This document discusses k-space and parallel imaging techniques in MRI. It can be summarized in 3 sentences: K-space is how MRI data is stored, with the center representing low spatial frequencies and edges representing high frequencies. Parallel imaging techniques like SENSE acquire undersampled k-space data using multiple receiver coils, and use the coils' sensitivity profiles to reconstruct a full k-space image without aliasing. Faster k-space filling methods like EPI acquire k-space along non-Cartesian trajectories like spirals to reduce scan time for applications like fMRI and perfusion imaging.

1. K SPACE
AND
PARALLEL IMAGING
ASHIK E H
DAMIT,SCTIMST
02/08/2018

2. OBJECTIVE
oProperties
oTrajectories of filling
oParallel imaging
oApplication

3. K STANDS FOR
• Wave number =k=1/Wavelength
• the number of waves or cycles per unit distance.
• kayser (K), where 1 K = 1 cm-1
• Greek word =krustallos kruos

4. K SPACE
•X Axis = Frequency encodings axis
•Y Axis = phase encodings axis
•Determine FOV
•Central line = seperate the + &- ve
half of k space
•Above and Below=determine + &- ve
half
•Stored-pfile

5. K SPACE
kx
ky

6. K SPACE
FT

7. PROPERTIES OF K SPACE
oCONTRAST
oRESOLUTION
oPOINT SYMMETRY
oFOV

8. CENTRE OF K-SPACE
oLow spatial frequency
oImage contrast, brightness, and general shapes
K-SPACE (ONLY CENTER FILLED ))
FT

9. PERIPHERY OF K-SPACE
oHigh spatial frequency
oedges, details, sharp transitions-resolution
FT

11. POINT SYMMETRY
Phase-conjugate symmetry lead to
Siemens - "Half Fourier
Philips and Hitachi -"Half scan".
GE-½-NEX" or "Fractional NEX"

12. FOV
o FOV refers the distance ( cm/mm) over which an MR
image is acquired or displayed.
o Δk = 1/FOV.
oΔk =spacing between samples in k space
oΔw = 1/kFOV. Δw is the pixel width
FT

13. K SPACE FILLING
oCartesian trajectories
oNon Cartesian trajectories.
oEcho planar.

14. Cartesian trajectories
 Uses a line by line rectilinear trajectory.
 One line is get filled for each TR.
 This trajectory can be done with
SE,GRE,IR,and other pulse sequences.

15. LINEAR REORDERING

16. CENTERIC REORDERING

17. REVERSE CENTERIC REORDERING

18. FAST K SPACE FILLING TECHNIQUES
 Partial Fourier imaging
 Radial imaging
 Spiral imaging
 Keyhole imaging
 EPI imaging

19. HALF K-SPACE” ACQUISITION
 Only part of k-space is measured.
 The unmeasured points are estimated by conjugate symmetry
through the center of k-space.

20. Siemens - "Half Fourier
Philips and Hitachi -"Half scan".
GE-½-NEX" or "Fractional NEX"

21. PARTIAL FOURIER IMAGING
PARTIAL FOURIER IMAGING
PARTIAL FOURIER IMAGING
The spatial information in either half of the k-space
is identical
If only half of the data along the Ky is acquired , we
can reduce the imaging time
It reduce the SNR by a factor of 2,but no loss in
spatial resolution
Routinely used for time-resolved perfusion & MRA
Commonly used in conjunction with HASTE &
Balanced SSFP

22. Radial trajectory
The first MR images reconstructed - radial trajectory
Samples k space on radial lines passing through the center.
These lines of k space is sampled more densely in the center
than in the periphery.
So the center of k space is filled almost immediately after
excitation.
The motion artifacts propagate radially rather than along
one axis.

23. Radial trajectory

24. PROPELLER/BLADE/MULTIVANE
 Use -
Uncooperative patients that cannot
remain motionless during exam
 Benefit -
Reduces artifact from in-plane
motion
Other names for similar sequence
BLADE (Sie)
Reduces artifact from in-plane motion

25. SPIRAL IMAGING
Two orthogonal gradients are applied simultaneously
& oscillated during read out
Producing spiral trajectory through the the k space
Data collection begins at the center, then curved
towards its edges
Center of the k-space is sampled more densely than
the periphery
Multiple interleaved spirals are needed to collect
enough data for an image of moderate resolution

26. SPIRAL IMAGING

27.  Very shot echo time.
 Employed in several applications like f MRI of brain, ASL
coronary MR angiography etc.
Advantages & applications
 Usually multiple interleaved spirals are required to collect
enough data for image of moderate resolution.
K-Space Representation of
Spiral Image Acquisition

28. EPI
•Very fast-capable to acquire an entire MR image only
in a fraction of second
•Proposed by Mansfield and pykett in 1977
•All the lines in k-space are filled by multiple gradient
reversals, producing multiple echoes after a single RF
excitation
•sequence highly vulnerable to susceptibility artifacts
Types of EPI
(a) single shot
(b) multi shot

29. Single short EPI
• All the spatial encoding data of an image can be obtained
after a single RF excitation
• Frequency-encoding gradient oscillates rapidly from a + to - a
negative amplitude, forming a train of gradient echoes .
•Each echo is phase encoded differently by phase-encoding
blips on the phase
•Reduced imaging time, decreased motion artifact, and the
ability to image rapid physiologic processes of the human
body

30. Filling K-space for EPI
1. Because of the alternating
positive/negative readout
gradients,
k-space is filled in a “Zig-zag”
pattern.
2. Because this is a long train of
gradient echoes, we get
geometric distortions in the
image. This happens
whenever we take too long to
fill k-space for EPI. To
reduce this problem, we often
use “half k-space”
acquisition.
We measure these
We estimate these
(w/ the complex conjugates)

31. Multishot EPI
•Also called segmental EPI
•Readout is divided into multiple shots or segments
•Only a portion of k-space data is acquired with each
shot
•Shots are repeated until a full set of data is collected

32. Clinical applications of EPI
Diffusion imaging of the brain
Dynamic perfusion studies
Cardiac and abdominal imaging free of motion
artifact
Imaging of coronary arteries free of cardiac motion
artifact
Cine cardiac imaging with a single heart beat

33. KEYHOLE -IMAGING
Arrival of contrast
injection
Fast dynamic
scanning
Reconstruction
ky
kz
ky
kz
ky
kz
ky
kz1 2 3
ky
kz
mask

34. Centric Keyhole (4D TRAK - Philips)
• 2 regions only
• Centric version of keyhole
• Oval central & peripheries

35. Semi randomized Centric Keyhole (TWIST – Siemens)
• 2 regions only
• Central k-space sampled alternately with
incomplete peripheral k-space
• Peripheral k-space is acquired over many cycles

36. Multi-Centric Keyhole (TRICKS – GE)
4 regions (3 central + 1 peripheral)
• A-BA-CA-DRepeat
• Central > intermediate > peripheral k-spaces sampled with
decremental frequency
A
D
B
c

37. LIMITATION OF KEYHOLE IMAGING
• If any motion between the baseline higher resolution
images& dynamic contrast enhanced images, it will
produce misregistration between the contrast & fine
detail of the image
• Dramatic changes in signal intensities of acquired and
replaced k space data will create ghost artifacts

38. PARALLEL
IMAGING

39. Basic Requirements For Pl
High field MRI magnet
Phased array coil
High fast computer reconstruction system

40. NON PARALLEL/REGULAR IMAGING
Single/multiple surface coils may be used to detect
the MR signal
but their individual outputs are combined into one
aggregate complex signal that is digitized and
processed into the final image



41. PARALLEL IMAGING –FULL FOV
 Consider image with the field of view (FOV) as shown
and two
coils with the following sensitivities


Full FOV


Half FOV

42. Acceleration factor (R)
Which reduce the aquisition time
If we have M coil elements covering the FOV, we can skip up to [M-1]
lines for each line in k-space .
This can be fractional as well:
no of phase-encodes to cover k-space
R = –––––––––––––––––––––––––
no of phase-encodes used in acquisition
iPAT factor (Siemens)
ASSET factor (GE)
SENSE factor (Philips)

43. K-space
#Profiles
Time
R=2
cut to half both
• scan duration
• FOV

44. FT
FT
+
unwrap

45. • Under sampled k space resulting in aliasing artifact
• More the lines skipped more will be the aliasing
Specific reconstruction algorithm are used to locate
the aliased part and under go PI Imaging
reconstruction
• So, fundamental problem is PI is how to "unfold“
/unwrap the wrap around

46. SIGNAL TO NOISE RATIO
parallel

47. PHASED ARRAY COIL ELEMENTS
 It has multiple no :of coil element
 Uneven distribution of SNR throughout
volume i . e
- Very high SNR at the edge
- Lower in the middle
+ + + =

48. Sensitivity map
sensitivity map = The spatial sensitivity of each coil element
 A calibration scan is usually done to get sensitivity map
S2S1

49. Uses of phased array coil
In regular /Non PI imaging only problem related to spatial
sensitivity
Conventional use of
phased array [unaliased]

50. Uses of phased array coil [PI]
•Spatial sensitivity varies for each coil element
•Along conjunction with undersampling

51. FT
+
unwrap

52. Two Families of PAT
Image-based PAT k-space-based PAT
SENSE [Philips] SMASH
ASSET [GE] ARC [GE]
mSENSE[Siemens] GRAPPA [Siemens]
RAPID [Hitachi] iPAT [Siemens]
SPEEDER [Toshiba] SPEEDER [Toshiba]

53. K-SPACE BASED pMRI
Reconstruct images from each
elements, then untangle
IMAGE BASED pMRI
Untangle data to create fully
filled k space, then
reconstruct image
SENSE/ASSET methods reconstruct, then correct.
GRAPPA/ARC methods correct, then reconstruct.

54. SENSE
Introduced by Pruessmann et al
 first commercially available PI method (by PHILIPS)
 1 -sensitivity maps for each coil element short,low
resolution calibration scan.
 2-A reduced k space is MR data formed by fewer phase
encoding gradient steps in conjunction with phased
array coil
 3. Reconstruct partial FOV images from each coil
 [Sub sampled k space shows aliasing]
 4. Unfold/Combine partial FOV image by matrix
inversion

55. FFT
FFT
SENSE
RECON
FULL FOV
IMAGE
r FOV
IMAGES
COILCALIBRATION
COIL ELEMENT 1
COIL ELEMENT 2
UNDER SAMPLING IN
K-SPACE
SENSE (IMAGE BASED)

56. SPATIAL SENSITIVITY MEASURED BY
A]Acquire quick images from each element of coil
B]Reconstruct the full image using all elements
C]Image (a) divided by (b) gives a noisy
sensitivity map[C]
=A
B
[C]
D]Filtering smoothes out the noise, yielding
our sensitivity map [D] [D]

57. SENSE Reduces SNR
SENSE factor =1.0 SENSE factor =3.0
As SENSE factor increases, noisiness of the image
increases
SENSE
Artifact

59. Acquire , Reconstruct and Unfold

60. • In pre scan calibration- calculate the point by point sensitivity
of each elements of coil
• sensitivities of Coils 1 and 2 @A =S1A and S2A
• sensitivities of Coils 1 and 2 @B =S1B and S2B
• Pixel values from Coils 1 and 2 = P1 and P2
• P1 = A•S1A + B•S1B
P2 = A•S2A + B•S2B
• 2]MATRIX INVERSION TECHNIQUE-similalar to it

61. • 2]MATRIX INVERSION TECHNIQUE-similalar to it
• I = (SHψ-1S + λ-1)-1SHψ-1P
• S = coarse sensitivity profiles from the individual coils,
normalized for uniform signal by the body coil
• ψ = noise covariance matrix, representing noise increase
due to patient-specific interactions between coil elements.
• P = partial FOV images with aliasing
• I = final image at full FOV

62. Applications of SENSE
1. Cardiovascular-breath hold, real-time
2. CEMRA
3. Brain-f MRI

63. mSENSE
•Modified SENSE is a version of SENSE
•Which does not require a separate calibration scan
•Additional lines are acquired at the centre of k space
during diagnostic scan
•Central lines are extracted and reconstruct low
resolution,unaliased images
•This images used to provide sensitivity map
•Reduction factor R cannot achieve-additional k space
lines are required for calibrations.

64. SMASH
•Described by sodickson and manning
•Requires a prior estimation of the individual coil
sensitivities of the receiver array
•A linear combination of these estimated coil
sensitivities can directly generate missing phase
encoding steps,which would normally be performed by
using phase encoding magnetic field gradient
•The missing k space lines are restored prior to the FT

65. Requires a prior estimation of the individual coil
sensitivities of the receiver array
 the sensitivity values Ck(x,y) are combined with
appropriate linear weights nk (m) to generate composite
sensitivity profiles with sinusoidal spatial sensitivity
variations of the order m
 sensitivity maps are fit to the desired harmonic
modulations.[m=-0,1]
Unser sampled data with desired harmonic generate full
FOV K Space
Fourier transformed to yield the full-FOV reconstructed
image
SMASH reconstruction process.

68. GRAPPA
• Variation of smash
• Less dependant on coil geometry than SMASH
• Better SNR than SMASH

69. FOUR MAJOR STEPS IN GRAPPA [ARC]
• Data Acquisition
• Estimation of Missing Lines
• Generate Individual Coil Images
• Combine images of each coil

70. 1- DATA ACQUISITION
• Acquired MR signals are digitized,
demodulated and used to fill k space
• center of k-space with ACS caliberation
• [ACS are used to calculate weighting factors for
each coil ]
• others k space are under sampled

71. 2 Estimation of Missing Lines
• weighting factors for each coil-
reflect how each coil distorts,
smears, and displaces spatial
frequencies within the full FOV k-
space data
• combined with local known data
for each small region (known a
block or kernel
• 3-Generate Individual Coil Images
• 4-Combine images of each coil

73. ARC-
• ARC uses a full 3D kernel to synthesize missing target data
from neighbouring source data from all three imaging
directions.
• Thus, improved reconstruction accuracy with fewer required
calibration lines
• The end result is highly accelerated MR data acquisition with
improved image quality and fewer artifacts.
• .

75. CAIPIRINHA
• Controlled aliasing in parallel imaging results in higher
acceleration
• PI offered by Siemens with R≥4
• used primarily for 3D breath-hold abdominal imaging
• Aliasing controlled by providing individual slice with
different phase cycle by means of altering multiband RF
pulse.

76. phase offset improves the accuracy of reconstruction while reducing noise and aliasing.
Aliasing artifacts are still present but they are shifted to the corners of image space and
are less likely to become concentrated in a few locations.

77. Choosing Of PI Method [SENSE/GRAPPA]
 FACTORS
 Total Imaging Time/Speed. GRAPPA/ARC is a somewhat
longer sequence than SENSE/ASSET becoz :extra time for the
self-calibration of k-space lines
• Signal-to-noise SENSE/ASSET provides slightly higher SNR
• [ But same SNR @ R=0 ]
• Body Region accurate coil sensitivity maps may difficult to
obtain for SENSE/ASSET ;SO, GRAPPA/ARC is preffered

78. Choosing Of PI Method [SENSE/GRAPPA]
 FACTORS
 Motion: SENSE/ASSET may do poorly preferred due to
motion /recontruction artifact arise b/w calibration and
acquisition scans
 difficulty suspending respiration to exactly the same degree
between SENSE/ASSET calibration and imaging
 Field-of-view (FOV) GRAPPA/ARC is more tolerant toward
small FOVs
 SENSE/ASSET produce aliasing/wrap around if
full FOV < OBJECT Size
 Use in Single-Shot EPI : GRAPPA/ARC prefered becoz of less
distortion during reconstruction

79. Clinical Applications
• wide applicability: PI can be applied to nearly any pulse
sequence
• gains in acquisition speed can be used in a no: of
different ways
MR Angiography:
• Because of high acquisition speed, SNR, minimal
artifacts, and relatively high spatial resolution-it become
standard technique
Patient cooperative to hold breath [reduced aqu - time]
thus also reduce motion artifact

80. Clinical Applications
Not only reduce motion artifact ,but also also
diminish venous contamination, particularly in regions
where there is rapid venous return, such as the renal
and carotid arteries

81. Clinical Applications
• Time-resolved pulmonary MR angiography
Performed with a high temporal resolution

82. • The gains in speed by PI can alternatively be applied to
improve spatial resolution [so additional space encoding
steps is acquired]

83. • Helps to reduce artifacts

84. • PI optimizing the length of the arterial phase
• There by, characterize lesions that enhance in the
arterial phase and rapidly wash out, such as small
hepatocellular carcinomas, certain metastatic lesions
microadenoma

85. Cardiac Imaging
• reduce the total number and/or length of breath holds
required in an examination and thereby significantly
reduce the total examination time

86. Cardiac Imaging
• PI Technique helps to improve spatial and temporal
resolution of Coronal cardiac images

87. Advantage of parallel imaging…
 To reduce scan time
 To speed up single shot MRI method
 To reduce TE on long echo train methods
 To mitigate susceptibility , chemical shift and
other artifacts
 To decrease RF heating [SAR] by minimizing
number of RF pulse

88. Thank you