nmr relaxation times
TRANSCRIPT
NMR Relaxation Times
Stuart Clare
Review
• NMR signal depends on the quantum mechanical properties of nuclei.
• Larmor equation relates field to frequency.
0B • Spins excited by a B1 field, perpendicular to
the B0, oscillating at this frequency.
• 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
TMM
dtdM zz
• 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
Lattice Thermal Processes
B0A
X
r
323 cossin
rBxy
Lattice Thermal Processes
• The frequency distribution of the motion of a randomly tumbling molecule is expressed in terms of the spectral density
• c is called the correlation time and is a characteristic time scale of molecular motion.
221 c
cJ
T1 Relaxation Time
• It can be shown that
where 0 is the resonant frequency of the spin system.
220
2
1 11
c
cxyBT
Recovery Curve
time
Signal
10 exp1
TtSS
What effect does T1 have on Images?
90° 90° 90° 90° 90°
Mz
What effect does T1 have on Images?
t = 0 t = 3s t = 6s t = 9s t = 12s
• Assume the steady state has been reached.• Use a flip angle of degrees.• Find a condition where the transverse
magnetization following the flip is maximized.
The Ernst Angle
1
expcosTTR
T1-Weighted Images
T1-Weighted Images
T1-Weighted Images
T1-Weighted Images
T1 Mapping
• Inversion recovery method.• Invert the magnetization with a 180° pulse.• Wait a period TI and inspect the recovery of
the longitudinal magnetization.
10 exp21
TTISS
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.
Transverse Relaxation• The return to equilibrium is governed by the Bloch equation.
• T2 is called the spin-spin relaxation time
2TM
dtdM xyxy
Transverse relaxation
Rotating frame
B0
t
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.
Transverse Relaxation
Long T2
Short T2
frequency
Relating T2 to Spectral Density
01 2
2
JBT z
02
1
1 JBT xy
Transverse relaxation
Longitudinal relaxation
cJ 0
220
0 12
c
cJ
Decay Curve
time
Signal
20 exp
TtSS
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
What is T2*?
The Spin Echo
The Spin Echo
The Spin Echo
The Spin Echo
The Spin Echo
The Spin Echo
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.
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.
What effect does T2* have on
Images?• Effect of echo time
What effect does T2* have on
Images?• Effect of echo time
What effect does T2* have on
Images?• Effect of echo time
What effect does T2* have on
Images?• Effect of echo time
What effect does T2 * have on
Images?
× =
=
FT FTFT
Perfect FID T2* Decay Actual FID
Perfect Image Point Spread Function Actual Image
What effect does T2 * have on
Images?
× =
=
FT FTFT
Perfect FID T2* Decay Actual FID
Perfect Image Point Spread Function Actual Image
What effect does T2 * have on
Images?
What effect does T2 * have on
Images?• Effect of linewidth (point spread function)
Acquire
Acquire
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)
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
TE2 TE
3 TE
90° 180° 180° 180°