Biomedical Engineering Reference
In-Depth Information
distributions [23] centered in the average radius
R
k
and having standard
deviation
η
k
corresponding to each arterial structures. Tissue scatterers
are represented by:
exp
k
o
a
k
η
k
(
R
−
R
k
)
2
2
η
A
(
R
)
=
(1.12)
−
2
k
k
=
1
where
a
k
is the maximal number of scatterers at
R
=
R
k
,
k
is the
k
th radial
simulated tissue layer, and
R
k
is the radial layer average position.
2.
Nontissue scatterers
. These contributions can be made by structures
formed by spatial calcium accumulation, which are characterized as hav-
ing greater DBC density than the rest of the arterial structures. They are
simulated by a Gaussian distribution in the radial, angular, and longitudinal
arterial positions of the simulated structure:
l
o
m
o
n
o
b
l
c
m
d
n
β
l
γ
m
ν
n
F
(
R
,,
Z
)
B
(
R
,,
Z
)
=
l
=
1
m
=
1
n
=
1
F
(
R
,,
Z
)
=
exp
(
R
−
R
l
)
2
β
(
−
m
)
2
γ
(
Z
−
Z
n
)
2
ν
1
2
−
+
+
2
l
m
n
where (
l
,
m
,
n
) correspond to the radial, angular, and longitudinal axes
directions, (
l
o
,
m
o
,
n
o
) are the structures number in radial, angular, and
longitudinal directions, (
b
l
,
c
m
,
d
n
) are the scatterer numbers that have a
maximum at
R
=
R
l
,
=
m
, and
Z
=
Z
n
,(
β
l
,γ
m
,ν
n
) are the radial, angu-
lar, and longitudinal standard deviations, and (
R
l
,
m
,
Z
n
) are the radial,
angular, and longitudinal average positions.
3.
Artifacts scatterers
. In our model we consider the artifact caused by the
sheathing transducer:
exp
a
o
α
o
(
R
−
R
o
)
2
2
α
C
(
R
)
=
−
o
where
a
o
is the scatterers number that has a maximum at
R
=
R
o
,
α
o
is the
artifact standard deviation, and
R
o
is the artifact radial average position.
1.5.2 1D Echogram Generation
To obtain a 1D echogram, an ultrasound pulse is generated in accordance
with Eq. (1.4) and emitted from the transducer position. The pulse moves
