Context-dependent influences of local and non-local connectivity on macroscale cortical activity
Rishi Maran (University of Sydney), Eli Muller (University of Sydney), Ben Fulcher (University of Sydney)
Introduction Despite the role of non-local long-range connections (LRCs) in integrating information across remote neural systems, many key properties of macroscale cortical dynamics can be accurately captured by simple geometric models that neglect the specific positions of LRCs 1,2 . Using a novel mathematical model, we aim to investigate why the cortex's local geometry sufficiently captures many such properties. Our results reveal a context-dependent role of LRCs that provide a plausible account of this open question: while LRCs predominantly shape the fast information processing of spatially precise stimuli, they play a relatively minor role in shaping spontaneous fluctuations over longer timescales, which are well captured by cortical geometry alone.
Methods: We develop and introduce a novel mathematical model of cortical dynamics, in which neural populations interact simultaneously via local geometry and a non-local connectome of LRCs (Fig. 1A), both in accordance to a non-local partial differential equation. Local connections propagate activity between any two populations as waves; whereas LRCs propagate activity rapidly between specific pairs of distant populations.
Results: We show that the model's evoked response to a focal stimulus is perturbed by a LRC most strongly when the response dynamics is resolved at short millisecond timescales, and the stimulus is proximate to the LRC (Fig. 1B,C). Contrastingly, a LRC's perturbation of cortical dynamics diminishes, both: (i) when the dynamics is measured in spontaneous settings (relative to the response to a focal input stimulus); and (ii) when restricted to its long-timescale dynamics (such as those measured by fMRI). Our results demonstrate that the extent to which geometric model well approximates brain dynamics varies with the settings under which the dynamics are generated and measured, and becomes sufficiently valid under the conditions of resting-state fMRI.
Discussion: We have developed a new model of macroscale cortical dynamics capable of simultaneous local geometric propagation and non-local connectomic propagation. Our model simulations indicate LRCs shape the model's dynamics strongly on short millisecond timescales in stimulus-response settings, but minimally on longer timescales accessible from fMRI and in spontaneous settings. Our findings provide an explanation for a major open problem in macroscale neuroscience, while providing a foundation on which future brain models can be developed and refined.
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1. Gabay, N. C., & Robinson, P. A. (2017). Cortical geometry as a determinant of brain activity eigenmodes: Neural field analysis. Physical Review E, 96(3), 032413. https://doi.org/10.1103/PhysRevE.96.032413 2. Pang, J. C., Aquino, K. M., Oldehinkel, M., Robinson, P. A., Fulcher, B. D., Breakspear, M., & Fornito, A. (2023). Geometric constraints on human brain function. Nature, 618(7965), 566-574. https://doi.org/10.1038/s41586-023-06169-z
