A rigorous framework for diffusion tensor calculus

@article{batchelor-et-al:2005, 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. {\copyright} 2004 Wiley-Liss, Inc.}, address = {Imaging Sciences Division, King's College London, London, United Kingdom; Laboratoire de Mod\'{e}lisation Math\'{e}matique et Num\'{e}rique dans les Sciences de l'Ing\'{e}nieur, Ecole Nationale d'Ing\'{e}nieurs de Tunis, B.P. 37, 1002 Tunis-Belv\'{e}d\`{e}re, Tunisia; Radiology and Physics Unit, Institute of Child Health, University College London, London, United Kingdom}, author = {Batchelor, P. G. and Moakher, M. and Atkinson, D. and Calamante, F. and Connelly, A. }, citeulike-article-id = {2051171}, doi = {http://dx.doi.org/10.1002/mrm.20334}, journal = {Magnetic Resonance in Medicine}, keywords = {dti, riemannian-geometry, tensor}, number = {1}, pages = {221--225}, posted-at = {2007-12-03 16:46:10}, priority = {0}, title = {A rigorous framework for diffusion tensor calculus}, url = {http://dx.doi.org/10.1002/mrm.20334}, volume = {53}, year = {2005} }

TY - JOUR ID - batchelor-et-al:2005 L3 - citeulike-article-id:2051171 TI - A rigorous framework for diffusion tensor calculus JF - Magnetic Resonance in Medicine VL - 53 IS - 1 SP - 221 EP - 225 AD - Imaging Sciences Division, King's College London, London, United Kingdom; Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur, Ecole Nationale d'Ingénieurs de Tunis, B.P. 37, 1002 Tunis-Belvédère, Tunisia; Radiology and Physics Unit, Institute of Child Health, University College London, London, United Kingdom N2 - 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. © 2004 Wiley-Liss, Inc. KW - dti KW - riemannian-geometry KW - tensor AU - Batchelor, PG AU - Moakher, M AU - Atkinson, D AU - Calamante, F AU - Connelly, A PY - 2005/// UR - http://dx.doi.org/10.1002/mrm.20334 ER -