title: Quantitative mapping of the per-axon diffusion coefficients in brain white matter.
abstract: OBJECTIVE
  This article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per-axon or microscopic diffusion coefficients.
  
  
  METHODS
  Diffusion MR imaging is used to probe the underlying tissue material. The key observation is that for a fixed b-value the spherical mean of the diffusion signal over the gradient directions does not depend on the axon orientation distribution. By exploiting this invariance property, we propose a simple, fast, and robust estimator of the per-axon diffusion coefficients, which we refer to as the spherical mean technique.
  
  
  RESULTS
  We demonstrate quantitative maps of the axon-scale diffusion process, which has factored out the effects due to fiber dispersion and crossing, in human brain white matter. These microscopic diffusion coefficients are estimated in vivo using a widely available off-the-shelf pulse sequence featuring multiple b-shells and high-angular gradient resolution.
  
  
  CONCLUSIONS
  The estimation of the per-axon diffusion coefficients is essential for the accurate recovery of the fiber orientation distribution. In addition, the spherical mean technique enables us to discriminate microscopic tissue features from fiber dispersion, which potentially improves the sensitivity and/or specificity to various neurological conditions. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.
authors.affiliation: Centre for Medical Image Computing, University College London, UK.
authors.forename: Enrico
authors.initials: E
authors.lastname: Kaden
authors.affiliation: Department of Biomedical Engineering, University of California, Irvine, California, USA.
authors.forename: Frithjof
authors.initials: F
authors.lastname: Kruggel
authors.affiliation: Centre for Medical Image Computing, University College London, UK.
authors.forename: Daniel C
authors.initials: DC
authors.lastname: Alexander
mesh_terms: D000328:Adult; D001921:Brain / Q000000981:diagnostic imaging*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008297:Male; D055815:Young Adult
keywords: diffusion MR imaging; fiber orientation distribution; microscopic diffusion anisotropy; per-axon diffusion coefficients; powder average; spherical mean technique