Encoding and Image
Formation
Gradients
Slice selection
Frequency encoding
Phase encoding
Sampling
Data collection
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.
►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
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.
► 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
negative
A
2 cm
9998 G
42.5614 MHz
B
10000 G
42.57 MHz
2 cm
gradient 1 G
per cm
C
10002 G
42.5785 MHz
X,Y,Z Gradient coils
► 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
Y
the magnet
Z
X
► The
magnetic isocentre is the centre point
of the axis of all three gradients, and the
bore of the magnet.
isocentre
Y
Z
X
► The
field strength remains unaltered at the
isocentre
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
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.
► Z-gradient
selects axial
slices
► Y gradient
selects coronal
slices
► X gradient
selects sagittal
slices
Y
Z
X
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.
► 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.
Shallow
gradient
slice select
gradient
Narrow
Bandwidth
Transmit
bandwidth
broad
Bandwidth
Steep
gradient
Thin slice
Thick slice
Thin slice
Thick slice
Gradient strength & slice thickness
Shallow (weaker gradient)
Steeper ( strong) gradient
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.
►
►
►
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.
900
Slice select
gradient
1800
900
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
A
Nuclei in column
A precess at
frequency A
B
Nuclei in column
B precess at
frequency B
C
Nuclei in column
C precess at
frequency C
For frequency encoding of
► Coronal & sagittal images – use z gradient
► Axial images – use X gradient
► Axial images of Head – use Y gradient
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
rephasing
FID
dephasing
Frequency
peak
encoding gradient
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.
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.
Gradient & phase difference
14998 G
63.852 MHz
nuclei travel
slower
Loose phase
15000 G
63.86 MHz
15002 G
63.868 MHz
Nuclei
travel
faster
gain phase
► 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).
In practice
► The phase encoding gradient is switched on just before the
application of the 1800 rephasing pulse in spin echo
sequences.
1800
900
Phase encoding
gradient
900
Summary of phase encoding
► The
phase encoding gradient alters the
phase along the short axis of the anatomy
Coronal images – x gradient
► In sagittal images - Y gradient
► In axial images - Y gradient
► In
► Axial
images of brain – x gradient
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)
► 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
Gradient timing in spin echo
TR
1800
900
slice
select
echo
Phase
encode
slice
select
Frequency
encode
900
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
► 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 f3 f4 f5 f6
Receive bandwidth
Frequencies
sampled are
mapped across
the FOV along
the frequency
axis
► 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
► 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
Nyquist theorum
Sampling once
Reproduced as a
straight line
Sampling twice
Reproduced more
accurately
Bandwidth versus sampling time
Sampling time (8 ms)
Bandwidth
16,000 Hz
128 cycles
occur
(256 samples
can be taken)
8,000 Hz
64 cycles occur
(only 128
samples can be
taken)
If bandwidth is reduced, the sampling time must be increased so
that the same number of samples can be taken
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)
3 cycles/s
Frequency shift
►
2 cycles/s
1 cycle/s
Phase shift
K space
►
The data information is stored in the computer memory location
called the K space. Maximum number of lines are 1024
frequency
+ve
phase
One line is filled
for one phase
encoding
gradient
-ve
outer
central
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
►
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
The pseudo frequency curve
time
Phase shift value
Phase encoding gradient & pseudo
frequency
► Steeper
gradients results in high pseudo
frequencies
► Shallow gradients results in low frequencies
► 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
K space
Line 1
Line 2
Line 128
phase encode 1 frequency/phase data
phase encode 2
phase encode 128
Fast Fourier Transform (FFT)
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
RF intensity
Amplitude
► The
Frequency
Time
Time domain
Frequency domain
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
Matrix
8 frequency samples
8 phase samples
4 phase samples
4 frequency samples
Coarse matrix 4x4
Fine matrix 8 x 8
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
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
TR & number of slices
180
90
TR
echo
Slice 1
TE
Slice 2
Slice 3
Phase encode 1
Slice 4
Phase encode 2
Slice 1
second TR
► 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
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
► 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
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
Phase encoding slope & signal
amplitude
Low amplitude
Steeper gradient
medium gradient
shallow gradient
medium amplitude
high amplitude
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
Signal amplitude & frequency
gradient
Peak
Rephasing
Dephasing
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)
► 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
Resolution & Amplitude
High spatial
resolution
High signal
High spatial
resolution
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
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
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
A
C
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
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
Minimum TE
Readout gradient
Partial echo imaging
Minimum TE reduced
This extrapolated
from filled segment
Only this half is read
Only half of the k Space is filled
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
►
If phase
encodings = 256
TR = 1s
NEX=1,
Partial averaging
75% of k
space is
filled with
data
Scan time = 256
x 1 x 1 = 256 s
If phase
encodings = 256
TR = 1s
NEX=3/4,
Scan time = 256
x ¾ x 1 = 192 s
25% is
filled with
zeros
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.
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
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)
►
End