Analytical error propagation in diffusion anisotropy calculations.

Purpose: To develop an analytical formalism describing how noise and selection of diffusion-weighting scheme propagate through the diffusion tensor imaging (DTI) computational chain into variances of the diffusion tensor elements, and errors in the relative anisotropy (RA) and fractional anisotropy (FA) indices.

Materials And Methods: Singular-value decomposition (SVD) was used to determine the tensor variances, with diffusion-weighting scheme and measurement noise incorporated into the design matrix. Anisotropy errors were then derived using propagation of error.