Generative model of the human connectome: a geometric approach

1556 

Abstract Submission 

Francis Normand¹, James Pang², Trang Cao³, Jace Cruddas², Alex Fornito¹

¹Monash University, Clayton, Victoria, ²Monash University, Melbourne, Victoria, ³Monash University, Clayton, VIC

Francis Normand  
Monash University
Clayton, Victoria

James Pang, PhD  
Monash University
Melbourne, Victoria

Trang Cao  
Monash University
Clayton, VIC

Jace Cruddas  
Monash University
Melbourne, Victoria

Alex Fornito  
Monash University
Clayton, Victoria

In what follows, the connectome refers to the structural connectivity matrix (SC) representing the large-scale network of physical connections (white-matter fiber tracts) between it's nodes (brain regions). The cortex is usually parcellated between 100 and 1000 brain regions. The connectome is a weighted and undirected network, where the weights (strengths of the connections) represent the total number or the density of fiber tracts between the regions. The interest in generating realistic connectome models stems from the desire to compress its complex network description (its connectivity matrix) to a few simple wiring rules, with a few parameters that are optimized to fit the empirical connectome. The current best generative models usually incorporate two rules that dictate the formation of connections, i.e., a spatial and a topological rule. The topological rule is usually the matching index, which assigns greater probability of connection to nodes who already share common neighbors. This family of generative models can successfully capture the topology of the empirical connectome, based on the four network measures of node degree, betweenness centrality, clustering coefficient and edge length distribution. On the other hand, these models fail to capture the topography of the empirical connectome, for e.g., the location of the hubs. In this work, we propose a generative model of the connectome based entirely on the geometry of the cortex, i.e., using the geometric modes and eigenvalues of the cortical surface mesh. The geometric modes, analogous to the resonant frequencies on a guitar string, represent the fundamental modes of vibrations of the cortical surface mesh representation, i.e., in the linear regime, any pattern of vibration can be decomposed into a combination of the geometric modes. Therefore, the basis of geometric modes is a tool of interest to describe the process through which brain anatomy shapes its function.

The spectral theorem tells us that we can reconstruct the connectome (SC) using its eigenvectors (connectome eigenmodes and eigenvalues. Reconstructing the connectome in this way is trivial, since the connectome itself is used as an input. In this work, we posit that we can approximate SC using instead the geometric modes as a starting point. The geometric modes are obtained by solving the Helmholtz equation using the Laplace-Beltrami operator (LBO) of the mesh.

The starting point is to consider what we term the geometric contribution to the functional connectivity matrix (FC). We posit that the geometric contribution to FC is given by a truncated LBO.

From this hypothesis, our framework lends itself well to the one proposed by Robinson (2012) that relates different representations of connectivity (SC and FC) together through neural field theory (NFT). This framework allows us to reconstruct SC with remarkable precision.

The results presented in the figure show the violin plots for 100 HCP subjects for max KS, reconstruction accuracy and ranked correlations for degree, betweenness, clustering and node connection distance. We also show a visualization of average empirical SC over 100 subjects and average model SC, and scatter plot of node degree for both average network.

Our framework captures both the topology and the topography of empirical connectomes and offers a novel approach to generative models of the connectome, and would seem to suggest that structural connectivity is heavily influenced by geometry.

Connectivity (eg. functional, effective, structural) ¹

fMRI Connectivity and Network Modeling ²

FUNCTIONAL MRI

Modeling

STRUCTURAL MRI

Tractography

White Matter