•A general approach is introduced to optimize relaxation dispersion sequences.•Optimizations are based on the relaxation and exchange rate dependence of the detectable signal.•The optimized windowless sequences are both amplitude and phase modulated.•The performance of ideal CPMG sequences is approached by energy-limited sequences.•The physical limits of relaxation dispersion experiments can be explored.A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.Download high-res image (147KB)Download full-size image

•Chemical shift correlations are obtained for on-going reactions by SHOT decoupling.•This method is used with dissolution dynamic nuclear polarization in a single scan.•A novel SHOT pulse increases the J-splitting up to 50% over the actual J-coupling.•The performance of two SHOT pulses with different J-splittings is evaluated.Off-resonance decoupling using the method of Scaling of Heteronuclear Couplings by Optimal Tracking (SHOT) enables determination of heteronuclear correlations of chemical shifts in single scan NMR spectra. Through modulation of J-coupling evolution by shaped radio frequency pulses, off resonance decoupling using SHOT pulses causes a user-defined dependence of the observed J-splitting, such as the splitting of 13C peaks, on the chemical shift offset of coupled nuclei, such as 1H. Because a decoupling experiment requires only a single scan, this method is suitable for characterizing on-going chemical reactions using hyperpolarization by dissolution dynamic nuclear polarization (D-DNP). We demonstrate the calculation of [13C, 1H] chemical shift correlations of the carbanionic active sites from hyperpolarized styrene polymerized using sodium naphthalene as an initiator. While off resonance decoupling by SHOT pulses does not enhance the resolution in the same way as a 2D NMR spectrum would, the ability to obtain the correlations in single scans makes this method ideal for determination of chemical shifts in on-going reactions on the second time scale. In addition, we present a novel SHOT pulse that allows to scale J-splittings 50% larger than the respective J-coupling constant. This feature can be used to enhance the resolution of the indirectly detected chemical shift and reduce peak overlap, as demonstrated in a model reaction between p-anisaldehyde and isobutylamine. For both pulses, the accuracy is evaluated under changing signal-to-noise ratios (SNR) of the peaks from reactants and reaction products, with an overall standard deviation of chemical shift differences compared to reference spectra of 0.02 ppm when measured on a 400 MHz NMR spectrometer. Notably, the appearance of decoupling side-bands, which scale with peak intensity, appears to be of secondary importance.

•Time–frequency representations of NMR pulses make hidden structures visible.•Approach provides clues to mode of action of highly optimized pulses.•Phase-sensitive spectrograms and pseudo-heteronuclear representations of pulses.•Visualization of frequency-dependent power deposition in decoupling sequences.•Distinction between noise pulses and seemingly random but highly optimized pulses.We study the utility of joint time–frequency representations for the analysis of shaped or composite pulses for magnetic resonance. Such spectrograms are commonly used for the visualization of shaped laser pulses in optical spectroscopy. This intuitive representation provides additional insight compared to conventional approaches, which exclusively show either temporal or spectral information. We focus on the short-time Fourier transform, which provides not only amplitude but also phase information. The approach is illustrated for broadband inversion pulses, multiple quantum excitation and broadband heteronuclear decoupling. The physical interpretation and validity of the approach is discussed.Download high-res image (137KB)Download full-size image

The control of the dynamics of spin systems by magnetic fields has opened intriguing possibilities in quantum computing and in Nuclear Magnetic Resonance spectroscopy. In this framework, optimal control theory has been used to design control fields able to realize a given task while minimizing a prescribed cost such as the energy of the field or the duration of the process. However, some of the powerful tools of optimal control had not been used yet for NMR applications in medical imagery. Here, we show that the geometric control theory approach can be advantageously combined with NMR methods to crucially optimize the imaging contrast. This approach is applied to a benchmark problem but it gives a strong evidence for the possibility of using optimal control theory for enhancing the contrast and the resolution of medical images.