Post on 26-Dec-2015
Statistical Parametric Statistical Parametric MappingMapping
Chapter 3
Principles of Nuclear Magnetic Resonance and MRI
Many thanks to those that share their MRI slides online
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Peter Bandettini NIH
MRI Has Many Layers Of Complexity
…
Physics … Engineering … Technology … Applications … Interpretation …
Even subdivisions below have multiple layers of complexity
History: MRI
• Paul Lauterbur and Peter Mansfield won the Nobel Prize in Physiology/Medicine (2003) for their pioneering work in MRI
• 1940s – Bloch & Purcell: Nuclear Magnetic Resonance
• 1990s - Discovery that MRI can be used to distinguish oxygenated blood from deoxygenated blood. Leads to Functional Magnetic Resonance imaging (fMRI)
• 1973 - Lauterbur: gradients for spatial localization of images
• 1977 – Mansfield: first image of human anatomy, first echo planar image (a fast imaging technique)
Basic Physics of MRI
• Why does neutron have magnetic properties?• What about electron(s) magnetic properties?
• 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
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.
Nuclear magnetic moments precess
about B0.
Nuclei spin axis not parallel to B0 field
direction.
Field Strength and the Net Magnetization (M)
NL
NU = 1,000,000
~ 1,000,000 + 10
1.5 T
~ 1,000,000 + 15
= 1,000,000 - 5
...
...
NL
NU
ΔE3.0T = 2*ΔE1.5T ΔE1.5T
..
...
NNLL = # /volume in low energy state = # /volume in low energy state
NNUU = # /volume high energy state = # /volume high energy stateM (N(NLL - N - NUU))
Lowering temperature increases M – Any volunteers?
MM3.0 T
Basic Physics of MRI• Frequency of precession of magnetic moments given
by Larmor relationship
~ 43 mHz/Tesla
Larmor frequencies of RICs MRIs
3T ~ 130 mHZ7T ~ 300 mHz
11.7T ~ 500 mHz
f = f = x B x B00
f = Larmor frequency (mHz) = Gyromagnetic ratio (mHz/Tesla)B0 = Magnetic field strength (Tesla)
NMRable Nuclei
Basic Physics of MRI
Body Body 11H content is high due to water (>67%)H content is high due to water (>67%) Hydrogen protons in mobile water are primary Hydrogen protons in mobile water are primary
source of signals in fMRI and aMRIsource of signals in fMRI and aMRI
• 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 anti-parallel 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.
Basic Physics of MRI
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.
RF at Larmor frequency will cause M to rotate
about B1 in rotating frame of reference.
Rotating B1 Rotating B1 from RF pulse?from RF pulse?
NOTE: coordinate system
Basic Physics of MRI
RF pulse duration and strength determine flip
angle
duration
strength
RF Pulse
Frequency of rotation of M about B1 determined by the magnitude (strength)
of B1.
Basic RF Pulse Concepts
Flip AngleRotation of Net Magnetization (M)
Mo
x’
Bo
α
B1
Bo: magnetic fieldB1: generated by the RF coilα : flip angle
When α = 90° then Mxy = M0 and Mz = 0When α = 180° then Mxy = 0 and Mz = - M0
y’RF coil
Sample
M0 : depends on proton density
Basic Physics of MRI
FID magnitude decays in an exponential manner with a time constant T2. Decay due to ‘spin-spin’ relaxation.
• 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. )2sin()( 2
0 fteStS Tt
π⋅=−
FID = Free Induction Decay
Need for 180° Pulse - Spin Echo
90°
180°0
TE
TE/2 -
timeTE/2+
• FID also diminishes due to local static FID also diminishes due to local static magnetic field inhomogeneitymagnetic field inhomogeneity
• Some spins precess faster and some Some spins precess faster and some slower than those due to Bslower than those due to B00
• 180 180 ° RF pulse reverses RF pulse reverses dephasing at TE (echo time)dephasing at TE (echo time)
• Residual decay due to T2Residual decay due to T2 Spin Echo Signal
Nuclear Magnetic Resonance (NMR) Signal: Spin Echo (SE)
TE/2 TE/2
90o
TR (repetition time) = time between RF excitation pulses
90o 180o
FID Spin Echo
TE = time from 90o pulse to center of spin echo
MRI Scanner Anatomy
• 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)
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
RF Coils or Antennas
Volume coil
• 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.
Surface coilHead coil
www.fmrib.ox.ac.uk/~karla/
Surface coil
NS
M-P
035
Per
man
ent
Mag
net
MR
I
Comprehensive Receiving coils
7 standard configuration:QD head coil QD Neck Coil QD Body Coil
QD Extremity Coil Flat Spine 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 Making Images of the NMR SignalSignal
• 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 encodingPhase 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 1
Coil 2
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
Gradient field decreases total
Gradient field increases total
B0 ~ 1mT
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)
€
B0 =G z⋅z
f ≅ γ B0 + ΔB0( )
B= 0.001 T z = 0.25 m B/ z = 0.004 T/m
~ 172 kHz/m
Slice SelectionDuring RF excitation, a linear gradient is applied. Only a “slice” of the sample is excited.
Slice Location
center of RF frequency range
f=(B0 + Gsss)
Thickness
TH = BWRF/ Gs
s
f
• RF Coils Transmit RF Field (B1)
—Transmitter at frequency f0 with bandwidth
ff Receive signal from Mxy
—Receiver tuned to frequency f0
RF Field Generation
tt
ffoo
ff = 1/ t= 1/ t
FTFT
ffoo
Body Transmitter/Receiver
Head Transmitter/Receiver
Frequency encoding
Mxy
f(x)
B(x) = B0 + Gxx
f(x) = {B0 + Gxx}
f(x) = Gxx
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.
During signal readout, a gradient is applied in one direction:
Phase encoding
Mxy
f (y)
B(y) = B0 + Gyyf(y) = {B0 + Gyy}
f (y) = Gyy
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.
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.
Frequency and Phase Encoding for a 2D MRI
Select slice (Gs)
Phase Encode (Gp)
Frequency encode (Gf)
Repeat this many times with Gp changed each time
Slice Select for Brain Orientation: GSlice Select for Brain Orientation: Gxx – sagittal; G – sagittal; Gyy – coronal; G – coronal; Gzz - axial - axial
RF Excitation
Readout
Making an ImageMaking an Image k-space k-space (frequency (frequency
domain)domain)
A k-space domain image is formed using
frequency and phase encoding
Two Spaces
FTFT
FTFT-1-1
k-spacek-space
kkxx
kkyy
Acquired DataAcquired Data
Image spaceImage space
xx
yy
Final ImageFinal Image
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.
MR image is the magnitude of the Fourier transform of the k-space image
The k-space Trajectory
kx = kx = 00tt GGxx(t) dt(t) dt
ky = ky = 00t’t’ GGyy(t) dt(t) dt
if Gif Gyy is constant is constant ky = ky = GGyyt’t’
Equations that govern 2D k-space trajectoryEquations that govern 2D k-space trajectory
The kx, ky frequency coordinates are established by durations (t) and strength of gradients (G).
if Gif Gxx is constant is constant kx = kx = GGxxtt
Simple MRI Frequency Encoding:
digitizer ondigitizer on
RF ExcitationRF Excitation
SliceSliceSelection (GSelection (Gzz))
FrequencyFrequency Encoding (GEncoding (Gxx))
ReadoutReadout
Exercise drawing k-space manipulationExercise drawing k-space manipulation
The k-space Trajectory
Frequency Frequency Encoding Encoding Gradient Gradient
((GGxx))
kx
ky
(0,0)
Digitizer records N samples along kx where ky = 0
Move to left side of k-space.
Simple MRI Frequency Encoding: Spin Echo
digitizer ondigitizer on
ExcitationExcitation
SliceSliceSelectionSelection
FrequencyFrequency Encoding (GEncoding (Gxx))
ReadoutReadout
Exercise drawing k-space representationExercise drawing k-space representation
Frequency and Phase Encoding for 2D Spin Echo Imaging
digitizer ondigitizer on
ExciteExcite
SliceSliceSelectSelect
FrequencyFrequencyEncodeEncode
PhasePhaseEncodeEncode
ReadoutReadout
9090 180180
kx
ky
2D Fourier Imaging
Magnitude of Fourier transform
Raw 2D k-space data Processed data
Imaging time - Np TR
Calculation of the Field of View (FOV)along frequency encoding direction
FOVFOVff = BW/( = BW/(*G*Gff ) )
Using Gx for frequency encoding let the readout FOV range from -xm to +xm
Within this FOV frequencies range from (B(B00 - G - Gx x xm) to + ) to + (B(B00 + G + Gx x xm))
Frequency change is 2 Frequency change is 2 G Gx x xm.
Since 2 xm = FOV then the frequency range is G Gxx FOV FOV
RF receiver bandwidth (BW) is adjusted to cover this range of frequencies. RF receiver bandwidth (BW) is adjusted to cover this range of frequencies. Therefore BW = Therefore BW = G Gxx FOV. FOV.
Same as equation for slice thickness seen before
• If BW is fixed increasing Gf reduces FOV• If Gf is fixed increasing BW increases FOV
RF Receiver Bandwidth and Digitizer RF Receiver Bandwidth and Digitizer Sampling RateSampling Rate
Example: For receiver with BW = 32 kHzExample: For receiver with BW = 32 kHz
With RWith Rss = 32K samples/second what is time to acquire = 32K samples/second what is time to acquire
one line of 256 samples along kx?one line of 256 samples along kx? 256 samples/32K samples/sec = 8 msec.256 samples/32K samples/sec = 8 msec.
BW = 2 fBW = 2 fmaxmax in MRI (-f in MRI (-fmaxmax to +f to +fmaxmax))
Digitizer must sample at rate RDigitizer must sample at rate Rss = 2 f = 2 fmaxmax to to
avoid aliasing so avoid aliasing so RRss = BW = BW..
Calculation of the Field of View (FOV)Calculation of the Field of View (FOV)along phase encoding directionalong phase encoding direction
GGp p FOV FOVpp = N = Npp / T / Tpp
where Twhere Tpp is the duration and N is the duration and Npp the number the number
of the phase encoding gradients, Gp is theof the phase encoding gradients, Gp is themaximum amplitude of the phase encodingmaximum amplitude of the phase encodinggradient.gradient.
FOVFOVpp = (N = (Npp / T / Tpp)/ ()/ (GGpp ) )
More Example CalculationsMore Example CalculationsWhat is BW/pixel if BW = 32 kHZ in 256x256 image?What is BW/pixel if BW = 32 kHZ in 256x256 image?
32 kHz/256 pixels = 125 Hz/sample.32 kHz/256 pixels = 125 Hz/sample.
What is spread in Larmor frequencies for a 3T magnet What is spread in Larmor frequencies for a 3T magnet with 0.1 ppm range in Bwith 0.1 ppm range in B00 within a voxel? within a voxel?
3T x 43 mHz/T = 129 MHz3T x 43 mHz/T = 129 MHz129 x10129 x1066 Hz x 0.1/1x10 Hz x 0.1/1x1066 = 12.9 Hz = 12.9 Hz
What is potential phase shift at TE = 20 msec due to this What is potential phase shift at TE = 20 msec due to this inhomogeneity?inhomogeneity?
12.9 cycles/sec12.9 cycles/sec-1-1 x 20 x10 x 20 x10-3-3 sec = 0.258 of a cycle sec = 0.258 of a cycle
kx
ky
256
256
256
256
128
Decreases y-direction spatial resolution.
Partial Fourier or K-Space Imaging to Shorten Scan Time
Decreasing number of phase (ky) lines reduces scan time proportionally.
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 TissuesTissue 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 Average Values of T1 and T2 in the Human BrainHuman 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.
T2 is shorter in fat and longer in CSF. Signal
contrast increased with TE.
• TR determines T1 contrast
• TE determines T2 contrast.
(msec)
(sec)
T1 & T2 Weighting – Spin Echo
• T1W Contrast Echo (TE) at T2 contrast min Repeat (TR) at T1 contrast max
• T2W Contrast Echo (TE) at T2 contrast max Repeat (TR) at T1 contrast min
T1 Contrast Weighting
T2 Contrast Weighting
TE
TR TE
TR
Min T2 Contrast Max T1 Contrast
Max T2 Contrast Min T1 Contrast
3214 34 21decay
T
TE
eryre
T
TR
eeSS ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
−−2
cov
10 1
Contrast, Imaging Parameters
- proton density- proton densitySE – spin echo imagingSE – spin echo imagingGRE – gradient echo imagingGRE – gradient echo imaging
Short TEs reduce T2WShort TEs reduce T2WLong TRs reduce T1WLong TRs reduce T1W
€
S(TR,TE)∝ ρ 1− e−TR /T1{ } e−TE /T2{ } SE
or ρ 1− e−TR /T1{ } e−TE /T2*
{ } GRE
T1W T2W
PDWPDW
T1WT1W
T2WT2W
Three Common Clinical MRIsThree Common Clinical MRIs
Note: Display contrast adjusted for best viewing of each.
Largest SignalLargest Signal
Good GM-WM ContrastGood GM-WM Contrast
Fluids are bright
Inversion Recovery T1 ContrastInversion Recovery T1 Contrast
-S-So
SSo
S = SS = Soo * (1 – 2 e * (1 – 2 e –t/T1–t/T1))
S = SS = Soo * (1 – 2 e * (1 – 2 e –t/T1’–t/T1’))
Sampling signal at this time suppresses tissue with T1’
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
digitizer ondigitizer on
ExcitationExcitation
SliceSliceSelectionSelection
FrequencyFrequency EncodingEncoding
PhasePhase EncodingEncoding
ReadoutReadout
€
cos(θE ) = e− TRT1Ernst angle (E) for optimum SNR .
E.
crus
her
crus
her
crus
her
crus
her
B1
Gz
Gx
Gy
B1
Gz
Gx
Gy
TR1 TR2
TRN/2 TRN
TR1
TR2
TRN/2
TRN
Fig. 3.19. Courtesy of Peter Jezzard.
refocus
acquire
FLASH Pulse Sequence
2D Gradient EchoRF (10-15 degrees)Short TR (10-50 msec)N= 256 (2.5-13 sec per slice)
3D Sequence (Gradient Echo)
Gx
Gy
Gz
B1
acq
kx
ky
kz
Scan time = NyNzTRGood for high resolution T1W images of brain
Select& phase
phase
read
RF
B1
Gz
Gx
Gy
Fig. 3.20. Courtesy of Peter Jezzard.
refocus
acquire
a) b)
2D Echo Planar Imaging (EPI)
2d Gradient EchoEntire 2D slice within one TR64x64 or 128x128Time per slice (30-50 msec)Whole volume (2-4 sec)Good for fMRI studies
Fig. 3.23 courtesy of Peter Jezzard.
FLASH Image T2* Weighted
TE = 30 msecCSF 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*
R2* = R2tis + R2ih + R2BOLD + R2suc
BOLD EPI Functional MRIBOLD EPI Functional MRI
RestTask
Subtraction converted to t- or z-values
3 %
0
R L
z = (Task - Rest)/SDTask-Rest
(Task - Rest)
fMRI (BOLD EPI) – With Statistical Parametric fMRI (BOLD EPI) – With Statistical Parametric MappingMapping
R Finger
Tongue
z-values > 3