Spins and Relaxation

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Spins and Relaxation
Daniel Bulte
FMRIB Graduate Program Lecture MR Physics
2
Objectives

• How does MRI work?
• What is resonance?
• Where does the signal come from?
• What are T1 and T2?
• Where does contrast come from?
• Please ask questions!

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Spin

• Fundamental property of particles, like mass and
  charge
• Spin comes in quanta of 1/2 (for Fermions)
• Electrons, protons and neutrons all have spin
  1/2
• Pairs of these subatomic particles tend to align
  with opposite spin and cancel out

4
Nuclear Spin
Some nuclei have Spin
If a nucleus has an unpaired proton it will have
spin and it will have a net magnetic moment or
field ? NMR phenomenon
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Common NMR Active Nuclei
Isotope Spin ? I abundance MHz/T
1H 1/2 99.985 42.575 2H 1 0.015 6.53 13C
1/2 1.108 10.71 14N 1 99.63 3.078 15N
1/2 0.37 4.32 17O 5/2 0.037 5.77 19F
1/2 100 40.08 23Na 3/2 100 11.27 31P
1/2 100 17.25
? gyromagnetic ratio
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Alignment of Spins in a Magnetic Field
M
M0
B0 field
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Energy in a Magnetic Field(Zeeman Splitting,
Spin ½)
E1/2 ???B0/2
E-1/2 ??B0/2
mI ½
mI ?½
P1/2 0. 5000049
P-1/2 0.4999951
P(E) ? exp(?E/kT)
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Larmor Frequency
mI ?½
mI ½
E1/2 ???B0/2
E-1/2 ??B0/2
Allowed transitions ?E ??B0
??0
?0 ?B0
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Larmor Frequency
Spins precess at Larmor frequency. Net
magnetisation M0 is static.
B0
?0 ?B0
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Precession
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Important Point 1

• When a particle with net spin is placed in a
  magnetic field it precesses at a rate determined
  by the field strength and the type of particle

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Resonance

• If a system that has an intrinsic frequency (such
  as a bell or a swing) can draw energy from
  another system which is oscillating at the same
  frequency the 2 systems are said to resonate

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The B1 Field

• A radio frequency (RF) field from an antenna is
  simply an alternating electromagnetic field
• We can thereby create a magnetic field which
  oscillates at a specific frequency

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A Night at the Disco

• Imagine if you will
• a new dance craze to rival the macarena.
• Everybody do the NMR!

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The B1 Field

• This secondary rotating field has the same effect
  on the spins as the B0 field it causes them to
  precess
• The precession is about the direction of the
  field, which is itself rotating

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Laboratory Frame
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Rotating Frame
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Spin Excitation
M
M
M
x
rotating frame
B0
laboratory frame
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Review

• NMR signal depends on the quantum mechanical
  properties of nuclei.
• Larmor equation relates field to frequency.
• ?0 ?B0

• Spins excited by a B1 field, perpendicular to the
  B0, rotate around the B1 direction

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Where does the signal come from?

• The net magnetic vector is the sum of all the
  spins from all of the protons
• Its magnitude in a given direction can be altered
  through clever application of the B1 field

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NMR Excitation
Resting state
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NMR Excitation
Excitation
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NMR Excitation
Saturation
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NMR Relaxation
T1 recovery
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Lattice Thermal Processes

• Frequency distribution of molecular motion can be
  expressed by the spectral density function
• J(?)
• Where ?c is the correlation time or
  characteristic time scale of the motion

?c
1 ?2 ?c2
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Lattice Thermal Processes

• The relaxation rate (1/T1) is given by
• R1
• Where ?0 is the resonant frequency of the spin
  system

? B2xy
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The Simplified Bloch Equation

• 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.

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Mz Recovery Following a 90º Pulse
Mz
M0
z
y
x
t
90o pulse
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What effect does T1 have on Images?
a
a
a
a
a
EPI
EPI
EPI
EPI
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What effect does T1 have on Images?
a
a
a
a
a
Mz
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What effect does T1 have on Images?
a
a
a
a
a
Mz
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What effect does T1 have on Images?
a
a
a
a
a
Mz
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What effect does T1 have on Images?
a
a
a
a
a
Mz
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What effect does T1 have on Images?
a
a
a
a
a
Mz
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What effect does T1 have on Images?
t 0 t 3s t
6s t 9s t 12s
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Effect of Flip Angle
High flip angle
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Effect of Flip Angle
Low flip angle
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The Ernst Angle

• Assume the steady state has been reached.
• Use a flip angle of q degrees.
• Find a condition where the transverse
  magnetization following the flip is maximized.

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T1 Recovery Curves
Short T1 (white matter)
Mz
Medium T1 (grey matter)
Long T1 (CSF)
Contrast
TR
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T1-Weighted Imageswith Inversion Recovery
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T1-Weighted Images with Inversion Recovery
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T1-Weighted Images with Inversion Recovery
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T1 Weighted Image
T1/s
R1/s-1
white matter
0.7
1.43
grey matter
1
1
CSF
4
0.25
1.5T
SPGR, TR14ms, TE5ms, flip20º
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NMR Relaxation
T2 relaxation
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T2 Decay Curve
FID dies away with increasing time
FIDAmplitude
æ
ö
t

-
ç

M
M
exp
0
è
ø
T
2
t
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Free Induction Decay
M
FT
time
frequency
FT
Note Signal only detected from Mxy component
time
frequency
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Transverse Relaxation

• Interactions between neighbouring spins causes
  loss of coherence in transverse magnetisation

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Transverse Relaxation

• Longitudinal relaxation is driven by field
  oscillations in the transverse plane.
• Transverse relaxation is driven by field
  oscillations in the longitudinal direction.
• Random fluctuations in B0 experienced by a
  nucleus cause the resonant frequency of that spin
  to change ? loss of coherence

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Transverse Relaxation

• The return to equilibrium is governed by the
  Bloch equation.
• T2 is called the spin-spin relaxation time

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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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Transverse relaxation
B0
t
Rotating frame
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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.

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Transverse Relaxation
Long T2
frequency
Short T2
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T2 Decay Curves
EchoAmplitude
Long T2 (CSF)
Medium T2 (grey matter)
Contrast
Short T2(white matter)
TE
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T2 Weighted Image
T2/ms
CSF
500
80?90
grey matter
70?80
white matter
1.5T
SE, TR4000ms, TE100ms
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Relaxation in a Nutshell
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What is T2

• Loss of coherence in transverse magnetisation
  also occurs as a result of bulk magnetic effects
• Spatial static B0 field variations within a voxel
  lead to identical effects on the signal as
  spin-spin interactions

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T2 vs. T2

• The T2 relaxation time depends primarily on
  spin-spin interactions - non-reversible
• T2 depends on both spin-spin interactions AND
  the homogeneity of the external magnetic field -
  reversible
• Homogeneity depends on how good your magnet is,
  and susceptibility-induced field distortions due
  to the presence of different tissues
• T2 can be considered as the observed or
  effective transverse relaxation time

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Optimal TR and TE for T1 Contrast
TR
TE
MR Signal
MR Signal
T1 contrast
T2 contrast
sec
ms
T1 Recovery
T2 Decay
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Optimal TR and TE for T2 and T2 Contrast
TR
TE
T2 Contrast
MR Signal
MR Signal
T1 Contrast
ms
sec
T2 Decay
T1 Recovery
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Important Point 2

• TR controls T1 weighting
• TE controls T2 weighting
• Short T2 tissues are dark on T2 images
• Short T1 tissues are bright on T1 images

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Reversing T2 Losses

• 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.

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The Spin Echo
t 0
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The Spin Echo
t gt 0
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The Spin Echo
t t
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The Spin Echo
t gt t
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The Spin Echo
t 2t
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Tutorial

• http//www.revisemri.com/questions/
• basicphysics/