Fractional anisotropy

Fractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally restricted) in all directions. 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.FA value of 0.9209, the DT matrix is diagonal()FA value of 0, the DT matrix is diagonal()FA value of 0.6030, the DT matrix is diagonal() Fractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally restricted) in all directions. 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. A Diffusion Ellipsoid is completely represented by the Diffusion Tensor, D. FA is calculated from the eigenvalues ( λ 1 , λ 2 , λ 3 {displaystyle lambda _{1},lambda _{2},lambda _{3}} ) of the diffusion tensor. The eigenvectors ϵ {displaystyle epsilon } give the directions in which the ellipsoid has major axes, and the corresponding eigenvalues λ {displaystyle lambda } give the magnitude of the peak in that direction. with λ ^ = ( λ 1 + λ 2 + λ 3 ) / 3 {displaystyle {hat {lambda }}=(lambda _{1}+lambda _{2}+lambda _{3})/3} being the mean value of the eigenvalues.