1. Spinning Nucleus Produces Magnetic Moment
A moving electric charge produces a magnetic field.
An atomic nucleus can be thought of as a spinning charged body,
which acts like a tiny magnet. p 
nuclear magnetic moment =p
p = angular momentum
I = nuclear spin (quantum number)
= gyromagnetic ratio
 is collinear with p
Magnetism is a property of matter that is a result of the orbiting of the electrons in atoms. The orbiting electrons cause the atoms to have a magnetic moment associated with an intrinsic angular momentum called "spin".
Normally, the direction that these tiny magnets point in is randomly distributed.

2. Macroscopic Alignment with B-fieldBo
A spinning nucleus placed within a large external magnetic field (B0) will align with the external field.
M = MBo 
In the magnetic field of an MRI scanner at room temperature, there is approximately the same number of proton nuclei aligned with the main magnetic field Bo as counter-aligned. The aligned position is slightly favored, as the nucleus is at a lower energy in this position. For every one-million nuclei, there is about one extra nucleus aligned with the Bo field as opposed to the field. This results in a net or macroscopic magnetization pointing in the direction of the main magnetic field.
I = 1/2 case
cM: magnetic susceptibility
For protons: cM~10-6

3. Precession at “Resonance” Frequency
The magnetic field exerts a torque on the spinning proton, causing it to precess, similar to a spinning top.
The magnetic moment precesses around the applied field at a rate proportional to the applied static field: the Larmor frequency.
Bo = 1 Tesla
H-1 : MHz (o/2)
Na-23 : MHz
P-31 : MHz
The Lamor frequency for conventional MRI
lies in the radio frequency range.

4. Excitation = Tip Magnetization into Transverse Plane
An additional magnetic field B1, perpendicular to the static field B0, can be added to tip the spins into the transverse plane.
B1 is most efficient when its frequency matches the Lamor frequency: resonance condition. Z Bo B1 a X Y
Rotation frequency
B1
Flip angle
 = g B1 t M

5. Relaxation  T1 and T2 Mz Mx,y Longitudinal Transverse
“Relaxation” = Return to equilibrium magnetization Bo B1 a
Mx,y Mz
Longitudinal Transverse

6. T1 Recovery and T2 Decay T1 Recovery Mxy T2 Decay Mz M0 exp(-t/T2)
time
time
T1 and T2 are independent processes, T2≤T1
Transverse magnetization, Mxy, is the detected signal
T2 = T1
T2 = 0.5T1
T2 = 0.25T1

7. B0 T1 T2

8. T2 is Dephasing of Transverse Signal
Spins precess in XY plane about B0.
Variation in B0 causes faster and slower
precession rates. z Bo
B0
B0
Mxy y x z
T1 recovery of Mz Bo MZ
MRI signal is “net” vector Mxy
Mxy y x

9. Terminology T1 is the time constant of Mz to return to equilibrium.
T2 and T2* are time constants of loss of Mxy
T2 signal loss is “entropic” -- it cannot be recovered.
T2* signal loss is reversable (sometimes) with a spin-echo.
TR, Repetition Time
Tissue with shorter T1 recovers Mz faster.
TE, Echo Time (signal acquisition time)
Tissue with shorter T2 (or T2*) loses Mxy faster.

10. The Spin Echo
90o pulse
spins dephase
180o pulse
spins re-align
spin echo
Spin echo refocuses dephasing from static field inhomogeneity, i.e T2*.
T2 dephasing is not refocused.
Gradient echo creates an artificial, gradient-induced echo.
No refocusing of T2 or T2*.

11. Contrast Contrast: Difference in signal intensity
Spatial contrast (e.g. tissue types)
Temporal contrast (changing properties, T1 or T2)
BOLD is a T2* (or T2) contrast
T1 Contrast
T2 Contrast
T1 Contrast
T2 Contrast
TR (s)
TE (ms)

12. T1 Contrast Example White Matter Gray Matter CSF
100
200
300
CSF GM WM T1
Contrast Example
White Matter
Gray Matter
CSF 5 4 3 2 1
TR (s) WM GM
CSF