A Geometric Generative Model of the Connectome

Brisbane Convention & Exhibition Centre 

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.