Extreme diffusion values for non-Gaussian diffusions

References

• Assaf , Y. and Pasternak , O. 2008 . Diffusion tensor imaging (DTI)-based white matter mapping in brain research: a review . J. Mol. Neurosci. , 34 : 51 – 61 .
   PubMed Web of Science ®Google Scholar
• Barmpoutis , A. , Jian , B. , Vemuri , B. C. and Shepherd , T. M. 2007 . “ Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI ” . In Information Processing and Medical Imaging , Edited by: Karssemeijer , M. and Lelieveldt , B. 308 – 319 . Berlin : Springer-Verlag .
   Google Scholar
• Basser , P. J. and Jones , D. K. 2002 . Diffusion-tensor MRI: theory, experimental design and data analysis – a technical review . NMR in Biomed. , 15 : 456 – 467 .
   PubMed Web of Science ®Google Scholar
• Chang , K. C. , Pearson , K. and Zhang , T. 2008 . On eigenvalues of real symmetric tensors , Beijing, , China : School of Mathematical Science, Peking University . preprint
   Google Scholar
• Cox , D. , Little , J. and O'Shea , D. 1998 . Using Algebraic Geometry , New York : Springer-Verlag .
   Google Scholar
• Jensen , J. H. , Helpern , J. A. , Ramani , A. , Lu , H. and Kaczynski , K. 2005 . Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of maganetic resonance imaging . Magn. Resonan. Med. , 53 : 1432 – 1440 .
   PubMed Web of Science ®Google Scholar
• Jones , D. K. and Basser , P. J. 2004 . ‘Squashing peanuts and smashing pumpkins’: how noise distorts diffusion weighted MR data . Magn. Resonan. Med. , 52 : 979 – 993 .
   PubMed Web of Science ®Google Scholar
• Le Bihan , D. , Mangin , J. F. , Poupon , C. , Clark , C. A. , Pappata , S. , Molko , N. and Chabriat , H. 2001 . Diffusion tensor imaging: concepts and applications . J. Magn. Resonan. Imag. , 13 : 534 – 546 .
   PubMed Web of Science ®Google Scholar
• Liu , C. , Bammer , R. , Acar , B. and Mosely , M. E. 2004 . Characterizing non-Gaussian diffusion by generalized diffusion tensors . Magn. Resonan. Med. , 51 : 924 – 937 .
   PubMed Web of Science ®Google Scholar
• Lu , H. , Jensen , J. H. , Ramani , A. and Helpern , J. A. 2006 . Three-dimensional characterization of non-Gaussian water diffusion in humans using diffusion kurtosis imaging . NMR Biomed. , 19 : 236 – 247 .
   PubMed Web of Science ®Google Scholar
• Moseley , M. E. , Cohen , Y. , Mintorovitch , J. , Chileuitt , L. , Shimizu , H. , Kucharczyk , J. , Wendland , M. F. and Weinstein , P. R. 1990 . Early detection of regional cerebral ischemia in cats: comparison of diffusion- and T2-weighted MRI and spectroscopy . Magn. Resonan. Med. , 14 : 330 – 346 .
   PubMed Web of Science ®Google Scholar
• Ni , G. , Qi , L. , Wang , F. and Wang , Y. 2007 . The degree of the E-characteristic polynomial of an even order tensor . J. Math. Anal. Appl. , 329 : 1218 – 1229 .
   Web of Science ®Google Scholar
• Özarslan , E. and Mareci , T. H. 2003 . Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging . Magn. Resonan. Med. , 50 : 955 – 965 .
   PubMed Web of Science ®Google Scholar
• Özarslan , E. , DeFord , S. M. , Mareci , T. H. and Hayes , R. L. 2002 . Qualification of diffusion tensor imaging predicts diffuse axonal injury following traumatic brain injury in rats . J. Neurotrauma , 19 : 1285
   Google Scholar
• Pierpaoli , C. and Basser , P. J. 1996 . Toward a quantitative assessment of diffusion anisotropy . Magn. Resonan. Med. , 36 : 893 – 906 .
   PubMed Web of Science ®Google Scholar
• Qi , L. 2005 . Eigenvalues of a real supersymmetric tensor . J. Symb. Comput. , 40 : 1302 – 1324 .
   Web of Science ®Google Scholar
• Qi , L. 2006 . Rank and eigenvalues of a supersymmetric tensor, a multivariate homogeneous polynomial and an algebraic surface defined by them . J. Symb. Comput. , 41 : 1309 – 1327 .
   Web of Science ®Google Scholar
• Qi , L. 2007 . Eigenvalues and invariants of tensors . J. Math. Anal. Appl. , 325 : 1363 – 1377 .
   Web of Science ®Google Scholar
• Qi , L. , Wang , Y. and Wu , E. X. in press . D-Eigenvalues of diffusion kurtosis tensors . J. Comput. Appl. Math. , DOI: 10.1016/j.cam.2007.10.012
   Google Scholar
• Sturmfels , B. 2002 . Solving Systems of Polynomial Equations , Providence, RI : American Mathematical Society . CBMS Regional Conferences Series, No. 97
   Google Scholar
• Hui , E. S. , Cheung , M. M. , Qi , L. and Wu , E. X. 2008 . Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis . Neuroimage , 42 : 122 – 134 .
   PubMed Web of Science ®Google Scholar