Biomedical Engineering Reference
In-Depth Information
16.9 EXERCISES
1.
Find the Fourier transform of
Q
½ð
t
t
0
Þ
c
=
L
given the Fourier transform pair
`
Q
ðÞ
.
2.
Select the correct answer. Ultrasound imaging for medical applications began to grow
significantly when
(a)
Wild and Reid demonstrated real-time imaging
(b)
Edler and Hertz started the science of echocardiography
(c)
Stewart found a connection between cancer in children and prenatal x-ray exposure
(d)
Satomura and his colleagues detected blood flow using Doppler techniques
3.
Compute the pressure reflection factor between blood and muscle at normal incidence in dB
(use Table 16.1). Compare the reflection factor at 45
incidence to this result. Which is greater?
4.
Derive the normal reflection and transmission factors in terms of intensity rather than amplitude.
Determine the normal transmission intensity factor between blood and (a) the liver, (b) an ideal
rigid boundary, and (c) air. How do these compare to the corresponding amplitude results?
½
¼
sin
ðp
f
Þ= pðÞ¼
sinc
ðÞ
5.
If the Q of the electrical part of a transducer equivalent circuit is defined as
Q
¼
f
0
=D
f
¼
f
0
is 5 MHz, compare the
fractional -6 dB bandwidths (in %) for the following two transducer materials: A k
T
¼
1
=½o
0
C
0
R
A
ð
f
0
Þ
, where
D
f
is the -6 dB bandwidth and
0.7,
680. (Hint: See Eq. (16.27c).)
6.
Calculate the electrical impedances of the following two transducer designs at resonance
using the constants from Example Problem 16.3: one with a direct water load and one with a
matching layer between the crystal and the water load, both with Z
B
¼
e
R
¼
1470 and k
T
¼
0.9 and e
R
¼
Z
C
. (Hint: Use
Eq. (16.34).) What is the improvement in acoustic loss by including the matching layer?
7.
Ultrasound is not used to image bone directly. (a) To estimate the strength of the reflection,
determine the normal amplitude reflection factor from muscle to bone. (b) Determine a
matching layer impedance to match the muscle better to bone. (c) What are the amplitude
reflection and transmission factors with the matching layer at resonance?
8.
A company can only afford either a tuning inductor or a matching layer for their transducer
product. Which would you recommend and why? Material details: area: A
400 mm
2
;
¼
4.35 km/s; e
R
=e
0
¼
thickness: d
¼
0.87 mm; crystal data: c
¼
830; e
0
¼
8.85 pF; k
T
¼
0.49.
50 ohms.
9.
Compare the frame rates for the following two cases: a 3 MHz cardiac sector scanner with
128 lines per frame for a depth of 10 cm, and a small parts 10 MHz linear array with 300 lines
per frame and a 1 cm depth.
10.
If a 5 MHz transducer in an imaging system has an overall round-trip dynamic range of 100 dB,
what is the greatest distance it can detect a pressure reflection between a liver-bone boundary?
Between a liver-muscle boundary? Assume average tissue properties to the boundary are the
same as that of liver. (Use Table 16.1 for relevant tissue and absorption data.)
11.
A small lesion about 2 mm in diameter at a depth of 6 cmmust be found. Which of the following
rectangular array transducers with apertures and center frequencies would you use and why?
(a)
L
Electrical source impedance: R
g
¼
¼
15 mm and 6 MHz
(b)
L
¼
11 mm and 5 MHz
(c)
L
¼
12 mm and 3 MHz
Assume c
¼
1.5 mm/m
s
and a focal length of F
¼
60 mm in the scan plane.
