Visualization of Diffusion Tensor Imaging Data
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.
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Using this technique the colour coding of the resulting image provides a segmentation by tissue type as demonstrated in the figure. The cyan and green regions represent areas of high mean diffusivity and low anisotropy and therefore indicate fluid filled compartments. The whitish regions represent areas of low anisotropy and low mean diffusivity and therefore indicate gray matter. Textured regions exhibit a high anisotropy and indicate white matter. Very long texture components indicate fiber tracts parallel to the image plane, eg. the splenium of the corpus callosum. In contrast a noise-like texture with very short texture components indicates fiber tracts almost orthogonal to the image plane, \eg the external capsule (1).
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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.
Acknowledgements
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.
Last Modified: 01/22/2003 14:51:59 by Burkhard Wünsche (Wuensche)