Diffusion anisotropy and white matter tracts
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Diffusion Anisotropy and White Matter Tracts V.J. W e d e e n 1, T.L. Davis 1, B.E. Lautrup 2, T.G. Reese ~ and B.R. Rosen ~ 1Harvard Medical School, Boston, USA 2CONNECT, The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark Objectives. Water diffusion anisotropy can provide information about the tissue microarchitecture (1). Images of diffusion anisotropy in the brain reveal the orientation of axons in white matter, and diffusion anisotropy data provide information about the large-scale structure of white matter tracts. Methods. Diffusion-weighted magnetic resonance images were obtained in a normal volunteer as described by Davis et al (2). Employing single-shot echo-planar MRI at 1.5 Tesla, diffusion data were sampled for 15 contiguous coronal slices at a 3 millimeter isotropic resolution. Total acquisition time was 15 minutes. From these data the water selfdiffusion tensor field was computed at each voxel location (3). We assume that the inverse of the diffusion tensor may be interpreted as a non-Euclidean metric tensor, and we test whether the shortest curves--the geodesics--in this geometry follow known white-matter tracts in the brain. These geodics were computed by numerically integrating the second-order geodesic equation (4). Initial data were constructed by selecting a point in a region of high anisotropy and setting the initial tangent vector equal to the diffusion tensor eigenvector corresponding to the largest eigenvalue, which is the Figure 1 direction of greatest water mobility. Results. Figure 1 depicts three-dimensional water diffusion in an axial slice through the brain at the level of the lateral ventricles. MRI magnitude data are shown in grayscale, and diffusion data are represented by small 3D rhomboids at each pixel location; rhomboid vertices represent the top two eigenvectors of the local diffusion tensor. In Fig. 1, the posterior horn of the left lateral ventricle appears as a large white structure. The long axes of the rhomboids indicate the principal orientation of local white matter. We identify the splenium of the corpus callosum (long vertical arrow), the optic radiations (three horizontal arrows) and examples of gyral U-fibers (two short arrows). Note that the fibers of the optic radiations are seen to arch upwards into the plane of section. Base points selected in the region of the corticospinal tract yielded geodesic trajectories which remained within this tract over distances of several centimeters (Fig. 2). A coronal slice through the data volume provides an anatomic reference. Local diffusion tensor data in this plane are represented by rhomboids. Fibers of the corona radiata are visualized as vertically oriented diffusivities (black arrows). The 3D geodesic solutions for seed points within the corona radiata track through planes that lie in front of this image plane and conform to the coronal diffusion. These solutions exhibit the expected medial-to-lateral fan of the corona. Pairs of fibers whose . . . . trajectories are parallel for several centimeters are joined by a ribbon. Figure 2 Conclusions. Diffusion tensor anisotropy provides a means of tracking axonal bundles over macroscopic distances. The identification of white-matter tracts is less obvious when these cross and the diffusion tensor becomes less anisotropic. A systematic analysis of these data may be undertaken by massive computation of the full set of diffusion geodesics between all voxels. The use of geodesics promises to provide an anatomic substrate for functional connectivity in vivo. Acknowledgement. Funded in part by Human Brain Project R01 DA092461. References 1. Moseley, ME et al. Mag Res Med. 1991, 19:321-326. 2. Davis, TL. et al. In Soc. Mag. Res. in Med., 12th meeting, New York, N.Y. 1993, 1:239. 3. Garrido, L. et al. Circ. Res. 1994, 74(5):789-793. 4. Carmo, DO. Differential Geometry of Curves and Surfaces. Prentiss Hall. 1976.
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