1. fMRI: Biological Basis and Experiment Design Lecture 7: Gradients and k-space FFT examples –Sampling and aliasing Gradient Gradient echo K-space www.hoghaven.com

2. Zooming in k-space is undersampling in real space

3. Zooming in real space is undersampling in k-space

4. 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.

5. 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  st = 20  st = 160  s G = 12mT/m B x G = 5.1kHz/cm f x --  0

6. Gradient echo Applying a gradient in the opposite direction reverses this process t = 160  st = 300  st = 320  s G = -12mT/m B x --  0

7. Applying a gradient produces a periodic spin phase pattern G RO --  0 Real part of signal in RF coil Magnitude of signal in RF coil Imaginary component of signal in RF coil

8. The read-out signal is the 1D FFT of the sample G RO --  0 Real part of signal in RF coil Magnitude of signal in RF coil Imaginary component of signal in RF coil

9. Applying simultaneous gradients rotates the coordinate system G RO G PE --  0

10. Phase encoding allows independent spatial frequency encoding on 2 axes G PE G RO 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

11. Phase encoding allows independent spatial frequency encoding on 2 axes G PE G RO 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

12. FLASH sequences read one line per excitation --  0 Relative phase of spins

13. Pulse sequence diagram: slow 2D FLASH (64 x 64) N rep = 64 64 points RF G SS G PE G RO DAC PE table increments each repetition Flip angle ~ 56 deg. TR ~ 640us

14. EPI sequences zig-zag back and forth across k-space --  0

15. Pulse sequence diagram: EPI (64 x 64 image) N rep = 32 64 pts RF G SS G PE G RO DAC Total read-out time ~40 ms Bandwidth (image): 100kHz (dwell time: 10us) 64 pts