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Mathematically, the eigenvalue is the factor by which a linear transformation multiplies one of its eigenvectors. In an appropriate spatial reference frame, the diffusion tensor 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.
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Diffusion Tensor ImagingInfoSheet: - Sequences - 
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(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 isotropic diffusion and a linear diffusion. The FA range is between 0 and 1 (0 = isotropic diffusion, 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.

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Further Reading:
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EVALUATION OF HUMAN STROKE BY MR IMAGING
2000
  News & More:
Imaging Technique for Spinal Cord Injury Shows Promise
Sunday, 22 December 2013   by www.wauwatosanow.com    
DTI: a New Diagnostic Tool for Injuries in Motor Vehicle Accidents
Saturday, 19 November 2011   by www.digitaljournal.com    
Imaging shows structural changes in mild traumatic brain injury
Thursday, 25 October 2007   by www.eurekalert.org    
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In trace images, the contrast is generated by the direction of the diffusion tensor. This parametric images contains the average of the three eigenvalues (independent of the frame of reference).
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