MRI Image Formation

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MRI Image Formation
Karla Miller FMRIB Physics Group
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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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MR imaging is based on precession
z
y
x
courtesy William Overall

• Spins precess at the Larmor rate
• g (B0 DB)

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Magnetic Gradients

• Gradient Additional magnetic field which varies
  over space
• Gradient adds to B0, so field depends on position
• Precessional frequency varies with position!
• Pulse sequence modulates size of gradient

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Magnetic Gradients

• Spins at each position sing at different
  frequency
• RF coil hears all of the spins at once
• Differentiate material at a given position by
  selectively listening to that frequency

Fast precession
Slow precession
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Simple imaging experiment (1D)
increasing field
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Simple imaging experiment (1D)
Signal
Fourier transform
Image
position
Fourier Transform determines amount of material
at a given location by selectively listening to
the corresponding frequency
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2D Imaging via 2D Fourier Transform
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Analogy Weather Mapping
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2D Fourier Transform
2DFT
Measured signal (frequency-, or k-space)
Reconstructed image
FT can be applied in any number of
dimensions MRI signal acquired in 2D frequency
space (k-space) (Usually) reconstruct image with
2DFT
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Gradients and image acquisition

• Magnetic field gradients encode spatial position
  in precession frequency
• Signal is acquired in the frequency domain
  (k-space)
• To get an image, acquire spatial frequencies
  along both x and y
• Image is recovered from k-space data using a
  Fourier transform

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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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Sampling k-space
Perfect reconstruction of an object would require
measurement of all locations in k-space
(infinite!) Data is acquired point-by-point in
k-space (sampling)
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Sampling k-space

1. What is the highest frequency we need to sample
   in k-space (kmax)?
2. How close should the samples be in k-space (Dk)?

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Frequency spectrum
What is the maximum frequency we need to
measure? Or, what is the maximum k-space value
we must sample (kmax)?
FT
kmax
-kmax
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Frequency spectrum
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Frequency spectrum
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Frequency spectrum
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Frequency spectrum
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Frequency spectrum
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Frequency spectrum
Higher frequencies make the reconstruction look
more like the original object! Large kmax
increases resolution (allows us to distinguish
smaller features)
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2D Extension
increasing kmax
kymax
kxmax
?kxmax
?kymax
2 kxmax
kmax determines image resolution Large kmax
means high resolution !
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Sampling k-space

1. What is the highest frequency we need to sample
   in k-space (kmax)?
2. How close should the samples be in k-space (Dk)?

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Nyquist Sampling Theorem
A given frequency must be sampled at least twice
per cycle in order to reproduce it accurately
1 samp/cyc
2 samp/cyc
Upper waveform is resolved!
Cannot distinguish between waveforms
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Nyquist Sampling Theorem
Insufficient sampling forces us to interpret that
both samples are at the same location aliasing
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Aliasing (ghosting) inability to differentiate
between 2 frequencies makes them appear to be at
same location
x
x
Aliased image
Applied FOV
max ?ive frequency
max ?ive frequency
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k-space relationsFOV and Resolution
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k-space relationsFOV and Resolution
k-space and image-space are inversely related
resolution in one domain determines extent in
other
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k-space
Image
Full-FOV, high-res
Full sampling
2DFT
Full-FOV, low-res blurred
Reduce kmax
Low-FOV, high-res may be aliased
Increase ?k
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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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Visualizing k-space trajectories
kx(t) ? ?Gx(t) dt ky(t) ? ?Gy(t) dt
k-space location is proportional to accumulated
area under gradient waveforms Gradients move us
along a trajectory through k-space !
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Raster-scan (2DFT) Acquisition
Acquire k-space line-by-line (usually called
2DFT) Gx causes frequency shift along x
frequency encode axis Gy causes phase shift
along y phase ecode axis
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Echo-planar Imaging (EPI) Acquisition
Single-shot (snap-shot) acquire all data at once
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Many possible trajectories through k-space
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Trajectory considerations

• Longer readout more image artifacts
• Single-shot (EPI spiral) warping or blurring
• PR 2DFT have very short readouts and few
  artifacts
• Cartesian (2DFT, EPI) vs radial (PR, spiral)
• 2DFT EPI ghosting warping artifacts
• PR spiral blurring artifacts
• SNR for N shots with time per shot Tread

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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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Partial k-space
If object is entirely real, quadrants of k-space
contain redundant information
2
1
aib
cid
a?ib
c?id
ky
3
4
kx
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Partial k-space
Idea just acquire half of k-space and fill in
missing data Symmetry isnt perfect, so must get
slightly more than half
1
aib
cid
measured data
a?ib
c?id
missing data
ky
kx
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Multiple approaches
Reduced phase encode steps
Acquire half of each frequency encode
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Parallel imaging(SENSE, SMASH, GRAPPA, iPAT, etc)
Surface coils
Object in 8-channel array
Single coil sensitivity
Multi-channel coils Array of RF receive
coils Each coil is sensitive to a subset of the
object
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Parallel imaging(SENSE, SMASH, GRAPPA, iPAT, etc)
Surface coils
Object in 8-channel array
Single coil sensitivity
Coil sensitivity to encode additional
information Can leave out large parts of
k-space (more than 1/2!) Similar uses to partial
k-space (faster imaging, reduced distortion,
etc), but can go farther
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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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Slice Selection
RF
frequency
?0
gradient
Gz
excited slice
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2D Multi-slice Imaging
excited slice
All slices excited and acquired sequentially
(separately) Most scans acquired this way
(including FMRI, DTI)
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True 3D imaging
excited volume
Repeatedly excite all slices simultaneously,
k-space acquisition extended from 2D to 3D
Higher SNR than multi-slice, but may take
longer Typically used in structural scans
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Image Formation

• Gradients and spatial encoding
• Sampling k-space
• Trajectories and acquisition strategies
• Fast imaging
• Acquiring multiple slices
• Image reconstruction and artifacts

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Motion Artifacts
PE

• Motion causes inconsistencies between readouts in
  multi-shot data (structurals)
• Usually looks like replication of object edges
  along phase encode direction

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Gibbs Ringing (Truncation)

• Abruptly truncating signal in k-space introduces
  ringing to the image

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EPI distortion (warping)
field offset
image distortion
Field map
EPI image (uncorrected)
Magnetization precesses at a different rate than
expected Reconstruction places the signal at the
wrong location
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EPI unwarping (FUGUE)
field map
uncorrected
corrected
Field map tells us where there are
problems Estimate distortion from field map and
remove it
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EPI Trajectory Errors
Left-to-right lines offset from right-to-left
lines Many causes timing errors, eddy currents
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EPI Ghosting
Shifted trajectory is sum of 2 shifted
undersampled trajectories Causes aliasing
(ghosting) To fix measure shifts with
reference scan, shift back in reconstruction
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Image Formation Tutorial

• Matlab exercises (self-contained, simple!)
• k-space sampling (FOV, resolution)
• k-space trajectories
• Get file from FMRIB network
• http//www.fmrib.ox.ac.uk/karla/misc/imageform.tar
  
• Instructions in PDF
• Go through on your own (or in pairs), well
  discuss on Thursday