Biomedical Engineering Reference
In-Depth Information
Table 10.1
Parameters used
in the finite element model
Parameter
Value
Source
Matrix material
c
23.63 kPa
Famaey et al. (
2012a
)
Collagen fibers
α
fib
±
5°
O'Connell et al. (
2008
)
k
1
32
.
51 kPa
k
2
3
.
05
(
−
)
Famaey et al. (
2012a
)
κ
0
.
16
(
−
)
Smooth muscle cells—chemical rate constants
κ
1
,κ
6
0
.
14 s
−
1
0
.
5s
−
1
κ
2
,κ
5
Hai and Murphy (
1988
)
0
.
44 s
−
1
κ
3
,
4
κ
4
0
.
01 s
−
1
κ
7
Smooth muscle cells—mechanical constants
μ
smc
0.25 MPa
Famaey et al. (
2012b
)
κ
c
0.93 MPa
Famaey et al. (
2012b
)
η
60 MPa s
Murtada et al. (
2010
)
α
smc
0°
O'Connell et al. (
2008
)
γ
smc
pas
0
.
9
(
−
)
Famaey et al. (
2012b
)
m
smc
pas
3
.
00 kPa
Famaey et al. (
2012b
)
were used as fixed input values into the mechanical model. Additional parameters
are related to the mechanical model of the smooth muscle cell contribution. Accord-
ing to O'Connell et al. (
2008
), the smooth muscle cells of rat abdominal arteries
are oriented circumferentially with
α
smc
0°. The parameter
μ
smc
depending on
the stiffness of the actin-myosin filament structure and the parameter
κ
c
related to
the driving force per cross-bridge were both tuned to fit the experimental contrac-
tion measured in the myograph due to addition of PE for a previously undamaged
segment, as described in Sect.
10.2
. The viscous damping constant
η
was set to
60 MPa s, corresponding to the value used in Murtada et al. (
2010
).
To characterize damage progression appropriately, two parameters need to be cal-
ibrated for each constituent, plus two additional ones for the smooth muscle cells,
resulting to ten parameters. Since the myograph experiment only allows for damage
quantification in the smooth muscle cells, with the current setup, no reasonable dam-
age parameters can be defined for the extracellular matrix and the collagen fibers.
Additional complementary experiments will be needed for this task, as discussed in
Sect.
10.7
. Accordingly, here,
γ
mat
and
γ
fib
were set to zero, such that
m
mat
and
m
fib
can take any arbitrary value. Secondly, the assumption was made that, during
clamping, the smooth muscle cells were completely passive, and thus not contribut-
ing to the stiffness. Consequently, no damage could accumulate here, so that
γ
smc
act
=
