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

MR imaging is based on precession z y x [courtesy William Overall] Spins precess at the Larmor rate: = g (B0 + DB) field strength field offset

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 B0 High field Low field Make color gradient on arrows & fast->slow precession?

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 B0 Fast precession High field Low field Make color gradient on arrows & fast->slow precession? Slow precession

Simple “imaging” experiment (1D) increasing field

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 1D Signal 1D “Image” 1DFT 2D Signal kx ky 2D Image x y 2DFT

Analogy: Weather Mapping

(frequency-, or k-space) 2D Fourier Transform 2DFT kx ky x y 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 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 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 FT 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-space kx ky kx 2 kxmax What is the highest frequency we need to sample in k-space (kmax)? How close should the samples be in k-space (Dk)?

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

Frequency spectrum

Frequency spectrum

Frequency spectrum

Frequency spectrum

Frequency spectrum

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 increasing kmax kymax kxmax kxmax kymax 2 kxmax kmax determines image resolution Large kmax means high resolution !

Sampling k-space kx ky kx 2 kxmax 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 A given frequency must be sampled at least twice per cycle in order to reproduce it accurately 1 samp/cyc 2 samp/cyc Cannot distinguish between waveforms Upper waveform is resolved!

Nyquist Sampling Theorem increasing field Insufficient sampling forces us to interpret that both samples are at the same location: aliasing

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 kx 2 kxmax x = 1/(2*kxmax) FOV = 1/kx

k-space relations: FOV and Resolution kx ky kx 2 kxmax 2 kxmax = 1/x xmax = 1/kx k-space and image-space are inversely related: resolution in one domain determines extent in other

k-space Image Full-FOV, Full sampling high-res 2DFT Full-FOV, low-res: blurred Reduce kmax Low-FOV, high-res: may be aliased Increase k

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 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 !

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

Many possible trajectories through k-space…

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 : SNR   Ttotal =  N  Tread

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 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-space c+id a+ib aib cid 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 ky missing data kx

Multiple approaches Acquire half of each frequency encode kx ky kx ky Acquire half of each frequency encode Reduced phase encode steps

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

Slice Selection RF frequency 0 gradient Gz excited slice

2D Multi-slice Imaging t1 t2 t3 t4 t5 t6 excited slice All slices excited and acquired sequentially (separately) Most scans acquired this way (including FMRI, DTI)

“True” 3D imaging excited volume 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 Formation Gradients and spatial encoding Sampling k-space Trajectories and acquisition strategies Fast imaging Acquiring multiple slices Image reconstruction and artifacts

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

Gibbs Ringing (Truncation) Abruptly truncating signal in k-space introduces “ringing” to the image

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

EPI unwarping (FUGUE) Field map tells us where there are problems uncorrected corrected Field map tells us where there are problems Estimate distortion from field map and remove it

EPI Trajectory Errors Left-to-right lines offset from right-to-left lines Many causes: timing errors, eddy currents…

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 = + undersampled

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