1
ECE 380 Biomedical Imaging Spring 2010
Homework 6 Solutions
_____________________________________________________
Problem 1
: (20 points)
a)
What is the precession frequency of protons in a main magnetic field Bo=3 T?
(10 points)
Using equation (4.6) from your book i.e.
00
wB
and the value of
/ 2
42.57
/
MHz T
from Table 4.1, the precession frequency is
0
0
0
6
0
2
(42.57 10 ) (3)
2
127.71
w
B
fB
B
f
f
MHz
b)
A 2 mm slice perpendicular to the zaxis at position z = 0.1 m is excited with a
radiofrequency pulse at frequency f. Assume Bo=1.5 T Gz=10 mT/m. What is the
frequency f (in Hz) of the RF pulse to excite this slice? And what is the
bandwidth? (10 points)
Using equation (4.33) from the book,
0
0
63
0
( )
(
)
2
(
)
()
(42.57 10 ) (1.5 (10 10 )(0.1))
2
63.89
z
z
z
w z
G z
B
f
B
G z
B
G z
f
f
MHz
Bandwidth
Using equation (4.35) from the book
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
3
3
6
2
2
(2 10 )(10 10 )(42.57 10 )
851.4
zz
z
f
z
GG
zG
f
f
f
Hz
Problem 2
:
NMR (30 points)
a)
Suppose a sample has a T
1
value of 0.6 seconds. The net magnetization from the
sample is set equal to zero. This sample is then allowed to recover towards its
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Prof.A
 Frequency, Magnetic Field, Nuclear magnetic resonance

Click to edit the document details