Biomedical Engineering Reference
In-Depth Information
using Eq. (1.11). Figure 1.21 shows the simulations of
N
scatterers located
in (
R
i
,
a
≤
j
≤
b
):
N
i
N
R
σ
(
R
i
,
o
±
j
)
ζ
(
t
,δ
i
)
|
R
i
|
S
(
t
,
o
)
=
(1.13)
i
=
1
j
=
1
N
θ
i
exp
−
(
t
−
δ
i
)
2
2
σ
sin(
ω
t
−
δ
i
)
N
R
σ
(
R
i
,
o
±
j
)
|
R
i
|
S
(
t
,
o
)
=
C
o
2
i
=
1
j
=
1
where
o
=
(
a
+
b
)
/
2,
C
o
defines the transducer constant parameters, and
N
i
is the total scatterers number at the angular position
θ
a
≤
≤
θ
b
for a radial
position
R
i
. The sum only operates on the scatterers located in the angular
position
θ
a
≤
≤
θ
b
that is the focal transducer zone (Figs. 1.9(b) and 1.13).
Therefore,
N
is the total scatterers number in this region. Equation (1.13) can be
written as a function of the penetration depth, replacing
t
=
x
/
c
. Equation (1.13)
can be rewritten on gray-level scale as:
N
θ
i
exp
−
(
t
−
δ
i
)
2
2
σ
sin(
ω
t
−
δ
i
)
N
R
256
max(
S
(
t
))
C
o
σ
(
R
i
,
o
±
j
)
|
R
i
|
S
(
t
,
o
)
=
2
i
=
1
j
=
1
(1.14)
where
δ
i
=
2
R
i
/
c
and
S
(
x
) is the 1D echogram generated by a set of
N
scatterers
located in (
R
i
,
a
≤
i
≤
b
). The overall distribution backscattering cross-
section
σ
i
(
R
i
,
i
±
δ
) is given by Eq. (1.11).
1.5.3 2D Echogram Generation
The procedure to obtain the 2D simulated IVUS is the following: A rotatory
transducer with angular velocity
ω
(Fig. 1.23(a)) is located at the center of
the simulated arterial configuration given by Eq. (1.11). The transducer emits
an ultrasound pulse radially focused at frequency
f
o
along angular direction
θ
1
(Fig. 1.23(a)). The pulse progressively penetrates each one of the layers of
the simulated arterial structure according to Eq. (1.15). Each one of the layers
generates a profile of amplitude or echoes in time, which can be transformed
into a profile of amplitude as a function of the penetration depth (Fig. 1.23(b)).
Therefore, the depth can be calculated using Eq. (1.1). As the penetration depth
is coincident with the axial beam direction, the radial coordinate
R
is thus
determined. This procedure is repeated
n
times for angles, (
θ
1
,...,θ
n
) and the
2D image is generated. The generated echo profiles are transformed to a polar
