2. Review
• NMR signal depends on the quantum
mechanical properties of nuclei.
• Larmor equation relates field to frequency.
0Bγω =
• Spins excited by a B1 field, perpendicular to
the B0, oscillating at this frequency.
3. • Time to reach equilibrium is governed by
thermal processes.
• The return to equilibrium is generally
exponential and governed by the equation
• T1 is called the spin-lattice relaxation time.
The Simplified Bloch Equation
1
0
T
MM
dt
dM zz −
=
4. • The relative populations of the spin states
can be altered in a well defined way by the
application of a resonant B1 field in the xy-
plane.
• Any fluctuating magnetic field that has a
component in the xy-plane that oscillates at
the resonant frequency can induce
transitions between the spin states.
The T1 Relaxation Process
6. Lattice Thermal Processes
• The frequency distribution of the motion of
a randomly tumbling molecule is expressed
in terms of the spectral density
• τc is called the correlation time and is a
characteristic time scale of molecular
motion.
( ) 22
1 c
c
J
τω
τ
ω
+
=
7. T1 Relaxation Time
• It can be shown that
where ω0 is the resonant frequency of the spin
system.
22
0
2
1 1
1
c
c
xyB
T τω
τ
+
∝
10. What effect does T1 have on
Images?
t = 0 t = 3s t = 6s t = 9s t = 12s
11. • Assume the steady state has been reached.
• Use a flip angle of θ degrees.
• Find a condition where the transverse
magnetization following the flip is
maximized.
The Ernst Angle
−=
1
expcos
T
TR
θ
16. T1 Mapping
• Inversion recovery method.
• Invert the magnetization with a 180° pulse.
• Wait a period TI and inspect the recovery of
the longitudinal magnetization.
−−=
1
0 exp21
T
TI
SS
17. Transverse Relaxation
• Longitudinal relaxation is driven by field
oscillations in the transverse plane.
• Transverse relaxation is driven by field
oscillations in the longitudinal plane.
• Random fluctuations in B0 experienced by a
nucleus cause the resonant frequency of that
spin to change.
18. Transverse Relaxation
• The return to equilibrium is governed by the
Bloch equation.
• T2 is called the spin-spin relaxation time
2T
M
dt
dM xyxy
−=
20. Transverse Relaxation
• If the field experienced by the molecule is
purely random then the effect would time
average to zero.
• Correlations in the motion cause a range of
frequencies.
• In solids where there is no molecular
tumbling the range of resonances is very
broad.
24. What is T2
*
?
• Spin-spin relaxation represents a loss of
coherence in the transverse magnetization
due to local effects on spin.
• Loss of the coherence of the transverse
magnetization also occurs as a result of bulk
magnetic effects
32. The Spin Echo
• A spin echo can refocus spins that are
sitting in a time invariant B0 field.
• A spin echo cannot refocus T2 dephasing.
• A spin echo cannot refocus spins that have
experienced a time varying field, for
example diffusing molecules.
33. What effect does T2
*
have on
Images?
• T2 and T2
*
have the same effect on images.
• T2
*
effects dominate when there is no spin
echo.
• From now on, we will assume that T2* is
more important, since in imaging it often is.
41. What effect does T2
*
have on
Images?
• Effect of linewidth (point spread function)
Acquire
Acquire
42. What effect does T2
*
have on
Images?
• 2DFT imaging
– Each line of k-space acquired with a new fid.
– No T2 effect in the phase encode direction. (taq= 0)
– Small T2 effect in the read direction. (taq≈ 5ms)
• EPI
– Whole of k-space acquired in one fid.
– Small T2 effect in the read direction. (taq≈ 0.5ms)
– Large T2 effect in the phase encode direction.
(taq≈ 40ms)
43. T2 Mapping
• Acquire a number of images with a different
value of echo time.
• Fit an exponential decay curve to the pixel
values for each TE.
• Multiple spin echo technique.
TE/2
TE
2 TE
3 TE
90° 180° 180° 180°
