Biomedical Engineering Reference
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Three-dimensional analyses have also been prepared to justify the accuracy of the
results based on the plane analyses of patient-specific case studies (Bluestein et al.
2008; Holzapfel et al. 2002; Kiousis et al. 2009; Li et al. 2006; Tang et al. 2005a,
b, 2008). Some plaque mechanics studies examine arterial wall bending along the
longitudinal axis since repetitive bending causes strain on an atherosclerotic plaque
resulting in rupture (Beaussier et al. 2008).
Plaque rupture is dependent on biomechanical events acting on the fibrous cap
such as haemodynamic shear stresses (Gertz and Roberts 1990), turbulent pressure
fluctuations (Loree et al. 1991), cyclic variation of intraluminal pressure and maxi-
mum principal stress by the pulsatile blood pressure (Loree et al. 1992; Richardson
et al. 1989a). In particular, large eccentric lipid cores are of mechanical disadvan-
tage since circumferential tensile stresses are configured in such a way that fibrous
caps have a tendency to rupture most of the time (Cheng et al. 1993b). This gives
rise to the relationship between plaque rupture and the critical stress acting on the
fibrous cap.
Autopsies of patients that are diagnosed with cardiac ischemia showed that the
level of macrophages is high, smooth muscle cells are reduced, the proportion of
crescentic acellular mass for a lipid core is significant, and the fibrous cap is thin
(Davies et al. 1993; Fayad and Fuster 2001; Moreno et al. 1994a; Richardson et al.
1989a). For plaque rupture, 65 μm thickness with an infiltrate of macrophages is
defined as the threshold after histological analysis (Burke et al. 1997). This can
guide critical risk analysis of plaque condition.
8.5.1.3
Design of Plaque Models
Idealized plane models of the longitudinal atherosclerotic arteries were implement-
ed to study the effects of stenotic severity on plaque circumferential stress. One set
pertains to stenosis based on a homogenous wall material while the other is based on
plaque with a lipid core where the constitutive model is assumed non-homogenous,
anisotropic, and elastic. To numerically simulate this type of plaque-vessel, all
plaque constituents were assigned with physiological mechanical properties.
For validation, a non-calcified plaque structural configuration was implemented.
Two subset models of plaques with and without the lipid core are shown in Fig.
8.30a
and
b
respectively. The effects of fibrous cap thickness
d
fc
and width of calcification
gap
d
cg
on the stress levels of plaque were examined by varying fibrous cap thick-
ness
d
fc
from 0.05 to 0.5 mm. We hypothesize that calcification plays an important
role in plaque vulnerability assessment, and therefore the calcification agglomerate
is modeled as a 140
o
crescent of variable thickness
d
cag
and positioned within the
lipid. Idealistic models for analysis of calcification structural variation were de-
signed with calcification gap
d
cg
, ranging from 0.05 to 0.33 mm (Fig.
8.30c
).
The following parameters were used in a plane-stress model: Young's modulus
(
E
) in circumferential (
θ
) and radial (
r
) directions,
ν
rθ
and
ν
rz
that are the Poisson
ratios in
r-θ
and
θ-z
planes respectively, as well as
G
rθ
that is the shear modulus in
r-θ
plane.
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