Biomedical Engineering Reference
In-Depth Information
Typically, the simulation results follow the same trend as that of the two-dimen-
sional plaque structural analysis. A drop in value of the blood-vessel interaction
model is found when compared based on the two-dimensional structural analysis.
However, the critical stress and maximum deformation follows a more accurate
trend due to the realism of the blood-plaque configuration being modeled. The two-
dimensional analysis can serve as a preliminary verification of the three-dimension-
al results.
The relationship between calcification gap and maximum principal stress
is based on the stress distribution on the fibrous cap having d cg varied from 0 to
0.25 mm and with E lp = 1 kPa and E cag = 100 kPa. Plaque rupture occurs when stress
levels exceed a 300 kPa threshold (Lendon et al. 1991; Vengrenyuk et al. 2006).
This stress threshold determines whether plaque fracture will occur and is based on
the morphological conditions assumed in our model and for a threshold calcifica-
tion gap. However it should not be assumed that all plaque fracture will occur at this
value (Cheng et al. 1993b).
8.5.4.5
Two-Dimensional Structural Analysis
For the non-calcified plaque with the same fibrous cap thickness, the stress can
reach as high as 370 kPa. However, the presence of calcification agglomerate at suf-
ficiently low calcification gap can lower stress levels to below 370 kPa and prevent
plaque rupture which may occur at 300 kPa. Since fibrous cap thinness threshold
for rupture is 0.065 mm, we implement the case of a fibrous cap as thin as 0.05 mm
as a limiting example. The calcification gap is specified as 0.02 mm consistent with
Fig. 8.38 .
Based on calcified plaque with fibrous cap thickness d fc at 0.05 mm, the relation-
ship between calcification gap d cg and peak maximum principal stress or critical
stress σ cr is shown in Fig. 8.40a .). For d fc at 0.05 mm as a conservative setting, a
calcification gap value of > 0.04 mm causes stress levels to exceed 300 kPa and
cause plaque rupture. As calcification gap increases, the critical stress tends to con-
verge to a peak maximum principal stress. The plaque is stabilized when the calci-
fication gap is less than 0.04 mm based on the assumed plaque configuration. The
critical stress σ cr has a positive correlation with maximum fibrous cap deformation
D max (Fig. 8.40b ). This is due to the correlation that exists for the calcification gap
with the maximum deformation. Here, D max > 0.165 mm causes plaque rupture. For
D max > 165 μm, which is 3.3 times the fibrous cap thickness (0.05 mm), stress levels
exceed 300 kPa.
8.5.4.6
Three-Dimensional Fluid-Structural Analysis
The critical stress profiles for a three-dimensional fluid-structure analysis are shown
in Fig. 8.41 . A similar trend to the two-dimensional analysis is found for the three-
dimensional model with calcified plaque where the calcification gap is specified at
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