Geometric constraints on human brain function

Abstract

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres1–3. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity4–6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity7,8. Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain’s geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics.

Reply to: Commentary on Pang et al. (2023) Nature

“…Faskowitz et al’s 2 critique of our paper’s framing is that it “can be perceived” as a “winner-takes-all… comparison between brain shape and structural connectivity”. This misperception evidently arises from quotes taken out of context and an oversight of the fundamental relationship between geometry and connectivity underlying our approach, as defined formally in Supplementary Information S8 of the original paper 1 . In brief, the use of cortical eigenmodes to model cortical activity rests irrevocably upon a form of distance-dependent connectivity that has been consistently identified in human and non-human data alike 3,4 .…”

“…3 in ref. 1 ) can be approximated analytically as a first-order perturbation of spherical geometry, where the perturbations describe the symmetry-breaking effect of cortical folding. As a result, cortical eigenmodes can be expressed as linear combinations of appropriately rotated spherical harmonics 8 (Figs.…”

“…(3) in ref. 1 ). In other words, at coarse scales relevant for fMRI, the “non-brain like shapes” used by Faskowitz et al 2 are indeed brain-like, and their comparison merely shows that modes obtained from objects with similar geometries reconstruct activity with similar accuracy.…”

“…1d of ref. 1 ). Thus, as previously shown 8 , low-order cortical modes can be approximated in terms of spherical modes, allowing them to have comparable reconstruction accuracies and explaining the effect shown by Faskowitz et al 2 .…”

“…As stated in ref. 1 , our goal was to identify a parsimonious basis set of physically constrained eigenmodes, not an arbitrary basis set that is optimal in some purely statistical sense. Alternative phenomenological (i.e., non-physiological) basis sets may reconstruct fMRI data at equivalent accuracy but they do not shed light on the anatomical constraints or generative processes that give rise to brain activity 9 .…”