Biomedical Engineering Reference
In-Depth Information
Fig. 6.6
Microstructure from DTI. Coherent fibers (
a
) can be inferred from the ellipsoid of the
diffusion tensor (DT) (
b
). The DT also provides a local coordinate system (
c
) that indicates the
preferential diffusion anisotropy directions
Fig. 6.7
Diffusion Tensor Imaging (DTI). (
a
) DTI ellipsoids from an axial slice of the brain.
(
b
) Zoom of highlighted box in (
a
). (
c
) Fractional Anisotropy (FA). (
d
) Colour FA where the
colour components RGB represent the unit major eigenvector of the diffusion tensor
e
1
=[
r, g, b
]
T
weighted by FA, or the colours indicate the preferential diffusion anisotropy directions
Scalar Measures:
The microstructure of the medium or the white matter can
be further characterized from a number of rotationally invariant scalar measures
derived from the DT that reveal diffusive properties of the underlying tissue. A
number of such scalar measures are of primary importance since they are often used
as bio-markers.
Thefi t s
mean diffusivity
(MD) [
4
]:
λ
=
tr
(
D
)
/
3
.
Fractional anisotropy
(FA) is the other measure which describes the amount of
anisotropy presented by the microstructure (Fig.
6.7
). It too is derived from the
eigenvalues of
D
(
λ
1
≥
λ
2
≥
λ
3
)[
4
]:
λ
1
−
λ
)
2
+(
λ
2
−
λ
)
2
+(
λ
3
−
λ
)
2
3
2
(
FA =
,
λ
1
+
λ
2
+
λ
3
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