Anisotropically weighted MRI

The intensity of an isotropically weighted MR image is proportional to a rotationally invariant measure of bulk diffusion, Trace((D) under bar) (where (D) under bar is the effective diffusion tensor). Such images can be acquired from as few as two diffusion-weighted images (DWIs). Analogously, the intensity of an anisotropically weighted MR image is proportional to a rotationally invariant measure of diffusion anisotropy derived from (D) under bar, such as the variance of the principal diffusivities of (D) under bar. By using linear algebra, we show that to produce an anisotropically weighted MR image requires acquiring at least seven DWIs, which is also the minimum number of DWIs sufficient to estimate the entire diffusion tensor, as well as the T-2-weighted amplitude image, A((b) under bar = (O) under bar), in each voxel. A general mathematical framework for constructing isotropically weighted and anisotropically weighted MR images is also provided.