Properties of shapes in geometry12/31/2023 ![]() In the linear regime, such as brain activity under normal (that is, non-seizure-like) conditions 13, eigenmodes (hereafter also referred to as modes) offer a particularly powerful and rigorous formalism for linking brain anatomy with the physical processes that shape activity. In diverse areas of physics and engineering, structural constraints on system dynamics can be understood via the system’s eigenmodes, which are fundamental spatial patterns corresponding to the natural, resonant modes of the system 12. Several studies have shown correlations between various properties of brain connectivity and activity 11, but precisely how spatiotemporal patterns of neural dynamics are constrained by a relatively stable neuroanatomical scaffold remains unclear. ![]() The nervous system is no exception, with the rich and complex spatiotemporal dynamics of anatomically distributed neuronal populations being supported by their intricate web of axonal interconnectivity 1, 10. For instance, the shape of a drum influences its acoustic properties, the morphology of a river bed shapes underwater currents and the geometry of a protein determines the molecules with which it can interact 9. ![]() The dynamics of many natural systems are fundamentally constrained by their underlying structure. 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. 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. 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. 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. ![]() Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity 4, 5, 6, suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity 7, 8. 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 fibres 1, 2, 3. The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. ![]()
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