Biomedical Engineering Reference
In-Depth Information
Table 8.4
Material properties for plaque constituents. The Young's modulus (
E
r
,
E
θ
), Poison ratios
(
G
rθ
) and shear modulus (
ν
rθ,
ν
rz
) are presented for the plaque, non-diseased wall of artery and lipid.
The data are revised from Loree et al. (1992)and Holzapfel et al.(2002) Fibrous tissue at
α
= 5 %,
lipid at
β
= 20 % and calcium
at
γ
= 75 % pertain to the homogenous calcification agglomerate
Parameter
Artery (ndw)
Fibrous tissue
(ft)
Lipid (lp)
Micro-calcium
(Ca)
Calcification
agglomerate (cag)
E
r
(kPa)
10
50
1
12,600
9452.7
E
θ
(kPa)
100
1000
1
12,600
9500.2
G
rθ
(kPa)
50
500
1
12,600
9475.2
ν
rθ
0.01
0.01
0.01
0.01
0.01
ν
rz
0.27
0.27
0.27
0.27
0.27
The elastic mechanical property of the calcification agglomerate is established
based on defined percentages of fibrous plaque tissue (
ft
), lipid core (
lc
) and cal-
cium (
Ca
):
cag
ft
lc
Ca
E
=
αβ
E EE
+
+
γ
,
i
i
i
i
cag
ft
lc
Ca
G
=
αβ
GGG
θ
+
+
γ
,
(8.2)
r
r
θ
r
θ
r
θ
where
i
denotes
r
and
θ
represents radial and circumferential orientations respec-
tively. The percentage of compositions
α, β,
and
γ
corresponds to fibrous tissue,
lipid and calcium, respectively. Young's modulus
E
i
cag
and shear modulus
cag
G
θ
are
based on a linear combination of
E
i
j
and
j
G
θ
with component
j = ft, lc
, and
Ca
.
The material properties of the plaque constituents are consolidated from Loree
et al. (1992) and Holzapfel et al. (2002) in Table
8.4
. In this study, we assumed a
combination of fibrous tissue (
α
= 5 %), lipid (
β
= 20 %) and calcium (
γ
= 75 %) as
components for a homogenous calcification agglomerate.
The ANSYS finite element program was used to relate the stress distribution
within plaque with a luminal pressure
P
of 14.6 kPa. The finite element mesh were
tetrahedral elements with minimal skewness. The axial strain is of the order of ves-
sel dimension and negligible with respect to the circumferential and principal strain,
and therefore the analysis is based on plane-stress models. Due to the symmetry of
the vessel, a half model was implemented to reduce computational costs of model-
ling stress. The symmetry condition was applied at the half-vessel that lies on a
symmetry line. Adaptive meshing for each component of the plaque was performed
to increase the mesh resolution at regions where high strain energies are localized.
Such non-homogenous distribution of mesh elements improves accuracy of the nu-
merical solution. Different grid densities were applied for the artery, fibrous plaque,
lipid and calcification agglomerate as a variation of strain energies pertain to these
elastic materials (Fig.
8.31
).
As atherosclerosis is a complex process, multiple parameters are required
to accurately model plaque vulnerability. As a prerequisite, preliminary analysis
was performed on a simplified version of the model to identify the correlations
between maximum principal stress, maximum deformation, fibrous cap thickness
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