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MRI Image Formation. Karla Miller FMRIB Physics Group. Image Formation. Gradients and spatial encoding Sampling k -space Trajectories and acquisition strategies Fast imaging Acquiring multiple slices Image reconstruction and artifacts. field strength. field offset.

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mri image formation
MRI Image Formation

Karla Miller

FMRIB Physics Group

image formation
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
mr imaging is based on precession

field strength

field offset

MR imaging is based on precession

z

y

x

[courtesy William Overall]

Spins precess at the Larmor rate:

  • = g (B0 + DB)
magnetic gradients

High field

B0

Low field

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
magnetic gradients5

High field

B0

Low field

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

slide7

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

2d imaging via 2d fourier transform

y

ky

1D Signal

1D “Image”

x

kx

2DFT

1DFT

2D Signal

2D Image

2D Imaging via 2D Fourier Transform
2d fourier transform

y

ky

x

kx

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

gradients and image acquisition
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
image formation12
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
sampling k space

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

x x x x x x x x x x x x x

FT

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)

sampling k space14

kx

ky

kx

2 kxmax

Sampling k-space
  • What is the highest frequency we need to sample in k-space (kmax)?
  • How close should the samples be in k-space (Dk)?
slide15

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

slide21

Frequency spectrum

Higher frequencies make the reconstruction look more like the original object!

Large kmax increases resolution (allows us to distinguish smaller features)

2d extension
2D Extension

increasing kmax

kymax

kxmax

kxmax

kymax

2 kxmax

kmaxdetermines image resolution

Large kmaxmeans high resolution !

sampling k space23

kx

ky

kx

2 kxmax

Sampling k-space
  • What is the highest frequency we need to sample in k-space (kmax)?
  • How close should the samples be in k-space (Dk)?
nyquist sampling theorem
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

nyquist sampling theorem25

increasing field

Nyquist Sampling Theorem

Insufficient sampling

forces us to interpret

that both samples are

at the same location:

aliasing

slide26
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

k space relations fov and resolution

kx

ky

FOV = 1/kx

kx

x= 1/(2*kxmax)

2 kxmax

k-space relations:FOV and Resolution
k space relations fov and resolution28

kx

ky

xmax = 1/kx

kx

2 kxmax = 1/x

2 kxmax

k-space relations:FOV and Resolution

k-space and image-space are inversely related: resolution in one domain determines extent in other

slide29

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

image formation30
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
visualizing k space trajectories
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 !

slide32

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

echo planar imaging epi acquisition
Echo-planar Imaging (EPI) Acquisition

Single-shot (snap-shot): acquire all data at once

trajectory considerations

SNR   Ttotal =  N  Tread

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 :
image formation36
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
partial k space
Partial k-space

If object is entirely real, quadrants of k-space contain redundant information

2

1

c+id

a+ib

aib

cid

ky

3

4

kx

partial k space38
Partial k-space

Idea: just acquire half of k-space and “fill in” missing data

Symmetry isn’t perfect, so must get slightly more than half

1

c+id

a+ib

measured data

aib

cid

missing data

ky

kx

multiple approaches

ky

ky

kx

kx

Multiple approaches

Acquire half of each

frequency encode

Reduced phase

encode steps

parallel imaging sense smash grappa ipat etc
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

parallel imaging sense smash grappa ipat etc41
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

image formation42
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
slice selection
Slice Selection

RF

frequency

0

gradient

Gz

excited slice

2d multi slice imaging

t1

t2

t3

t4

t5

t6

2D Multi-slice Imaging

excited slice

All slices excited and acquired sequentially (separately)

Most scans acquired this way (including FMRI, DTI)

true 3d imaging

excited volume

“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

image formation46
Image Formation
  • Gradients and spatial encoding
  • Sampling k-space
  • Trajectories and acquisition strategies
  • Fast imaging
  • Acquiring multiple slices
  • Image reconstruction and artifacts
motion artifacts
Motion Artifacts

Motion causes inconsistencies between readouts in multi-shot data (structurals)

Usually looks like replication of object edges along phase encode direction

PE

gibbs ringing truncation
Gibbs Ringing (Truncation)

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

slide49

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

slide50

EPI unwarping (FUGUE)

field map

uncorrected

corrected

Field map tells us where there are problems

Estimate distortion from field map and remove it

epi trajectory errors
EPI Trajectory Errors

Left-to-right lines offset from right-to-left lines

Many causes: timing errors, eddy currents…

epi ghosting

=

+

undersampled

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

image formation tutorial
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), we’ll discuss on Thursday