Biomedical Engineering Reference
In-Depth Information
b
ML-EM
Method
ML-EM
Method
S'
p
A
p
a
B'
n, k+1
p
B
n, k+1
p
B'
n,0
p
B
0
Figure 4.22
(a) Preliminary thickness slice reconstruction
B
n,k
p
from
thickness sinogram
A
n
p
and irst cross section initial guess
B
0
p
. b) Average stress slice reconstruction
B
a
n,k
p
from iltered
average stress sinogram
S
a
0
p
and irst cross section initial guess
B
a
n,
0
p
.
Let us name
A
n
P
(a, b)
the pixel located at row
a
and column
b
of
A
n
P
, the limits of the ROI for the row
a
are deined by the external
wall location
L
oa
and the inner wall location
L
ia
.
When
A
n
P
(a, b)
reaches 1200
b
when
A
n
P
(a, b)
reaches the irst
local maximum. The average stress sinogram
S
n
P
is calculated by the
boundaries deined by the ROI by
μ
m,
L
oa
b
, and
L
ia
=
=
L
ia
¤
n
n
RabcAab
(,)/
(,)
p
p
bL
n
Sab
(,)
(4.37)
oa
p
LL
ia
oa
Pixels outside the ROI were set as zero. Finally the average stress
sinogram
S
n
P
is iltered by multiplying it with the sinogram of
B'
n, 0
P
to obtain
S'
n
P
. Then the ML-EM was applied to images
S'
n
P
and
B'
n,
0
P
, after ive iterations a slice of average stress was reconstructed
B'
n, 5
P.
During the application of the ML-EM method if a pixel value
of
B'
n, 0
P
or
S'
n
P
was zero, the detection probability was brought
to zero for that pixel. For accuracy evaluation, we used the model
for longitudinal stress variation in a cylinder according to [9]; this
model describes the stress on the blood vessel model edge:
2
(
rt
)
T
2
P
in
(4.38)
2
2
r
(
r
t
)
where
P
in
is the pressure inside the cylinder,
r
the cylinder radius
and
t
the wall thickness.
Slices of average stress corresponding to the sinograms of
Fig. 4.21 were reconstructed relying on ML-EM method, as shown
in Fig. 4.23. Ten stress distribution slices within the region of
interest were loaded to the
Volume Viewer
of
ImageJ
to display the
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