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![Spins precess at the Larmor rate:
= (B0 + B)
MR imaging is based on precession
]
field strength field offset
x
y
z](https://image.slidesharecdn.com/mriimageformation-k-space1-250908130950-119babbc/85/MRI-IMAGE-FORMATION-K-SPACE-5-320.jpg)
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MRI IMAGE FORMATION -K-SPACE .
- 1. MRI Image Formation DARSHAN.B.S. MEDICAL IMAGING TECHNOLOGIST. DEPARTMENT OF RADIODIAGNOSIS.KMIO.BENGALORE
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- 4. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
- 5. Spins precess atthe Larmor rate: = (B0 + B) MR imaging is based on precession ] field strength field offset x y z
- 6. Magnetic Gradients Gradient: Additionalmagnetic 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 High field Low field B0
- 7. • Spins ateach 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 Magnetic Gradients Fast precession Slow precession B0 High field Low field
- 8. Simple “imaging” experiment(1D) increasing field
- 9. Simple “imaging” experiment(1D) Fourier transform Signal “Image” Fourier Transform: determines amount of material at a given location by selectively “listening” to the corresponding frequency position
- 10. 2D Imaging via2D Fourier Transform 2DFT 2D Image x y 2D Signal kx ky 1D Signal 1D “Image” 1DFT
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- 12. 2D Fourier Transform 2DFT Measuredsignal (frequency-, or k-space) Reconstructed image Fourier Transform can be applied in any number of dimensions MRI: signal acquired in 2D frequency space (k-space) (Usually) reconstruct image with 2DFT x y kx ky
- 13. Gradients and imageacquisition • 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
- 14. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
- 15. Sampling k-space Perfect reconstructionof an object would require measurement of all locations in k-space (infinite!) Data is acquired point-by-point in k-space (sampling) 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
- 16. Sampling k-space 1. Whatis the highest frequency we need to sample in k-space (kmax )? 2. How close should the samples be in k-space (k)? kx ky kx 2 kx max
- 17. Frequency spectrum What isthe 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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- 23. Frequency spectrum Higher frequencies makethe reconstruction look more like the original object! Large kmax increases resolution (allows us to distinguish smaller features)
- 24. 2D Extension increasing kmax 2kx max kx max kx max ky max ky max kmax determines image resolution Large kmax means high resolution !
- 25. Sampling k-space 1. Whatis the highest frequency we need to sample in k-space (kmax )? 2. How close should the samples be in k-space (k)? kx ky kx 2 kx max
- 26. Nyquist Sampling Theorem Agiven 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!
- 27. Insufficient sampling forces usto interpret that both samples are at the same location: aliasing Nyquist Sampling Theorem increasing field
- 28. Aliasing (ghosting): inabilityto differentiate between 2 frequencies makes them appear to be at same location Applied FOV Aliased image max ive frequency max ive frequency x x
- 29. k-space relations: FOV andResolution x = 1/(2*kx max ) FOV = 1/kx kx ky kx 2 kx max
- 30. k-space relations: FOV andResolution 2 kx max = 1/x xmax = 1/kx kx ky kx 2 kx max k-space and image-space are inversely related: resolution in one domain determines extent in other
- 31. k-space Image Full samplingFull-FOV, high-res Full-FOV, low-res: blurred Low-FOV, high-res: may be aliased Reduce kmax Increase k 2DFT
- 32. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
- 33. Visualizing k-space trajectories k-spacelocation is proportional to accumulated area under gradient waveforms Gradients move us along a trajectory through k- space ! kx(t) = Gx() d ky(t) = Gy() d
- 34. Raster-scan (2DFT) Acquisition Acquirek-space line-by-line (usually called “2DFT”) Gx causes frequency shift along x: “frequency encode” axis G causes phase shift along y: “phase ecode” axis
- 35. Echo-planar Imaging (EPI)Acquisition Single-shot (snap-shot): acquire all data at once
- 36. Many possible trajectoriesthrough k-space…
- 37. Trajectory considerations • Longerreadout = 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
- 38. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
- 39. Partial k-space If objectis entirely real, quadrants of k-space contain redundant information a+ib aib c+id cid ky kx 1 2 4 3
- 40. Partial k-space Idea: justacquire half of k-space and “fill in” missing data Symmetry isn’t perfect, so must get slightly more than half measured data missing data a+ib aib c+id cid ky kx 1
- 41. Multiple approaches kx ky Reduced phase encodesteps Acquire half of each frequency encode kx ky
- 42. Parallel imaging (SENSE, SMASH,GRAPPA, iPAT, etc) Object in 8-channel array Single coil sensitivity Surface coils Multi-channel coils: Array of RF receive coils Each coil is sensitive to a subset of the object
- 43. Object in 8-channel array Singlecoil sensitivity Surface coils 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 Parallel imaging (SENSE, SMASH, GRAPPA, iPAT, etc)
- 44. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
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- 46. 2D Multi-slice Imaging excitedslice All slices excited and acquired sequentially (separately) Most scans acquired this way (including FMRI, DTI) t1 t2 t3 t4 t5 t6
- 47. “True” 3D imaging Repeatedlyexcite 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 excited volume excited volume
- 48. Image Formation • Gradientsand spatial encoding • Sampling k-space • Trajectories and acquisition strategies • Fast imaging • Acquiring multiple slices • Image reconstruction and artifacts
- 49. Motion Artifacts Motion causesinconsistencies between readouts in multi-shot data (structurals) Usually looks like replication of object edges along phase encode direction PE
- 50. Gibbs Ringing (Truncation) Abruptlytruncating signal in k-space introduces “ringing” to the image
- 51. EPI distortion (warping) Fieldmap EPI image (uncorrected) field offset Magnetization precesses at a different rate than expected Reconstruction places the signal at the wrong location image distortion
- 52. EPI unwarping (FUGUE) fieldmap uncorrected Field map tells us where there are problems Estimate distortion from field map and remove it corrected
- 53. EPI Trajectory Errors Left-to-rightlines offset from right-to-left lines Many causes: timing errors, eddy currents…
- 54. EPI Ghosting = + undersampled Shiftedtrajectory is sum of 2 shifted undersampled trajectories Causes aliasing (“ghosting”) To fix: measure shifts with reference scan, shift back in reconstruction
- 55. Image Formation Matlab exercises(self-contained, simple!) k-space sampling (FOV, resolution) k-space trajectories
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