spatial encoding part_2
TRANSCRIPT
Topics
• spatial encoding - part 2
Slice Selection
z
y
x
0
imaging plane
z gradientz gradient
Slice Selectionslice thickness is determined by gradient strength
RF bandwidth
tt11
tt22
tt33
Slice Selection
Selection of an axial slice is accomplished by the z gradient.
zz gradient direction gradient direction
graph of the z magnetic gradient
z-axis
Slice Selectionslice location is determined by the null point of the z gradient
RF bandwidthslice 1
slice 2 slice 3
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
z
y
x
x gradientx gradient
higher frequency
lower frequency
LR
Frequency Encoding
RF signal RF signal from from entireentire slice slice
A/D conversion, 256 pointsA/D conversion, 256 points 1 line ofk-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
z
y
x
yy gradient, gradient, phase step #192phase step #192
yy gradient, gradient, phase step #64phase step #64
Phase Encoding
2D k-space matrixgradient strength +128
RF in RF outRF out A/D conversion
gradient strength N
RF in RF outRF out A/D conversion
gradient strength -128
RF in RF outRF out A/D conversion
END
BEGIN
line 128
line N
line -128
Spin Echo Imaging
RF
z gradient
echo
echo
echo
y gradient
x gradient
slice select
phase
readout
Spin Echo Imaging
view -128
view -55view 40
k-space256 x 256 points
row 40
row -55
row -128
A/D, 256 points
kx = frequencyky = phase
• 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.
MR Image Reconstruction
Discrete Fourier Transform
F(kx,ky) is the 2D discrete Fourier transform of the image f(x,y)
f x yN
F k k exk yk
kkx y
jN
x jN
yNN
yx
( , ) ( , )
12
2 2
0
1
0
1
x
y
f(x,y)
kx
ky
k-space
F(kx,ky)
MR image
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
TR number phase encodings NEXmsec 60,000
• Example, TR 2000, 192 phase steps, 1 NEXimaging 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.
Image Acquisition Time
Multi-slice Imaging
echo
echo
echo
echo
slice 1
slice 2
slice 3
TRTR
TETE
• The maximum number of slices that can be obtained in a single acquisition is calculated as follows:
Multi-slice Imaging
TR
TEmsec
msec + C
C msec 10 20
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.
• 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.
k-space Traversal
kx
ky
256
256
256
128
256
128
decreased resolution
• 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
Half Fourier Imaging
kx
ky
256
256
kx
ky
256
128
full resolution
• 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
Half Fourier Imaging
kx
ky
256
256
256
kx
ky
128
normal phase symmetry
kx
ky
128
256
read symmetry
kx
ky
128
128 ??
128
kx
ky
256
128
kx
ky
192
128
kx
ky
128
3D Acquisition
• 3D is an extension of the 2D technique.
advantages:true contiguous slicesvery thin slices (< 1 mm)no partial volume effectsvolume data acquisition
disadvantages:gradient echo imaging only(3D FSE now available)motion sensitive
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)
• 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
3D Acquisition
TR number phase encodings number phase encodings NEXmsec 1 260,000
3D Imaging
RF
z gradient
echo
echo
echo
y gradient
x gradient
slice select
phase
readout
3D Imaging
kx
ky
256
256
z step 1
z step 4
z step N3D k-space3D k-space