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Pulse Techniques

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Off-Resonance Effects Initial magnetization along z x-pulse ( = 0) On-resonance: M z -> -M y Off-resonance: phase

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Off-Resonance Effects – 90º Pulse 90º hard pulse works well for < 1 Phase shift is approximately linear Effective flip angle increases

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

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Off-Resonance Effects – 90º Pulse Initial magnetization state is irrelevant Result: z - x - z

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

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Pulse calibration – 180º or 360º? 180º pulse: Poor off-resonance performance M xy ~ Linear phase twist Saturation in repeated experiments 360º pulse Better off-resonance performance < 0.1 1 Uniform phase Minimal saturation

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Off-Resonance Effects – 180º Pulse Inversion: Poor off-resonance performance Refocusing: Orthogonal better than parallel Phase twist is the same Both work only for < 0.2 1

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Composite Pulses Trains of rectangular pulses instead of a single pulse Off-resonance performance Tolerance to B 1 inhomogeneity 90º – historic 180º inversion – most common

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

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x -2 y - x Composite Pulse 90 x -180 y -90 x has better broadband inversion performance < 1 90 x -225 y -90 x has smoother, but narrower profile < 0.7 1 x -2 y - x composite pulse is less sensitive to mis- calibration of 90º pulse Cannot be used for refocusing

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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

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Soft Rectangular Pulses Find 1, which produces a null in the excitation (inversion) profile at a certain offset off-resonance

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Shaped Pulses Approximated by a series of short rectangular pulses Every point i : Amplitude i Phase i

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

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

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

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Examples - Q5 Gaussian Cascade ~300 s pulse used as 90º 13C excitation pulse in Bruker pulse sequences Better than a soft rectangular 90º pulse For I y -> I z application needs to be time-reversed

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Q5 Gaussian Cascade – Excitation Profile

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Examples - Q3 Gaussian Cascade ~200 s pulse used as 180º 13C refocusing pulse in Bruker pulse sequences

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Q3 Gaussian Cascade – Refocusing Profile

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Q3 Gaussian Cascade – Inversion Profile It also provides good inversion

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Examples - E-BURP2 Used in L-optimized experiments

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E-BURP2 – Excitation Profile

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Phase-Modulated Pulses – Frequency shifting Linear phase ramp 0 controls the phase of the resulting pulse: 90º ( I z -> I y ): N = 0 90º ( I y -> I z ): 0 = 0 180º ( I y -> -I y ): N/2 = 0 180º ( I z -> -I z ): arbitrary

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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

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

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

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Adiabatic Pulses – Performance Conditions B eff magnitude should be changed gradually

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Adiabatic Pulses – Performance Conditions A second rotating frame {x r, y r, z r } within the first rotating frame B eff magnitude should be tilted slowly

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Adiabatic Pulses – Performance Conditions Adiabatic condition Adiabaticity factor

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

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

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Adiabatic Pulses – Tolerance B 1 Inhomogeneity Power 3 dB higher than calibrated Power 3 dB lower than calibrated

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Adiabatic Pulses - Wurst Smoothed ramp-up and ramp-down

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Adiabatic Pulses - sech

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

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Pseudo Bloch-Siegert Shifts The result is a z-rotation by an angle In the absence of 1 the rotation = p – the chemical shift evolution! Pulse phase and initial magnetization phase are irrelevant

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Pseudo Bloch-Siegert Shifts An off-resonance pulse incurs a phase shift PBS It is proportional to time- averaged square of 1 Also valid for shaped pulses Continuous application of 1 leads to a frequency shift PBS SEDUCE decoupling during chemical shift evolution

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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

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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

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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

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

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PBS Frequency Shifts – SEDUCE decoupling 600 MHz example 15 s hard 13C pulse 252 s SEDUCE-1 1 max = 2.1 kHz Scaling factor = 0.36 For squared shapes, relative to a rectangle of the same amplitude mod = 17.7 kHz For 80 ppm spectral width 0.2 ppm shift at edges Unsuitable for 15N-, 13C ali -, 13C aro -NOESY

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