Mri system block diagram

SHAPE Society

1. MRI System Block Diagram
RF
amp
spectrometer
r.f.coil
gradient coil
X
amp
Y
amp
Z
amp

2. Principle of Gradient Coil
¶Bz
¶x
¶Bz
¶z

3. Isotope Spin %age g
I abundanceMHz/T
1
H 1/2 99.985 42.575
2
H 1 0.015 6.53
13
C 1/2 1.108 10.71
14
N 1 99.63 3.078
15
N 1/2 0.37 4.32
17
O 5/2 0.037 5.77
19
F 1/2 100 40.08
23
Na 3/2 100 11.27
31
P 1/2 100 17.25
Common NMR Active Nuclei

4. Alignment of Spins in a
Magnetic Field
spin
magnetic moment
B
0
field
M
M=0

5. Energy in a Magnetic Field
(Zeeman Splitting, Spin ½)
E
+1/2
= -gB
0
/2 E
-1/2
= +gB
0
/2
P
+1/2
= 0. 5000049 P
-1/2
= 0.4999951
1.5T, T=310K, P(E)µexp(-E/kT)
m
I
= +½ m
I
= -½

6. Larmor Frequency
E
+1/2
= -gB
0
/2 E
-1/2
= +gB
0
/2
Allowed transitions DE = gB
0
= w
0
m
I
= -½
m
I
= +½
w
0
= gB
0

7. Quantum Mechanical Description
(Spin ½ Case)
½y> = a
-½
½-½> + a
+½
½+½>
I=½, 2I+1 Zeeman splittings
m
I
= -½
m
I
= +½
M
z
= <y½I
z
½y> =½ a
+½
½
2
-½ a
-½
½
2
M
xy
= <y½I
x
+ iI
y
½y>

8. Coupling with a B1 Field
B0
B1
Birdcage coil
A
time

9. Spin Excitation
M M
M
rotating frame
laboratory frame

10. Free Induction Decay
FT
FT
frequency
frequency
time
time
M

11. Free Induction Decay
M
M
M
90°
90°
90°
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set

12. Free Induction Decay
M
M
M
90°
90°
90°
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set

13. Product Operators
M
x
® M
x
M
y
® M
y
cosq + M
z
sinq
M
z
® M
z
cosq - M
y
sinq
q
x
q
x
q
x
M
x
® M
y
cosq - M
z
sinq
M
y
® M
y
M
z
® M
z
cosq + M
x
sinq
q
y
q
y
q
y
M
x
® M
x
coswt + M
y
sin wt
w t
M
y
® M
y
coswt - M
x
sin wt
w t
M
z
® M
z
w t
r.f.
free
precession
x
y
z

14. Bloch Equations
dM
z
(t) = - [M
z
(t) - M
0]
dt T1
dM
xy
(t) = - M
xy
(t)
dt T2
M
z
M
xy
M
z
M
z
M
xy
M
xy

15. T1 Relaxation
M
z
(t) = M
0
+ {M
z
(0) - M
0}exp(-t/T1)
M
z
M
z
t t
saturation–
recovery
inversion–recovery
dM
z
(t) = - [M
z
(t) - M
0]
dt T1
M
0
M
0
M
z
(0) = 0 M
z
(0) = -M
0

16. Spin Echo
M
M
M
180°
180°
180°90°
90°
90°
small positive shim mis-set
medium positive shim mis-set
large positive shim mis-set

17. Spin Echo
M
M
M
180°
180°
180°90°
90°
90°
small negative shim mis-set
medium negative shim mis-set
large negative shim mis-set

18. T2 Relaxation
M
xy
(t) = M
xy
(0) exp(-t/T2)
M
xy
t
dM
xy
(t) = - M
xy
(t)
dt T2

19. Slice Selection
w
0
w
0
time
time
frequency
frequency
FT
FT

20. Slice Selection
w
0
time frequency
G