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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
• Normally, the direction that these tiny
magnets point in is randomly distributed.
CMROI
Slide 1
Macroscopic Alignment with B-field
• A spinning
nucleus placed within a large external
magnetic field (B0) will align with the external
field.
Bo
M =  M Bo

I = 1/2 case
M: magnetic susceptibility
For protons: M~10-6
CMROI
Slide 2
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.
0  B0
Bo = 1 Tesla
H-1 : 42.58 MHz (o/2)
Na-23 : 11.26 MHz
P-31 : 17.24 MHz
• The Lamor frequency for conventional MRI
lies in the radio frequency range.
CMROI
Slide 3
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.
Z
Bo
X
Y
• B1 is most efficient when its
frequency matches the Lamor
frequency: resonance condition.
Rotation frequency
  B1
Flip angle

M
B1
   B t
CMROI
Slide 4
Relaxation  T1 and T2
“Relaxation” = Return to equilibrium magnetization
Bo
Mz
B1 dM
dt
Longitudinal
CMROI

z

M z  M0
T1
Mx,y
Transverse
Slide 5
T1 Recovery and T2 Decay
Mxy
T2 Decay
Mz
M0 exp(-t/T2)
time
T1 Recovery
M0 [1-exp(-t/T1)]
time
T2 = T1
• T1 and T2 are independent processes, T2≤T1
T2 = 0.5T1
• Transverse magnetization, Mxy, is the detected signal
T2 = 0.25T1
CMROI
Slide 6
B0
T1
T2
CMROI
Slide 7
T2 is Dephasing of Transverse Signal
Spins precess in XY plane about B0.
Variation in B0 causes faster and slower
precession rates.
z
Bo
Mxy
y
  B0
x
z
Bo
  B0
T1 recovery of Mz
MZ
MRI signal is “net” vector Mxy
Mxy
y
CMROI
x
Slide 8
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.
CMROI
Slide 9
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*.
CMROI
Slide 10
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)
CMROI
TE (ms)
Slide 11
300
CSF
GM
200
T1
Contrast Example
White Matter
Gray Matter
CSF
WM
100
0
0
1
2
3
4
5
TR (s)
WM
GM
CSF
CMROI
Slide 12