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Introduction to Nuclear
Magnetic Resonance
• Topics
– Nuclear spin and magnetism
– Resonance behavior and the Larmor
Frequ...
Nuclear Magnetism
• Nucleons (protons, neutrons) have a quantum
property known as spin.
• Nucleons have been shown to obey...
single
voxel
single
voxel
net magnetizationnet magnetization
Individual nuclear spinsIndividual nuclear spins
Nuclear Magnetic Resonance:
Properties in Matter
• Relaxation
– After we have delivered energy to the nuclei
in our sample...
• Spontaneous emission:
– negligible effect at RF frequencies (dominant
at visible frequencies)
• Induced emission
– Energ...
• NMR Spectroscopy is the study of the
chemistry of matter using the NMR
absorption spectrum
• Relaxometry is the study of...
x
y
x
y
x
y
x
y
Spin Dephasing after excitation
Bo
Alignment of Spins in a
Magnetic Field
spin
magnetic moment
B0 field
M
M=0
Energy in a Magnetic Field
(Zeeman Splitting, Spin ½)
E+1/2= −γB0/2 E-1/2= +γB0/2
P+1/2= 0. 5000049 P-1/2= 0.4999951
1.5...
Larmor Frequency
E+1/2= −γB0/2 E-1/2= +γB0/2
Allowed transitions ∆E = γB0
= ω0
mI = −½
mI = +½
ω0 = γB0
T1 Relaxation
Mz(t) = M0 + {Mz(0) − M0}exp(-t/T1)
Mz Mz
t t
saturation–recovery inversion–recovery
dMz(t) = − [Mz(t) − M0]...
T2 Relaxation
Mxy(t) = Mxy(0) exp(−t/T2)
Mxy
t
dMxy(t) = − Mxy(t)
dt T2
• The relative populations of the spin states
can be altered in a well defined way by the
application of a resonant B1 fie...
Recovery Curve
time
Signal












−−=
1
0 exp1
T
t
SS
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 θdegrees.
• Find a condition where the transverse
magnet...
T1-Weighted Images
T1-Weighted Images
T1-Weighted Images
T1-Weighted Images
Transverse Relaxation
• Longitudinal relaxation is driven by field
oscillations in the transverse plane.
• Transverse rela...
Transverse Relaxation
• If the field experienced by the molecule is
purely random then the effect would time
average to ze...
Transverse Relaxation
Long T2
Short T2
frequency
Decay Curve
time
Signal






−=
2
0 exp
T
t
SS
PD
T1
T2
What is T2
*?
• Spin-spin relaxation represents a loss of
coherence in the transverse magnetization
due to local effects o...
What is T2
*?
What effect does T2
* have on
Images?
• T2 and T2
* have the same effect on images.
• T2
* effects dominate when there 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 Fu...
What effect does T2
* have on
Images?
× =
⊗ =
⇓ ⇓ ⇓FT FTFT
Perfect FID T2
*
Decay Actual FID
Perfect Image Point Spread Fu...
Contrast in MRI
• Contrast based on Relaxation Time
• Contrast Agents
• BOLD Contrast
• Perfusion and Diffusion Contrast
To start with….
• No Spins, no contrast.
• Spin density is the most fundamental of
contrasts in MRI.
• In our case spin de...
Water Content of Tissue
Tissue % Water Content
Grey Matter 70.6
White Matter 84.3
Heart 80.0
Blood 93.0
Bone 12.2
Enhancing the Signal
from Spin Density
• Gastrointestinal imaging
– Drinking water
• Lung imaging
– Inhaling hyperpolarize...
T1 Contrast
• The shorter the repetition time (TR) the
greater the T1 contrast.
• Prepare the magnetisation with a saturat...
T2 or T2
* Contrast
• Sequences without a spin echo will be T2
*-
weighted rather than T2-weighted.
• The longer the echo ...
Magnetism
• units of magnetism
– 1T = 10,000 Gauss
– Earth’s field = 0.5 Gauss
• types of magnetism
– ferromagnetism
– par...
Magnetic Susceptibility
• the degree to which a material
becomes magnetized when placed
in a magnetic field
• magnetizabil...
Ferromagnetism
• Property of certain metals
– iron
– nickel
– cobalt
• Positive susceptibility
• consist of magnet domains...
Paramagnetism
• Oxygen
• metal ions with unpaired electrons
resulting in positive susceptibility
– Fe
– Gd
– Mg
• less tha...
Superparamagnetism
• halfway between ferro and
paramagnetic
• property of individual domains of
elements that have ferroma...
Diamagnetism
• no intrinsic atomic magnetic moment
• In a magnetic field weakly repel the field
– negative magnetic suscep...
Contrast Agents
• Sometimes it is desirable to enhance the
natural contrast in the images.
– Highlighting a tumour.
– Meas...
Contrast Agents
• Contain an ion with a large number of
unpaired electrons.
• This gives it a larger magnetic moment than
...
Contrast Agents
• These are usually paramagnetic ions.
e.g. Gadolinium
• By themselves these ions are highly toxic so
they...
Gadolinium
• shortens T1 relaxation of water
– high SI on T1 weighted images in lower
concentrations
• shortens T2 relaxat...
Gd-DTPA
COO-
CH2
N - CH2 - CH2 - N - CH2 - CH2 - N
Gd3
+
CH2 - COO-
CH2 - COOH
COO- - CH2
COOH - CH2
Haemoglobin
Haemoglobin
Oxy-haemoglobin
Deoxy-haemoglobin
Paramagnetic
Diamagnetic
Perfusion Imaging
• Contrast agent methods
• Spin tagged methods
– Continuously labelled
– IVIM
– Pulse labelled
Perfusion Imaging
• Perfusion is the rate constant determining
the delivery of metabolic substrates to the
local tissue an...
Contrast Agent Methods
• Inject contrast agent.
• Causes a bolus of blood to have a different
signal intensity to the bloo...
Contrast Agent Methods
Artery
Capillary Bed
Vein
Contrast Agent Methods
Artery
Capillary Bed
Vein
Contrast Agent Methods
Artery
Capillary Bed
Vein
What is k-space?
• a mathematical concept
• not a real “space” in the patient nor in
the MR scanner
• key to understanding...
k-space and the MR Image
x
y
f(x,y)
kx
ky
KKK---spacespacespace
F(kx,ky)
ImageImageImage---spacespacespace
ℑ
k-space and the MR Image
• each individual point in the MR image
is reconstructed from every point in
the k-space represen...
Discrete Fourier Transform
F(kx,ky) is the 2D discrete Fourier transform of the
image f(x,y)
x
y
f(x,y)
kx
ky
ℑ
K-space
F(...
k-space and the MR Image
• If the image is a 256 x 256 matrix size,
then k-space is also 256 x 256 points.
• The individua...
low spatial
frequencies
low spatial
frequencies
high spatial
frequencies
high spatial
frequencies
all
frequencies
all
freq...
Spatial Frequencies
• low frequency = contrast
• high frequency = detail
• The most abrupt change occurs at an
edge. Image...
Properties of k-space
• k-space is symmetrical
• all of the points in k-space must be known
to reconstruct the signal fait...
MRI and k-space
• The nuclei in an MR experiment
produce a radio signal (wave) that
depends on the strength of the main
ma...
RF signal
A/D
conversion
image space
FT
k-space
MRI
• Spatial encoding is accomplished by
superimposing gradient fields.
• There are three gradient fields in the
x, y, an...
MRI
• For most clinical MR imagers using
superconducting main magnets, the main
magnetic field is oriented in the z direct...
MRI
• The three magnetic gradients work together
to encode the NMR signal with spatial
information.
• Remember: the resona...
Gradients
• Consider the example of MR imaging in the
transverse (axial) plane.
Z gradient: slice select
X gradient: frequ...
Slice Selection
• For axial imaging, slice selection occurs
along the long axis of the magnet.
• Superposition of the slic...
Slice Selection
ββ
z
y
x
0
imaging plane
ββ++
ββ−−
ββ00
z gradientz gradient
Slice Selection
slice thickness is determined by gradient strength
β
β0
ω
ω0
RF bandwidth
1
3
2
ΖΖ
tt11
tt22
tt33
Slice Selection
Selection of an axial
slice is accomplished
by the z gradient.
zz gradient directiongradient direction
ω =...
Slice Selection
slice location is determined by the null point of the z gradient
β
β0
ω
ω0
RF bandwidth
slice 1
ΖΖ
slice 2...
Frequency Encoding
• Within the imaging plane, a small gradient is
applied left to right to allow for spatial
encoding in ...
Frequency Encoding
z
y
x
x gradientx gradient
higher frequency
lower frequency
LR
Frequency Encoding
RF signalRF signal
fromfrom entireentire sliceslice
A/D conversion, 256 pointsA/D conversion, 256 point...
Phase Encoding
• An additional gradient is applied in the
y direction to encode the image in the
remaining direction.
• Be...
Phase Encoding
• The technique of phase encoding the second
dimension in the imaging plane is
sometimes referred to as spi...
Phase Encoding
z
y
x
yy gradient,gradient,
phase step #192phase step #192
yy gradient,gradient,
phase step #64phase step #...
Phase Encoding
2D k-space matrix
gradient strength +128
RF in RF outRF out A/D conversion
gradient strength N
RF in RF out...
Spin Echo Imaging
RF
z gradient
echo
90°180°
echo
90°180°
echo
90°180°
y gradient
x gradient
slice select
phase
readout
Spin Echo Imaging
view -128
view -55
view 40
                 
       ...
• Acquisition of spatially encoded data as
described allows for reconstruction of the
MR image.
• The frequency and phase ...
Energy Absorption
β0
M0=x M0=z
900 tip
900 RF pulse
ω=ω0
Relaxation
β0
t=t0
RF
t=t1
ML=0
t=t2
ML=a
t=t3
ML=b
t=∞
ML=1
….
t
ML
t0 t1 t2 t3
Relaxation and Imaging
• FID (free induction decay) is
the relaxation behavior
following a single RF pulse
• most imaging ...
Relaxation
β0
t=t0
900 RF
t=t3
ML=b
t=t4
ML<b
900 RF
t=t3+
ML=0
900 RF
t=t4+
ML=0
t=t5
ML<<b
TR TR
Equilibrium
• after 5 or so
repetitions, the
system reaches
equilibrium
• similar to water
flowing into a
leaky bucket
rel...
Differential Relaxation
• short TR
• lower absolute ML
• marked difference
in relative signal
• long TR
• higher absolute ...
Image Contrast and T1
Relaxation
• shorter TRs maximize
differences in T1 relaxation,
generating tissue contrast
• longer ...
Goals of Imaging
Sequences
• generate an RF signal
perpendicular to β0
• generate tissue contrast
• minimize artifacts
Measuring the MR Signal
z
y x
RF signal from
precessing protons
RF signal from
precessing protons
RF antennaRF antenna
β0
Gradient Echo
• simplest sequence
–alpha flip-gradient recalled echo
• 3 parameters
–TR
–TE
–flip angle
• reduced SAR
• ar...
Gradient Echo
FID gradient recalled
echo
α
RF pulse
rephase
dephase
signal
gradient
z
y x
z
y x
α0 RF
t=t0 t=t0+
Partial Flip
α0 ML
MXY
M
MXY = M sin(α)
ML = M cos(α)
Dephasing in the xy-plane
view from the top
y
x
z Mxy
y
x
z
Mxy≈0
dephase
phase coherency phase dispersion
y
x
z Mxy
phase coherency
minus t2* decay
Rephasing in the xy-plane
view from the top
rephase
y
x
z
Mxy≈0
phase dispersion
MR Signal During
Rephasingz
y x
RF signal
“echo”
RF signal
“echo”
RF antennaRF antennaβ0
T2* decay
• occurs between the dephasing and
the rephasing gradients
• rephasing incompletely recovers
the signal
• signal...
T2* decay
• T2* decay is always faster than
T2 decay
• gradient echo imaging cannot
recover signal losses from
–magnetic f...
T2 and T2* Relaxation
• T2* relaxation influences
contrast in gradient echo
imaging
• T2 relaxation influences
contrast in...
Gradient Echo
pulse timing
echo
RF
signal
readout
α0
phase
slice
TE
Gradient Echo
advantages
• faster imaging
–can use shorter TR and shorter
TEs than SE
• low flip angle deposits less
energ...
Gradient Echo
disadvantages
• difficult to generate good T2
weighting
• magnetic field inhomogeneities
cause signal loss
–...
Gradient Echo
changing TE
TE 9
FA 30
TE 9
FA 30
TE 30
FA 30
TE 30
FA 30
susceptibility effectsusceptibility effect T2* wei...
Gradient Echo
magnetic susceptibility
post-surgical change
“blooming” artifact
post-surgical change
“blooming” artifact
Gradient Echo
• image contrast depends on
sequence
• conventional GR scan
– aka GRASS, FAST
– decreased FA causes less T1
...
Conventional GR
TE 20, FA 15
Gradient Echo
• Spoiled GR
–aka SPGR, RF-FAST
–spoiling destroys accumulated
transverse coherence
–maximizes T1 contrast
Gradient Echo
• Contrast enhanced GR
–aka SSFP, CE-FAST
–infrequently used because of
poor S/N
–generates heavily T2* weig...
Gradient Echo
• other varieties
–MTC
• T2 - like weighting
–IR prepped
• 180 preparatory pulse
–DE (driven equilibrium) pr...
MTC GR
TE 13, FA 50
Spin Echo
• widely used sequence
–90-180-echo
• 2 parameters
–TR
–TE
• generates T1, PD, and T2
weighted images
• minimize...
Spin Echo
FID spin
echo
900 RF pulse
readoutfrequency encode
signal
gradient
1800 RF pulse
Gradient versus Spin Echo
Spin Echo
FID spin
echo
900RF pulse
readoutfrequency encode
signal
gradient
1800RF pulse
Gradien...
900 Flip
z
y x
z
y x
900 RF
t=t0 t=t0+
900
After
ML=0
MXY=M
Before
ML=M
MXY=0
Dephasing in the xy-plane
view from the top
y
x
z Mxy
y
x
z
Mxy≈0
phase coherency phase dispersion
Dephasing begins
immedi...
y
x
z Mxy
phase coherency
minus t2 decay
Rephasing in the xy-plane
view from the top
y
x
z
Mxy≈0
phase dispersion
t=TE/2 t...
z
y x
z
y x
z
y x
z
y x
t=TE/2 t=TE
1800 RF
t=0
900 RF
dephased
rephased
1800 Flip
Spin Echo
pulse timing
echo
RF
signal
readout
900
phase
slice
TE
1800
WNMR Race
t=0
900 RF
WNMR Race
WNMR Race
t=TE/2
1800 RF
t=TE
WNMR Race
Effects of the 1800 Pulse
• eliminates signal loss due to
field inhomogeneities
• eliminates signal loss due to
susceptibi...
Spin Echo
advantages
• high signal to noise
• least artifact prone sequence
• contrast mechanisms easier to
understand
Spin Echo
disadvantages
• high SAR than gradient echo
because of 900 and 1800 RF
pulses
• long TR times are incompatible
w...
Spin Echo Contrast
• T1 weighted
–short TR (450-850)
–short TE (10-30)
• T2 weighted
–long TR (2000 +)
–long TE (> 60)
• P...
Spin Echo Contrast
T2 Relaxation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500
msec
Mxy
long T2
short T2
T...
T1 weightedT1 weighted T2 weightedT2 weighted
Spin Echo Contrast
Spin Echo Contrast
PD weightedPD weighted T2 weightedT2 weighted
Contrast
• the ability to discriminate different
tissues based on their relative
brightness
Caveat
• windowing affects the relative
contrast of tissues
– intensity values of pixels are relative
to one another, unli...
T1 SET1 SET2 FSET2 FSE
“CYST”“CYST”
T1 SET1 SET2 FSET2 FSE
CYST?CYST?
T2 FSET2 FSE T2 FSET2 FSE
CYST?CYST?
Summary
• need visible differences in intensity
to discriminate tissues
• surrounding tissues can make an
intermediate sig...
Noise
• constant at a given machine setup
• reduces the ability to visualize low
contrast structures
• adds to or subtract...
Noise
• increasing the available signal will
reduce the relative effects of noise
• machine parameters must be
chosen to m...
frequency
SI
frequency
SI
Signal versus Noise
• high signal
• high SNR
• low signal
• low SNR
Noiseless Conditions
0
10
20
30
40
50
60
70
80
90
100
Tissue A Tissue B
Tissue Type
RelativeSignalIntensity
High Signal/Low Noise
0
10
20
30
40
50
60
70
80
90
100
Tissue A Tissue B
Tissue Type
RelativeSignalIntensity
Low Signal/High Noise
0
10
20
30
40
50
60
70
80
90
100
Tissue A Tissue B
Tissue Type
RelativeSignalIntensity
Noiseless Conditions
0
10
20
30
40
50
60
70
80
90
100
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Relative Pixel Location
Rela...
High Signal/Low Noise
0
10
20
30
40
50
60
70
80
90
100
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Relative Pixel Location
Rel...
Low Signal/High Noise
0
10
20
30
40
50
60
70
80
90
100
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
Relative Pixel Location
Rel...
Image Contrast
100% noise
Image Contrast
80% noise
Image Contrast
60% noise
Image Contrast
40% noise
Image Contrast
20% noise
Image Contrast
0% noise
Factors Affecting SNR
• strength of main magnet
• coil selection
• voxel size
• phase encoding
• number of averages
• rece...
• stronger main magnet
• proper imaging coil
• larger voxel size
• decreased phase encoding
• increased number of averages...
Stronger Main Magnet
S/N effect Downside
• linear increase • less T1 weighting
at high fields
• increased
chemical shift
e...
Coil Selection
S/N effect Downside
• increase in signal
with surface coils
• quadrature
provides 40%
increase S/N over
lin...
Larger Voxel Size
S/N effect Downside
• linear increase in
either RO or PE
direction
• linear increase
with increased
slic...
Decreased Phase Encodings
S/N effect Downside
• square root
increase in signal
to noise
• linear decrease in
scan time
• d...
Increased Signal Averages
S/N effect Downside
• square root
increase in signal
to noise
• linear increase in
scan time
Decreased Receiver BW
S/N effect Downside
• square root
increase in signal
to noise
• increase in
chemical shift
artifact ...
Pulse Sequence Parameters
• SE imaging
– increased TR provides nonlinear
increase in SNR with linear increase
in scan time...
Pulse Sequence Parameters
• GE imaging
– complex effects
– maximum SNR typically between 30
and 60 degrees
– long TR seque...
SNR Application
• pituitary imaging
– baseline:
• 16 cm FOV, 3 mm slice thickness, 192
phase encodes, 4 NEX
– new goal:
• ...
FOV RO PE
Slice
Thickness
(mm) NEX
Imaging Time
(TR=500
msec)
Relative
SNR
160 256 192 3 4 6.40 43.30
160 256 170 4 2 2.83...
Fat Suppression and SNR
• non fat-suppressed image
– each image pixel comprised of signal
from water and fat in the imagin...
frequency
SI
frequency
SI
Fat Suppression
• without fat
suppresion
• high SNR
• with fat
suppression
• lower SNR
water
plu...
Introduction to mri
Introduction to mri
Introduction to mri
Introduction to mri
Introduction to mri
Introduction to mri
Introduction to mri
Introduction to mri
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Introduction to mri

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Introduction to mri

  1. 1. Introduction to Nuclear Magnetic Resonance • Topics – Nuclear spin and magnetism – Resonance behavior and the Larmor Frequency • Larmor frequency • flip angle – Energy Absorption and Emission • NMR spectroscopy • Energy absorption in tissue (safety issues) • Relaxometry – T1,T2,T2* relaxation
  2. 2. Nuclear Magnetism • Nucleons (protons, neutrons) have a quantum property known as spin. • Nucleons have been shown to obey Fermi statistics, and thus have a maximum spin magnitude of 1/2 Bohr magneton. (spin=1/2) • In the absence of a magnetic field, nuclear spin is not an observable • In the presence of a homogeneous magnetic field, the energy of the nucleus depends on the relative orientation of the magnetic field and the nuclear spin vector
  3. 3. single voxel single voxel net magnetizationnet magnetization Individual nuclear spinsIndividual nuclear spins
  4. 4. Nuclear Magnetic Resonance: Properties in Matter • Relaxation – After we have delivered energy to the nuclei in our sample at the Larmor frequency, there are two possible ways for the sample to lose this energy (back to lowest energy state): • spontaneous emission • induced emission
  5. 5. • Spontaneous emission: – negligible effect at RF frequencies (dominant at visible frequencies) • Induced emission – Energy emission requires interaction of the nucleus with its external environment The nature of energy emission depends strongly on the environment of the excited nucleus (Relaxation) 3ω∝
  6. 6. • NMR Spectroscopy is the study of the chemistry of matter using the NMR absorption spectrum • Relaxometry is the study of the chemistry of matter using the NMR relaxation properties. MRI generates tissue contrast based (mostly) on NMR relaxation differences.
  7. 7. x y x y x y x y Spin Dephasing after excitation Bo
  8. 8. Alignment of Spins in a Magnetic Field spin magnetic moment B0 field M M=0
  9. 9. Energy in a Magnetic Field (Zeeman Splitting, Spin ½) E+1/2= −γB0/2 E-1/2= +γB0/2 P+1/2= 0. 5000049 P-1/2= 0.4999951 1.5T, T=310K, P(E)∝exp(−E/kT) mI = +½ mI = −½
  10. 10. Larmor Frequency E+1/2= −γB0/2 E-1/2= +γB0/2 Allowed transitions ∆E = γB0 = ω0 mI = −½ mI = +½ ω0 = γB0
  11. 11. T1 Relaxation Mz(t) = M0 + {Mz(0) − M0}exp(-t/T1) Mz Mz t t saturation–recovery inversion–recovery dMz(t) = − [Mz(t) − M0] dt T1 M0 M0 Mz(0) = 0 Mz(0) = −M0
  12. 12. T2 Relaxation Mxy(t) = Mxy(0) exp(−t/T2) Mxy t dMxy(t) = − Mxy(t) dt T2
  13. 13. • 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
  14. 14. Recovery Curve time Signal             −−= 1 0 exp1 T t SS
  15. 15. What effect does T1 have on Images? 90° 90° 90° 90° 90° Mz
  16. 16. What effect does T1 have on Images? t = 0 t = 3s t = 6s t = 9s t = 12s
  17. 17. • Assume the steady state has been reached. • Use a flip angle of θdegrees. • Find a condition where the transverse magnetization following the flip is maximized. The Ernst Angle       −= 1 expcos T TR θ
  18. 18. T1-Weighted Images
  19. 19. T1-Weighted Images
  20. 20. T1-Weighted Images
  21. 21. T1-Weighted Images
  22. 22. 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.
  23. 23. 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. 24. Transverse Relaxation Long T2 Short T2 frequency
  25. 25. Decay Curve time Signal       −= 2 0 exp T t SS
  26. 26. PD T1 T2
  27. 27. 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
  28. 28. What is T2 *?
  29. 29. 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.
  30. 30. What effect does T2 * have on Images? • Effect of echo time
  31. 31. What effect does T2 * have on Images? • Effect of echo time
  32. 32. What effect does T2 * have on Images? • Effect of echo time
  33. 33. What effect does T2 * have on Images? • Effect of echo time
  34. 34. What effect does T2 * have on Images? × = ⊗ = ⇓ ⇓ ⇓FT FTFT Perfect FID T2 * Decay Actual FID Perfect Image Point Spread Function Actual Image
  35. 35. What effect does T2 * have on Images? × = ⊗ = ⇓ ⇓ ⇓FT FTFT Perfect FID T2 * Decay Actual FID Perfect Image Point Spread Function Actual Image
  36. 36. Contrast in MRI • Contrast based on Relaxation Time • Contrast Agents • BOLD Contrast • Perfusion and Diffusion Contrast
  37. 37. To start with…. • No Spins, no contrast. • Spin density is the most fundamental of contrasts in MRI. • In our case spin density is related to the water content of the tissue.
  38. 38. Water Content of Tissue Tissue % Water Content Grey Matter 70.6 White Matter 84.3 Heart 80.0 Blood 93.0 Bone 12.2
  39. 39. Enhancing the Signal from Spin Density • Gastrointestinal imaging – Drinking water • Lung imaging – Inhaling hyperpolarized inert gas. A laser polarises the helium gas increasing its magnetisation.
  40. 40. T1 Contrast • The shorter the repetition time (TR) the greater the T1 contrast. • Prepare the magnetisation with a saturation or inversion pulse followed by a suitable delay.
  41. 41. T2 or T2 * Contrast • Sequences without a spin echo will be T2 *- weighted rather than T2-weighted. • The longer the echo time (TE) the greater the T2 contrast.
  42. 42. Magnetism • units of magnetism – 1T = 10,000 Gauss – Earth’s field = 0.5 Gauss • types of magnetism – ferromagnetism – paramagnetism – superparamagnetism – diamagnetism
  43. 43. Magnetic Susceptibility • the degree to which a material becomes magnetized when placed in a magnetic field • magnetizability
  44. 44. Ferromagnetism • Property of certain metals – iron – nickel – cobalt • Positive susceptibility • consist of magnet domains • able to remain magnetized without the influence of an external field
  45. 45. Paramagnetism • Oxygen • metal ions with unpaired electrons resulting in positive susceptibility – Fe – Gd – Mg • less than 1/1000 th effect of ferromagnetism • shortens T1 and T2 times
  46. 46. Superparamagnetism • halfway between ferro and paramagnetic • property of individual domains of elements that have ferromagnetic properties in bulk • iron containing contrast agents for bowel and lymph nodes are superparamagnetic
  47. 47. Diamagnetism • no intrinsic atomic magnetic moment • In a magnetic field weakly repel the field – negative magnetic susceptibility • water, copper, nitrogen, barium sulfate, and most tissues are diamagnetic. • contributes to the loss of signal seen in bowel on MRI after administration of barium sulfate suspensions.
  48. 48. Contrast Agents • Sometimes it is desirable to enhance the natural contrast in the images. – Highlighting a tumour. – Measuring perfusion rates. • MR contrast agents act to change the relaxation times of the substrate they are in.
  49. 49. Contrast Agents • Contain an ion with a large number of unpaired electrons. • This gives it a larger magnetic moment than the proton. • This enhances the local magnetic fields that fluctuate, due to thermal motion, in the vicinity of a proton.
  50. 50. Contrast Agents • These are usually paramagnetic ions. e.g. Gadolinium • By themselves these ions are highly toxic so they are bound up in large molecules. e.g. DTPA • They tend not to permeate the blood brain barrier and so enhance tumours that lack this barrier.
  51. 51. Gadolinium • shortens T1 relaxation of water – high SI on T1 weighted images in lower concentrations • shortens T2 relaxation of water – lowers SI on T1 weighted images in high concentrations • seven unpaired electrons – high magnetic moment – unpaired electrons react with protons in adjacent water molecules shortening their relaxation time
  52. 52. Gd-DTPA COO- CH2 N - CH2 - CH2 - N - CH2 - CH2 - N Gd3 + CH2 - COO- CH2 - COOH COO- - CH2 COOH - CH2
  53. 53. Haemoglobin
  54. 54. Haemoglobin Oxy-haemoglobin Deoxy-haemoglobin Paramagnetic Diamagnetic
  55. 55. Perfusion Imaging • Contrast agent methods • Spin tagged methods – Continuously labelled – IVIM – Pulse labelled
  56. 56. Perfusion Imaging • Perfusion is the rate constant determining the delivery of metabolic substrates to the local tissue and clearance of products of metabolism. • If a volume of tissue V is supplied with arterial blood at a rate of F then perfusion f = F / V (ml/100g/min)
  57. 57. Contrast Agent Methods • Inject contrast agent. • Causes a bolus of blood to have a different signal intensity to the blood in the brain. • This tagged bolus perfuses the brain. • Level of signal change gives an indication of rate of perfusion.
  58. 58. Contrast Agent Methods Artery Capillary Bed Vein
  59. 59. Contrast Agent Methods Artery Capillary Bed Vein
  60. 60. Contrast Agent Methods Artery Capillary Bed Vein
  61. 61. What is k-space? • a mathematical concept • not a real “space” in the patient nor in the MR scanner • key to understanding spatial encoding of MR images
  62. 62. k-space and the MR Image x y f(x,y) kx ky KKK---spacespacespace F(kx,ky) ImageImageImage---spacespacespace ℑ
  63. 63. k-space and the MR Image • each individual point in the MR image is reconstructed from every point in the k-space representation of the image – like a card shuffling trick: you must have all of the cards (k-space) to pick the single correct card from the deck • all points of k-space must be collected for a faithful reconstruction of the image
  64. 64. Discrete Fourier Transform F(kx,ky) is the 2D discrete Fourier transform of the image f(x,y) x y f(x,y) kx ky ℑ K-space F(kx,ky) f x y N F k k e xk yk kk x y j N x j N yNN yx ( , ) ( , )= +       = − = − ∑∑ 1 2 2 2 0 1 0 1 π π image-space
  65. 65. k-space and the MR Image • If the image is a 256 x 256 matrix size, then k-space is also 256 x 256 points. • The individual points in k-space represent spatial frequencies in the image. • Image contrast is represented by low spatial frequencies; detail is represented by high spatial frequencies.
  66. 66. low spatial frequencies low spatial frequencies high spatial frequencies high spatial frequencies all frequencies all frequencies
  67. 67. Spatial Frequencies • low frequency = contrast • high frequency = detail • The most abrupt change occurs at an edge. Images of edges contain the highest spatial frequencies.
  68. 68. Properties of k-space • k-space is symmetrical • all of the points in k-space must be known to reconstruct the signal faithfully • truncation of k-space results in loss of detail, particularly at edges • most important information centered around the middle of k-space • k-space is the Fourier representation of the waveform
  69. 69. MRI and k-space • The nuclei in an MR experiment produce a radio signal (wave) that depends on the strength of the main magnet and the specific nucleus being studied (usually H+). • To reconstruct an MR image we need to determine the k-space values from the MR signal.
  70. 70. RF signal A/D conversion image space FT k-space
  71. 71. MRI • Spatial encoding is accomplished by superimposing gradient fields. • There are three gradient fields in the x, y, and z directions. • Gradients alter the magnetic field resulting in a change in resonance frequency or a change in phase.
  72. 72. MRI • For most clinical MR imagers using superconducting main magnets, the main magnetic field is oriented in the z direction. • Gradient fields are located in the x, y, and z directions.
  73. 73. MRI • The three magnetic gradients work together to encode the NMR signal with spatial information. • Remember: the resonance frequency depends on the magnetic field strength. Small alterations in the magnetic field by the gradient coils will change the resonance frequency.
  74. 74. Gradients • Consider the example of MR imaging in the transverse (axial) plane. Z gradient: slice select X gradient: frequency encode (readout) Y gradient: phase encode
  75. 75. Slice Selection • For axial imaging, slice selection occurs along the long axis of the magnet. • Superposition of the slice selection gradient causes non-resonance of tissues that are located above and below the plane of interest.
  76. 76. Slice Selection ββ z y x 0 imaging plane ββ++ ββ−− ββ00 z gradientz gradient
  77. 77. Slice Selection slice thickness is determined by gradient strength β β0 ω ω0 RF bandwidth 1 3 2 ΖΖ tt11 tt22 tt33
  78. 78. Slice Selection Selection of an axial slice is accomplished by the z gradient. zz gradient directiongradient direction ω = ω0 graph of the z magnetic gradient z-axis β β = β0 β > β0 β < β0
  79. 79. Slice Selection slice location is determined by the null point of the z gradient β β0 ω ω0 RF bandwidth slice 1 ΖΖ slice 2 slice 3 Ζ1 Ζ2 Ζ3
  80. 80. Frequency Encoding • Within the imaging plane, a small gradient is applied left to right to allow for spatial encoding in the x direction. • Tissues on the left will have a slightly higher resonance frequency than tissues on the right. • The superposition of an x gradient on the patient is called frequency encoding. • Frequency encoding enables spatial localization in the L-R direction only.
  81. 81. Frequency Encoding z y x x gradientx gradient higher frequency lower frequency LR
  82. 82. Frequency Encoding RF signalRF signal fromfrom entireentire sliceslice A/D conversion, 256 pointsA/D conversion, 256 points 1 line of k-space
  83. 83. Phase Encoding • An additional gradient is applied in the y direction to encode the image in the remaining direction. • Because the x gradient alters the frequencies in the received signal according to spatial location, the y gradient must alter the phase of the signal. • Thus, the points of k-space are revealed by recording the digitized RF signal after a phase encoding gradient application.
  84. 84. Phase Encoding • The technique of phase encoding the second dimension in the imaging plane is sometimes referred to as spin warping. • The phase encoding gradient is “stepped” during the acquisition of image data for a single slice. Each step provides a unique phase encoding. • For a 256 x 256 square image matrix, 256 unique phase encodings must be performed for each image slice. The second 256 points in the x direction are obtained by A to D conversion of the received signal.
  85. 85. Phase Encoding z y x yy gradient,gradient, phase step #192phase step #192 yy gradient,gradient, phase step #64phase step #64
  86. 86. Phase Encoding 2D k-space matrix gradient strength +128 RF in RF outRF out A/D conversion gradient strength N RF in RF outRF out A/D conversion gradient strength -128 RF in RF outRF out A/D conversion                         END BEGIN line 128 line N line -128                                    
  87. 87. Spin Echo Imaging RF z gradient echo 90°180° echo 90°180° echo 90°180° y gradient x gradient slice select phase readout
  88. 88. Spin Echo Imaging view -128 view -55 view 40                                                       k-space 256 x 256 points row 40 row -55 row -128 A/D, 256 points kx = frequency ky = phase
  89. 89. • Acquisition of spatially encoded data as described allows for reconstruction of the MR image. • The frequency and phase data are acquired and form points in a 2D array . • Reconstruction of the image is provided by 2D inverse Fourier transform of the 2D array. • This method of spatially encoding the MR image is called 2D FT imaging. MR Image Reconstruction
  90. 90. Energy Absorption β0 M0=x M0=z 900 tip 900 RF pulse ω=ω0
  91. 91. Relaxation β0 t=t0 RF t=t1 ML=0 t=t2 ML=a t=t3 ML=b t=∞ ML=1 …. t ML t0 t1 t2 t3
  92. 92. Relaxation and Imaging • FID (free induction decay) is the relaxation behavior following a single RF pulse • most imaging done with repetitive RF energy deposition • the interval between the RF energy pulses is called the TR interval (time to repetition)
  93. 93. Relaxation β0 t=t0 900 RF t=t3 ML=b t=t4 ML<b 900 RF t=t3+ ML=0 900 RF t=t4+ ML=0 t=t5 ML<<b TR TR
  94. 94. Equilibrium • after 5 or so repetitions, the system reaches equilibrium • similar to water flowing into a leaky bucket relaxation RF in equilibriumequilibrium
  95. 95. Differential Relaxation • short TR • lower absolute ML • marked difference in relative signal • long TR • higher absolute ML • minimal difference in relative signal fat protons water protons
  96. 96. Image Contrast and T1 Relaxation • shorter TRs maximize differences in T1 relaxation, generating tissue contrast • longer TRs minimize differences in T1 relaxation, reducing T1 tissue contrast
  97. 97. Goals of Imaging Sequences • generate an RF signal perpendicular to β0 • generate tissue contrast • minimize artifacts
  98. 98. Measuring the MR Signal z y x RF signal from precessing protons RF signal from precessing protons RF antennaRF antenna β0
  99. 99. Gradient Echo • simplest sequence –alpha flip-gradient recalled echo • 3 parameters –TR –TE –flip angle • reduced SAR • artifact prone
  100. 100. Gradient Echo FID gradient recalled echo α RF pulse rephase dephase signal gradient
  101. 101. z y x z y x α0 RF t=t0 t=t0+ Partial Flip α0 ML MXY M MXY = M sin(α) ML = M cos(α)
  102. 102. Dephasing in the xy-plane view from the top y x z Mxy y x z Mxy≈0 dephase phase coherency phase dispersion
  103. 103. y x z Mxy phase coherency minus t2* decay Rephasing in the xy-plane view from the top rephase y x z Mxy≈0 phase dispersion
  104. 104. MR Signal During Rephasingz y x RF signal “echo” RF signal “echo” RF antennaRF antennaβ0
  105. 105. T2* decay • occurs between the dephasing and the rephasing gradients • rephasing incompletely recovers the signal • signal loss is greater with longer TEs • decay generates image contrast
  106. 106. T2* decay • T2* decay is always faster than T2 decay • gradient echo imaging cannot recover signal losses from –magnetic field inhomogeneity –magnetic susceptibility –water-fat incoherence
  107. 107. T2 and T2* Relaxation • T2* relaxation influences contrast in gradient echo imaging • T2 relaxation influences contrast in spin echo imaging
  108. 108. Gradient Echo pulse timing echo RF signal readout α0 phase slice TE
  109. 109. Gradient Echo advantages • faster imaging –can use shorter TR and shorter TEs than SE • low flip angle deposits less energy –more slices per TR than SE –decreases SAR • compatible with 3D acquisitions
  110. 110. Gradient Echo disadvantages • difficult to generate good T2 weighting • magnetic field inhomogeneities cause signal loss –worse with increasing TE times –susceptibility effects –dephasing of water and fat protons
  111. 111. Gradient Echo changing TE TE 9 FA 30 TE 9 FA 30 TE 30 FA 30 TE 30 FA 30 susceptibility effectsusceptibility effect T2* weightingT2* weighting
  112. 112. Gradient Echo magnetic susceptibility post-surgical change “blooming” artifact post-surgical change “blooming” artifact
  113. 113. Gradient Echo • image contrast depends on sequence • conventional GR scan – aka GRASS, FAST – decreased FA causes less T1 weighting – increased TE causes more T2* weighting
  114. 114. Conventional GR TE 20, FA 15
  115. 115. Gradient Echo • Spoiled GR –aka SPGR, RF-FAST –spoiling destroys accumulated transverse coherence –maximizes T1 contrast
  116. 116. Gradient Echo • Contrast enhanced GR –aka SSFP, CE-FAST –infrequently used because of poor S/N –generates heavily T2* weighted images
  117. 117. Gradient Echo • other varieties –MTC • T2 - like weighting –IR prepped • 180 preparatory pulse –DE (driven equilibrium) prepped • 90-180-90 preparatory pulses • T2 contrast
  118. 118. MTC GR TE 13, FA 50
  119. 119. Spin Echo • widely used sequence –90-180-echo • 2 parameters –TR –TE • generates T1, PD, and T2 weighted images • minimizes artifacts
  120. 120. Spin Echo FID spin echo 900 RF pulse readoutfrequency encode signal gradient 1800 RF pulse
  121. 121. Gradient versus Spin Echo Spin Echo FID spin echo 900RF pulse readoutfrequency encode signal gradient 1800RF pulse Gradient Echo FID gradient recalled echo α RF pulse rephase dephase signal gradient
  122. 122. 900 Flip z y x z y x 900 RF t=t0 t=t0+ 900 After ML=0 MXY=M Before ML=M MXY=0
  123. 123. Dephasing in the xy-plane view from the top y x z Mxy y x z Mxy≈0 phase coherency phase dispersion Dephasing begins immediately after the 900 RF pulse. t=0 t=TE/2 900 RF
  124. 124. y x z Mxy phase coherency minus t2 decay Rephasing in the xy-plane view from the top y x z Mxy≈0 phase dispersion t=TE/2 t=TE 1800 RF
  125. 125. z y x z y x z y x z y x t=TE/2 t=TE 1800 RF t=0 900 RF dephased rephased 1800 Flip
  126. 126. Spin Echo pulse timing echo RF signal readout 900 phase slice TE 1800
  127. 127. WNMR Race t=0 900 RF
  128. 128. WNMR Race
  129. 129. WNMR Race t=TE/2 1800 RF
  130. 130. t=TE WNMR Race
  131. 131. Effects of the 1800 Pulse • eliminates signal loss due to field inhomogeneities • eliminates signal loss due to susceptibility effects • eliminates signal loss due to water/fat dephasing • all signal decay is caused by T2 relaxation only
  132. 132. Spin Echo advantages • high signal to noise • least artifact prone sequence • contrast mechanisms easier to understand
  133. 133. Spin Echo disadvantages • high SAR than gradient echo because of 900 and 1800 RF pulses • long TR times are incompatible with 3D acquisitions
  134. 134. Spin Echo Contrast • T1 weighted –short TR (450-850) –short TE (10-30) • T2 weighted –long TR (2000 +) –long TE (> 60) • PD weighted –long TR, short TE
  135. 135. Spin Echo Contrast T2 Relaxation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 msec Mxy long T2 short T2 T1 Relaxation 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1000 2000 3000 4000 5000 msec ML long T1 short T1 T1 weighted - T1 relaxation predominates •Short TE minimizes differences in T2 relaxation •Short TR maximizes differences in T1 relaxation T2 weighted - T2 relaxation predominates •Long TE maximizes differences in T2 relaxation •Long TR minimizes differences in T1 relaxation
  136. 136. T1 weightedT1 weighted T2 weightedT2 weighted Spin Echo Contrast
  137. 137. Spin Echo Contrast PD weightedPD weighted T2 weightedT2 weighted
  138. 138. Contrast • the ability to discriminate different tissues based on their relative brightness
  139. 139. Caveat • windowing affects the relative contrast of tissues – intensity values of pixels are relative to one another, unlike CT • windowing can make a solid tumor look like a “cyst”
  140. 140. T1 SET1 SET2 FSET2 FSE “CYST”“CYST”
  141. 141. T1 SET1 SET2 FSET2 FSE CYST?CYST?
  142. 142. T2 FSET2 FSE T2 FSET2 FSE CYST?CYST?
  143. 143. Summary • need visible differences in intensity to discriminate tissues • surrounding tissues can make an intermediate signal tissue appear dark or bright • windowing affects image and tissue contrast
  144. 144. Noise • constant at a given machine setup • reduces the ability to visualize low contrast structures • adds to or subtracts from the average signal intensity of a given pixel
  145. 145. Noise • increasing the available signal will reduce the relative effects of noise • machine parameters must be chosen to maximize signal without significantly extending exam times • S/N is a relative measure allowing for comparison in a variety of circumstances
  146. 146. frequency SI frequency SI Signal versus Noise • high signal • high SNR • low signal • low SNR
  147. 147. Noiseless Conditions 0 10 20 30 40 50 60 70 80 90 100 Tissue A Tissue B Tissue Type RelativeSignalIntensity
  148. 148. High Signal/Low Noise 0 10 20 30 40 50 60 70 80 90 100 Tissue A Tissue B Tissue Type RelativeSignalIntensity
  149. 149. Low Signal/High Noise 0 10 20 30 40 50 60 70 80 90 100 Tissue A Tissue B Tissue Type RelativeSignalIntensity
  150. 150. Noiseless Conditions 0 10 20 30 40 50 60 70 80 90 100 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Relative Pixel Location RelativeSignalIntensity
  151. 151. High Signal/Low Noise 0 10 20 30 40 50 60 70 80 90 100 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Relative Pixel Location RelativeSignalIntensity
  152. 152. Low Signal/High Noise 0 10 20 30 40 50 60 70 80 90 100 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Relative Pixel Location RelativeSignalIntensity
  153. 153. Image Contrast 100% noise
  154. 154. Image Contrast 80% noise
  155. 155. Image Contrast 60% noise
  156. 156. Image Contrast 40% noise
  157. 157. Image Contrast 20% noise
  158. 158. Image Contrast 0% noise
  159. 159. Factors Affecting SNR • strength of main magnet • coil selection • voxel size • phase encoding • number of averages • receiver bandwidth • pulse sequence parameters
  160. 160. • stronger main magnet • proper imaging coil • larger voxel size • decreased phase encoding • increased number of averages • decreased receiver bandwidth • (pulse sequence parameters) Factors INCREASING SNR
  161. 161. Stronger Main Magnet S/N effect Downside • linear increase • less T1 weighting at high fields • increased chemical shift effects in RO direction
  162. 162. Coil Selection S/N effect Downside • increase in signal with surface coils • quadrature provides 40% increase S/N over linear • phased array increased over quadrature • limited coverage with surface coils • more complex coils are more expensive
  163. 163. Larger Voxel Size S/N effect Downside • linear increase in either RO or PE direction • linear increase with increased slice thickness • decreased resolution
  164. 164. Decreased Phase Encodings S/N effect Downside • square root increase in signal to noise • linear decrease in scan time • decreased resolution in PE direction • Gibb’s phenomenon in PE direction
  165. 165. Increased Signal Averages S/N effect Downside • square root increase in signal to noise • linear increase in scan time
  166. 166. Decreased Receiver BW S/N effect Downside • square root increase in signal to noise • increase in chemical shift artifact in RO direction
  167. 167. Pulse Sequence Parameters • SE imaging – increased TR provides nonlinear increase in SNR with linear increase in scan time – decreased TE provides nonlinear increase in SNR with no effect on scan time and less T2 weighting
  168. 168. Pulse Sequence Parameters • GE imaging – complex effects – maximum SNR typically between 30 and 60 degrees – long TR sequences (2D) • increase SNR with increased flip angle – short TR sequences (TOF & 3D) • decreased SNR with increased flip angle
  169. 169. SNR Application • pituitary imaging – baseline: • 16 cm FOV, 3 mm slice thickness, 192 phase encodes, 4 NEX – new goal: • reduced scan time, same SNR
  170. 170. FOV RO PE Slice Thickness (mm) NEX Imaging Time (TR=500 msec) Relative SNR 160 256 192 3 4 6.40 43.30 160 256 170 4 2 2.83 43.39 190 256 192 3 2 3.20 43.18 160 256 144 3 3 3.60 43.30 SNR Example
  171. 171. Fat Suppression and SNR • non fat-suppressed image – each image pixel comprised of signal from water and fat in the imaging voxel • fat-suppression – reduces total signal by suppression of fat from the voxel – reduces SNR
  172. 172. frequency SI frequency SI Fat Suppression • without fat suppresion • high SNR • with fat suppression • lower SNR water plus fat water only

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