title: A rigorous framework for diffusion tensor calculus.
abstract: In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data.
authors.affiliation: Imaging Sciences Division, 5th Floor Thomas Guy House, King's College London, London Southern 9RT, UK. phillip.batchelor@kcl.ac.uk
authors.forename: P G
authors.initials: PG
authors.lastname: Batchelor
authors.forename: M
authors.initials: M
authors.lastname: Moakher
authors.forename: D
authors.initials: D
authors.lastname: Atkinson
authors.forename: F
authors.initials: F
authors.lastname: Calamante
authors.forename: A
authors.initials: A
authors.lastname: Connelly
mesh_terms: D016880:Anisotropy; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods; D006801:Humans; D008433:Mathematics