A Linear Relationship Exists among Brain Diffusion Eigenvalues Measured by Diffusion Tensor Magnetic Resonance Imaging

Diffusion in biological tissues can be measured by magnetic resonance diffusion tensor imaging The complex nature of anisotropic diffusion in the brain has been described by a diffusion tensor which contains information about the magnitude of diffusion in different directions. Each tensor contains a set of three eigenvalues which are related to the major, intermediate, and minor axes of a diffusion ellipsoid. This investigation demonstrates that the various sets of diffusion eigenvalues from different regions of the brain lie along a line in ordered eigenvalue space. Sets of ordered diffusion eigenvalues were considered points in ordered eigenvalue space. The line which best fit the data by minimizing the total squared deviations was determined. A new coordinate system was constructed through translation and rotation which spanned ordered eigenvalue space. Eigenvalues from both monkey brain and human brain were studied. It was found that the sets of eigenvalues from both species have significant linear trends. Moreover, the same line may describe the brain eigenvalues from both species. It is likely that this linear relationship of the eigenvalues observed in an ordered eigenvalue plot is related to a combination of (1) conservation of total isotropic diffusion and (2) the degree of orientational dispersion of the microfibers within each voxel.