title: (Mathematical) Necessary conditions for the selection of gradient vectors in DTI.
abstract: A set of necessary conditions for the choice of diffusion gradient vectors to make the linear equations nonsingular for the estimation of the diffusion matrix are given in a coordinate free manner. The conditions assert that the initial step in the design of a DTI experiment with six or more acquisitions must be to select six valid diffusion gradients first and then add new ones.
authors.affiliation: Biomedical MR Laboratory, Mallinckrodt Institute of Radiology, Washington University in Saint Louis, School of Medicine, Box 8227, St. Louis, MO 63110, USA. ozcan@zach.wustl.edu
authors.forename: Alpay
authors.initials: A
authors.lastname: Ozcan
mesh_terms: D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D016014:Linear Models; D008433:Mathematics