This document provides an overview of MRI system components and basic MRI physics concepts. It includes: 1) A diagram of the main components of an MRI system, including RF coils, gradient coils, and amplifiers. 2) Tables listing common NMR-active nuclei and their properties important for MRI. 3) Explanations of spin alignment in magnetic fields, Larmor frequency, spin excitation, free induction decay, Bloch equations, T1 and T2 relaxation, and slice selection techniques.

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