Directed-graph communities of the human connectome
Poster No:
1164
Submission Type:
Abstract Submission
Authors:
Alexandre Cionca1, Michael Chan1, Maciej Jedynak2, Yasser Alemán-Gómez3, Olivier David2, Patric Hagmann3, Dimitri Van De Ville1
Institutions:
1École polytechnique fédérale de Lausanne (EPFL), Geneva, Switzerland, 2Univ. Aix Marseille, Marseille, France, 3Lausanne University Hospital and University of Lausanne (CHUV-UNIL), Lausanne, Switzerland
First Author:
Co-Author(s):
Yasser Alemán-Gómez
Lausanne University Hospital and University of Lausanne (CHUV-UNIL)
Lausanne, Switzerland
Lausanne University Hospital and University of Lausanne (CHUV-UNIL)
Lausanne, Switzerland
Patric Hagmann
Lausanne University Hospital and University of Lausanne (CHUV-UNIL)
Lausanne, Switzerland
Lausanne University Hospital and University of Lausanne (CHUV-UNIL)
Lausanne, Switzerland
Introduction:
Underlying processes of brain function can be extracted from the topological feature of its network representation (i.e. connectome) (Bassett & Sporns, 2017, Margulies et al., 2016; Meunier et al., 2010). These models however usually fail to capture how information is transmitted within the brain, as brain graphs often describe undirected, symmetric relationships between nodes (e.g. regions). Here we showcase a novel framework for community detection in directed graphs, "bicommunities", that we extract from a map of the human brain effective connectivity obtained from electrophysiology, thus informed with directionality. Bicommunities can reveal patterns of directed brain communication that would otherwise remain unseen by conventional community detection.
Methods:
A directed human connectome is built by aggregating a population-level white-matter bundle atlas (Alemán-Gómez et al., 2022) and cortico-cortical evoked potentials (CCEP) from stereo-encephalographic responses to direct electrical stimulation of the multi-centric F-TRACT database (Lemaréchal et al., 2022). The strength of connections sij between brain regions are computed as the number of streamlines from diffusion MRI. The directionality of connections is estimated from the directed communication fij which represents the probability to record an early CCEP (< 100ms) in area j when stimulating area i. The directed connectivity strength kij is derived by redistributing the undirected weight to the outgoing or incoming connection based on the proportion of outgoing or incoming communication:
$$\mathbf{k}_{ij}=2\mathbf{s}_{ij}\frac{\mathbf{f}_{ij}}{\mathbf{f}_{ij}+\mathbf{f}_{ji}}$$
The connectivity matrix is thresholded to obtain an asymmetric, binary adjacency matrix.
Brain bicommunities are identified through the bimodularity framework. This approach is an extension of the spectral optimization of modularity (Newman, 2006) for directed graphs. It separates a network into a set of sending patterns and their corresponding receiving clusters. The bimodularity Qbi is defined as the difference between the fraction of edges from sending communities Ckout to their respective receiving communities Ckin and the expected value of this fraction (from a null configuration model):
$$Q_\text{bi}=\frac{1}{m}\sum_{k=1}^K \sum_{\substack{i\in C_{k}^\text{out}\\j\in C_{k}^\text{in}}} \left[A_{ij}-\mathbf{E}(A_{ij}|{\mathcal H}_0)\right]$$
Bicommunities are extracted using k-means on graph edges projected on embeddings that maximize the bimodularity index. The sending part of a bicommunity can overlap with its corresponding receiving part or with the sending/receiving patterns of other bicommunities.
$$\mathbf{k}_{ij}=2\mathbf{s}_{ij}\frac{\mathbf{f}_{ij}}{\mathbf{f}_{ij}+\mathbf{f}_{ji}}$$
The connectivity matrix is thresholded to obtain an asymmetric, binary adjacency matrix.
Brain bicommunities are identified through the bimodularity framework. This approach is an extension of the spectral optimization of modularity (Newman, 2006) for directed graphs. It separates a network into a set of sending patterns and their corresponding receiving clusters. The bimodularity Qbi is defined as the difference between the fraction of edges from sending communities Ckout to their respective receiving communities Ckin and the expected value of this fraction (from a null configuration model):
$$Q_\text{bi}=\frac{1}{m}\sum_{k=1}^K \sum_{\substack{i\in C_{k}^\text{out}\\j\in C_{k}^\text{in}}} \left[A_{ij}-\mathbf{E}(A_{ij}|{\mathcal H}_0)\right]$$
Bicommunities are extracted using k-means on graph edges projected on embeddings that maximize the bimodularity index. The sending part of a bicommunity can overlap with its corresponding receiving part or with the sending/receiving patterns of other bicommunities.
Results:
We highlight four bicommunities through the maximization of bimodularity. The two patterns with the highest contribution to bimodularity show the interconnectivity within both hemispheres. The two remaining bicommunities however distinguish inter-hemispheric connectivity from left to right and from right to left respectively. The negative bimodularity indices hint dissortative community structures.
Finer clustering (k=12) further separates each hemisphere in two distinct sets of regions located in the anterior and posterior half respectively. The directed communication between each pair of hemisphere half is highlighted in a specific bicommunity.
Finer clustering (k=12) further separates each hemisphere in two distinct sets of regions located in the anterior and posterior half respectively. The directed communication between each pair of hemisphere half is highlighted in a specific bicommunity.
·Bicommunities (k = 4) of the human brain. Colors show the contribution of a brain region to the sending (red) pattern or its corresponding receiving (blue) community. LH (RH): Left (Right) Hemisphere.
·Bicommunities (k = 12) of the human brain. Colors show the contribution of a brain region to the sending (red) pattern or its corresponding receiving (blue) community. LH (RH): Left (Right) Hemisphere
Conclusions:
Bicommunities of the directed human connectome show coherent brain networks with a novel perspective. Unlike traditional clustering approaches, our method distinguishes the directed relationship both within and between hemispheres. Bicommunities go beyond the trivial symmetric structure of the brain and identify regions that predominantly send or receive information in each pattern. This stresses the potential of bimodularity as an innovative approach to disentangle the complex pathways of neural communication.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
fMRI Connectivity and Network Modeling 2
Keywords:
Computational Neuroscience
Data analysis
MRI
STRUCTURAL MRI
1|2Indicates the priority used for review
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Provide references using APA citation style.
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Margulies, D. S., et al. (2016). Situating the default-mode network along a principal gradient of macroscale cortical organization. Proceedings of the National Academy of Sciences, 113(44), 12574–12579. https://doi.org/10.1073/pnas.1608282113
Meunier, D., et al. (2010). Modular and Hierarchically Modular Organization of Brain Networks. Frontiers in Neuroscience, 4. https://doi.org/10.3389/fnins.2010.00200
Newman, M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23), 8577–8582. https://doi.org/10.1073/pnas.0601602103