Image Processing Reference
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tors of the diffusion tensors, are extracted and displayed [
2
]. Care must to be taken
to terminate the streamlines in areas of isotropic or planar diffusion. Hyperstream-
lines take into account more of the tensor information [
109
]. Many tractography
approaches require one or more regions of interest to be selected
before
tracts can
be seeded starting only from those regions, while more recent efforts allow for full-
brain fiber tracking followed by more intuitive interactive selection within the brain's
tracked fiber bundles [
8
,
85
] (see the right image in Fig.
21.2
for an example). For a
simplified visual representation, the envelopes of clustered streamline bundles can be
shown [
25
], or illustrative techniques such as depth-dependent halos can be used [
26
].
With probabilistic tractography, local probability density functions of diffusion or
connectivity are estimated and can in turn be used to estimate the global connectivity,
that is, the probability that two points in the brain are structurally connected [
4
]. This
type of data is arguably a higher fidelity representation of structural connectivity.
Connectivity between two points can be visualized with, e.g., constant-probability
isosurfaces, with direct volume rendering of the probability field, or using topolog-
ical methods from flow visualization [
82
]. Calculating and effectively visualizing a
full-brain probabilistic tractography would be challenging.
DSI and HARDI.
As explained above, DTI is not able to capture more than one
principal direction per sample point. In order to reconstruct the full diffusion proba-
bility density function (PDF), that is, the function describing the probability of water
diffusion from each voxel to all possible displacements in the volume, about 500
or more diffusion-weighted MRI volumes need to be acquired successively. This is
called diffusion spectrum imaging or DSI [
34
] and is the canonical way of acquir-
ing the complete 3-D water diffusion behavior. However, the time and processing
required to perform full DSI complicate its use in research and practice.
In High Angular Resolution Diffusion Imaging, or HARDI, 40 or more direc-
tions are typically acquired in order to sample the 3-D diffusion profile around every
point [
95
]. Based on such data, multiple diffusion tensors can be fit to the data [
95
],
higher order tensors can be used [
69
], or a model-free method such as Q-Ball imag-
ing [
96
] can be applied. Q-Ball yields as output an orientation distribution function,
or ODF. The ODF is related to the diffusion PDF in that it describes for each direction
the sum of the PDF values in that direction. It can be visualized as a deformed sphere
whose radii represent the amount of diffusion in the respective direction.
HARDI visualization follows much the same lines as DTI visualization, except
that the data are more complex. Analogous to DTI, HARDI scalar metrics, such as
generalized (fractional) anisotropy and fractional multifiber index, can be used to
reduce the data to one or more scalar values that can be visualized with traditional
techniques. Multiple diffusion tensors can be represented as glyphs, or the diffusion
ODF can be directly represented using a tessellated icosahedron or by raycasting
the spherical harmonics describing the ODF [
70
]. This results in a field of complex
glyphs representing at each point the diffusion profile at that position. In contrast to
DTI glyph techniques, regions of crossing fibers can in general be identified.
Although there are fewer examples, especially in the visualization literature,
(probabilistic) fiber tracking can be performed based on HARDI data [
72
]. More
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