fmri: biological basis and experiment design lecture 7: gradients and k-space fft examples...
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fMRI: Biological Basis and Experiment DesignLecture 7: Gradients and k-space
• FFT examples– Sampling and aliasing
• Gradient• Gradient echo• K-space
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Zooming in k-space is undersampling in real space
Zooming in real space is undersampling in k-space
General imaging considerations
• K-space resolution (sampling rate) determines field of view (FOV)– Sampling bandwidth, for a fixed read-out gradient, determines FOV
• K-space coverage (matrix size) determines resolution• Image "bandwidth per pixel" (different on different axes) determines
sensitivity to susceptibility-induced artifacts.
Gradient echo
Immediately after excitation, all the spins in a sample are in phase
When a gradient is applied, the spins begin to pick up a phase difference
The phase depends on both space and time (and gradient strength)
t = 0 s t = 20 s t = 160 s
G = 12mT/mB
x
G = 5.1kHz/cm
f
x- 0
Gradient echo
Applying a gradient in the opposite direction reverses this process
t = 160 s t = 300 s t = 320 s
G = -12mT/mB
x
- 0
Applying a gradient produces a periodic spin phase pattern
GRO
- 0
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Real part of signal in RF coil
Magnitude of signal in RF coil
Imaginary component of signal in RF coil
The read-out signal is the 1D FFT of the sample
GRO
- 0Real part of signal in RF coil
Magnitude of signal in RF coil
Imaginary component of signal in RF coil
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Applying simultaneous gradients rotates the coordinate system
GRO
GPE
- 0
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Phase encoding allows independent spatial frequency encoding on 2 axes
GPE
GRO
PE gradient imposes phase pattern on one axis
Read "refocusing" gradient rewinds phase pattern on another axis
Read gradient creates phase evolution while one line of k-space is acquired
PE
RO
- 0
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Phase encoding allows independent spatial frequency encoding on 2 axes
GPE
GRO
PE gradient imposes phase pattern on one axis
Read "refocusing" gradient rewinds phase pattern on another axis
Read gradient creates phase evolution while one line of k-space is acquired
PE
RO
- 0
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
FLASH sequences read one line per excitation
- 0
Relative phase of spins
Pulse sequence diagram: slow 2D FLASH (64 x 64)
Nrep = 64
64 points
RF
GSS
GPE
GRO
DAC
PE table increments each repetition
Flip angle ~ 56 deg. TR ~ 640us
EPI sequences zig-zag back and forth across k-space
- 0
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
Pulse sequence diagram: EPI (64 x 64 image)
Nrep = 32
64 pts
RF
GSS
GPE
GRO
DAC
Total read-out time ~40 msBandwidth (image): 100kHz (dwell time: 10us)
64 pts