Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

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.