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Investigation of anomalous estimates of tensor‐derived quantities in diffusion tensor imaging
Author(s) -
Koay Cheng Guan,
Carew John D.,
Alexander Andrew L.,
Basser Peter J.,
Meyerand M. Elizabeth
Publication year - 2006
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.20832
Subject(s) - tensor (intrinsic definition) , eigenvalues and eigenvectors , diffusion mri , estimator , least squares function approximation , mathematics , nonlinear system , tensor density , anisotropy , non linear least squares , mathematical analysis , physics , tensor field , exact solutions in general relativity , statistics , pure mathematics , quantum mechanics , medicine , radiology , magnetic resonance imaging
The diffusion tensor is typically assumed to be positive definite. However, noise in the measurements may cause the eigenvalues of the tensor estimate to be negative, thereby violating this assumption. Negative eigenvalues in diffusion tensor imaging (DTI) data occur predominately in regions of high anisotropy and may cause the fractional anisotropy (FA) to exceed unity. Two constrained least squares methods for eliminating negative eigenvalues are explored. These methods, the constrained linear least squares method (CLLS) and the constrained nonlinear least squares method (CNLS), are compared with other commonly used algebraic constrained methods. The CLLS tensor estimator can be shown to be equivalent to the linear least squares (LLS) tensor estimator when the LLS tensor estimate is positive definite. Similarly, the CNLS tensor estimator can be shown to be equivalent to the nonlinear least squares (NLS) tensor estimator when the NLS tensor estimate is positive definite. The constrained least squares methods for eliminating negative eigenvalues are evaluated with both simulations and in vivo human brain DTI data. Simulation results show that the CNLS method is, in terms of mean squared error for estimating trace and FA, the most effective method for correcting negative eigenvalues. Magn Reson Med, 2006. Published 2006 Wiley‐Liss, Inc.