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Fiber Crossing in Human Brain Depicted with Diffusion Tensor MR Imaging¹

¹ From the Department of Radiology, Nuclear Magnetic Resonance Center, Massachusetts General Hospital-East, Bldg 149, 13th St, Charlestown, MA 02129 (M.R.W., V.J.W.); and the Danish Research Center for Magnetic Resonance, Hvidovre Hospital, Denmark (M.R.W., H.B.W.L.). Received June 21, 1999; revision requested August 10; final revision received March 13, 2000; accepted March 20. Supported in part by the Sol Goldman Charitable Trust and National Institutes of Health grant 5RO1H256727. M.R.W supported by Apoteker fonden af 1991 (Copenhagen, Denmark). Address correspondence to V.J.W. (e-mail: van@nmr.mgh.harvard.edu).

View larger version (26K): [in a new window]   Figure 1. The probability function for water displacement can be depicted as an ellipsoid. The ellipsoid represents an isocontour of the 3D Gaussian solution to the diffusion equation. The axes are directed along the eigenvectors (v1, v2, v3, principal diffusion orientations), and the lengths are scaled by the corresponding eigenvalues (1, 2, 3, diffusion magnitudes). The eigensystem is conventionally ordered so 1 > 2 > 3, with anisotropic diffusion characterized by 1 2 3 and isotropic diffusion by 1 2 3.

View larger version (52K): [in a new window]   Figure 2. Two representations of 3D graphic displays emphasizing the differences between the eigenvalues (23 = 2 - 3) were used. The first eigenvector (v1) represents the mean direction of fiber populations. The second eigenvector (v2) represents angular dispersion of the first eigenvector. The third eigenvector (v3) represents the normal to the plane of the mean direction and its angular dispersion. The uniaxial model (23 0) is best depicted with the first eigenvector, whereas the plane spanned by the first and second eigenvectors better emphasizes the planar model (23 > 0).

View larger version (67K): [in a new window]   Figure 3. Color sphere represents the colors related to the anatomic orientation of the brain. The color coding applies the three principal colors—red, green, and blue—to the elements of a vector, resulting in a color that represents its 3D direction.

View larger version (95K): [in a new window]   Figure 4. Color-coded transverse images of mean diffusion direction (v1) masked by the 12 anisotropy (left) and the normal (v3) to the plane of the mean direction and its angular dispersion masked by the 23 anisotropy (right). Left: Uniaxial architecture is emphasized by the corpus callosum (CC, red), corona radiata (CR, blue), and superior longitudinal fascicle (SLF, green). Right: Planar architecture is emphasized by the intersection of the corpus callosum and corona radiata (area 1, green) and fanning of the superior longitudinal fascicle into the U fibers (area 4, green laterally anteriorly and laterally posteriorly, red anteriorly and posteriorly).

View larger version (72K): [in a new window]   Figure 5. Color-coded coronal images of mean diffusion direction (v1) masked by the 12 anisotropy (left) and the normal (v3) to the plane of the mean direction and its angular dispersion masked by the 23 anisotropy (right). Left: Uniaxial architecture is emphasized (corpus callosum [CC, red], corticospinal tracts [CS, blue], pontocerebellar fibers [Po, red], and cingulum [Ci, green]). Right: Planar architecture is emphasized by the intersection of the corpus callosum and corona radiata (area 2, green), the intersection of pontocerebellar fibers and corticospinal tracts (area 3, green), and fanning of the superior frontal gyrus (area 5, red).

View larger version (91K): [in a new window]   Figure 6. Three-dimensional renderings of area 1 show a transverse view of the crossing between the corona radiata and radiation of the corpus callosum, as viewed with the two diffusion models: uniaxial (left) and planar (right). Left: Scaling of the cylinders according to their 12 anisotropy highlights voxels dominated by uniaxial diffusion. The longitudinal orientation and color coding of the cylinders were determined with the first eigenvector to indicate the direction of mean diffusion. Right: Scaling of the cylinders according to their 23 anisotropy reveals voxels dominated by planar diffusion. The longitudinal axis and color coding of the cylinders were determined by the third eigenvector. The end plane of the cylinders then represents the plane spanned by the first and second eigenvectors. The color coding represents the orientation of the third eigenvector, which is perpendicular to the plane of maximal diffusion. The area of the crossing between the corpus callosum and corona radiata is determined with a mediolateral-superoinferior fiber plane (left), which can be explained in terms of mediolateral-directed collosal fibers and superoinferior-directed corticospinal tracts (right).

View larger version (85K): [in a new window]   Figure 7. Three-dimensional renderings of area 2 show a coronal view of the crossing between the corona radiata and radiation of the corpus callosum, as viewed with the uniaxial model (left) and the planar model (right). The colors, orientations, and scaling of the cylinders were determined as in The mediolateral-superoinferior fiber plane (right), which can be explained in terms of left-to-right-directed collosal fibers and superoinferior-directed corticospinal tracts (left), determines the crossing area between the corpus callosum and corona radiata.

View larger version (66K): [in a new window]   Figure 8. Three-dimensional renderings of area 3 show a coronal view of the crossing between the pontocerebellar fibers and the corticospinal tracts, as viewed with the uniaxial model (left) and the planar model (right). The colors, orientations, and scaling of the cylinders were set as in The crossing area between the corticospinal tracts and the pontocerebellar fibers shows mediolateral-superoinferior planar architecture (right), which can be described in terms of the left-to-right-directed pontocerebellar fibers and the superoinferior-oriented corticospinal tracts (left).

View larger version (89K): [in a new window]   Figure 9. Three-dimensional renderings of area 4 show a transverse view of fanning of the superior longitudinal fascicle, as viewed with the uniaxial model (left) and the planar model (right). The colors, orientations, and scaling of the cylinders were determined as in Right: Dispersion of the superior longitudinal fascicle can be appreciated as anteroposterior or mediolateral planar architecture, and curvature of the U fiber around the sulcus can be seen.

View larger version (82K): [in a new window]   Figure 10. Three-dimensional renderings of area 5 show a coronal view of fanning of the middle and superior frontal gyri, as viewed with the uniaxial model (left) and the planar model (right). Left: The color coding and longitudinal orientation of the cylinders were determined with the first eigenvector, and scaling was determined with fractional anisotropy. Right: The planar model represents the color coding and longitudinal axis of the cylinder with the third eigenvector. The plane of maximal diffusion, spanned by the first and second eigenvectors can be appreciated as the end plane of the cylinder. The scaling was determined with fractional anisotropy. Radial dispersion of the frontal gyri is found to be in the superoinferior or anteroposterior direction, in accordance with the directions of the gyri.