New scalar measures for diffusion-weighted MRI visualization

Abstract

We present new scalar measures for diffusion-weighted MRI visualization which are based on operations of tensor calculus and have a connection to topological visualization. These operators are generalizations of the familiar divergence and curl operations in vector calculus. We also present a method for computing the Helmholtz decomposition of tensor fields which can make the new scalar measures more robust. The methods we present are general with respect to tensor order, so they apply to traditional 2nd order diffusion tensor MRI, as well as 4th and high order models used in high angular resolution diffusion imaging. Results are shown for synthetic tensor fields of orders 2 and 4 and also real diffusion tensor MRI data of orders 2 and 4. © 2009 Springer-Verlag.