fmri: biological basis and experiment design lecture 7: gradients and k-space fft examples...

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

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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

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Applying simultaneous gradients rotates the coordinate system

GRO

GPE

- 0

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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

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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

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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

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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