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Abstract #1066

The Asymptotic Distribution of Diffusion Tensor and Fractional Anisotropy Estimates

Wahba G, Alexander A, Basser P, Meyerand M, Carew J, Koay C
University of Wisconsin

Error propagation in diffusion tensor imaging (DTI) has general interest since it tells us how noise in diffusion-weighted images propagates to estimates of the tensor and functions of the tensor estimate (e.g., fractional anisotropy (FA)). In this paper we derive asymptotic properties of the nonlinear least squares estimator (NLSE) of the diffusion tensor. We show that the NLSE of the diffusion tensor is a maximum likelihood estimator under normal noise assumptions. This connection allows us to directly apply the theory of maximum likelihood estimation to obtain asymptotic properties. In particular, we show that the NLSE is consistent and asymptotically normal. Furthermore, any continuously differentiable function of the tensor estimate is also consistent and asymptotically normal. To illustrate and validate the theory we derive the asymptotic distribution of FA and show, with simulations, that for as little as 6 directions, the asymptotic distribution of FA is very close to the empirical distribution