Biomedical Engineering Reference
In-Depth Information
where
λ
=
c
/
f
and
D
is the transducer diameter. For a typical transducer of 30
MHz,
c
=
1540 m/sec and transducer dimensions given in Fig. 1.14, the lateral
resolution is
d
θ
≈
0
.
10
◦
and the focal length is
F
=
2 mm.
1.4.2 The Beam Intensity
The beam ultrasound intensity, as a function of the penetration depth and the
ultrasound frequency, is given by [13, 14, 16]:
I
(
r
)
=
I
o
exp(
−
α
(
N
θ
)
rf
)
(1.8)
where
I
o
is the beam intensity at
r
=
0 and the coefficient
α
gives the rate of
diminution of average power with respect to the distance along a transmission
path [17]. It is composed of two parts, one (absorption) proportional to the
frequency and the other (scattering) dependent on the particle size, or the scat-
terer number
N
θ
located along the ultrasound beam path (see Section 1.5.2).
Since the attenuation is frequency dependent, a single attenuation coefficient
only applies to a single frequency. The attenuation coefficient of ultrasound is
measured in units of dB/cm, which is the logarithm of relative energy loss per
centimeter traveled. In biological soft tissues, the ultrasound attenuation coef-
ficient is roughly proportional to the ultrasound frequency (for the frequency
range used in medical imaging). This means that the attenuation coefficient di-
vided by the frequency (unit dB/MHz cm) is nearly constant in a given tissue.
Typical soft tissue values are 0.5-1.0 dB/MHz cm. In our model we assumed that
the attenuation coefficient
α
is only dependent on the scatterer number in the
way beam. Figure 1.15 shows the beam intensity dependence on penetration
depth for several typical frequencies used by IVUS.
1.4.3 Ultrasound Beam Sweeping Criterion
Let us explore a criterion that assures that all the reflected echoes reach the
transducer before it moves to the following angular position. Let us define
β
as
the ratio between transducer diameter
D
and arc length
(Fig. 1.16):
D
β
=
where
D
is the transducer diameter and
is the arc segment swept by the beam
