Error Propagation Framework for Diffusion Tensor Imaging via Diffusion Tensor Representations

An analytical framework of error propagation for diffusion tensor imaging (DTI) is presented. Using this framework, any uncertainty of interest related to the diffusion tensor elements or to the tensor-derived quantities such as eigenvalues, eigenvectors, trace, fractional anisotropy (FA), and relative anisotropy (RA) can be analytically expressed and derived from the noisy diffusion-weighted signals. The proposed framework elucidates the underlying geometric relationship between the variability of a tensor-derived quantity and the variability of the diffusion weighted signals through the nonlinear least squares objective function of DTI. Monte Carlo simulations are carried out to validate and investigate the basic statistical properties of the proposed framework.