Biomedical Engineering Reference
In-Depth Information
So, for example,
a
(
1
)
0
a
(
2
)
0
=
cos
β
e
θ
+
sin
β
e
z
,
=
cos
β
e
θ
−
sin
β
e
z
.
(6.63)
Since acute vessel injury following PTA has been found to be limited to the intima
and media layers [57, 122], we only consider damage to the mechanisms in the intima
and media. The damage to each layer will be modelled using the isotropic structural
damage model introduced in Sect. 6.3. Here, only mechanical damage is considered
since the time scale is too short for a secondary response of hemodynamic loads to be
important [72]. Further, due the low number of loading cycles and large magnitude
of the load, only discontinuous mechanical damage is considered.
For all layers, the isotropic contributions will be assumed to be of the form,
e
(
γ
iso
(
I
0
−
3
))
−
1
⎧
⎨
⎩
I
0
)=
η
iso
2
W
iso
(
γ
iso
W
iso
(
W
iso
=(
1
−
d
(
α
iso
))
I
0
)
,
where
W
iso
(
s
)
(6.64)
α
iso
=
max
s
∈
[
0
,
t
]
d
(
α
iso
)
is given in Eq. (6.52)
where
γ
iso
are layer dependent material constants.
The components of the anisotropic mechanism in the medial layer are modelled
using a two fibre model. It is assumed the fibre families in the two directions have
the same material properties, differing only in their fibre orientation. As introduced
in (6.19),(6.41),(6.53),
η
iso
and
i
=
1
1
−
d
(
α
(
i
)
W
aniso
(
λ
(
i
)
2
W
aniso
=
aniso
)
)
,
where
t
e
γ
aniso
(
λ
(
i
)
2
1
⎧
⎨
)=
η
aniso
2
W
aniso
(
λ
(
i
)
−
3
)
t
−
t
γ
aniso
1
λ
λ
(
i
)
t
C
0
:
a
(
i
)
a
(
i
)
0
=
⊗
0
2
a
(6.65)
⎩
α
(
i
)
]
λ
(
i
)
aniso
=
max
s
t
∈
[
0
,
t
d
(
α
aniso
)
is given in Eq. (6.52)
where
are material constants associated with the families of fi-
bres. The components of the anisotropic mechanism in the adventitial layer are mod-
elled using a generalized structure tensor approach. As introduced in (6.36),(6.38)
are defined as,
η
aniso
,
γ
aniso
,
λ
a
,and
β
i
=
1
1
−
d
(
i
)
W
aniso
(
λ
(
i
)
2
=
)
,
W
aniso
t
