Fractional anisotropy

A value of one means that diffusion occurs only along one axis and is fully restricted along all other directions.

FA is a measure often used in diffusion imaging where it is thought to reflect fiber density, axonal diameter, and myelination in white matter.

The FA is an extension of the concept of eccentricity of conic sections in 3 dimensions, normalized to the unit range.

The FA can reach a maximum value of 1 (this rarely happens in real data), in which case D has only one nonzero eigenvalue and the ellipsoid reduces to a line in the direction of that eigenvector.

FA quantifies the pointedness of the ellipsoid, but does not give information about which direction it is pointing to.

Note that the FA of most liquids, including water, is 0 unless the diffusion process is being constrained by structures such as network of fibers.

In some regions, such as the corpus callosum the fibers are aligned over a large enough scale (on the order of a mm) for their directions to mostly agree within the resolution element of a magnetic resonance image, and it is these regions that stand out in an FA image.

Liquid crystals can also exhibit anisotropic diffusion because the needle or plate-like shapes of their molecules affect how they slide over one another.

Due to this, higher order models using spherical harmonics and Orientation Distribution Functions (ODF) have been used to define newer and richer estimates of the anisotropy, called Generalized Fractional Anisotropy.

GFA computations use samples of the ODF to evaluate the anisotropy in diffusion.