Geodesic theory of long association fibers guidance on the human fetal cortex

Association fibers connect different areas of the cerebral cortex over long distances and integrate information to achieve higher brain functions, particularly in humans. Prototyped association fibers are developed to the respective tangential direction throughout the cerebral hemispheres in the subplate layer during the fetal period. However, the directional guidance principle for forming association fibers is unknown. Because the subplate is located below the cortical surface, the tangential direction of the fibers may be biased by the curved surface geometry due to Sylvian fissure and cortical poles. The fiber length can be minimized if the tracts follow the shortest paths (geodesics) of the curved cortical surface. Here, we propose and examine a theory that geodesics guide the tangential direction of long association fibers by analyzing how geodesics are spatially distributed on the fetal human brains. Unlike the homogeneous distribution on spherical surfaces, we found that the geodesics were dense on the saddle-shaped surface of the perisylvian region and sparse on the dome-shaped cortical poles. The geodesics corresponded with the positions of five typical association fibers, supporting the geodesic theory. Thus, the geodesic theory provides directional guidance and suggests that long association fibers emerge from minimizing their tangential length on fetal brains.