Image Processing of Diffusion Tensor MRI Data - Advance Image Processing in Magnetic Resonance Imaging - page 431

(b)

(a)

FIGURE 13.10 (a) Visualization of diffusion tensors. The tensors are color-coded according
to the shape: the linear case is blue, planar case is yellow, and spherical case is red. The radius
of the sphere is the smallest eigenvalue of the diffusion tensor; the radius of the disk is the
second largest; and the length of the rod is twice the largest eigenvalue. (b) Simulated tensor
field of three crossing white matter tracts. Due to partial voluming effects, the tensors in the
area where the fibers are crossing have spherical shape. (From Westin, C.-F., Maier, S.,
Mamata, H., Nabavi, A., Jolesz, F., and Kikinis, R. (2002). Processing and visualization of
diffusion tensor MRI. Med. Image Anal. 6(2): 93-108.)

are here scaled according to the eigenvalues, but can alternatively be scaled according
to the shape measures c l , c p , and c s .
Additionally, coloring based on the shape measures c l , c p , and c s can be used
for visualization of shape. Figure 13.10 shows a coloring scheme in which the
color is interpolated between the blue linear case, the yellow planar case, and the
red spherical case.

13.5 CONNECTIVITY ANALYSIS

Determination of neural fiber architecture from diffusion tensors measured in the
brain is a complex problem with many potential applications in neurosurgery and
neuroscience. The phrase “white matter connectivity” refers to a measure of the
neural connection strength between points or regions in the brain. In animal
research, connectivity measurements can be made using injected tracers in com-
bination with histological analysis. These methods are not applicable to human
neuroanatomical study, but a wealth of information can be acquired noninvasively
through the analysis of diffusion MRI.
Initial work on DT-MRI connectivity focused on tractography [1,2,18], or the
interpolation of paths through the principal eigenvector field. An extension of this
method evolved a surface using a fast marching method, in which the speed
function was dependent on the principal eigenvector field [13]. Another approach
iteratively simulated diffusion in a 2-D tensor volume, and quantified connection
strengths based on a probabilistic interpretation of the arrival time of the diffusion
front [4]. A new level-set-based method evolved a surface in a field of vectors