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A rigorous framework for diffusion tensor calculus

✍ Scribed by P. G. Batchelor; M. Moakher; D. Atkinson; F. Calamante; A. Connelly

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
262 KB
Volume
53
Category
Article
ISSN
0740-3194

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✦ Synopsis

Abstract

In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data. Magn Reson Med 53:221–225, 2005. Β© 2004 Wiley‐Liss, Inc.

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