A Geometric Generative Model of the Connectome
Presented During:
Saturday, June 28, 2025: 11:30 AM - 12:45 PM
Brisbane Convention & Exhibition Centre
Room:
P2 (Plaza Level)
Poster No:
1773
Submission Type:
Abstract Submission
Authors:
Francis Normand1, James Pang1, Trang Cao1, Jace Cruddas1, Mehul Gajwani1, Arshiya Sangchooli1, Alex Fornito1
Institutions:
1Monash University, Clayton, Victoria
First Author:
Co-Author(s):
Introduction:
Understanding the organizational principles that shape the network architecture of the brain remains a fundamental challenge in neuroscience. The prevailing view is that the brain is a discrete network of intricately connected neurons and neuronal populations (Bullmore and Sporns 2009). From this framework, several generative network models have been proposed to identify the wiring rules that might shape connectome architecture (Betzel 2017). These models are generally able to capture topological properties of empirical data, but fail to capture topographical (i.e., spatial) properties (Oldham 2023).
An alternative view, informed by neural field theory (NFT)(Robinson 1997), involves treating brain structures, particularly the cortex, as continuous. Spatiotemporally patterned neocortical dynamics are then viewed as emerging from waves of excitation travelling through the continuous cortical sheet (Robinson 1997). Critically, it can be shown that these waves arise from a superposition of a fundamental basis set of resonant standing wave patterns that correspond to the eigenmodes of cortical geometry, an equivalence given by the well-known Helmholtz equation used in diverse diverse areas of physics and engineering (Robinson et al., 1997 ;Pang et al., 2023). These eigenmodes thus correspond to preferred, resonant modes of cortical excitation.
A corollary of this view is that anatomical connections in the brain may preferentially link different areas to support resonance of the geometric modes, under a Hebbian-like plasticity mechanism (i.e., cells that fire together wire together). Here, we test this hypothesis by using a simple model that preferentially connects distinct cortical areas according to their profiles of geometric resonance. The model is simple and highly scalable, yielding, to our knowledge, the first generative model of weighted conectome architecture at the vertex level. Our model out-performs traditional models assuming discretized graph-like structures, highlighting the utility of continuous approaches that prioritize the physical and spatial properties of the brain.
An alternative view, informed by neural field theory (NFT)(Robinson 1997), involves treating brain structures, particularly the cortex, as continuous. Spatiotemporally patterned neocortical dynamics are then viewed as emerging from waves of excitation travelling through the continuous cortical sheet (Robinson 1997). Critically, it can be shown that these waves arise from a superposition of a fundamental basis set of resonant standing wave patterns that correspond to the eigenmodes of cortical geometry, an equivalence given by the well-known Helmholtz equation used in diverse diverse areas of physics and engineering (Robinson et al., 1997 ;Pang et al., 2023). These eigenmodes thus correspond to preferred, resonant modes of cortical excitation.
A corollary of this view is that anatomical connections in the brain may preferentially link different areas to support resonance of the geometric modes, under a Hebbian-like plasticity mechanism (i.e., cells that fire together wire together). Here, we test this hypothesis by using a simple model that preferentially connects distinct cortical areas according to their profiles of geometric resonance. The model is simple and highly scalable, yielding, to our knowledge, the first generative model of weighted conectome architecture at the vertex level. Our model out-performs traditional models assuming discretized graph-like structures, highlighting the utility of continuous approaches that prioritize the physical and spatial properties of the brain.
Methods:
The starting point of our model is the eigenmodes of cortical geometry, derived from the Laplace-Beltrami operator of the cortical surface. Each eigenmode defines the spatial pattern of resonant excitation ordered from coarse to fine-scale wavelengths. Our connectome model corresponds to the spatial propagator, or Green function of a specific NFT (Robinson 2005), which assigns connection weights based on how correlated are spatial locations on the neocortical surface across a certain number of geometric eigenmodes. Our model has two free parameters, i.e., the number of geometric modes considered κ, and r, which prescribes the spatial length scale of the wave propagation. We optimize our model to maximize the binary rank degree correlation, as well as the rank correlation of the edge weights of between empirical and model connectomes.
Models were fitted to empirical connectomes derived from diffusion MRI from eh HCP dataset, both at the vertex and parcel levels, using parcellations comprising 100, 300 and 500 regions (Schaefer). We also compared our model with connectomes from three non-human primate species (chimpanzee, marmoset and macaque) and a voxel-wise representation of the mouse connectome.
Models were fitted to empirical connectomes derived from diffusion MRI from eh HCP dataset, both at the vertex and parcel levels, using parcellations comprising 100, 300 and 500 regions (Schaefer). We also compared our model with connectomes from three non-human primate species (chimpanzee, marmoset and macaque) and a voxel-wise representation of the mouse connectome.
Results:
While classical generative models of the connectome fell short of capturing the topography of empirical connectomes, our model captures both their topology and topography, for all the species investigated. In Fig 1 we show an overview of our model's performance for a group template empirical connectome from the HCP dataset.
Conclusions:
Our model suggests that the connectome is to some extent tuned to facilitate the excitation of the geometric modes of the neocortical surface. This work demonstrates the utility of continuum approaches to modelling the brain and the important role that geometry plays in shaping its architecture.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural)
Diffusion MRI Modeling and Analysis
Neuroanatomy, Physiology, Metabolism and Neurotransmission:
Cortical Anatomy and Brain Mapping 2
Normal Development
White Matter Anatomy, Fiber Pathways and Connectivity 1
Keywords:
Cross-Species Homologues
Development
Modeling
White Matter
1|2Indicates the priority used for review
Abstract Information
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Provide references using APA citation style.
Bullmore, E. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nature Reviews. Neuroscience, 10(3), 186–198. https://doi.org/10.1038/nrn2575
Robinson, P. A. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Physical Review E, 56(1), 826–840. https://doi.org/10.1103/PhysRevE.56.826
Pang, J. C. (2023). Geometric constraints on human brain function. Nature, 618(7965), 566–574. https://doi.org/10.1038/s41586-023-06098-1
Oldham, S. (2022). Modeling spatial, developmental, physiological, and topological constraints on human brain connectivity. Science Advances, 8(22), eabm6127. https://doi.org/10.1126/sciadv.abm6127
Robinson, P. A. (2005). Propagator theory of brain dynamics. Physical Review E, 72(1), 011904. https://doi.org/10.1103/PhysRevE.72.011904
Arnatkeviciute, A. (2021). Genetic influences on hub connectivity of the human connectome. Nature Communications, 12(1), 4237. https://doi.org/10.1038/s41467-021-24306-2