Biomedical Engineering Reference
In-Depth Information
Table 1.3:
An example of simulated values of arterial structures
R
k
η
k
(
DBC
)
µ
k
σ
k
k
Structure
N
k
[mm]
[mm]
[m
2
]
E
6
[
2
]
E
6
×
−
×
−
0
Transducer
475
0.59
0.05
7.2E
1
2.68E
2
−
−
1
Blood
6204
1.57
1.22
9.0E
2
9.48E
1
−
−
2
Intima
729
2.18
0.25
8.2E
1
2.86E
2
−
−
3
Media
150
2.38
0.35
3.3E
−
3
1.82E
−
1
4
Adventitia
25794
3.44
3.02
7.3E
−
1
2.71E
−
2
N
k
is the scatterer number,
R
k
is the mean radial position,
η
k
is the radial deviation,
µ
k
is the backscattering
cross section, and
σ
k
is the DBC deviation.
“voxel” volume. For the RBCs,
V
o
=
0
.
04
×
0
.
04
×
0
.
04
≈
6
.
4
×
10
−
5
mm
3
. The
total number of RBCs per voxel is
N
t
=
V
o
×
N
≈
360 cells
/
voxel. Now, we can
calculate the total RBCs “voxel” number as
N
RBC
=
N
o
/
N
t
≈
1
.
5
×
10
4
voxels
for the sweeping volume by the ultrasound beam. This “voxel” number is even
computer intractable. Therefore, we must consider that the typical structure
dimensions that can be measured by IVUS image are greater than 0.04 mm. A
well contrasted image structure dimension by IVUS begins from 0.06 mm. Using
these “voxel” dimensions,
V
o
=
2
.
14
×
10
−
4
mm
3
, the total “voxel” number is
N
t
≈
880 cells
/
voxel, and the RBC “voxels” number is approximately
N
1
≈
6200
voxels. An example of RBCs “voxel” number used in this simulation is given in
Table 1.3.
(2)
The intima, media,
and
adventitia.
The numerical values necessary for
the evaluation of the scatterer number for the intima, media, and adventitia
were taken from results of Perelman
et al.
[22], which give the typical nuclear
cells size
l
(
µ
m) distribution for human cells. The “voxel” number for each layer
was computed taking into account the typical dimensions of intima, media, and
adventitia of a normal artery.
(3)
The voxel number for the sheathing transducer
was calculated taking
into account the minimal scatterers that can be observed at maximal resolution
when the frequency is fixed at 40 MHz, a typical IVUS frequency. From Figs. 1.14
and 1.19, the transducer sweeping volume is
V
t
=
π
a
(
D
2
M
−
D
2
m
)
/
4, where
a
≈
0
.
60 mm is the transducer diameter, and
D
M
≈
0
.
84 mm and
D
m
≈
0
.
72 mm
are the exterior and interior transducer sheathing diameters respectively. Us-
ing these dimensions,
V
t
≈
0
.
08 mm
3
. The sheathing “voxel” number
N
o
can be
calculated as
N
o
=
V
t
/
V
o
, where
V
t
≈
0
.
08 mm
3
is the sheathing volume by the
beam and
V
o
=
4
π
d
r
/
3 is formed by the minimal spherical scatterers with radius
