Biomedical Engineering Reference
In-Depth Information
The
Relative anisotropy
(RA)isgivenby[
4
]:
(
λ
1
−
λ
)
2
+(
λ
2
−
λ
)
2
+(
λ
3
−
λ
)
2
√
3
RA =
.
λ
Westin et al. [
73
] proposed anisotropy measures to discern
linear
c
l
,
planar
c
p
and
spherical
c
s
diffusion tensor shapes:
λ
1
−
λ
2
2(
λ
2
−
λ
3
)
λ
3
λ
1
+
3
λ
1
+
λ
1
+
c
l
=
λ
3
;
c
p
=
λ
3
;
c
s
=
.
λ
2
+
λ
2
+
λ
2
+
λ
3
6.4.2
Beyond DTI
In DTI, the Gaussian assumption over-simplifies the diffusion of water molecules.
While it is adequate for voxels in which there is only a single fiber orientation
(or none), it breaks down for voxels in which there are more complex internal
structures. This is an important limitation, since the resolution of dMRI acquisitions
is between 1 mm
3
and 3 mm
3
while the physical diameter of fibers can be between
1
m[
8
,
54
]. Research groups currently agree that there is complex fiber
architecture in most fiber regions of the brain [
53
]. In fact, it is currently thought
that between one third and two thirds of imaging voxels in the human brain white
matter contain multiple fiber bundle crossings [
9
]. This has led to the development of
various High Angular Resolution Diffusion Imaging (HARDI) techniques [
69
]such
as Q-Ball Imaging or Diffusion Spectrum Imaging for exploring the microstructure
of biological tissues with greater accuracy.
HARDI samples q-space along as many directions as possible in order to
reconstruct estimates of the true diffusion PDF—also referred as the EAP—of water
molecules. This true diffusion PDF is model-free and can recover the diffusion
of water molecules in any underlying fiber population. HARDI depends on the
number of measurements
N
and the gradient strength (
b
-value), which directly
affects acquisition time and signal to noise ratio in the signal.
μ
m and 30
μ
6.4.2.1
Diffusion Spectrum Imaging: Recovering the Diffusion EAP
Diffusion spectrum imaging
(DSI) introduced by Wedeen et al. [
67
,
71
] in 2000, was
the first dMRI method that applied the q-space formalism to measure or estimate
the EAP in biological tissue. The forte of the q-space formalism, where diffusion
could reveal more than just the intrinsic properties like the diffusion coefficient,
and show how it could probe the complex microstructure of the underlying tissue,
became quickly apparent. Crossing fiber microstructures were clearly revealed by
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