1. Steady-state magnetization
Repeated measurements: combined T1 and T2* weighting
Ernst angle
Steady-state magnetization

2. Steady-state magnetization
T1 and T2 re-cap
Equilibrium
Excitation
Relaxation M0
M(0) = M0sin() 
Steady-state magnetization

3. Steady-state magnetization
T2 vs.T2* recap T2
intrinsic (unrecoverable) spin-spin relaxation
describes transverse magnetization decay in spin echo pulse sequences
T2*
dephasing of spin isochromats due to microscopic field inhomogeneities
Free induction decay (FID)
describes transverse magnetization decay in gradient echo pulse sequences
Steady-state magnetization

4. Steady-state magnetization
T2 vs.T2* recap
Excitation pulse
Refocusing pulse
Echo
Read-out MT T2
T2* S
Steady-state magnetization

5. But who has time to wait for equilibrium?
Magnetization preparation
Excitation
Read-out
Nrep = 128
TR = 6s
Tacq = 13 min. RF
GSS
GPE
GRO
DAC
Steady-state magnetization

6. Experiments with TR < T1
Steady-state magnetization

7. Ernst angle: maximizing steady-state signal
Excerpt from BPhy 8147 notes …
Setting derivative with respect to alpha equal to zero finds the expression for the Ernst angle.
Steady-state magnetization

8. Ernst angle calculation
Typical EPI parameters
Gray matter T1: ms
Volume TR: ms
Flip angle (Matlab code): alpha_ernst = acos(exp(-TR/T1))*180/pi = acos(exp(-1.36))*180/pi = 75º
Steady-state magnetization

9. Gray/white contrast at steady-state
1st image
Steady-state
Steady-state magnetization