Multi-shelled q-ball Imaging: Moment-based Orientation Distribution Function

Purpose: q-ball imaging (QBI) reconstructs the orientation distribution function (ODF) that describes the probability for a spin to diffuse in a given direction, and it is capable of identifying intravoxel multiple fiber orientations. The local maxima of ODF are assumed to indicate fiber orientations, but there is a mismatch between the orientation of a fiber crossing and the local maxima. We propose a novel method, multi-shelled QBI (MS-QBI), that gives a new ODF based on the moment of the probability density function of diffusion displacement. We test the accuracy of the fiber orientation indicated by the new ODF and test fiber tracking using the new ODF. Methods: We performed tests using numerical simulation. To test the accuracy of fiber orientation, we assumed that 2 fibers cross and evaluated the deviation of the measured crossing angle from the actual angle. To test the fiber tracking, we used a numerical phantom of the cerebral hemisphere containing the corpus callosum, projection fibers, and superior longitudinal fasciculus. In the tests, we compared the results between MS-QBI and conventional QBI under the condition of approximately equal total numbers of diffusion signal samplings between the 2 methods and chose the interpolation parameter such that the stabilities of the results of the angular deviation for the 2 methods were the same. Results: The absolute value of the mean angular deviation was smaller in MS-QBI than in conventional QBI. Using the moment-based ODF improved the accuracy of fiber pathways in fiber tracking but maintained the stability of the results. Conclusion: MS-QBI can more accurately identify intravoxel multiple fiber orientations than can QBI, without increasing sampling number. The high accuracy of MS-QBI will contribute to the improved tractography.