Biomedical Engineering Reference
In-Depth Information
Table 19.1
Material parameters for numerical simulations of CED
Symbol
Value
Unit
Description/reference
ρ
IR
10
+
3
[kg/m
3
]
0
.
993
·
effective density interstitial fluid (water at 37 °C) and
ρ
BR
10
+
3
[kg/m
3
]
1
.
055
·
effective density of blood plasma according to
The Physics
Factbook
by Glenn Elert (
http://hypertextbook.com
)
μ
IR
10
−
3
[Ns/m
2
]
0
.
7
·
dynamic viscosity interstitial fluid (water at 37 °C) and
μ
BR
10
−
3
[Ns/m
2
]
3
.
5
·
dynamic viscosity of blood at 37 °C according to
The Physics
Hypertextbook
by Glenn Elert (
http://physics.info/viscosity
)
n
I
0
S
0.20
[-]
initial interstitial fluid volume fraction, according to Baxter
and Jain (
1989
) and citations therein
n
0
S
0.05
[-]
initial blood volume fraction, according to Baxter and Jain
(
1989
) and citations therein
n
0
S
0.75
[-]
initial solidity (cells & vascular walls), remaining term in
(
19.1
)
μ
S
10
+
3
[N/m
2
]
·
elastic Lamé constants (
E
=
2
.
8kPa;
ν
=
1
.
0
0
.
417), chosen in
λ
S
10
+
3
[N/m
2
]
5
.
0
·
magnitude according to Smith and Humphrey (
2007
), Chen
and Sarntinoranont (
2007
) and citations therein
D
ij
10
−
11
-10
−
12
[m
2
/s]
order of magnitude of spatial varying drug diffusion coeffi-
cient, cf. Sect.
19.2.2
, according to Baxter and Jain (
1989
)
and citations therein
K
ij
10
−
7
-10
−
8
[m/s]
order of magnitude of spatial varying Darcy permeability for
the interstitial fluid, cf. Sect.
19.2.2
, according to Kaczmarek
et al. (
1997
)
K
ii
10
−
3
3
.
0
·
[m/s]
isotropic Darcy permeability coefficient, blood in vascular
10
−
5
3
.
0
·
[m/s]
and non-vascular regions, based on Su and Payne (
2009
)
κ
1.4
[-]
deformation-dependent permeability (assumption)
19.3.1 Simulation of CED on a Human Brain Slice
As is well known in biomechanics, the in-vivo determination of patient-specific ma-
terial data is an almost impossible task. Lacking of an alternative, the simulation
parameters are predominantly extracted from the related literature on phantom ex-
periments and numerical studies on animals or gels, see Table
19.1
. However, since
the focus of this contribution is mainly motivated by making available a model-
ing approach for numerical studies, we do not claim the accuracy for all included
material parameters.
For the present numerical study, a realistic geometry of slice of a human brain is
spatially discretized using 2,100 hexahedral Taylor-Hood elements (one element in
thickness direction). As is shown in Fig.
19.4
, the catheter is virtually placed in the
brain tissue applying the corresponding boundary conditions for the CED. Further-
more, plane-strain conditions for the brain section are considered in combination
with a horizontally fixed exterior of the brain (cortex). In addition, the blood flow is
neglected in combination with a constant blood volume fraction. Figure
19.5
shows
