Cortical folding is closely linked to brain functions, with gyri acting more like local functional "hubs" to integrate information than sulci do. However, understanding how anatomical constraints relate to complex functions remains fragmented. One possible reason is that the relationship is estimated on brain mosaics divided by brain functions and cortical folding patterns. The boundaries of these hypothetical hard-segmented mosaics could be subject to the selection of functional/morphological features and as well as the thresholds. In contrast, functional gradient and folding gradient could provide a more feasible and unitless platform to mitigate the uncertainty introduced by boundary definition. Based on the MRI datasets, we used cortical surface curvature as the folding gradient and related it to the functional connectivity transition gradient. We found that, at the local scale, the functional gradient exhibits different function transition patterns between convex/concave cortices, with positive/negative curvatures, respectively. At the global scale, a cortex with more positive curvature could provide more function transition efficiency and play a more dominant role in more abstractive functional networks. These results reveal a novel relation between cortical morphology and brain functions, providing new clues to how anatomical constraint is related to the rise of an efficient brain function architecture.
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