Network Curvature as a Hallmark of Brain Structural Connectivity

AbstractStudies show that while brain networks are remarkably robust to a variety of adverse events, such as injuries and lesions due to accidents or disease, they may be fragile when the disturbance takes place in specific locations. This seems to be the case for diseases in which accumulated changes in network topology dramatically affect certain sensitive areas. To this end, previous attempts have been made to quantify robustness and fragility of brain functionality in two broadly defined ways: (i) utilizing model-based techniques to predict lesion effects, and (ii) studying empirical effects from brain lesions due to injury or disease. Both directions aim at assessing functional connectivity changes resulting from structural network variations. In the present work, we follow a more geometric viewpoint that is based on a notion of curvature of networks, the so-called Ollivier-Ricci curvature. A similar approach has been used in recent studies to quantify financial market robustness as well as to differentiate biological networks corresponding to cancer cells from normal cells. The same notion of curvature, defined at the node level for brain networks obtained from MRI data, may help identify and characterize the effects of diseases on specific brain regions. In the present paper, we apply the Ollivier-Ricci curvature to brain structural networks to: i) Demonstrate its unique ability to identify robust (or fragile) brain regions in healthy subjects. We compare our results to previously published work which identified a unique set of regions (called structural core) of the human cerebral cortex. This novel characterization of brain networks, complementary to measures such as degree, strength, clustering or efficiency, may be particularly useful to detect and monitor candidate areas for targeting by surgery (e.g. deep brain stimulation) or pharmaco-therapeutic agents; ii) Illustrate the power our curvature-derived measures to track changes in brain connectivity with healthy development/aging and; iii) Detect changes in brain structural connectivity in people with Autism Spectrum Disorders (ASD) which are in agreement with previous morphometric MRI studies.

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Network curvature as a hallmark of brain structural connectivity

Nature Communications ◽

10.1038/s41467-019-12915-x ◽

2019 ◽

Vol 10 (1) ◽

Cited By ~ 3

Author(s):

Hamza Farooq ◽

Yongxin Chen ◽

Tryphon T. Georgiou ◽

Allen Tannenbaum ◽

Christophe Lenglet

Keyword(s):

Financial Market ◽

Biological Networks ◽

Healthy Subjects ◽

Structural Changes ◽

Brain Connectivity ◽

Empirical Studies ◽

Structural Connectivity ◽

Brain Regions ◽

Autism Spectrum ◽

Structural Networks

Abstract Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies.

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New graph-theoretical-multimodal approach using temporal and structural correlations reveal disruption in the thalamo-cortical network in patients with schizophrenia

10.1101/489997 ◽

2018 ◽

Author(s):

Paolo Finotteli ◽

Caroline Garcia Forlim ◽

Paolo Dulio ◽

Leonie Klock ◽

Alessia Pini ◽

...

Keyword(s):

Functional Connectivity ◽

Resting State ◽

Brain Connectivity ◽

Brain Networks ◽

Structural Connectivity ◽

Network Models ◽

Brain Regions ◽

Cortical Network ◽

Future Research ◽

Connectivity Matrix

Schizophrenia has been understood as a network disease with altered functional and structural connectivity in multiple brain networks compatible to the extremely broad spectrum of psychopathological, cognitive and behavioral symptoms in this disorder. When building brain networks, functional and structural networks are typically modelled independently: functional network models are based on temporal correlations among brain regions, whereas structural network models are based on anatomical characteristics. Combining both features may give rise to more realistic and reliable models of brain networks. In this study, we applied a new flexible graph-theoretical-multimodal model called FD (F, the functional connectivity matrix, and D, the structural matrix) to construct brain networks combining functional, structural and topological information of MRI measurements (structural and resting state imaging) to patients with schizophrenia (N=35) and matched healthy individuals (N=41). As a reference condition, the traditional pure functional connectivity (pFC) analysis was carried out. By using the FD model, we found disrupted connectivity in the thalamo-cortical network in schizophrenic patients, whereas the pFC model failed to extract group differences after multiple comparison correction. We interpret this observation as evidence that the FD model is superior to conventional connectivity analysis, by stressing relevant features of the whole brain connectivity including functional, structural and topological signatures. The FD model can be used in future research to model subtle alterations of functional and structural connectivity resulting in pronounced clinical syndromes and major psychiatric disorders. Lastly, FD is not limited to the analysis of resting state fMRI, and can be applied to EEG, MEG etc.

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On the structural connectivity of large-scale models of brain networks at cellular level

Scientific Reports ◽

10.1038/s41598-021-83759-z ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Giuseppe Giacopelli ◽

Domenico Tegolo ◽

Emiliano Spera ◽

Michele Migliore

Keyword(s):

Large Scale ◽

Brain Networks ◽

Structural Connectivity ◽

Network Models ◽

Brain Regions ◽

Cellular Level ◽

Scale Model ◽

Mathematical Framework ◽

Underlying Mechanisms ◽

Experimental Findings

AbstractThe brain’s structural connectivity plays a fundamental role in determining how neuron networks generate, process, and transfer information within and between brain regions. The underlying mechanisms are extremely difficult to study experimentally and, in many cases, large-scale model networks are of great help. However, the implementation of these models relies on experimental findings that are often sparse and limited. Their predicting power ultimately depends on how closely a model’s connectivity represents the real system. Here we argue that the data-driven probabilistic rules, widely used to build neuronal network models, may not be appropriate to represent the dynamics of the corresponding biological system. To solve this problem, we propose to use a new mathematical framework able to use sparse and limited experimental data to quantitatively reproduce the structural connectivity of biological brain networks at cellular level.

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Integrative Structural Brain Network Analysis In Diffusion Tensor Imaging

10.1101/129015 ◽

2017 ◽

Cited By ~ 1

Author(s):

Moo K. Chung ◽

Jamie L. Hanson ◽

Nagesh Adluru ◽

Andrew L. Alexander ◽

Richard J. Davidson ◽

...

Keyword(s):

Diffusion Tensor Imaging ◽

Diffusion Tensor ◽

Structural Connectivity ◽

Brain Regions ◽

Brain Network ◽

Node Degree ◽

Fiber Tracts ◽

White Matter Fiber Tracts ◽

Structural Brain Network ◽

Structural Networks

AbstractIn diffusion tensor imaging, structural connectivity between brain regions is often measured by the number of white matter fiber tracts connecting them. Other features such as the length of tracts or fractional anisotropy (FA) are also used in measuring the strength of connectivity. In this study, we investigated the effects of incorporating the number of tracts, the tract length and FA-values into the connectivity model. Using various node-degree based graph theory features, the three connectivity models are compared. The methods are applied in characterizing structural networks between normal controls and maltreated children, who experienced maltreatment while living in post-institutional settings before being adopted by families in the US.

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Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Network Neuroscience ◽

10.1162/netn_a_00150 ◽

2020 ◽

Vol 4 (3) ◽

pp. 871-890

Author(s):

Arseny A. Sokolov ◽

Peter Zeidman ◽

Adeel Razi ◽

Michael Erb ◽

Philippe Ryvlin ◽

...

Keyword(s):

White Matter ◽

Dynamic Range ◽

Diffusion Processes ◽

Brain Connectivity ◽

Effective Connectivity ◽

Structural Connectivity ◽

Laplacian Matrix ◽

Graph Laplacian ◽

Brain Regions ◽

High Order

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

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Brain Network Organization Correlates with Autistic Features in Preschoolers with Autism Spectrum Disorders and in Their Fathers: Preliminary Data from a DWI Analysis

Journal of Clinical Medicine ◽

10.3390/jcm8040487 ◽

2019 ◽

Vol 8 (4) ◽

pp. 487 ◽

Cited By ~ 2

Author(s):

Billeci ◽

Calderoni ◽

Conti ◽

Lagomarsini ◽

Narzisi ◽

...

Keyword(s):

Autism Spectrum Disorders ◽

Brain Connectivity ◽

Brain Regions ◽

Autism Spectrum ◽

Brain Network ◽

Local Network ◽

Network Organization ◽

Frontal Pole ◽

Structural Network ◽

Spectrum Disorders

Autism Spectrum Disorders (ASD) is a group of neurodevelopmental disorders that is characterized by an altered brain connectivity organization. Autistic traits below the clinical threshold (i.e., the broad autism phenotype; BAP) are frequent among first-degree relatives of subjects with ASD; however, little is known regarding whether subthreshold behavioral manifestations of ASD mirror also at the neuroanatomical level in parents of ASD probands. To this aim, we applied advanced diffusion network analysis to MRI of 16 dyads consisting of a child with ASD and his father in order to investigate: (i) the correlation between structural network organization and autistic features in preschoolers with ASD (all males; age range 1.5–5.2 years); (ii) the correlation between structural network organization and BAP features in the fathers of individuals with ASD (fath-ASD). Local network measures significantly correlated with autism severity in ASD children and with BAP traits in fath-ASD, while no significant association emerged when considering the global measures of brain connectivity. Notably, an overlap of some brain regions that are crucial for social functioning (cingulum, superior temporal gyrus, inferior temporal gyrus, middle frontal gyrus, frontal pole, and amygdala) in patients with ASD and fath-ASD was detected, suggesting an intergenerational transmission of these neural substrates. Overall, the results of this study may help in elucidating the neurostructural endophenotype of ASD, paving the way for bridging connections between underlying genetic and ASD symptomatology.

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An Autism Spectrum Disorder Adaptive Identification Based on the Elimination of Brain Connections: A Proof of Long-Range Underconnectivity

10.21203/rs.3.rs-982098/v1 ◽

2021 ◽

Author(s):

Fatima zahra Benabdallah ◽

Ahmed Drissi El Maliani ◽

Dounia Lotfi ◽

Rachid Jennane ◽

Mohammed El hassouni

Keyword(s):

Autism Spectrum Disorder ◽

Functional Connectivity ◽

Long Range ◽

Data Exchange ◽

Brain Connectivity ◽

Brain Regions ◽

Autism Spectrum ◽

Spectrum Disorder ◽

Imaging Data ◽

Brain Imaging Data

Abstract Autism spectrum disorder (ASD) is theoretically characterized by alterations in functional connectivity between brain regions. Many works presented approaches to determine informative patterns that help to predict autism from typical development. However, most of the proposed pipelines are not specifically designed for the autism problem, i.e they do not corroborate with autism theories about functional connectivity. In this paper, we propose a framework that takes into account the properties of local connectivity and long range under-connectivity in the autistic brain. The originality of the proposed approach is to adopt elimination as a technique in order to well emerge the autistic brain connectivity alterations, and show how they contribute to differentiate ASD from controls. Experimental results conducted on the large multi-site Autism Brain Imaging Data Exchange (ABIDE) show that our approach provides accurate prediction up to 70% and succeeds to prove the existence of deficits in the long-range connectivity in the ASD subjects brains.

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Unique mapping of structural and functional connectivity on cognition

10.1101/296913 ◽

2018 ◽

Author(s):

J. Zimmermann ◽

J.G. Griffiths ◽

A.R. McIntosh

Keyword(s):

Functional Connectivity ◽

Brain Connectivity ◽

Structural Connectivity ◽

Brain Regions ◽

Unique Mapping ◽

Human Connectome Project ◽

Behavioural Patterns ◽

Wide Range ◽

Psychological Tasks ◽

New Evidence

AbstractThe unique mapping of structural and functional brain connectivity (SC, FC) on cognition is currently not well understood. It is not clear whether cognition is mapped via a global connectome pattern or instead is underpinned by several sets of distributed connectivity patterns. Moreover, we also do not know whether the pattern of SC and of FC that underlie cognition are overlapping or distinct. Here, we study the relationship between SC and FC and an array of psychological tasks in 609 subjects from the Human Connectome Project (HCP). We identified several sets of connections that each uniquely map onto different aspects of cognitive function. We found a small number of distributed SC and a larger set of cortico-cortical and cortico-subcortical FC that express this association. Importantly, SC and FC each show unique and distinct patterns of variance across subjects and differential relationships to cognition. The results suggest that a complete understanding of connectome underpinnings of cognition calls for a combination of the two modalities.Significance StatementStructural connectivity (SC), the physical white-matter inter-regional pathways in the brain, and functional connectivity (FC), the temporal co-activations between activity of brain regions, have each been studied extensively. Little is known, however, about the distribution of variance in connections as they relate to cognition. Here, in a large sample of subjects (N = 609), we showed that two sets of brain-behavioural patterns capture the correlations between SC, and FC with a wide range of cognitive tasks, respectively. These brain-behavioural patterns reveal distinct sets of connections within the SC and the FC network and provide new evidence that SC and FC each provide unique information for cognition.

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The R1-weighted connectome: complementing brain networks with a myelin-sensitive measure

Network Neuroscience ◽

10.1162/netn_a_00179 ◽

2020 ◽

pp. 1-15

Author(s):

Tommy Boshkovski ◽

Ljupco Kocarev ◽

Julien Cohen-Adad ◽

Bratislav Mišić ◽

Stéphane Lehéricy ◽

...

Keyword(s):

White Matter ◽

Diffusion Mri ◽

Brain Connectivity ◽

Structural Connectivity ◽

Brain Regions ◽

Added Value ◽

Modular Organization ◽

Sensitive Measure ◽

Higher Order Functions ◽

Insight Into

Myelin plays a crucial role in how well information travels between brain regions. Complementing the structural connectome, obtained with diffusion MRI tractography, with a myelin-sensitive measure could result in a more complete model of structural brain connectivity and give better insight into white-matter myeloarchitecture. In this work we weight the connectome by the longitudinal relaxation rate (R1), a measure sensitive to myelin, and then we assess its added value by comparing it with connectomes weighted by the number of streamlines (NOS). Our analysis reveals differences between the two connectomes both in the distribution of their weights and the modular organization. Additionally, the rank-based analysis shows that R1 can be used to separate transmodal regions (responsible for higher-order functions) from unimodal regions (responsible for low-order functions). Overall, the R1-weighted connectome provides a different perspective on structural connectivity taking into account white matter myeloarchitecture.

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Structurally constrained effective brain connectivity

10.31219/osf.io/4erqd ◽

2021 ◽

Author(s):

Alessandro Crimi

Keyword(s):

Community Detection ◽

Autoregressive Model ◽

Brain Connectivity ◽

Effective Connectivity ◽

Structural Connectivity ◽

Ground Truth ◽

Autism Spectrum ◽

Case Control ◽

Functional Dependencies ◽

The Brain

The relationship between structure and function is of interest in many research fields involving the study of complex biological processes. In neuroscience in particular, the fusion of structural and functional data can help to understand the underlying principles of the operational networks in the brain. To address this issue, this paper proposes a constrained autoregressive model leading to a representation of effective connectivity that can be used to better understand how the structure modulates the function. Or simply, it can be used to find novel biomarkers characterizing groups of subjects. In practice, an initial structural connectivity representation is re-weighted to explain the functional co-activations. This is obtained by minimizing the reconstruction error of an autoregressive model constrained by the structural connectivity prior. The model has been designed to also include indirect connections, allowing to split direct and indirect components in the functional connectivity, and it can be used with raw and deconvoluted BOLD signal.The derived representation of dependencies was compared to the well known dynamic causal model, giving results closer to known ground-truth. Further evaluation of the proposed effective network was performed on two typical tasks. In a first experiment the direct functional dependencies were tested on a community detection problem, where the brain was partitioned using the effective networks across multiple subjects. In a second experiment the model was validated in a case-control task, which aimed at differentiating healthy subjects from individuals with autism spectrum disorder. Results showed that using effective connectivity leads to clusters better describing the functional interactions in the community detection task, while maintaining the original structural organization, and obtaining a better discrimination in the case-control classification task.

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