Transcript L1_SPM_Chap3

Textbook
for the
Statistical
Parametric
Mapping
(SPM) class
Statistical Parametric
Mapping
Chapter 3
Principles of Nuclear Magnetic
Resonance and MRI
Many thanks to those that share their MRI slides online
Physical Science
Technology
Methodology
Engineering
Physics
Computer
Science
Statistics
Cognitive
Science
Neuroscience
Physiology
Interpretation
Medicine
Applications
Peter Bandettini NIH
MRI Has Many Layers Of
Complexity
Even subdivisions
below have multiple
layers of complexity
…
Physics … Engineering … Technology … Applications … Interpretation …
History: MRI
• 1940s – Bloch & Purcell: Nuclear Magnetic
Resonance
• 1973 - Lauterbur: gradients for spatial localization of
images
• 1977 – Mansfield: first image of human anatomy, first
echo planar image (a fast imaging technique)
• 1990s - Discovery that MRI can be used to
distinguish oxygenated blood from deoxygenated
blood. Leads to Functional Magnetic Resonance
imaging (fMRI)
• Paul Lauterbur and Peter Mansfield won the Nobel
Prize in Physiology/Medicine (2003) for their
pioneering work in MRI
Venography
Fiber Track Imaging
Anatomy
Angiography
Perfusion
Peter Bandettini NIH
fMRI
R
P
Peter Bandettini NIH
Basic Physics of MRI
• All magnetic fields are the result of charge in motion
• Nucleus of an atom has a magnetic moment when it
has an odd number of protons (or neutrons). Single
proton in Hydrogen yields strongest magnetic effect.
Model of
spin as
motion
• Why does neutron have magnetic properties?
• What about electron(s) magnetic properties?
Basic Physics of MRI
• The orientation of nuclear magnetic moments are
affected by an external magnetic field (that not due to
the local nuclear magnetic moments).
No external magnetic
field. Orientation is
random.
External magnetic field
B0. Orientation follows
direction of external
magnetic field.
Basic Physics of MRI
• Nuclei line up with magnetic moments either in a parallel or
anti-parallel configuration.
• In body tissues more line up in parallel creating a small
additional magnetization M in the direction of B0.
Nuclei spin axis not
parallel to B0 field
direction.
Nuclear magnetic
moments precess
about B0.
Field Strength and the Net
Magnetization (M)
..
...
NU= 1,000,000 - 5
NU = 1,000,000
ΔE3.0T = 2*ΔE1.5T
ΔE1.5T
...
1.5 T
NL ~ 1,000,000 + 10
M
NL = # /volume in low energy state
NU = # /volume high energy state
NL~ 1,000,000 + 15
...
3.0 T
M
M  (NL - NU)
Lowering temperature increases M – Any volunteers?
Basic Physics of MRI
• Frequency of precession of magnetic moments given
by Larmor relationship
f = g x B0
f = Larmor frequency (mHz)
g = Gyromagnetic ratio (mHz/Tesla)
B0 = Magnetic field strength (Tesla)
g ~ 43 mHz/Tesla
Larmor frequencies of RICs MRIs
3T ~ 130 mHZ
7T ~ 300 mHz
11.7T ~ 500 mHz
Basic Physics of MRI
NMRable Nuclei
 Body 1H content is high due to water (>67%)
 Hydrogen protons in mobile water are primary
source of signals in fMRI and aMRI
Basic Physics of MRI
• M is parallel to B0 since
transverse components of
magnetic moments are randomly
oriented.
• The difference between the
numbers of protons in the
parallel (up here) and antiparallel states leads to the net
magnetization (M).
• Proton density relates to the
number of parallel states per unit
volume.
• Signal producing capability
depends on proton density.
B0
Proton Signal
•
•
•
•
•
6.023x1023 molecules in 18 gm of H2O
3.35x1022 molecules in 1 gm (1 cc ~ cm3)
3.35x1019 molecules in 1 mg (1 mm3)
7.70x1019 hydrogen atoms/mm3
7.70x1014 signal producing protons/mm3
So the approximately 1 in 105 signal producing protons is still a lot.
Note: The number of protons contributing to signal will depend on volume
from which the signal arises (voxel size).
Basic Physics of MRI
• Radio Frequency (RF)
• B1(f) is magnetic field
rotating at frequency = f
• Resonance Condition:
f = Larmor frequency
B1 is rotating
magnetic field
associated with
the RF pulse.
NOTE: coordinate system
Rotating B1
from RF pulse?
RF at Larmor frequency
will cause M to rotate
about B1 in rotating frame
of reference.
Basic Physics of MRI
Frequency of rotation of M
about B1 determined by
the magnitude (strength)
of B1.
Basic RF Pulse Concepts
RF Pulse
strength
duration
RF pulse duration and
strength determine flip
angle
Flip AngleRotation of Net
Magnetization (M)
Mo
Bo: magnetic field
B1: generated by the RF coil
α : flip angle
Bo
M0 : depends on proton density
α
B1
RF coil
y’
x’
When α = 90° then Mxy = M0 and Mz = 0
When α = 180° then Mxy = 0 and Mz = - M0
Sample
Basic Physics of MRI
FID = Free Induction Decay
• 90° RF pulse rotates M into
transverse (x-y) plane
• Rotation of M within transverse
plane induces signal in receiver
coil at Larmor frequency.
• Magnitude signal dependent on
Mxy.
FID magnitude decays in an
exponential manner with a
time constant T2. Decay due
to ‘spin-spin’ relaxation.
S (t )  S 0 e
t
T2
 sin( 2 ft )
Need for 180° Pulse - Spin
Echo
• FID also diminishes due to local static
magnetic field inhomogeneity
• Some spins precess faster and some
slower than those due to B0
90
°
180°
• 180 ° RF pulse reverses
dephasing at TE (echo time)
• Residual decay due to T2
Spin Echo Signal
Nuclear Magnetic Resonance
(NMR) Signal: Spin Echo (SE)
TR (repetition time) = time between RF excitation pulses
90o
90o
180o
FID
TE/2
Spin Echo
TE/2
TE = time from 90o pulse to center of spin echo
• A helium-cooled
superconducting magnet
generates the static field.
– Always on: only quench
field in emergency.
– niobium titanium wire.
• Coils allow us to
– Make static field
homogenous (shims:
solenoid coils)
– Briefly adjust magnetic
field (gradients: solenoid
coils)
– Transmit, record RF
signal (RF coils:
antennas)
MRI Scanner
Anatomy
Superconductor Magnet
Necessary Equipment
3T magnet
Magnet
RF Coil
gradient coils
(inside)
Gradient Coils
RF Coil
Gradient Coils
Sounds generated during imaging due to mechanical stress within gradient coils.
MRI Scanner Components
RF Coil
• RF Coils can transmit and receive RF signals
(i.e. apply B1 and monitor Mxy)
• A typical coil is a tuned LC circuit and may be
considered a near-field antenna
www.fmrib.ox.ac.uk/~karla/
RF Coils or Antennas
• The MRI antenna is called a coil.
• Use different coils for different body parts.
• For brains, the most common antenna is the head coil
(surrounds the volume of interest)
• S coils: better signal for a small region near the coil.
Head coil
Surface coil
Volume coil
Surface coil
NSM-P035 Permanent Magnet MRI
Comprehensive Receiving coils
 7 standard configuration：
QD head coil
QD Extremity Coil
QD Neck Coil
Flat Spine Coil
QD Body Coil
Breast Coil
Signal and Field Strength
• In theory:
– Signal increases with square of
field strength
– Noise increases linearly with
field strength
– A 3T scanner should have twice
SNR of 1.5T scanner; 7T should
have ~4.7 times SNR of 1.5T.
• Unfortunately, physiological
artifacts also increase, so advantage
is less in practice.
• Benefits: speed, resolution
• Costs: Artifacts, RF heating,
wavelength effects, auditory noise, $
Making Images of the NMR
Signal
• Uniform magnetic field to set the stage (Main
Magnet)
• Gradient coils for positional information
• RF transceiver (excite and receive)
• Digitizer (convert received analog to digital)
• Pulse sequencer (controls timing of gradients,
RF, and digitizer)
• Computer (FFT to form images, store pulse
sequences, display results, archive, etc.)
Role of Gradient Coils
• Coils that produce magnetic field gradients
along x-,y-,and z-directions to encode spatial
information
• Selective excitation: (during RF) excite those
spins within a thin “slice” of the subject
• Frequency encoding: (during readout) make the
signal’s frequency depend on position
• Phase encoding: (between excitation and
readout) make the signal’s phase depend on
position
Gradient Magnetic
Fields for Gz
• Field Characteristics
• Gradient field direction parallel to B0
• Created by Maxwell Pair
— currents are anti-parallel (opposite direction)
Coil 2
Coil 1
BG
Total Field
• Total Field
• Sum of Main Magnet and Gradient Fields
• In practice a “shim” field is also used to “flatten” the field.
B0=BM+BG
DB0 ~ 1mT
Gradient field
decreases total
Gradient field
increases total
Spatial Encoding by Gradient
Fields
• Field varies (almost) linearly
• Field magnitude changes with z
here
• Frequency changes with z
• Delta B0 = 0 at z = 0 for balanced
system
• Gradient units (T/m)
DB0  G z z
f  g B 0  D B 0 
DB= 0.001 T
Dz = 0.25 m
DB/ Dz = 0.004 T/m
~ 172 kHz/m
Slice Selection
During RF excitation, a linear gradient is applied. Only a “slice” of the sample is
excited.
f
f=g(B0 + Gss)
Thickness
Slice Location
center of RF
frequency range
s
TH = BWRF/ g Gs
RF Field Generation
• RF Coils
 Transmit RF Field (B1)
— Transmitter at frequency
f0
with bandwidth
Df
 Receive signal from Mxy
— Receiver tuned to frequency f0
Head
Transmitter/
Receiver
Body
Transmitter/
Receiver
fo
t
fo
FT
Df = 1/ t
Frequency encoding
During signal readout, a gradient is applied in one direction:
B(x) = B0 + Gxx
f(x) = g{B0 + Gxx}
D f(x) = g Gxx
Mxy
f(x)
The precession frequency of the net magnetization Mxy depends on x-location. A
Fourier transform of the time signal can determine where the nuclei are along the
x-direction.
Phase encoding
Between excitation and readout a gradient is applied in one direction. This is
done in small increments (once per TR) such that the summed effect is similar
to frequency encoding.
B(y) = B0 + Gyy
f(y) = g{B0 + Gyy}
Df (y) = g Gyy
Mxy
f (y)
The phase difference depends on y-location. When phase encoding is
complete a Fourier transform of the signal tells us where the nuclei are along
the y-direction.
Frequency and Phase Encoding
for a 2D MRI
RF Excitation
Select slice (Gs)
Phase Encode (Gp)
Repeat this
many times
with Gp
changed
each time
Frequency encode (Gf)
Readout
Slice Select for Brain Orientation: Gx – sagittal; Gy – coronal; Gz - axial
Making an Image
k-space (frequency
domain)
A k-space domain
image is formed using
frequency and phase encoding
Two Spaces
Image space
y
k-space
ky
FT-1
kx
x
FT
Acquired Data
MRI task is to acquire k-space image then
transform to a spatial-domain image. kx is
sampled (read out) in real time to give N
samples. ky is adjusted before each readout.
Final Image
MR image is the magnitude
of the Fourier transform of
the k-space image
The k-space Trajectory
Equations that govern 2D k-space trajectory
kx = g0t Gx(t) dt
if Gx is constant
kx = gGxt
ky = g0t’ Gy(t) dt
if Gy is constant
ky = gGyt’
The kx, ky frequency coordinates are established
by durations (t) and strength of gradients (G).
Simple MRI Frequency Encoding:
RF Excitation
Slice
Selection (Gz)
Frequency
Encoding (Gx)
digitizer on
Readout
Exercise drawing k-space manipulation
The k-space Trajectory
Frequency
Encoding
Gradient
(Gx)
Move to left
side of k-space.
(0,0)
ky
Digitizer records N
samples along kx
where ky = 0
kx
Simple MRI Frequency Encoding: Spin
Echo
Excitation
Slice
Selection
Frequency
Encoding (Gx)
digitizer on
Readout
Exercise drawing k-space representation
The K-space Trajectory
180 pulse
Digitizer records N
samples of kx
where ky = 0
Frequency and Phase Encoding for 2D
Spin Echo Imaging
90
180
Excite
Slice
Select
kx
ky
Frequency
Encode
Phase
Encode
digitizer on
Readout
The 2D K-space Trajectory
180 pulse
Digitizer records N
samples of kx and
N samples of ky
2D Fourier Imaging
Raw 2D k-space data
Processed data
Magnitude of Fourier transform
Imaging time - Np TR
Calculation of the Field of View (FOV)
along frequency encoding direction
Using Gx for frequency encoding let the readout FOV range from -xm to +xm
Within this FOV frequencies range from g(B0 - Gx xm) to + g(B0 + Gx xm)
Frequency change is 2 g Gx xm.
Since 2 xm = FOV then the frequency range is g Gx FOV
RF receiver bandwidth (BW) is adjusted to cover this range of frequencies.
Therefore BW = g Gx FOV.
FOVf = BW/(g*Gf )
• If BW is fixed increasing Gf reduces FOV
• If Gf is fixed increasing BW increases FOV
Same as equation for slice
thickness seen before
RF Receiver Bandwidth and Digitizer
Sampling Rate
BW = 2 fmax in MRI (-fmax to +fmax)
Digitizer must sample at rate Rs = 2 fmax to
avoid aliasing so Rs = BW.
Example: For receiver with BW = 32 kHz
With Rs = 32K samples/second what is time to acquire
one line of 256 samples along kx?
256 samples/32K samples/sec = 8 msec.
Calculation of the Field of View (FOV)
along phase encoding direction
g Gp FOVp = Np / Tp
where Tp is the duration and Np the number
of the phase encoding gradients, Gp is the
maximum amplitude of the phase encoding
gradient.
FOVp = (Np / Tp)/ (gGp )
More Example Calculations
What is BW/pixel if BW = 32 kHZ in 256x256 image?
32 kHz/256 pixels = 125 Hz/sample.
What is spread in Larmor frequencies for a 3T magnet
with 0.1 ppm range in B0 within a voxel?
3T x 43 mHz/T = 129 MHz
129 x106 Hz x 0.1/1x106 = 12.9 Hz
What is potential phase shift at TE = 20 msec due to this
inhomogeneity?
12.9 cycles/sec-1 x 20 x10-3 sec = 0.258 of a cycle
Partial Fourier or K-Space Imaging to Shorten
Scan Time
k
y
2
5
6
kx
256
256
Decreasing number of phase (ky) lines reduces
scan time proportionally.
1
2
8
256
Decreases y-direction spatial resolution.
Half Fourier Imaging
ky
2
5
6
kx
256
ky
1
2
8
kx
256
Retains resolution but decreased SNR
Developing Contrast Using
Weighting
• Contrast = difference in image values between different
tissues
• T1 weighted example: gray-white contrast is possible
because T1 differs between these two types of tissue
T1 and T2
• T1-Relaxation: Recovery
– Recovery of longitudinal
orientation of M along z-axis.
– ‘T1 time’ refers to time interval for
63% recovery of longitudinal
magnetization.
– Spin-Lattice interactions.
• T2-Relaxation: Dephasing
– Loss of transverse magnetization
Mxy.
– ‘T2 time’ refers to time interval for
37% loss of original transverse
magnetization.
– Spin-spin interactions,and more.
Properties of Body Tissues
Tissue
T1 (ms) T2 (ms)
Grey Matter (GM)
950
100
White Matter (WM)
600
80
Muscle
900
50
Cerebrospinal Fluid (CSF) 4500
2200
Fat
250
60
Blood
1200
100-200
T1 values for B0 ~ 1Tesla.
T2 ~ 1/10th T1 for soft tissues
Average Values of T1 and T2 in the
Human Brain
Relaxation Times (msec)
Tissue
1.5T
3.0T
4.0T
WM-T1
640
860
1040
GM-T1
880
1200
1410
WM-T2
80
80
50
GM-T2
80
110
50
Large frequency dependence for T1 values.
Data from textbook.
Basic Physics of MRI: T1 and T2
T1 is shorter in fat (large
molecules) and longer in
CSF (small molecules). T1
contrast is higher for lower
TRs.
(sec)
T2 is shorter in fat and longer
in CSF. Signal contrast
increased with TE.
(msec)
• TR determines T1 contrast
• TE determines T2 contrast.
T1 & T2 Weighting – Spin Echo
T1 Contrast Weighting
• T1W Contrast
 Echo (TE) at T2 contrast min
 Repeat (TR) at T1 contrast max
• T2W Contrast
TR
 Echo (TE) at T2 contrast max
 Repeat (TR) at T1 contrast min
TE
Min T2 Contrast
Max T1 Contrast
T2 Contrast Weighting






T1
T2
  e

S  S 0  1  e
   
TR
re cov ery
TE
TR
TE
decay
Min T1 Contrast
Max T2 Contrast
Contrast, Imaging Parameters
T1W
S (TR ,TE )  r 1  e
or

r 1  e
T2W
 TR / T1
 TR / T1

e
e
 TE / T 2
*
 TE / T 2


SE
GRE
r- proton density
SE – spin echo imaging
GRE – gradient echo imaging
Short TEs reduce T2W
Long TRs reduce T1W
PDW
Three Common Clinical MRIs
T1W
T2W
Largest Signal
Good GM-WM Contrast
Note: Display contrast adjusted for best viewing of each.
Fluids are bright
Inversion Recovery T1 Contrast
So
S = So * (1 – 2 e –t/T1)
S = So * (1 – 2 e –t/T1’)
-So
Sampling signal at this time
suppresses tissue with T1’
T2W
Inversion Recovery
(CSF Attenuated)
Gradient Echo Imaging
• Signal is generated by magnetic field
refocusing mechanism only (the use of
negative and positive gradient)
• Signal intensity is governed by
S = So e-TE/T2*
• Can be used to measure T2* value of the
tissue
• R2* = R2 + R2ih +R2ph (R2=1/T2)
• Used in 3D and BOLD fMRI
ph – other phase related
MRI Pulse Sequence for Gradient
Echo Imaging
E.
Excitation
Slice
Selection
Frequency
Encoding
Phase
Encoding
digitizer on
Readout
Ernst angle (E) for optimum SNR .
cos(  E )  e
 TR
T1
FLASH Pulse Sequence
Gz
refocus
TR2
crusher
TR1
crusher
B1
Gy
Gx
acquire
Gy
Gx
Fig. 3.19. Courtesy of Peter Jezzard.
crusher
Gz
TRN/2
TRN
TRN/2
crusher
B1
TRN
TR2
TR1
2D Gradient Echo
RF (10-15 degrees)
Short TR (10-50 msec)
N= 256 (2.5-13 sec per slice)
3D Sequence (Gradient Echo)
read
acq
Gx
phase
Gy
Select
& phase
Gz
RF
B1
kz
kx
Scan time = NyNzTR
Good for high resolution T1W images of brain
ky
3D T1W
brain image
0.8mm spacing
Time = 25 min
2D Echo Planar
Imaging (EPI)
a)
b)
B1
Gz
refocus
Gy
Gx
acquire
Fig. 3.20. Courtesy of Peter Jezzard.
2d Gradient Echo
Entire 2D slice within one TR
64x64 or 128x128
Time per slice (30-50 msec)
Whole volume (2-4 sec)
Good for fMRI studies
FLASH Image T2* Weighted
TE = 30 msec
CSF is bright
Signal loss and distortions due
to local differences in
magnetic field
Sources of Contrast in Brain
- Endogenous - BOLD
- Exogenous - could be
contrast agent (Gd based)
- Other - Susceptibility
R2* = net T2 relaxation rate = 1/T2*
Fig. 3.23 courtesy of Peter Jezzard.
R2* = R2tis + R2ih + R2BOLD + R2suc
BOLD EPI Functional MRI
Task
Rest
3%
Subtraction converted
to t- or z-values
(Task - Rest)
z = (Task - Rest)/SDTask-Rest
0
R
L
fMRI (BOLD EPI) – With Statistical Parametric
Mapping
R Finger
Tongue
z-values > 3
3D Surface Views
R Finger
Movement
Tongue
Movement