EE415 Solutions of Homework 2

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Nov 15, 2013 (3 years and 7 months ago)

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EE415 Solutions of Homework 2


1
.
132
.
0
27
.
5
693
.
0


k

.
00876
.
0
01
.
0
)
1
(
132
.
0
gr
e
N





2.

I) Attenuation correction is easily accomplished in PET. The attenuation experienced
by a given pair of annihilated photons is independent of the position of the annihlat
ion.

II) collimation is done electronically, no collimator is required.

III) uniformity of sensitivity

IV) positron emitting isotopes of carbon, nitrogen, oxygen, and flourine occur naturally
in many compounds of biological interest and can therefore be re
adily incorporated into a
wide variety of useful pharmaceuticals.

V) The above given isotopes have short physical half
-
lives.


3.

Cu
Bq
10
10
7
.
3
1
1




Cu
atoms
hr
atoms
hr
N
A
071
.
0
sec
/
10
64
.
2
sec/
3600
)
10
)(
10
49
.
9
(
9
15
1
3











4.

I) in TCT x
-
ray attenuation coefficient is determined, in ECT the distribu
tion of
activity A is determined in the precence of unknown attenuation coefficient.

II) ECT images physiological and metabolic processes with a spatial resolution
(ranging from about 5 mm for PET to 15
-
20 mm for SPECT) much poorer than
the anatomical reso
lution of TCT (about 1 mm).

III) In ECT the radiation dose is distributed throughout much of the body for the
effective life time, whereas in TCT the radiation dose is limited to the duration of
x
-
ray exposure and to the section of the body irradiated.


5.

dB
I
I
dB
13
20
1
log
10
log
10
0












6.


)
(
1
1
1
x
k
wt
j
i
e
A
p


,
)
(
1
1
1
x
k
wt
j
r
e
B
p



)
(
2
2
2
x
k
wt
j
t
e
A
p


,
)
(
2
2
2
x
k
wt
j
r
e
B
p


,
))
(
(
3
3
3
l
x
k
wt
j
t
e
A
p




at
x

= 0 from continuity of pressure

p
i1

p
r1

p
r2

p
t3

p
t
2

x=0

x=
l

Z
1

Z
3

Z
2

2
2
1
1
B
A
B
A




Continuity of particle velocity


)
(
)
(
2
2
1
1
1
2
B
A
Z
B
A
Z




3
2
2
2
2
A
e
B
e
A
l
jk
l
jk




cont. of particle velocity



3
3
2
2
3
2
2
A
Z
e
B
e
A
Z
l
jk
l
jk





2
2
1
2
2
1
2
1
2
)
(
)
(
Z
B
Z
Z
A
Z
Z
A





l
jk
e
A
Z
Z
Z
A
2
3
3
2
3
2
2



l
jk
e
A
Z
Z
Z
B
2
3
3
2
3
2
2






2
3
2
3
1
2
2
3
1
2
3
1
4
)
)(
(
)
)(
(
2
2
Z
Z
e
Z
Z
Z
Z
e
Z
Z
Z
Z
A
A
l
jk
l
jk











2
3
2
3
1
2
2
2
2
1
3
2
3
1
2
sin
)
(
cos
)
(
Z
Z
l
k
j
Z
Z
Z
l
k
Z
Z
Z
Z
A
A





2
1
3
3
1









A
A
Z
Z


l
k
Z
Z
Z
Z
l
k
Z
Z
Z
Z
2
2
2
2
3
1
2
2
2
2
3
1
3
1
sin
cos
)
(
4















7.

38
.
1

fat
Z
,
62
.
1

kidney
Z

0064
.
0
2
2
1
2
1












Z
Z
Z
Z
R

,


9936
.
0
4
2
2
1
2
1



Z
Z
Z
Z
T



8.

mm
m
4
.
2
sec
/
10
5
.
2
sec
/
6000
6





thickness =

/2 = 1.2 mm


9.

Hz
MHz
m
cm
f
V
c
V
V
f
V
c
V
c
f
S
S
R
S
S
S
R
D
325
10
sec
/
1540
sec
/
5
1






















The frequency is shifted to a higher value.