Encoding and Image Formation

1
Encoding and Image Formation

• Gradients
• Slice selection
• Frequency encoding
• Phase encoding
• Sampling
• Data collection

2
Introduction

• Encoding means the location of the MR signal and
  positioning it on the correct place in the image
• RF at precessional frequency of hydrogen applied
  at 900 to B0 resonates and flips the NMV into
  transverse plane.
• The individual magnetic moments of hydrogen is
  put into phase.
• The coherent transverse magnetization precesses
  at Larmor frequency in the transverse plane.

3

• A voltage (signal) is induced in the receiver
  coil placed in the transverse plane
• This signal has a frequency equal to Larmor
  frequency of hydrogen (at 1.5 T 63.86 MHz)
• The system must be able to locate the signal
  spatially in three dimensions, so that it can
  position each signal at the correct point on the
  image.
• First it locates a slice.
• Then it is located or encoded along both axes of
  the image.
• This task is performed by magnetic gradients

4
Magnetic Gradients

• Gradients are alterations to the main magnetic
  field and are generated by coils of wire located
  within the bore of the magnet.
• The passage of current through a gradient coil
  induces a gradient magnetic field.
• The gradient field either adds to or subtracts
  from B0.
• B0 is altered in a linear fashion.

5

• Magnetic field strength and therefore the
  precessional frequency of the nuclei situated in
  the long axis is deferent and is predictable.
• This is called spatial encoding

positive
gradient 1 G per cm
negative
A
B
C
2 cm
2 cm
9998 G 42.5614 MHz
10002 G 42.5785 MHz
10000 G 42.57 MHz
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X,Y,Z Gradient coils
7

• There are three gradient coils (X,Y,Z) situated
  within the bore of the magnet
• Z gradient alters the magnetic field strength
  along the Z- (long) axis
• Y gradient alters the magnetic field strength
  along the Y- (vertical) axis of the magnet
• X gradient alters the magnetic field strength
  along the X- (horizontal /transverse) axis of
  the magnet

Y
Z
X
8

• The magnetic isocentre is the centre point of
  the axis of all three gradients, and the bore of
  the magnet.
• The field strength remains unaltered at the
  isocentre

isocentre
Y
Z
X
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Steep shallow gradients

• When a gradient coil is switched on, the magnetic
  field strength is either subtracted from or added
  to B0 relative to the isocentre
• The slope of the resulting magnetic field is the
  amplitude of the magnetic field gradient and it
  determines the rate of change of the magnetic
  field strength along the gradient axis.
• Steep gradient slopes alter the magnetic field
  strength between two points more than shallow
  gradient slopes.
• Steep gradient slopes therefore alter the
  precessional frequency of nuclei between two
  points, more than shallow gradients slopes

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Slice selection

• This is done by
• first switching the appropriate gradient coil to
  alter the field strength and the precessional
  frequency at points along the corresponding axis,
  and
• then by transmitting a selected band of RF
  frequencies to selectively excite the nuclei
  which precess in that particular frequencies.
• Resonance of nuclei within the slice occurs
  because RF appropriate to that position is
  transmitted
• Nuclei situated in other slices does not resonate
  because their precessional frequency is different.

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• Z-gradient selects axial slices
• Y gradient selects coronal slices
• X gradient selects sagittal slices

Y
Z
X
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Slice thickness

• To give each slice a thickness, a band of nuclei
  must be excited by the excitation pulse
• The slope of the slice-select gradient determines
  the difference in precessional frequency between
  two points on the gradient.
• Once a certain gradient slope is applied, the RF
  pulse transmitted to excite the slice, must
  contain a range of frequencies to match the
  difference in precessional frequency between two
  points
• This frequency range is called the bandwidth.
• As the RF is being transmitted at this point it
  is called the transmit bandwidth.

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• To achieve thin slices, a steep slice select
  slope and/or narrow bandwidth is applied
• To achieve thick slices, a shallow slice select
  slope and/or broad transmit bandwidth is applied.

Steep gradient
Shallow gradient
slice select gradient
broad Bandwidth
Transmit bandwidth
Narrow Bandwidth
Thick slice
Thin slice
Thin slice
Thick slice
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Gradient strength slice thickness
Shallow (weaker gradient)
Steeper ( strong) gradient
15
In Practice

• The system automatically applies the appropriate
  gradient slope and transmit bandwidth according
  to the thickness of slice required.
• The slice is excited by transmitting RF at the
  centre frequency corresponding to the
  precessional frequency of nuclei in the middle of
  the slice,
• The bandwidth and gradient slope determine the
  range of nuclei that resonate on either side of
  the centre.

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• The gap between the slices is determined by the
  gradient slope and by the thickness of the slice.
• In spin echo pulse sequences, the slice select
  gradient is switched on during the application of
  the 900 excitation pulse and during the 1800
  rephasing pulse, to excite and rephase each slice
  selectively.
• In gradient echo, the slice select gradient is
  switched on during the excitation pulse only.

1800
900
900
Slice select gradient
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Frequency encoding

• Once a slice has been selected, the signal coming
  from it must be spatially located (encoded) along
  both axes of the image
• Locating the signal along the long axis of
  anatomy is done by a process called frequency
  encoding
• A gradient is applied along the selected axis
• The precessional frequency of signal along the
  axis is therefore altered in a linear fashion.
• The signal can now be located along the axis of
  the gradient according to its frequency

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A
B
C
Nuclei in column A precess at frequency A
Nuclei in column C precess at frequency C
Nuclei in column B precess at frequency B

• For frequency encoding of
• Coronal sagittal images use z gradient
• Axial images use X gradient
• Axial images of Head use Y gradient

19

• In practice
• The frequency encoding gradient is switched on
  when the signal is received and is often called
  the readout gradient

1800
900
900
FID
Echo
FID
rephasing
dephasing
Frequency encoding gradient
peak
The steepness of the slope of the frequency
encoding gradient determines the size of the
anatomy covered Field Of View (FOV) along the
axis during scan.
20
Phase encoding

• The location of the signal along the remaining
  third axis is achieved by a process called phase
  encoding.
• This is achieved by applying a gradient along
  this remaining axis
• A gradient is switched on it alters the speed of
  precession as well as the accumulated phase of
  the nuclei along their precessional path.
• It produces a phase difference or shift between
  nuclei positioned along the axis.

21
Gradient phase difference
nuclei travel slower
14998 G 63.852 MHz
Loose phase
15000 G 63.86 MHz
Nuclei travel faster
15002 G 63.868 MHz
gain phase
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• When the phase encoding gradient is switched off,
  the magnetic field strength experienced by the
  nuclei returns to B0 and the precessional
  frequency of all the nuclei returns to the larmor
  frequency.
• However the phase difference between nuclei
  remains
• The nuclei travel at the same speed around their
  precessional paths, but their phases or positions
  are different.
• This difference in phase between the nuclei is
  used to determine their position along the phase
  encoding gradient (axis).

23

• In practice
• The phase encoding gradient is switched on just
  before the application of the 1800 rephasing
  pulse in spin echo sequences.

1800
900
900
Phase encoding gradient
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Summary of phase encoding

• The phase encoding gradient alters the phase
  along the short axis of the anatomy
• In Coronal images x gradient
• In sagittal images - Y gradient
• In axial images - Y gradient
• Axial images of brain x gradient

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Summary spatial encoding

• The slice-select gradient is switched on
• during the 90 and 180 pulses in spin echo pulse
  sequences , and
• during the excitation pulse only in gradient echo
  pulse sequences
• The slope of the slice-select gradient determines
  the slice thickness and slice gap (along with
  transmit bandwidth)

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• The phase encoding gradient is switched on
• just before the 180 pulse in spin echo, and
• between excitation and the signal collection in
  gradient echo.
• The slope of the phase encoding gradient
  determines the degree of phase shift along the
  phase encoding axis.
• The frequency encoding gradient is switched on
  during the collection of the signal
• The amplitude of the frequency encoding gradient
  and the phase encoding gradient determines the
  two dimensions of the FOV

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Gradient timing in spin echo
TR
1800
900
900
echo
Phase encode
slice select
slice select
Frequency encode
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Sampling

• The signal is collected during the frequency
  encoding gradient (readout gradient)
• The duration of readout gradient is called
  sampling time
• The system samples up to 1024 frequencies during
  sampling time
• The rate at which the samples are taken is called
  the sampling rate

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• The number of samples taken determines the number
  of frequencies sampled
• The range of frequencies is called the receive
  bandwidth

Frequency columns in FOV
f1
f2
f4
f3
f5
f6
Frequencies sampled are mapped across the FOV
along the frequency axis
Receive bandwidth
30

• Sampling time, sampling rate and receive
  bandwidth are linked by a mathematical principle
  called the Nyquist theorem.
• It states that any signal must be sampled at
  least twice per cycle in order to represent or
  reproduced it acurately.
• In addition enough cycles must occur during the
  sampling time to achieve enough frequency samples
  ( if 256 samples are to be taken 128 cycles must
  occur during the sampling time)
• Number of cycles occurring per second is
  determined by the receive bandwidth
• Receive bandwidth is proportional to the Sampling
  rate

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• Sampling time is inversely proportional to
• The sampling rate
• The receive bandwidth
• The receive bandwidth affect the minimum TE (
  because the sampling time is changed)
• Reducing the receive bandwidth increase the TE
  (sampling time increases) vise versa
• Usually the receive bandwidth sampling time are
  fixed

32
Nyquist theorum
Sampling once
Reproduced as a straight line
Sampling twice
Reproduced more accurately
33
Bandwidth versus sampling time
Sampling time (8 ms)
Bandwidth
128 cycles occur (256 samples can be taken)
16,000 Hz
64 cycles occur (only 128 samples can be taken)
8,000 Hz
If bandwidth is reduced, the sampling time must
be increased so that the same number of samples
can be taken
34
Data collection

• Location of individual signals within the image
  by measuring the number of times the magnetic
  moments cross the receiver coil (frequency), and
  their position around their precessional path
  (phase)

Frequency shift
3 cycles/s
2 cycles/s
1 cycle/s
Phase shift
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K space

• The data information is stored in the computer
  memory location called the K space. Maximum
  number of lines are 1024

frequency
ve
outer
One line is filled for one phase encoding gradient
central
phase
-ve
36
Data collection step 1

• During each TR the signal from each slice is
  phase encoded and frequency encoded.
• A certain value of frequency shift is obtained
  according to the slope of the frequency encoding
  gradient, which is determined by the size of the
  FOV.
• As the FOV remains unchanged during the scan, the
  frequency shift value remains the same.
• A certain value of phase shift is also obtained
  according to the slope of the phase encoding
  gradient
• The slope of the phase encoding gradient will
  determine which line of K space is filled with
  the data from that frequency and phase encoding

37
Phase shift pseudo-frequency

• The system cannot measure the phase values
  directly
• It can measure frequency
• The phase shift values are converted to a sine
  wave
• The frequency of this sine wave is called a
  pseudo-frequency
• Different phase shift gradient produce different
  sine waves with different pseudo-frequency

38
The pseudo frequency curve
time
Phase shift value
39
Phase encoding gradient pseudo frequency

• Steeper gradients results in high pseudo
  frequencies
• Shallow gradients results in low frequencies

40

• In order to fill out different lines of K space,
  the slope of the phase encoding gradient must be
  altered after each TR
• With each phase encoding one line of K space is
  filled
• Different lines in K space are filled after every
  TR
• The phase encoding gradient is altered for every
  TR
• In order to complete the acquisition all the
  lines of selected K space must have been filled
• The number of lines that are filled is determined
  by the number of different phase encoding slopes
  that are applied

41
K space
Line 1 phase encode 1 frequency/phase data
Line 2 phase encode 2





Line 128 phase encode 128
42
Fast Fourier Transform (FFT)

• The data in K space is converted into an image
  mathematically by Fourier Transform.
• The receive signal is a composite of multiple
  signals with different frequencies and amplitudes
• The signal intensity/time domain is converted to
  a signal intensity/frequency domain

Amplitude
RF intensity
Frequency
Time
Frequency domain
Time domain
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Matrix FOV

• The FOV relates to the amount of anatomy covered
• It can be square or rectangular
• Image consists of a matrix of pixels
• Te number of pixels depends on the number of
  frequency samples and phase encodings
• Matrix frequency samples x phase encodings

44
Matrix
4 frequency samples
8 frequency samples
8 phase samples
4 phase samples
Coarse matrix 4x4
Fine matrix 8 x 8
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Data collection - step 2, NSA (NEX)

• When all the lines of K space is filled the
  acquisition is over
• But the signal can be sampled more than once with
  the same slope of phase encoding gradient.
• Doing so each line of K space is filled more than
  once
• The number of times each signal is sampled with
  the same slope of phase encoding gradient is
  usually called the number of signal averages
  (NSA) or the number of excitations (NEX).
• The higher the NEX, the more data is stored and
  the amplitude of the signal at each frequency and
  phase shift is greater

46
Scan timing

• Every TR, each slice is selected, phase encoded
  and frequency encoded.
• The maximum number of slices that can be selected
  and encoded depends on the length of the TR.
• E.g.
• TR of 500ms may allow 12 slices.
• TR of 2000 ms may allow 18 slices

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TR number of slices
180
TR
90
echo
Slice 1
TE
Slice 2
Slice 3
Phase encode 1
Slice 4
Slice 1 second TR
Phase encode 2
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• The phase encoding gradient slope is altered
  every TR and is applied to each selected slice in
  order to phase encode it.
• At each phase encode a different line of k space
  is filled. The number of phase encoding steps
  therefore affects the length of the scan
• E.g. 256 phase encodings require 256 x TR to
  complete the scan.
• The scan time is also affected by the number of
  times the signal is phase encoded with the same
  phase encoding gradient slope, or NEX . So,
• Scan time TR x Number of phase encodings x NEX

49
K space filling

• The negative half of the k space is a mirror
  image of the positive half.
• The polarity of the phase gradient determines
  whether the positive or negative half is filled
• Gradient polarity depends on the direction of the
  current through the gradient coil
• The central lines are filled with data produced
  after the application of shallow phase encoding
  gradients
• The outer lines are filled with data produced
  with steep phase encoding gradients

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• The steepness of the slope of the phase encoding
  gradient depends on the current driven through he
  coil.
• The central lines of K space are usually filled
  first. (if 256 phase encodings are performed 128
  positive lines and 128 negative lines are filled.
• The lines are usually filled sequentially either
  from top to bottom or from bottom to top

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Signal amplitude phase shift gradient

• The shallow phase encoding gradients have smaller
  phase shifts. The resultant signal therefore has
  a large amplitude
• The steeper phase encoding gradients have larger
  phase shift along their axis and therefore small
  signal amplitudes

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Phase encoding slope signal amplitude
Low amplitude
Steeper gradient
medium amplitude
medium gradient
shallow gradient
high amplitude
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Signal amplitude frequency gradient

• The vertical axis of k space correspond to the
  frequency encoding
• The left of the k space is a mirror image of the
  right
• The centre represents the maximum signal
  amplitude because all the magnetic moments are in
  phase
• The magnetic moments on either side are either
  rephasing and dephasing and therefore the
  amplitude is less

54
Signal amplitude frequency gradient
Peak
Rephasing
Dephasing
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K space filling spatial resolution

• Number of phase encodings determines the number
  of pixels in the FOV along the phase encoding
  direction
• If the FOV is fixed voxels of smaller dimensions
  result in an image with high spatial resolution
• The steeper gradients result in high spatial
  resolution (two adjacent points have different
  phase values and can be differentiated)

56

• The outer lines of K space contain data with high
  spatial resolution
• The central lines of k space contain data with a
  low spatial resolution
• The central portion of k space contains data that
  has high signal amplitude low spatial
  resolution
• The outer portion of k space contains data that
  has low signal amplitude and high spatial
  resolution

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Resolution Amplitude
High spatial resolution
High signal
High spatial resolution
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Way of filling K space

• The amplitude of frequency encoding gradient
  determines how far to the left and right K space
  is traversed and this in turn determines the size
  of the FOV in the frequency direction of the
  image
• The amplitude of the phase encoding gradient
  determines how far up and down a line of K space
  is filled and in turn determines the size of the
  FOV in the phase direction of the image (or the
  spatial resolution when the FOV is square)
• The polarity of each gradient defines the
  direction traveled through K space

59
K space filling in gradient echo

• The frequency encoding gradient switches
  negatively to forcibly dephase the FID and then
  positively to rephase and produce a gradient echo
• Frequency encoding gradient is negative, k space
  traversed from left to right
• Frequency encoding gradient is positive, k space
  traversed from right to left
• Phase encode gradient is positive , fills top
  half of K space
• Phase encode gradient is negative, fills bottom
  half of K space

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K space filling in gradient echo
Phase encode amplitude determines distance B
Positive gradient traverse from centre through
distance C
Negative gradient traverse from centre through
distance A
Line of k space filled
B
C
A
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Manipulation of K space filling

• The way in which K space is filled depends on how
  the data is acquired and can be manipulated to
  suit the circumstances of the scan e.g. in the
  following
• Rectangular field of view
• Anti-aliasing
• Ultra fast pulse sequences
• Respiratory compensation
• Echo planar imaging

62
Partial or fractional echo imaging

• This refers to when only part of the signal is
  read (sampled) during application of frequency
  encoding gradient
• As the sampling time is reduced minimum TE can be
  reduced
• This allows maximum T1 and proton density
  weighting and number of slices for a given TR

63
Minimum TE
Readout gradient
Partial echo imaging
Only this half is read
Minimum TE reduced
Only half of the k Space is filled
This extrapolated from filled segment
64
Partial or fractional averaging

• The negative and positive halves of K space on
  each side of the phase axis are symmetrical and
  mirror image of each other
• The filling of at least half of the lines is
  adequate to produce an image
• If 60 of lines are to be filled only 60 of
  phase encodings are required and the remaining
  lines are filled with zeros
• The scan time is there fore reduced
• E.g. 256 phase encodings and, 1 TR and ¾ NEX is
  selected
• This is called partial or fractional averaging

65
Partial averaging
If phase encodings 256 TR 1s NEX1, Scan
time 256 x 1 x 1 256 s
75 of k space is filled with data
If phase encodings 256 TR 1s NEX3/4, Scan
time 256 x ¾ x 1 192 s
25 is filled with zeros
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PRE-SCAN

• This is a method of calibration that should be
  performed before every data acquisition. It
  includes
• Finding the centre frequency on which to transmit
  RF. I.e. Resonant frequency of water protons
  within the area under examination
• Finding the exact magnitude of RF that must be
  transmitted to generate maximum signal in the
  coil. (to flip the NMV through 900)
• Adjustment of the magnitude of the received
  signal so that it is not too large nor too small.

67
Reasons for failing pre-scan

• The coil is not plugged in properly
• The coil is faulty
• Chemical saturation techniques are utilized and
  there is an uneven distribution of fat and water
  in the area to be saturated
• The patient is either very large or very small

68
Types of acquisition

• Sequential data collected for slice by slice
  (k- space for each slice is filled one by one)
• Two-dimensional volumetric data collected for
  all the slices simultaneously (line 1 in first
  slice, then line 1 in slice 2)
• Three-dimensional volumetric (volume
  imaging)-collect data from total volume. The
  excitation pulse is not slice selective, and the
  whole prescribed volume is excited. At the end of
  acquisition the volume is divided into partitions
  by slice select gradient which separates the
  slices according to their phase value along the
  gradient. (This is called slice encoding)

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End