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Gradient Measurement

Gradient Measurement. Hochong Wu 2008/06/06. Outline. Imaging with Gradients Measurement Methods Signal Phase Model Phantom Calibration Self-Encoding Off-isocenter Slice Selection Simple Experiment. 1. Imaging with Gradients. Gradient encoding Acquisition k -space

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Gradient Measurement

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  1. Gradient Measurement Hochong Wu 2008/06/06

  2. Outline • Imaging with Gradients • Measurement Methods • Signal Phase Model • Phantom Calibration • Self-Encoding • Off-isocenter Slice Selection • Simple Experiment

  3. 1. Imaging with Gradients • Gradient encoding • Acquisition k-space • Excitation k-space • Gradient imperfections lead to artifacts • FOV scaling, shifting • Signal loss, shading • Image blurring, geometric distortion • Distorted spatial/spectral excitation profile

  4. Sources of Gradient Errors • Eddy currents(B0, linear, …) • Group delays (RF filters, A/D, etc.) • Amplifier limitations (BW, freq response) • Concomitant-field gradients • Gradient warping • Coil misalignment, acoustic vibration, …

  5. Eddy Currents • Spatial Dependence • Be(x, t) = b0(t) + x*g(t) + … • Time Dependence • Impulse response as a sum of decaying exponentials • Short time constant linear term is approximately a delay

  6. Compensation Options • Shielded gradient coils • Waveform preemphasis • Lower slew rate/gradient amplitude • Magnetic field monitoring • Measurement (and correction) • System characterization

  7. 2. Measurement Methods • Phantom calibration • RF landmarking • Self-encoding • peak fitting • Fourier transform • Off-isocenter slice selection

  8. Phase Terms in Signal • Linear w.r.t. the test gradient waveform • Test gradient itself (including group delays, eddy currents, amplifier limitations) • B0 eddy current term • Independent of test gradient polarity • Receiver coil response • Off-resonance • Eddy currents from other gradients • Concomitant-field Gurney, PhD Thesis, Stanford, 2007

  9. Common Considerations • Spin-Echo for long gradient waveforms • Phase unwrapping • Noise amplification (differentiation) • Polynomial curve fitting

  10. Phantom Calibration Signal Equation: Point source at (x0, y0): Ideally, the phase should be: Model measured phase difference as: Mason, et al., MRM 1997

  11. Practical Considerations • Need to move phantom manually • Need to measure (x0, y0) • Can’t perform directly on subject • Should use special coil • Has a limit on k-space resolution

  12. Self Encoding (Peak Fitting) Gradient encoding on one axis: Signal max (echo) occurs at k=0: To find k(t) at each time point: Onodera, et al., J P E: S I 1987 Takahashi, et al., MRM 1995

  13. Self Encoding (Fourier Transform) Gradient encoding on one axis: FT w.r.t. the self-encodings: Including other sources of phase contribution: With 2 acquisition (pos/neg): Alley, et al., MRM 1998

  14. Practical Considerations • Doesn’t need special hardware • Needs many self encodings • Ne,axis≥ max{k(t)} x FOV • Assumes the self-encodings are accurate

  15. Off-isocenter Slice Selection Signal equation for a slice at x0 and gradients on x: Taking the phase difference btwn two slices x1 and x2: Zhang, et al., MRM 1998 Duyn, et al., JMR 1998

  16. Practical Considerations • Potentially, 2 measurements per axis • More to boost SNR, k-space coverage • Should measure X on X, Y on X, … • Combine results, assuming linearity • Need thin, close slices • Should measure actual slice position

  17. 3. Simple Experiment • Interleaved Spiral • 2-mm spatial resolution • Off-iso Measurement • 6 slices: 2-mm thick / 5-mm spacing • X on X, Y on X, X on Y, Y on Y • Spin-Echo sequence

  18. Magnitude

  19. Unwrapped Phase

  20. 2 3 1

  21. 2 1 3 Difference

  22. X on X Y on X X on Y Y on Y

  23. References • Reese TG, et al., JMRI 1994 • Mason GF, et al., MRM 1997 • Onodera T, et al., J Phys E: Sci Instrum 1987 • Takahashi A, et al., MRM 1995 • Alley MT, et al., MRM 1998 • Zhang Y, et al., MRM 1998 • Duyn JH, et al., JMR 1998 • Beaumont M, et al., MRM 2007 • Kerr AB, PhD Thesis, Stanford, 1998 • Gurney PT, PhD Thesis, Stanford, 2007

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