Biomedical Engineering Reference
In-Depth Information
12.
For a spherically focusing transducer with an aperture a
5 mm and a frequency of 5 MHz,
show which of the following combinations places the effective focal length for a target at a
depth of 40 mm.
(a)
F
¼
¼
50 mm
(b)
F
¼
40 mm
80 mm
13.
For the Doppler detection of blood, a certain 2 MHz ultrasound system cannot sense signals
below a threshold of -35 dB. Assume a layer of muscle with negligible absorption loss above
a blood vessel where blood is flowing at a velocity of 1 m/s. Find the range of incident angles
(to the nearest degree) that will provide adequate signal strength and the corresponding
Doppler frequencies. Use Table 16.1 and note the Doppler angle
(c)
F
¼
90
—incident angle.
14.
For the arrangement of the whirling magnet in Figure 16.29, as d is increased, does the
intercepted voltage increase or decrease? What is a physical explanation for this effect?
(Note: Volt
¼
Weber/s.)
15.
Determine the nuclear magnetic dipole moments, m
z
, for
1
H,
19
F, and
23
Na. Use Table 16.2.
16.
Calculate the net magnetization moment M
0
for water at a temperature of T
¼
300
K and a
¼
10
19
protons/mm
3
. Use a form
magnetic field of B
0
¼
0.5 T and a proton density of N
¼
6.7
X
M
0
¼
^
of Eq. (16.54),
m
n
¼ m
n
þ
n
ð
Þ
and assume n
þ
¼
N/2.
n
If
B
y
ð
t
Þ¼
yB
1
sin o
, what will the field be in the rotated frame? After low-pass filtering to
eliminate 2o frequencies, what components are left?
ðÞ
17.
10
-5
T, what is
t
p
for
1
H? (b) Find the total flip time
18.
(a) For a flip angle of p
=
2 radians and B
1
¼
2 angle followed by a p angle rotation.
19.
Determine the relative decay for two individual rotations of p
for a p
=
=
2 and p in white matter and a
malignant tumor at the time
t
¼
250 ms. Which angle provides more contrast between the two
tissue types? Repeat at
t
¼
500 ms, and compare the contrast to the previous case.
20.
(a) Derive an expression for the spectrum of an F. I. D. pulse,
v
'(
t
)
¼
v
(
t
)H(
t
), where H(
t
)is
the step function, H(
t
)
¼
1 for
t
>
0, and H(
t
)
¼
0 for
t
<
0. Utilize the Fourier transform pair,
¼
1
i
2p
f
=
a
`
e
a
j
t
j
H
ð
t
Þ
h
i
. (b) What is the complex ratio of the F.I.D. spectrum to that of
2
j
a
j
1
þð
2p
f
=
a
Þ
the spin echo? (c) Find the value of this ratio at the Larmor frequency. (d) Can you find an
explanation for this ratio based on the time waveforms involved?
2
21.
(a) If
5 ms for the F. I. D. pulse of problem 20, find the spectral component at
the Larmor frequency of 5 MHz for the conditions
T
2
¼
T
¼
1cm
3
, and
B
1
¼
20 m
T
,I
¼
1A,V
oxel
¼
10
12
J/(T-mm
3
). (b) How does this value compare for a similar spectral magnitude
of a spin echo with T
2
for fat at the same Larmor frequency?
22.
Find the -6 dB width of the envelope of a time pulse and the two end frequencies needed
to scan a 1-mm-thick slice from -15 cm to
0
xy
¼
M
5
þ
15 cm around an isocenter on the
-axis. Assume
z
G
z
¼
0.5
/
.
T
m
23.
(a) In order to cover a range of
10 cm about an isocenter along the
y
-axis, phase encoding is
for
1
H and an overall phase shift of p
applied with a pulse length
t
p
¼
10 m
s
=
2. Find the
slopes, G
ym
, at the end points and the slope resolution for 256 steps.
Continued
