Mathematically, the eigenvalue is the factor by which a linear transformation multiplies one of its eigenvectors.
In an appropriate spatial reference frame, the diffusiontensor is diagonal (contains only three nonzero elements). These elements in diffusion tensor imaging are called the eigenvalues.
The vectors characterizing the reference frame are the eigenvectors.
(DTI) Diffusion tensor imaging is the more sophisticated form of DWI, which allows for the determination of directionality as well as the magnitude of water diffusion. This kind of MR imaging can estimates damage to nerve fibers that connect the area of the brain affected by the stroke to brain regions that are distant from it, and can be used to determine the effectiveness of stroke prevention medications.
DTI (FiberTrak) enables to visualize white matter fibers in the brain and can map (trace image) subtle changes in the white matter associated with diseases such as multiple sclerosis and epilepsy, as well as assessing diseases where the brain's wiring is abnormal, such as schizophrenia.
The fractional anisotropy (FA) gives information about the shape of
the diffusion tensor at each voxel. The FA is based on the normalized
variance of the eigenvalues. The fractional anisotropy reflects differences between an isotropicdiffusion and a linear diffusion. The FA range is between 0 and 1 (0 = isotropicdiffusion, 1 = highly directional).
The development of new imaging methods and some useful analysis techniques, such as 3-dimensional anisotropy contrast (3DAC) and spatial tracking of the diffusion tensor tractography (DTT), are currently under study.