Dyadic tensor-based interpolation of tensor orientation: Application to cardiac DT-MRI

Abstract

Objective: To develop an accurate and mathematically unambiguous method for interpolation of tensor orientation, specifically for the interpolation of cardiac microstructural orientation. Methods: A dyadic tensor-based (DY) orientation interpolation method, which sidesteps the eigenvector sign ambiguity problem by interpolating between the dyadic tensors of eigenvectors, is proposed and evaluated. The quaternion-based (QT) orientation interpolation method, which interpolates along the minimum rotation path between tensor orientations, is also revised and evaluated. DY and QT are compared to conventional tensor-based interpolation methods using both synthetic and cardiac DT-MRI data. Results: All methods (except QT) perform similarly well for recovery of the primary eigenvector. DY has significantly less bias than all other methods for recovery of the secondary and tertiary eigenvector, which is especially important for interpolating myolaminar sheet orientation. Conclusion: DY is a fast, commutative, and mathematically unambiguous tensor orientation interpolation method that accurately interpolates cardiac microstructural orientation. © Springer-Verlag Berlin Heidelberg 2014.