Fig. 3. Generation of the diffusion tensor. The physical basis for diffusion-weighted imaging is that a magnetic gradient is first dephased and then rephased, and the resulting loss of signal coherence (yielding signal attenuation) represents diffusive motion in the direction of the applied gradient. The set of spatially arrayed diffusion coefficients may be viewed as a second-order tensor, so constituting a method for visualizing 3-D diffusivity in space. The 3-D diffusion tensor may be computed for each voxel and visualized as individual octahedra (A) whose axes are scaled by the size of the eigenvalues and oriented along the corresponding eigenvectors. The principal eigenvector, V₁, corresponds to the direction of greatest diffusion, and is equivalent to the principal fiber direction. Octahedra may then be color coded based on the principal eigenvector {x, y, z} mapped to the red–green–blue color space: {|V_1x|} (B).