Diffusion tensor analysis with invariant gradients and rotation tangents.
Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.
Department of Radiology, Brigham and Womens Hospital, Harvard Medical School, Cambridge, MA 02139, USA. gk@bwh.harvard.edu
Gordon
G
Kindlmann
Daniel B
DB
Ennis
Ross T
RT
Whitaker
Carl-Fredrik
CF
Westin
D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D015203:Reproducibility of Results; D012399:Rotation; D012680:Sensitivity and Specificity