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Med Image Anal. 2015 Apr;21(1):15-28. doi: 10.1016/j.media.2014.11.013. Epub 2015 Jan 3.

A 4D hyperspherical interpretation of q-space.

Author information

1
Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA. Electronic address: hosseinbor@wisc.edu.
2
Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA; Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA.
3
Center for Neuroimaging, Indiana University, Indianapolis, IN, USA.
4
Geriatric Research, Education and Clinical Center (GRECC), William S. Middleton Memorial Veteran's Hospital, University of Wisconsin-Madison, Madison, WI, USA.
5
Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA; Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, USA; Department of Psychiatry, University of Wisconsin-Madison, Madison, WI, USA.

Abstract

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.

KEYWORDS:

Diffusion MRI; Diffusion propagator; Hyperspherical harmonics; ODF; q-Space indices

PMID:
25624043
PMCID:
PMC4330109
DOI:
10.1016/j.media.2014.11.013
[Indexed for MEDLINE]
Free PMC Article

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