502 nmr relaxation times

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 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


• 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.


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

• 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?

× =

=

FT FTFT

Perfect FID T2* Decay Actual FID

Perfect Image Point Spread Function Actual Image


Images?


Images?• Effect of linewidth (point spread function)

Acquire

Acquire


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°

502 nmr relaxation times

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