) and by means of structural-functional (SC-FC) coupling measured by combining DWI and resting-state functional magnetic resonance imaging. Connectome rich club organization was found to be significantly disrupted in medication-naïve patients as compared with healthy controls (P = .012, uncorrected), with rich club connection strength (P = .032, uncorrected) and SC-FC coupling (P < .001, corrected for false discovery rate) decreased in patients. Similar results were found in the replication dataset. Our findings suggest that a disruption of rich club organization and functional dynamics may reflect an early feature of schizophrenia pathophysiology. These findings add to our understanding of the neuropathological mechanisms of schizophrenia and provide new insights into the early stages of the disorder

Severity of current depression and remission status are associated with structural connectome alterations in major depressive disorder

Major depressive disorder (MDD) is associated to affected brain wiring. Little is known whether these changes are stable over time and hence might represent a biological predisposition, or whether these are state markers of current disease severity and recovery after a depressive episode. Human white matter network ("connectome") analysis via network science is a suitable tool to investigate the association between affected brain connectivity and MDD. This study examines structural connectome topology in 464 MDD patients (mean age: 36.6 years) and 432 healthy controls (35.6 years). MDD patients were stratified categorially by current disease status (acute vs. partial remission vs. full remission) based on DSM-IV criteria. Current symptom severity was assessed continuously via the Hamilton Depression Rating Scale (HAMD). Connectome matrices were created via a combination of T1-weighted magnetic resonance imaging (MRI) and tractography methods based on diffusion-weighted imaging. Global tract-based metrics were not found to show significant differences between disease status groups, suggesting conserved global brain connectivity in MDD. In contrast, reduced global fractional anisotropy (FA) was observed specifically in acute depressed patients compared to fully remitted patients and healthy controls. Within the MDD patients, FA in a subnetwork including frontal, temporal, insular, and parietal nodes was negatively associated with HAMD, an effect remaining when correcting for lifetime disease severity. Therefore, our findings provide new evidence of MDD to be associated with structural, yet dynamic, state-dependent connectome alterations, which covary with current disease severity and remission status after a depressive episode

Genetic mapping and evolutionary analysis of human-expanded cognitive networks

Cognitive brain networks such as the default-mode network (DMN), frontoparietal network, and salience network, are key functional networks of the human brain. Here we show that the rapid evolutionary cortical expansion of cognitive networks in the human brain, and most pronounced the DMN, runs parallel with high expression of human-accelerated genes (HAR genes). Using comparative transcriptomics analysis, we present that HAR genes are differentially more expressed in higher-order cognitive networks in humans compared to chimpanzees and macaques and that genes with high expression in the DMN are involved in synapse and dendrite formation. Moreover, HAR and DMN genes show significant associations with individual variations in DMN functional activity, intelligence, sociability, and mental conditions such as schizophrenia and autism. Our results suggest that the expansion of higher-order functional networks subserving increasing cognitive properties has been an important locus of genetic changes in recent human brain evolution

10Kin1day: A Bottom-Up Neuroimaging Initiative.

We organized 10Kin1day, a pop-up scientific event with the goal to bring together neuroimaging groups from around the world to jointly analyze 10,000+ existing MRI connectivity datasets during a 3-day workshop. In this report, we describe the motivation and principles of 10Kin1day, together with a public release of 8,000+ MRI connectome maps of the human brain

The laplacian spectrum of neural networks

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks

Structural and functional connectivity reconstruction with CATO - A Connectivity Analysis TOolbox

We describe a Connectivity Analysis TOolbox (CATO) for the reconstruction of structural and functional brain connectivity based on diffusion weighted imaging and resting-state functional MRI data. CATO is a multimodal software package that enables researchers to run end-to-end reconstructions from MRI data to structural and functional connectome maps, customize their analyses and utilize various software packages to preprocess data. Structural and functional connectome maps can be reconstructed with respect to user-defined (sub)cortical atlases providing aligned connectivity matrices for integrative multimodal analyses. We outline the implementation and usage of the structural and functional processing pipelines in CATO. Performance was calibrated with respect to simulated diffusion weighted imaging from the ITC2015 challenge, test-retest diffusion weighted imaging data and resting-state functional MRI data from the Human Connectome Project. CATO is open-source software distributed under the MIT License and available as a MATLAB toolbox and as a stand-alone application at www.dutchconnectomelab.nl/CATO

Connection strength of the macaque connectome augments topological and functional network attributes

Mammalian brains constitute complex organized networks of neural projections. On top of their binary topological organization, the strength (or weight) of these neural projections can be highly variable across connections and is thus likely of additional importance to the overall topological and functional organization of the network. Here we investigated the specific distribution pattern of connection strength in the macaque connectome. We performed weighted and binary network analysis on the cortico-cortical connectivity of the macaque provided by the unique tract-tracing dataset of Markov and colleagues (2014) and observed in both analyses a small-world, modular and rich club organization. Moreover, connectivity strength showed a distribution augmenting the architecture identified in the binary network version by enhancing both local network clustering and the central infrastructure for global topological communication and integration. Functional consequences of this topological distribution were further examined using the Kuramoto model for simulating interactions between brain regions and showed that the connectivity strength distribution across connections enhances synchronization within modules and between rich club hubs. Together, our results suggest that neural pathway strength promotes topological properties in the macaque connectome for local processing and global network integration

The role of symmetry in neural networks and their Laplacian spectra

Human and animal nervous systems constitute complexly wired networks that form the infrastructure for neural processing and integration of information. The organization of these neural networks can be analyzed using the so-called Laplacian spectrum, providing a mathematical tool to produce systems-level network fingerprints. In this article, we examine a characteristic central peak in the spectrum of neural networks, including anatomical brain network maps of the mouse, cat and macaque, as well as anatomical and functional network maps of human brain connectivity. We link the occurrence of this central peak to the level of symmetry in neural networks, an intriguing aspect of network organization resulting from network elements that exhibit similar wiring patterns. Specifically, we propose a measure to capture the global level of symmetry of a network and show that, for both empirical networks and network models, the height of the main peak in the Laplacian spectrum is strongly related to node symmetry in the underlying network. Moreover, examination of spectra of duplication-based model networks shows that neural spectra are best approximated using a trade-off between duplication and diversification. Taken together, our results facilitate a better understanding of neural network spectra and the importance of symmetry in neural networks