We present a quantitative statistical analysis of pairwise crossings for all fibers obtained from whole brain tractography that confirms with high confidence that the brain grid theory (Wedeen et al., 2012a) is not supported by the evidence. The overall fiber tracts structure appears to be more consistent with small angle treelike branching of tracts rather than with near-orthogonal gridlike crossing of fiber sheets. The analysis uses our new method for high-resolution whole brain tractography that is capable of resolving fibers crossing of less than 10 degrees and correctly following a continuous angular distribution of fibers even when the individual fiber directions are not resolved. This analysis also allows us to demonstrate that the whole brain fiber pathway system is very well approximated by a lamellar vector field, providing a concise and quantitative mathematical characterization of the structural connectivity of the human brain.

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