PURPOSE: 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. CONCLUSION: GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost.
PURPOSE: 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. CONCLUSION:GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost.
Authors: Geoffrey L Kung; Tom C Nguyen; Aki Itoh; Stefan Skare; Neil B Ingels; D Craig Miller; Daniel B Ennis Journal: J Magn Reson Imaging Date: 2011-09-19 Impact factor: 4.813
Authors: Feng Yang; Yue-Min Zhu; Isabelle E Magnin; Jian-Hua Luo; Pierre Croisille; Peter B Kingsley Journal: Med Image Anal Date: 2011-11-17 Impact factor: 8.545
Authors: Daniel B Ennis; Gordon Kindlman; Ignacio Rodriguez; Patrick A Helm; Elliot R McVeigh Journal: Magn Reson Med Date: 2005-01 Impact factor: 4.668
Authors: Gordon Kindlmann; Raúl San José Estépar; Marc Niethammer; Steven Haker; Carl-Fredrik Westin Journal: Med Image Comput Comput Assist Interv Date: 2007
Authors: Luigi E Perotti; Patrick Magrath; Ilya A Verzhbinsky; Eric Aliotta; Kévin Moulin; Daniel B Ennis Journal: Funct Imaging Model Heart Date: 2017-05-23
Authors: Luigi E Perotti; Ilya A Verzhbinsky; Kévin Moulin; Tyler E Cork; Michael Loecher; Daniel Balzani; Daniel B Ennis Journal: Med Image Anal Date: 2020-12-05 Impact factor: 8.545
Authors: Shankarjee Krishnamoorthi; Luigi E Perotti; Nils P Borgstrom; Olujimi A Ajijola; Anna Frid; Aditya V Ponnaluri; James N Weiss; Zhilin Qu; William S Klug; Daniel B Ennis; Alan Garfinkel Journal: PLoS One Date: 2014-12-10 Impact factor: 3.240
Authors: Geoffrey L Kung; Marmar Vaseghi; Jin K Gahm; Jane Shevtsov; Alan Garfinkel; Kalyanam Shivkumar; Daniel B Ennis Journal: Front Physiol Date: 2018-08-22 Impact factor: 4.566