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fMRI: Biological Basis and Experiment Design Lecture 7: Gradients and k-space

Understand the biological basis and experiment design of fMRI through lectures covering gradients, k-space, FFT examples, sampling, aliasing, and more. Explore the nuances of k-space resolution, sampling bandwidth, and sensitivity to artifacts for optimal imaging outcomes.

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fMRI: Biological Basis and Experiment Design Lecture 7: Gradients and k-space

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  1. fMRI: Biological Basis and Experiment DesignLecture 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. -  0 Gradient echo 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) Immediately after excitation, all the spins in a sample are in phase G = 5.1kHz/cm G = 12mT/m B f x x t = 0 s t = 20 s t = 160 s

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

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

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

  9. -  0 Applying simultaneous gradients rotates the coordinate system GRO GPE

  10. - 0  Phase encoding allows independent spatial frequency encoding on 2 axes PE Read gradient creates phase evolution while one line of k-space is acquired PE gradient imposes phase pattern on one axis GPE GRO RO Read "refocusing" gradient rewinds phase pattern on another axis

  11. - 0  Phase encoding allows independent spatial frequency encoding on 2 axes PE Read gradient creates phase evolution while one line of k-space is acquired PE gradient imposes phase pattern on one axis GPE GRO RO Read "refocusing" gradient rewinds phase pattern on another axis

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

  13. Pulse sequence diagram: slow 2D FLASH (64 x 64) Nrep = 64 Flip angle ~ 56 deg. TR ~ 640us RF GSS PE table increments each repetition GPE GRO 64 points DAC

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

  15. Pulse sequence diagram: EPI (64 x 64 image) Total read-out time ~40 ms Bandwidth (image): 100kHz (dwell time: 10us) Nrep = 32 RF GSS GPE GRO 64 pts 64 pts DAC

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