### Abstract

Fractional anisotropy (FA) and relative anisotropy (RA) are the two most commonly used scalar measures of anisotropy in diffusion tensor (DT) MRI. While a few published studies have shown that FA has superior noise immunity relative to RA, no theoretical basis has been proposed to explain this behavior. In the current study, the diffusion tensor invariants were used to derive a simple analytical expression that directly relates RA and FA. An analysis based on that analytical expression demonstrated that the FA images have a higher signal-to-noise ratio (SNR) than RA for any value of tensor anisotropy RA or FA > 0. This theoretical behavior was verified using both Monte Carlo simulations and bootstrap analysis of DT-MRI data acquired in a spherical water phantom and normal human subjects. Magn Reson Med 51:413–417, 2004. © 2004 Wiley-Liss, Inc.