Computation of the fractional anisotropy and mean diffusivity maps without tensor decoding and diagonalization: Theoretical analysis and validation

Diffusion tensor MRI (DT‐MRI) is a promising modality for in vivo mapping of the organization of deep tissues. The most commonly used DT‐MRI invariant maps are the mean diffusivity, μ(D), relative anisotropy (RA), and fractional anisotropy (FA). Because of the computational burden, anisotropy maps are generally computed offline. The availability of a simple procedure to compute RA, FA, and μ(D) online would make DT‐MRI more useful in clinical applications that require immediate feedback. In this study, analytical expressions that relate the commonly used tensor anisotropy measures obtained from the decoded and diagonalized DT with those obtained from the first and second moments of the measured diffusion‐weighted (DW) data are derived. Specifically, it is shown that for the principal icosahedron encoding scheme, RA is related to the mean and standard deviation (SD) of the DW measurements that can be computed online. Since FA is commonly used as an anisotropy measure, an analytical expression relating RA and FA was derived from the tensor invariants. These results were validated using both Monte Carlo simulations and high‐resolution, normal whole‐brain DT‐MRI measurements acquired with different b‐factors, encoding schemes, and signal‐to‐noise ratio (SNR) levels. The bias introduced by the rotationally variant encoding schemes into the diffusion measures is also investigated. Magn Reson Med 50:589–598, 2003. © 2003 Wiley‐Liss, Inc.