Biomedical Engineering Reference
In-Depth Information
Fig. 19.3
Left
: visualization of diffusion tensors as ellipsoids at a brain slice.
Middle
: selected
values for all coefficients of the symmetric and anisotropic diffusion tensor
D
D
obtained by DTI.
Right
: vascular (
grey
) and non-vascular (
black
) areas on a brain slice
Therein, n denotes the voxel number,
v
i
are the eigenvectors and
γ
i,
awd
the eigenval-
ues of
D
awd
at each voxel. The basic assumption to obtain the required parameters
is that
D
awd
possesses the same eigenvectors as
D
D
and
K
SI
0
S
, as it is proposed by
Tuch et al. (
2001
). Therefore, a calibration as was shown by Sarntinoranont et al.
(
2006
) or Linninger et al. (
2008
) is carried out via
γ
i,
D
D
,
n
=
D
D
γ
i,
awd
and
γ
i,
K
I
,
n
=
K
I
γ
i,
awd
,
(19.15)
γ
awd
γ
awd
¯
¯
γ
awd
D
D
K
I
are adjusting
where
¯
is the mean value of the eigenvalues and
and
reference values. Thus, the effective drug diffusion tensor
D
D
,
n
and the anisotropic
permeability tensor
K
SI,
n
0
S
are computed for each evaluated voxel via
3
3
D
D
,
n
γ
n
K
SI,
n
0
S
γ
n
=
i,
D
D
,
n
(
v
i
⊗
v
i
)
and
=
i,
K
I
,
n
(
v
i
⊗
v
i
).
(19.16)
i
=
1
i
=
1
To show the general feasibility of this procedure, a patient-specific voxel data set
is used here (available at
http://www.sci.utah.edu/~gk/DTI-data/
). In this regard, a
custom M
ATLAB
algorithm was programmed to process the raw binary data. Due to
the irregular distribution of the anisotropic diffusion parameters, cf. Fig.
19.3
(left),
it is not possible to define a closed analytical function for the anisotropic perfusion
parameters. Therefore, the diffusion data is stored in a look-up table and loaded in
a preceding calculation step to provide the full anisotropic perfusion parameters
D
D
for the drug, cf. Fig.
19.3
(middle), and
K
SI
0
S
for the interstitial fluid, respectively.
In order to include micro-structural information of the blood-vessel system, mag-
netic resonance angiography (MRA) is a promising in vivo approach to locate and
image blood vessels within the brain tissue. In the present study, a blood-vessel
segmentation of a MRA image was carried out using A
MIRA
, a software platform
allowing for bio-medical data processing. With this tool, it is possible to assign
vascular and non-vascular areas by varying blood perfusion parameters
K
SB
0
S
,cf.
Fig.
19.3
(right). In this contribution, a microscopical isotropic perfusion is as-
sumed, which varies in magnitude between vascular and non-vascular regions.
