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Pulse Techniques

Pulse Techniques. Off-Resonance Effects. Initial magnetization along z x-pulse ( f = 0) On-resonance: M z -> -M y Off-resonance: phase b. Off-Resonance Effects – 90 º Pulse. 90 º hard pulse works well for W < w 1 Phase shift b is approximately linear

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Pulse Techniques

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  1. Pulse Techniques

  2. Off-Resonance Effects • Initial magnetization along z • x-pulse (f = 0) • On-resonance: Mz -> -My • Off-resonance: phase b

  3. Off-Resonance Effects – 90º Pulse • 90º hard pulse works well for W < w1 • Phase shift b is approximately linear • Effective flip angle a increases

  4. Off-Resonance Effects – 90º Pulse • Assume: • Close to resonance • 90º pulse (a0=p/2) • First-order approximation • Phase angle is proportional to offset • First-order phase correction

  5. Off-Resonance Effects – 90º Pulse • Initial magnetization state is irrelevant • Result: zz-ax-zz

  6. Off-Resonance Effects - Compensation • Not constant-time • Subtract 2t90/p for each 90º pulse, or • Add a short echo • Constant-time • No compensation needed if 90º pulses are identical • Shaped 90º pulses?

  7. Pulse calibration – 180º or 360º? • 180º pulse: • Poor off-resonance performance • Mxy ~W • Linear phase twist b • Saturation in repeated experiments • 360º pulse • Better off-resonance performance • W< 0.1w1 • Uniform phase • Minimal saturation

  8. Off-Resonance Effects – 180º Pulse • Inversion: • Poor off-resonance performance • Refocusing: • Orthogonal better than parallel • Phase twist is the same • Both work only for W< 0.2w1

  9. Composite Pulses • Trains of rectangular pulses instead of a single pulse • Off-resonance performance • Tolerance to B1 inhomogeneity • 90º – historic • 180º inversion – most common

  10. 90x-180y-90x Composite Pulse • 90x-180y-90x replaces 180x for inversion • The middle 180º compensates for off-resonance behavior of the outer 90º pulses

  11. ax-2ay-ax Composite Pulse • 90x-180y-90x has better broadband inversion performance • W < w1 • 90x-225y-90x has smoother, but narrower profile • W < 0.7 w1 • ax-2ay-ax composite pulse is less sensitive to mis-calibration of 90º pulse • Cannot be used for refocusing

  12. Selective Pulses • Requirements: • Uniform excitation (inversion) profile • Minimal perturbation outside the target frequency range • Uniform resulting phase (for excitation) • Short pulse length • Low peak power • Easy to implement shape

  13. Soft Rectangular Pulses • Find w1, which produces a null in the excitation (inversion) profile at a certain offset off-resonance

  14. Shaped Pulses • Approximated by a series of short rectangular pulses • Every point i: • Amplitude wi • Phase fi

  15. Examples - Gaussian Pulse • Truncated at 1% of max amplitude • Excitation profile - gaussian

  16. Examples - Sinc Pulse • One-lobe of the sinc function • Needs less power for the same length • Similar excitation profile

  17. Examples - SEDUCE-1 • Essentially a gaussian, smoothed at both ends • Used mostly for decoupling

  18. Examples - Q5 Gaussian Cascade • ~300 ms pulse used as 90º 13C excitation pulse in Bruker pulse sequences • Better than a soft rectangular 90º pulse • For Iy -> Iz application needs to be time-reversed

  19. Q5 Gaussian Cascade – Excitation Profile

  20. Examples - Q3 Gaussian Cascade • ~200 ms pulse used as 180º 13C refocusing pulse in Bruker pulse sequences

  21. Q3 Gaussian Cascade – Refocusing Profile

  22. Q3 Gaussian Cascade – Inversion Profile • It also provides good inversion

  23. Examples - E-BURP2 • Used in L-optimized experiments

  24. E-BURP2 – Excitation Profile

  25. Phase-Modulated Pulses – Frequency shifting • Linear phase ramp • f0 controls the phase of the resulting pulse: • 90º (Iz -> Iy): fN = 0 • 90º (Iy -> Iz): f0 = 0 • 180º (Iy -> -Iy): fN/2 = 0 • 180º (Iz -> -Iz): arbitrary

  26. Phase-Modulated Pulses – Resolution Issues • Time resolution • More points = better shape approximation • Minimal pulse delay • Phase resolution • More points = smaller phase steps • Minimal phase step

  27. Phase-Modulated Pulses – Multi-band excitation • Cosine modulation • 10 kHz • Needs 2x more power

  28. Adiabatic Pulses • “Conventional” pulses: • Stationary Beff orientation • Magnitude may be variable • Precession around Beff • Adiabatic pulses: • Non-stationary Beff orientation • Magnetization follows Beff, while precessing around it

  29. Adiabatic Pulses –Performance Conditions • Beff magnitude should be changed gradually

  30. Adiabatic Pulses –Performance Conditions • A second rotating frame {xr, yr, zr} within the first rotating frame • Beff magnitude should be tilted slowly

  31. Adiabatic Pulses –Performance Conditions • Adiabatic condition • Adiabaticity factor

  32. Adiabatic Pulses - Chirp • 180 13C inversion on Bruker • 60 kHz sweep • 500 us • 20% smoothing

  33. Chirp – Inversion Profile • Very broad inversion profile • Low peak power • ~50% of high power

  34. Adiabatic Pulses – Tolerance B1 Inhomogeneity • Power 3 dB higher than calibrated • Power 3 dB lower than calibrated

  35. Adiabatic Pulses - Wurst • Smoothed ramp-up and ramp-down

  36. Adiabatic Pulses - sech

  37. Pseudo Bloch-Siegert Shifts • Assume: • x-pulse (f = 0) • Very far off-resonance • Magnetization along y • Third order approximation

  38. Pseudo Bloch-Siegert Shifts • The result is a z-rotation by an angle a • In the absence of w1 the rotation a = Wtp – the chemical shift evolution! • Pulse phase and initial magnetization phase are irrelevant

  39. Pseudo Bloch-Siegert Shifts • An off-resonance pulse incurs a phase shiftjPBS • It is proportional to time-averaged square of w1 • Also valid for shaped pulses • Continuous application of w1 leads to a frequency shiftwPBS • SEDUCE decoupling during chemical shift evolution

  40. PBS Phase Shifts - Compensation • Small-phase adjustment of a 90º pulse or phase correction in the frequency domain • Depends on whether there is chemical shift evolution • Works only for a narrow range of resonances far off-resonance • Partial compensation • Used in BioPack

  41. PBS Phase Shifts - Compensation • Using a second identical pulse and an echo • Perfect compensation over a broad spectral range • Limited by the broadband performance of refocusing 180º pulse • Default for Bruker sequences

  42. PBS Phase Shifts - Compensation • A second pulse with opposite offset • Must be far off-resonance • Imperfect compensation – first-order phase correction required • Not widely used • Cosine modulation • Requires twice the power

  43. PBS Frequency Shifts – SEDUCE decoupling • Train of cosine modulated SEDUCE-1 shaped pulses • Modulation frequency Wmod • Signals of interest are near the carrier • Decoupling is very far off resonance • The result is a scaling of the spectrum by a factor l • Compression around the center

  44. PBS Frequency Shifts – SEDUCE decoupling • 600 MHz example • 15 ms hard 13C pulse • 252 ms SEDUCE-1 • w1max = 2.1 kHz • Scaling factor x = 0.36 • For squared shapes, relative to a rectangle of the same amplitude • Wmod = 17.7 kHz • For 80 ppm spectral width • 0.2 ppm shift at edges • Unsuitable for 15N-, 13Cali-, 13Caro-NOESY

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