Biomedical Engineering Reference
In-Depth Information
is present for pressure above 60
mmHg. Error is large for pressure
ranges below 60
mmHg [7].
Photoelastic Stress Analysis
Reference Stress
40
1600
30
1200
800
20
HBPS Range
10
400
HBPS Range
0
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
160
180
Pressure (mmHg)
Pressure(mmHg)
Figure 4.15
Stress in the model wall variation against pressure inside the
model, calculated using photoelastic stress analysis and model
radius variation as reference stress (left). Variation of error of
photoelastic stress analysis with pressure changes inside the
vasculature model (right).
4.8
Angular Distortion Correction
To obtain the measurements shown in Fig. 4.14, a correction method
for angular distortion is needed. This distortion is produced as the
photoelastic crystals orientation changes related to the camera
orientation by the blood vessel model shape, producing more
retardation near the cylinder's axis and less in the borders of the
ROI (Fig. 4.16). Provided that the error obtained by applying the
photoelastic stress analysis to the average green light intensity value
in ROI is low, we could then apply equations (4.6, 4.26) to deduce
the stress in
(
2
)
(
P, x, y
)
, a pixel located in row
x
and column
y
of a
source image set corresponding to a pressure
P
inside the model. For
correcting this, we used
T
1
−
T
TT
a
xy
TT
(
)
(
)
1
2
(,)
1
2
(,)
xy
Q
¥
§
¦
2
40
y
µ
·
¶
¨
ª
¸
º
k
cos
(
TT
)
(
TT
)
(4.32)
1
2
AVG x ROI
(,
)
1
2
min(,
x ROI
)
where for each column of ROI,
(
T
1
−
T
2
)
min
(P, y
)
is the minimum and
(
T
1
−
T
2
)
AVG(P, y
)
the average stress value, and
k
=
0.8 is correction
factor.
For the stress analysis in every pixel of the ROI, the applied
correction eliminated the distortion introduced by the blood vessel
shape, as the stress distribution is more homogeneous in Fig.
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