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 γ
I abundance MHz/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
B0 field
M
M=0

5. Energy in a Magnetic Field
(Zeeman Splitting, Spin ½)
E+1/2= −γB0/2 E-1/2= +γB0/2
P+1/2= 0. 5000049 P-1/2= 0.4999951
1.5T, T=310K, P(E)∝exp(−E/kT)
mI = +½ mI = −½

6. Larmor Frequency
E+1/2= −γB0/2 E-1/2= +γB0/2
Allowed transitions ∆E = γB0
= ω0
mI = −½
mI = +½
ω0 = γB0

7. Quantum Mechanical Description
(Spin ½ Case)
ψ> = a−½−½> + a+½+½>
I=½, 2I+1 Zeeman splittings
mI = −½
mI = +½
Mz = <ψIzψ> = a+½2
− a−½2
Mxy = <ψIx+ iIyψ>

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
Mx → Mx
My → Mycosθ + Mzsinθ
Mz → Mzcosθ − Mysinθ
θx
θx
θx
Mx → Mycosθ − Mzsinθ
My → My
Mz → Mzcosθ + Mxsinθ
θy
θy
θy
Mx → Mxcosωt + Mysin ωt
ω t
My → Mycosωt − Mxsin ωt
ω t
Mz → Mz
ω t
r.f.
free
precession x
y
z

14. Bloch Equations
dMz(t) = − [Mz(t) − M0]
dt T1
dMxy(t) = − Mxy(t)
dt T2
Mz
Mxy
Mz Mz
Mxy
Mxy

15. T1 Relaxation
Mz(t) = M0 + {Mz(0) − M0}exp(-t/T1)
Mz Mz
t t
saturation–
recovery
inversion–recovery
dMz(t) = − [Mz(t) − M0]
dt T1
M0 M0
Mz(0) = 0 Mz(0) = −M0

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
Mxy(t) = Mxy(0) exp(−t/T2)
Mxy
t
dMxy(t) = − Mxy(t)
dt T2

19. Slice Selection
ω0
ω0
time
time
frequency
frequency
FT
FT

20. Slice Selection
ω0
time frequency
G