title: Linear invariant tensor interpolation applied to cardiac diffusion tensor MRI.
abstract: OBJECTIVE
  Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape.
  
  
  METHODS
  Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets.
  
  
  RESULTS
  EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI.
  
  
  CONCLUSIONS
  GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost.
authors.affiliation: Department of Radiological Sciences, UCLA, CA 90095, USA. gahmj@ucla.edu
authors.forename: Jin Kyu
authors.initials: JK
authors.lastname: Gahm
authors.forename: Nicholas
authors.initials: N
authors.lastname: Wisniewski
authors.forename: Gordon
authors.initials: G
authors.lastname: Kindlmann
authors.forename: Geoffrey L
authors.initials: GL
authors.lastname: Kung
authors.forename: William S
authors.initials: WS
authors.lastname: Klug
authors.forename: Alan
authors.initials: A
authors.lastname: Garfinkel
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Ennis
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006321:Heart / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016014:Linear Models; D019028:Magnetic Resonance Imaging, Cine / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity