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: = (B 0 + B) field strength field offset

Magnetic Gradients Gradient: Additional magnetic field which varies over space – Gradient adds to B 0, so field depends on position – Precessional frequency varies with position! – “Pulse sequence” modulates size of gradient High field B 0 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 High field Fast precession Low field Slow precession B 0

Simple “imaging” experiment (1 D) increasing field

Simple “imaging” experiment (1 D) Signal Fourier transform “Image” position Fourier Transform: determines amount of material at a given location by selectively “listening” to the corresponding frequency

2 D Imaging via 2 D Fourier Transform 1 DFT 1 D Signal 1 D “Image” 2 DFT ky y kx 2 D Signal x 2 D Image

Analogy: Weather Mapping

2 D Fourier Transform 2 DFT ky kx Measured signal (frequency-, or k-space) y x Reconstructed image FT can be applied in any number of dimensions MRI: signal acquired in 2 D frequency space (k-space) (Usually) reconstruct image with 2 DFT

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 x x x x x x x x x x 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 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)?

Frequency spectrum What is the maximum frequency we need to measure? FT Or, what is the maximum k-space value we must sample (kmax)? -kmax

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)

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

Sampling k-space kx ky kx 2 kxmax 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)?

Nyquist Sampling Theorem A given frequency must be sampled at least twice per cycle in order to reproduce it accurately 1 samp/cyc Cannot distinguish between waveforms 2 samp/cyc 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 max ive frequency Applied FOV x max ive frequency Aliased image

k-space relations: FOV and Resolution kx ky FOV = 1/ kx x = kx 1/(2*kxmax) 2 kxmax

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

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

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 kspace !

Raster-scan (2 DFT) Acquisition Acquire k-space line-by-line (usually called “ 2 DFT”) 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 & 2 DFT have very short readouts and few artifacts • Cartesian (2 DFT, EPI) vs radial (PR, spiral) – 2 DFT & 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 ky 1 c+id a+ib a ib c id 3 4 kx

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 ky a ib kx a+ib c id measured data missing data

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

Parallel imaging (SENSE, SMASH, GRAPPA, i. PAT, 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, i. PAT, 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 0 frequency gradient Gz excited slice

2 D Multi-slice Imaging excited slice t 1 t 2 t 3 t 4 t 5 t 6 All slices excited and acquired sequentially (separately) Most scans acquired this way (including FMRI, DTI)

“True” 3 D imaging excited volume Repeatedly excite all slices simultaneously, k-space acquisition extended from 2 D to 3 D 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 Field map image distortion EPI image (uncorrected) Magnetization precesses at a different rate than expected Reconstruction places the signal at the wrong location

EPI unwarping (FUGUE) field map uncorrected 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