Diffusion tensor imaging (DTI) is used to measure the intrinsic properties of water diffusion in the brain by an orientation invariant quantity, the diffusion tensor D. This is possible since the spatial distribution of water molecules originating at a point location after an infinitesimal time period is described by an ellipsoid. The lengths and orientations of the principal axes of this diffusion ellipsoid are given by the eigenvalues and eigenvectors, respectively, of the symmetric second-order tensor D which is represented by a symmetric 3x3 matrix.
In the brain DTI can be used to differentiate two types of structures. Fluid filled compartments are characterized by a very high isotropic diffusion, ie. the diffusion is similar in all directions. In contrast white matter consists of nerve fibers which restrict the diffusion to one direction only due to the presence of cell membranes and myelin sheaths surrounding the axons. Fiber tracts, consisting of parallel nerve fibers, are therefore identified as areas of a high anisotropic diffusion. The orientation of such fiber tracts is determined from the principal directions (eigenvectors) of the diffusion tensor. Finally gray matter consists of neural cell bodies, support cells, intermingling nerve fibers and connecting contacts, and is characterized by a low, isotropic diffusion.
As an improved visualization method for fiber direction in slice images we propose transparency modulated Line Integral Convolution. Line Integral Convolution (LIC) has been originally proposed by Cabral and Leedom as a method to visualize vector fields by convolving a noise texture with the field. We use the principal diffusion direction as a vector field but additionally define transparency values inversely proportional to the diffusion anisotropy in order to remove regions not corresponding to white matter. The resulting texture is then blended with a colour mapped image of the mean diffusivity. The three dimensional direction of a nerve fiber is encoded by varying the length of a convolution kernel with the normal component of the principal diffusion direction.
A 3D representation of nerve fiber tracts can be achieved by integrating streamlines along the principal diffusion in regions of high diffusion anisotropy. In order to improve the 3D perception of the streamlines we fit cylindrical tubes around them.
We would like to thank Peter J. Basser from the National Institute of Health, Bethesda, MD, for valuable discussions and Carlo Pierpaoli for providing us with the diffusion tensor data set of a healthy brain.
Modified: 01/22/2003 14:51:59 by Burkhard Wünsche (Wuensche)