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Mathematics of Crossing Fibers 

Mathematics of Crossing Fibers
Mathematics of Crossing Fibers

Daniel C. Alexander

and Kiran K. Seunarine

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date: 19 February 2019

A limitation of diffusion tensor imaging is that it estimates only one fiber orientation and does not give reliable information at fiber crossings or other complex sub-voxel fibre configurations. This chapter discusses the nature of this problem and reviews a variety of alternative techniques that have emerged to try to address it. Published methods differ in three key ways: the set of diffusion-weighted images they require (e.g., grid sampling or high angular resolution diffusion imaging), the object they aim to estimate (e.g., diffusion or fibre orientation distribution function), and the representation of that object (e.g., spherical harmonics or wavelets). It explains the significance of these different choices and refers to empirical comparisons in the literature that can guide their optimization. The chapter concludes with a discussion of limitations of the techniques and areas for further work.

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