Biomedical Engineering Reference
In-Depth Information
where
e
γ
aniso
(
λ
(
i
)
t
−
3
)
1
⎧
⎨
)=
η
aniso
2
(
i
)
t
W
aniso
(
λ
−
γ
aniso
1
λ
(
i
)
t
C
0
:
H
(
i
)
λ
=
0
2
a
(6.66)
⎩
H
(
i
)
0
a
(
i
)
0
a
(
i
)
0
=
κ
I
+(
1
−
3
κ
)
⊗
1
λ
(
i
)
<
λ
a
,
for
d
(
i
)
=
λ
(
i
)
≥
λ
,
0
for
a
where this model has similar material constants as for the medial anisotropic mech-
anism with the addition of
, the measure of fibre dispersion.
Further, each of the three mechanisms in the intima and media have three con-
stants associated with the damage model, Eq. 6.52,
κ
c
. Representative material
parameters for arterial layers used in the balloon-artery interaction are shown in Ta-
ble 6.1.
α
s
,
α
f
,
Angioplasty model
In this section, cerebral PTA is simulated using a general purpose finite element
code ANSYS 14.0 PREVIEW 1 (ANSYS, Inc., Canonsburg, PA, USA) in which the
damage model of Sect. 6.4 was implemented using user subroutines. The numeri-
cal implementation of the inelastic constitutive model in an implicit finite element
code requires the derivation of its stress response and elasticity tensor as well as a
reformulation of the constitutive equation as a slightly compressible material. This
reformulation requires some care because of the multiple reference configurations
used in the model. Details of the finite element formulation can be found in [70, 75].
Table 6.1.
Representative material parameters for three arterial layers in balloon-artery interaction
Intima-isotropic mechanism
η
(
KPa
)
γ
c
α
(
KPa
)
α
(
KPa
)
iso
iso
s
f
4.55
0.565
2.1
80.0
2100
Media-isotropic mechanism
η
iso
(
KPa
)
γ
iso
c
α
s
(
KPa
)
α
f
(
KPa
)
4.55
0.565
1.8
100.0
1800
Media-anisotropic mechanism
η
aniso
(
KPa
)
a
γ
aniso
λ
β
c
α
s
(
KPa
)
α
f
(
KPa
)
7
◦
0.006
125.0
1.88
1.54
1.5
6.0
Adventitia-isotropic
Adventitia-anisotropic
a
η
(
KPa
)
γ
η
(
KPa
)
γ
λ
κ
β
iso
iso
aniso
aniso
56
◦
2.27
1.13
500.0
7.53
1.5
0.20