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 ) 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 (kPa)
50
500
1
12,600
9475.2
ν
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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