Diffusion interactions between crossing fibers of the brain.

Purpose: Recent observations of several preferred orientations of diffusion in deep white matter may indicate either (a) that axons in different directions are independently bundled in thick sheets and function noninteractively, or more interestingly, (b) that the axons are closely interwoven and would exhibit branching and sharp turns. This study aims to investigate whether the dependence of dMRI Q-ball signal on the interpulse time can decode the smaller-than-voxel-size brain structure, in particular, to distinguish scenarios (a) and (b).

Methods: High-resolution Q-ball images of a healthy brain taken with  s/mm for 3 different values of were analyzed. The exchange of water molecules between crossing fibers was characterized by the fourth Fourier coefficient of the signal profile in the plane of crossing. To interpret the empirical results, a model consisting of differently oriented parallel sheets of cylinders was developed. Diffusion of water molecules inside and outside cylinders was simulated by the Monte Carlo method.

Results: Simulations predict that , agreeing with the empirical results, must increase with for large b-values, but may peak at a typical that depends on the thickness of the cylinder sheets for intermediate b-values. Thus, the thickness of axon layers in voxels with 2 predominant orientations can be detected from empirical taken at smaller b-values.

Conclusion: Based on the simulation results, recommendations are made on how to design a dMRI experiment with optimal b-value and range of in order to measure the thickness of axon sheets in the white matter, hence to distinguish (a) and (b).