Transcript Slice Selection

Topics
• spatial encoding - part 2
Slice Selection


y
0
z
z gradient
x




imaging plane
Slice Selection
slice thickness is determined by gradient strength



RF bandwidth




t1
t2
t3

Slice Selection

z gradient direction
Selection of an axial
slice is accomplished
by the z gradient.



z-axis
graph of the z magnetic gradient

Slice Selection
slice location is determined by the null point of the z gradient

slice 1 slice 2 slice 3
RF bandwidth







Frequency Encoding
• Within the imaging plane, a small gradient is
applied left to right to allow for spatial
encoding in the x direction.
• Tissues on the left will have a slightly higher
resonance frequency than tissues on the right.
• The superposition of an x gradient on the
patient is called frequency encoding.
• Frequency encoding enables spatial localization
in the L-R direction only.
Frequency Encoding
y
higher frequency
x
R
L
x gradient
lower frequency
z
Frequency Encoding
A/D conversion, 256 points
RF signal
from entire slice
1 line of
k-space
Phase Encoding
• An additional gradient is applied in the
y direction to encode the image in the
remaining direction.
• Because the x gradient alters the
frequencies in the received signal according
to spatial location, the y gradient must alter
the phase of the signal.
• Thus, the points of k-space are revealed by
recording the digitized RF signal after a
phase encoding gradient application.
Phase Encoding
• The technique of phase encoding the second
dimension in the imaging plane is
sometimes referred to as spin warping.
• The phase encoding gradient is “stepped”
during the acquisition of image data for a
single slice. Each step provides a unique
phase encoding.
• For a 256 x 256 square image matrix, 256
unique phase encodings must be performed
for each image slice. The second 256 points
in the x direction are obtained by A to D
conversion of the received signal.
Phase Encoding
y
x
z
y gradient,
phase step #64
y gradient,
phase step #192
Phase Encoding
BEGIN
RF in
RF out
A/D conversion



gradient strength +128
RF in
RF out
A/D conversion



gradient strength N
RF in
RF out
gradient strength -128
line 128
2D k-space matrix

line N
line -128
A/D conversion
END


Spin Echo Imaging


RF
echo

echo
echo
z gradient
slice select
y gradient
phase
x gradient
readout
Spin Echo Imaging
k-space
256 x 256 points
A/D, 256 points
row 40                  
row -55                  
view 40
view -55
view -128
row -128                  
kx = frequency
ky = phase
MR Image Reconstruction
• Acquisition of spatially encoded data as
described allows for reconstruction of the
MR image.
• The frequency and phase data are acquired
and form points in a 2D array .
• Reconstruction of the image is provided by
2D inverse Fourier transform of the
2D array.
• This method of spatially encoding the MR
image is called 2D FT imaging.
Discrete Fourier Transform
F(kx,ky) is the 2D discrete Fourier transform of the
image f(x,y)
N 1
N 1
1
f ( x, y )  2   F ( kx, ky )e
N k x 0 k y 0
 2
j
 N
xkx  j 2N yky 
y
x
f(x,y)
MR image
ky

kx
F(kx,ky)
k-space
Image Resolution and Phase Encoding
• Resolution is always maximum in the
frequency encoding direction because the MR
signal is always digitized into 256 points.
• Resolution can vary in the phase encoding
direction depending on the number of phase
steps used to acquire the image.
• Because each phase encoding requires a
separate 90 and 180 degree pulse, image
acquisition time is proportional to the number
of phase encode steps.
Image Acquisition Time
TRmsec  number phase encodings NEX
60,000
Image Acquisition Time
• Example, TR 2000, 192 phase steps, 1 NEX
imaging time = 6.4 minutes
• At this rate, it would take 128 minutes to do
an average 20 slice exam.
• Because TR is typically much longer than
TE, we can acquire the data for the other
slices between the 90 degree RF pulses.
Multi-slice Imaging
TR


echo
slice 1
echo

slice 2
TE
echo

slice 3
echo
Multi-slice Imaging
• The maximum number of slices that
can be obtained in a single acquisition
is calculated as follows:
TRmsec
TEmsec + C
C  10  20msec
k-space Traversal
• The most important phase encoding
information is centered around the
middle of k-space.
• Typically, k-space is filled in an orderly
manner, beginning with the returned
echos obtained at the maximum negative
y gradient strength and continuing to the
maximum positive value.
k-space Traversal
• For images obtained with less than
256 views, the number of phase
encodings is evenly divided between
positive and negative values centered
around zero.
• Images reconstructed with less than
256 phase encodings have less detail in
the phase encoding direction.
ky
2
5
6
kx
256
1
2
8
256
1
2
8
256
decreased resolution
Half Fourier Imaging
• Because k-space is symmetrical, one
half of the space can be determined
from knowledge of the other half.
• Imaging time can be reduced by a
factor of 2 by collecting either the
positive or the negative phase
encodings and filling the remainder of
k-space with the mirrored data.
Half Fourier Imaging
ky
2
5
6
kx
256
ky
1
2
8
kx
256
full resolution
Half Fourier Imaging
• This technique is sometimes referred
to as ‘half NEX’ imaging or ‘PCS’
(phase conjugate symmetry).
• Penalty: reduced signal decreases the
signal to noise ratio, typically by a
factor of 0.71.
Half Fourier Imaging
• The frequency half of k-space can also
be mirrored.
• This technique is called fractional
echo or ‘RCS’ (read conjugate
symmetry).
• Decreased read time enables more
slices per acquisition at the expense of
reduced signal.
Half Fourier Imaging
ky
2
5
6
ky
kx
256
normal
1
2
8
ky
kx
256
phase symmetry
2
5
6
kx
128
read symmetry
ky
1
2
8
?
kx
128
ky
ky
2
5
6
kx
128
1
9
2
ky
kx
128
1
2
8
kx
128
3D Acquisition
• 3D is an extension of the 2D technique.
advantages:
disadvantages:
true contiguous slices
gradient echo imaging only
very thin slices (< 1 mm)
(3D FSE now available)
no partial volume effects
motion sensitive
volume data acquisition
3D Acquisition
• no slice select gradient
• entire volume of tissue is excited
• second phase encoding gradient
replaces the slice select gradient
• after the intial RF pulse (), both y
and z gradients are applied, followed
by application of the x gradient
during readout (echo)
3D Acquisition
• the z gradient is changed only after all
of the y gradient phase encodes have
generated an echo, then the z gradient
is stepped and the y gradient phase
encodes are repeated
TRmsec  number 1 phase encodings  number 2 phase encodings NEX
60,000
3D Imaging

RF

echo

echo
echo
z gradient
slice select
y gradient
phase
x gradient
readout
3D Imaging
ky
z step 1
kx
z step 4



2
5
6
z step N
3D k-space
256