Efficient measurement and calculation of MR diffusion anisotropy images using the Platonic variance method.

The Platonic variance method produces MR diffusion anisotropy (DA) images with a minimum amount of computational effort. It can be programmed in a self-contained MR sequence, thus eliminating the need for postprocessing on a separate workstation. The method uses gradient acquisition schemes, based on Platonic solids: the "icosahedric" scheme (N = 6), the "dodecahedric" scheme (N = 10), and combinations thereof. For these schemes the average of the diffusion tensor eigenvalues equals the average of the measured apparent diffusion coefficients (ADCs), and the variance of the eigenvalues equals 5/2 times the variance of the diffusion coefficients. This results in compact expressions for anisotropy measures, directly in terms of the acquired images, i.e., without calculating the eigenvalues or even the tensor elements. The resulting anisotropy images were shown to be identical to the ones traditionally derived. It is expected that this method will considerably promote the routine use of DA imaging.