title: A 4D hyperspherical interpretation of q-space.
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.
authors.affiliation: Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison, Madison, WI, USA. Electronic address: hosseinbor@wisc.edu.
authors.forename: A
authors.initials: A
authors.lastname: Pasha Hosseinbor
authors.affiliation: 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.
authors.forename: Moo K
authors.initials: MK
authors.lastname: Chung
authors.affiliation: Center for Neuroimaging, Indiana University, Indianapolis, IN, USA.
authors.forename: Yu-Chien
authors.initials: YC
authors.lastname: Wu
authors.affiliation: Geriatric Research, Education and Clinical Center (GRECC), William S. Middleton Memorial Veteran's Hospital, University of Wisconsin-Madison, Madison, WI, USA.
authors.forename: Barbara B
authors.initials: BB
authors.lastname: Bendlin
authors.affiliation: 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.
authors.forename: Andrew L
authors.initials: AL
authors.lastname: Alexander
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D062211:Spatio-Temporal Analysis
keywords: Diffusion MRI; Diffusion propagator; Hyperspherical harmonics; ODF; q-Space indices