Spatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description

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dc.citation.firstpage1
dc.citation.issueNumber1
dc.citation.journalTitleConcepts in Magnetic Resonance Part A
dc.citation.lastpage27
dc.citation.volumeNumber43
dc.contributor.authorShetty, Anil N.
dc.contributor.authorChiang, Sharon
dc.contributor.authorMaletic-Savatic, Mirjana
dc.contributor.authorKasprian, Gregor
dc.contributor.authorVannucci, Marina
dc.contributor.authorLee, Wesley
dc.date.accessioned2017-08-17T19:19:42Z
dc.date.available2017-08-17T19:19:42Z
dc.date.issued2014
dc.description.abstractIn this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.
dc.identifier.citationShetty, Anil N., Chiang, Sharon, Maletic-Savatic, Mirjana, et al.. "Spatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description." <i>Concepts in Magnetic Resonance Part A,</i> 43, no. 1 (2014) Wiley: 1-27. https://doi.org/10.1002/cmr.a.21288.
dc.identifier.digitalSpatial_Mapping_Translational_Diffusion_Coefficients
dc.identifier.doihttps://doi.org/10.1002/cmr.a.21288
dc.identifier.urihttps://hdl.handle.net/1911/97342
dc.language.isoeng
dc.publisherWiley
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Wiley.
dc.subject.keyworddiffusion
dc.subject.keyworddiffusion anisotropy
dc.subject.keyworddiffusion tensor
dc.subject.keywordtractography
dc.titleSpatial mapping of translational diffusion coefficients using diffusion tensor imaging: A mathematical description
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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