Regional heterogeneity shapes macroscopic wave dynamics of the human and non-human primate cortex

Growing evidence indicates that macroscopic cortical activity is dominated by propagating waves of excitation. However, many computational models of such wave dynamics assume that the cortex is a spatially homogeneous medium, ignoring the rich regional variations in cellular, molecular, and physiological properties that are known to shape how brain activity evolves through both space and time. Here, we develop a general framework grounded in neural field theory to model how regional heterogeneities in diverse cortical properties shape spatiotemporal brain activity evolving on cortical surface meshes. This enables high resolution, vertex-level simulations without requiring predefined parcellations. The model requires only a standard mesh model of the cortical manifold and a spatial heterogeneity map, providing a biologically grounded and computationally efficient framework that can be generalised to human and non-human species. Using multiple cellular, molecular, and physiological maps in humans--and analogous maps in macaques and marmosets--we show that our model can consistently recapitulate known relationships between regional heterogeneities and variations in cortical wave speed. In particular, we find that models parameterised by heterogeneities in intracortical myelin and excitation-inhibition balance yield the largest performance improvements relative to spatially homogeneous models. Our results identify a key role for regional variations in myelin, receptor, and genetic architecture in shaping the spatial patterning of macroscale cortex-wide activity that is conserved across primate species with diverse cortical geometries.