Biomedical Engineering Reference
In-Depth Information
Fig. 22.3
Schematic represents the transfer restrictions placed on the MPET model. For example,
it can be seen that there is no provision allowing for flow to occur between the CSF and arterial
networks
−
k
ν
∂
2
p
ν
∂r
2
∂p
ν
∂r
2
r
−
−|
s
c
→
e
|+|
s
e
→
ν
|=
0
,
(22.6)
k
e
∂
2
p
e
∂r
2
∂p
e
∂r
2
r
−
−
−|˙
s
c
→
ν
|−|˙
s
e
→
ν
|=
0
.
(22.7)
In the above,
G
is the shear modulus and
ν
is the Poisson's ratio. In addition, if
one observes the set of Eqs. (
22.3
)-(
22.7
), there is an evident alternation of signs
for the
terms. A negative/positive sign indicates an addition/loss of fluid to that
particular network, see Fig.
22.3
. It is noted that in Eqs. (
22.3
)-(
22.7
), the transfer
between networks is via a hydrostatic pressure gradient (for the current stata of de-
velopment of the model), hence
|˙
s
|
˙
s
s
→
t
=
ξ
st
(p
t
−
p
s
)
. Here,
ξ
st
is a constant scaling
the flow between networks
s
and
t
.
22.3.3 Anatomy Acquisition
The three dimensional anatomy of the ventricular system, choroid plexuses and the
arterial system was reconstructed from a series of 511
(xy)
, 314
(xz)
, 511
(yz)
DI-
COM files produced from a T2-weighted MRI scan of a healthy male volunteer aged
in his sixties. The images of the entire cranial area were acquired in the sagittal, axial
and coronal directions. The slice spacing was 0.5 mm. The acquired images were
manually segmented for the ventricular system using Amira (Mercury Computer
Systems, San Diego, CA, USA) and the raw segmented geometry from this process
was saved as a stereo lithography (STL) file. In order to preserve key anatomical
features such as the aqueduct of Sylvius, subsequent smoothing of the STL file was
done using the open-source modeling software, Blender (The Blender Foundation,
Owing to its powerful individual nodal manipulation capabilities, Blender was
also used to apply the smooth and local stenosis (Tully and Ventikos,
2011
)tothe
three-dimensional patient specific geometries for the cases involving the three de-
grees of HCP severity, namely open (3.00 mm diameter), mild (1.25 mm diameter)
and severe (0.80 mm diameter). The aforementioned dimensions are those of the
hydraulic diameter defined in Sect.
22.4
. It must be noted that the current standard
