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P2 PHYSICS > Image formation 1: k-space > Flashcards

Image formation 1: k-space Flashcards

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1
Q

How do you visualise phase?

A

Imagining a vector V of magnitude A rotating at a constant rate

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2
Q

What is the component of the vector in the x direction?

A

(co)sine wave

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3
Q

What is the phase of the wave?

A

The angle the vector makes with the axis at time t=0

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4
Q

How are pixels arranged in an MR image?

A

rows and columns in a matrix

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5
Q

What does each pixel in the reconstructed image contain?

A

A number related to signal intensity (location in the computer memory)

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6
Q

What does matrix control?

A

Not only image size but also raw data space (k-space)

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7
Q

What happens each time the sequence is repeated?

A

A full line of k-space is acquired
- Frequency encode direction [ x-direction]

This is repeated for every line in the phase encode [y-direction]

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8
Q

What happens as sequence is acquired?

A

K-space if filled line by line

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9
Q

What does the phase encode matrix define?

A

How many times the sequence must be repeated and therefore acquisition time

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10
Q

What doesn’t frequency encode matrix have?

A

Effect on scan time

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11
Q

• In each direction of pixel size = FOV/matrix

A
  • E.g. PE pixel size = PE FOV/PE matrix

* E.g. FE pixel size = FE FOV/FE matrix

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12
Q

What is k-space?

A

Array of numbers representing spatial frequencies in the MR image

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13
Q

What is each star in k-space?

A

data point derived directly from MR signal

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14
Q

What does all the points in k-space contain?

A

Little information about every voxel

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15
Q

What does each individual point in image space depend on?

A

All of the points contained in k-space

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16
Q

What does k-space data related to?

A

Image data by Fourier Transform

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17
Q

How are the cells of k-space commonly displayed?

A

Rectangular grid with principal axes kx and ky

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18
Q

What does kx and ky axes of k-space correspond to?

A

Horizontal to horizontal and vertical axes of the image

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19
Q

What does k-axes represent?

A

spatial frequencies in the x- and y- directions rather than positions

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20
Q

What does individual points (kx,ky) in k-space do not correspond to?

A

one-to-one with individual pixels in image

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21
Q

What does each k-space point contain?

A

spatial frequency and phase information about every pixel in the final image

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22
Q

What does each pixel in image map to?

A

every point in k-space

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23
Q

What does the centre of k-space contain?

A

signal-to-noise and contrast information

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24
Q

What does data from the edges of k-space contain?

A

Information about resolution (edges and boundaries)

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25
Q

What happens when a frequency encoding gradient is applied during evolution of MR signal?

A

successive data points in the echo reflect progressively increasing spatial frequencies

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26
Q

What is Free Induction Decay (FID)?

A

The signal unaffected by any gradient

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27
Q

What is the time constant that determines the rate of decay?

A

T2

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28
Q

What does FID not have?

A

Positional information

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29
Q

What does FID induce?

A

A current in the receiver coil at the Larmor frequency

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30
Q

How can you think voltage as?

A

pure sine wave at f0 , modul0ated by much lower frequency signals that represent the slight differences in resonant frequency caused by
• applied gradients
• inherent susceptibility
• magnet inhomogeneity, etc.

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31
Q

Why are magnetic field gradients required?

A

Translate signals into seperate locations

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32
Q

What are magnetic field gradient?

A

Variations in the magnetic field with respect to position

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33
Q

What is a one-dimensional magnetic field gradient?

A

Variation with respect to one direction

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34
Q

What does a one-dimensional magnetic field gradient along x-axis in a magnetic field B0 indicate?

A

Magnetic field is increasing in the x direction

35
Q

What is a gradient?

A

A measure of the change in something over a specific distance

  • Linear variation in static field strength
  • Can be applied in any direction - 3 gradient coils, Gx, GymGz
36
Q

What happens when a gradient is applied?

A

The total field experienced by nuclei will be dependent upon position in space e.g. in the x-direction • B(x) = B0 + x Gx

37
Q

What is the equation of gradient?

A

42.57*(field+(gradient x position)= resonant freq

38
Q

Where is all of information of interest in?

A

426Hz and -213Hz frequency differences (from Larmor freq)

39
Q

What is resultant effect?

A

Sum of two signals at the two different frequencies

40
Q

What does field gradient cause?

A

A variation of MR signal frequency

41
Q

What does frequency variation cause?

A

spins to precess at different rates

42
Q

What happens when spins precess faster?

A

Appear to dephase

43
Q

What does the amount of dephasing depend on?

A

gradient strength

44
Q

How can you re-phase spin?

A

Reverse this effect using equal and opposite grafient

45
Q

What can dephasing be caused by?

A

B0 field inhomogeneities

- results in change in frequency

46
Q

What are the 3 steps that signal can be localised?

A
  1. Slice selection
  2. Frequency encoding
  3. Phase encoding
47
Q

What is frequency encoding?

A

Encode spatial information along the rows

48
Q

What is phase encoding?

A

Encode spatial information along the columns

49
Q

What is decoding of spatial information performed by?

A

Inverse Fourier Transform

50
Q

What is the slice selection gradient perpendicular to?

A

desired slice plane

Simultaneously with RF excitation pulse

51
Q

What does the RF pulse contain?

A

Narrow bandwidth centred at Larmor frequency

52
Q

What is the slice thickness determined by?

A

Bandwidth of RF pulse and slice select gradient strength

53
Q

What is the process of slice selection?

A
  1. A magnetic field gradient is applied in the z-axis
  2. The Larmor frequencies of the nuclei varies along the z-axis
  3. An RF pulse with a frequency matching the Larmor frequency of the nuclei we want to select is applied
  4. In this way a slice along the z-axis is selected (correlates with an axial slice of the patient)
  5. The phases of the nuclei are reset by reversing the gradients
54
Q

How can you flip the precession of the nuclei?

A

The RF pulse frequency should be the same as the Larmor frequency of the nuclei

55
Q

What does changing the RF pulse frequency move?

A

Slice selected up and down the z axis

56
Q

What does altering the gradient strength alter?

A

The steepness of the gradient

  • Larger gradient = smaller image slice
  • Smaller gradient = larger image slice
57
Q

What does the Phase Encoding (PE)

A

The spin resonance frequencies - induces dephasing

58
Q

What do all of the protons precess at?

A

same frequency but with different phases

- Y direction

59
Q

Where is FE gradient applied?

A

Perpendicular to the phase encoding direction

60
Q

What does FE gradient alter?

A

main magnetic fiekd
causing the resonance frequency to vary as a function of position \
-X direction

61
Q

What is the duration of 2D acquisition?

A

RTNPENFE

62
Q

What are the two ways signals can be described?

A
  1. Give all the frequencies that make it up, along with their relative proportion
  2. Give amplitude of the total signal at each instant of time
63
Q

What can any image be decomposed into?

A

spectrum of periodic (sinusoidal) brightness variation

64
Q

High spatial frequencies

A
  1. Describes things that are changing rapidly from pixel to pixel in an image
  2. Detail of the image (edges)
65
Q

Low spatial frequencies

A
  1. Describes things that are changing slowly from pixel to pixel
  2. Overall form of the image (contrast)
66
Q

What does zero spatial frequency describe?

A

Overall intensity of the whole image

67
Q

What is the contrast of image largely determined by?

A

Spatial frequencies close to zero

68
Q

What does the centre of k-space contain?

A

Low spatial frequency information

-Determines the overall image contrast, brightness and general shapes

69
Q

What does the periphery of k-space contain?

A

High spatial frequency

- edges, details, sharp transitions

70
Q

What does small objects have?

A

Ripples far out into the periphery of k-space

71
Q

What does larger objects have?

A

Their spectral energies more concentrated at the centre

72
Q

• What happens if we don’t measure the signal at all the points in a ‘square’ of k-space?

A
  • Simply don’t acquire largest phase encoded k-space lines
  • Replace omitted lines by zero filling
  • Time saving proportional to no of lines missed out
  • Loss of spatial resolution in PE axis (y resolution reduced -> blurring) –k ymax reduced
  • small improvement in SNR
  • NO change in field of view –Spacing between k-space lines unchanged
73
Q

What is the spatial resolution given by?

A

Selected FOV divided by matrix size in either direction

74
Q

How is the spatial resolution gradually improved?

A

Increasing numbers of Fourier lines around the centre of K-space

75
Q

What happens if we reduce the number of phase encode steps, but leave their range the same?

A
  1. Reduced matrix size
  2. Changed FOV
  3. Not changed Y-resolution
  4. This is a rectangular field of view with square pixels
76
Q

What happens if we change both the range and spacing of PE gradient steps?

A
  1. Still end up with a rectangular field of view
  2. Reduced matrix size
  3. Changed FOV
  4. Changed Y-resoltuon
77
Q

When is spin echo symmetric about its centre?

A

Perfectly homogenous field

78
Q

What happens if the echo is symmetric?

A

Only have to sample half of the k-space

79
Q

How can you fill in the missing points of echo?

A

Taking the complex conjugate of the data points we have measured

80
Q

Why is the number of PE steps necessary?

A

Reconstruct image reduced

Scan time reduced

81
Q

Scan percentage at 30%

A

reduction of the spatial resolution in the image as well as in a increase of the SNR in the image

82
Q

How do you increase the resolution for fixed FOV?

A
  1. Increase gradient strengths
  2. Increase the acquisition matrix size
  3. Increase sampling time (in frequency encoding directions only)
83
Q

How can you reduce the FOV for fixed matrix size?

A
  1. Increase gradient

2. Increase sampling time

84
Q

What is SNR proportional to?

A

Voxel volume

P2 PHYSICS (16 decks)

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