Novel Methods for High Resolution NMR in Inhomogeneous Fields

• Applicant: Professor Dr. Steffen Glaser
• Subject Area: Analytical Chemistry
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 49580800

• Final Report Year: 2014

Final Report Abstract

The project provided novel NMR pulses with unprecedented robustness with respect to large frequency offsets (due to chemical shifts or B0 inhomogeneity) and B1 scaling (due to imperfections in pulse calibration or B1 inhomogeneity). The pulse designs are based on numerical and geometric optimal control methods. Both broadband and band-selective pulses were investigated. Systematic studies provided libraries of point-to-point (PP) excitation, inversion and saturation pulses and of universal rotation (UR) 90◦ and 180◦ pulses. From these libraries, pulses can be chosen that are most appropriate for the bandwidth and robustness that is required for a given application. One of the highlights of the project was the first two-dimensional correlation experiment using toroid probes with a B1 inhomogeneity of 600%, which was made possible by extremely B1-tolerant universal rotation pulses. For coupled spin systems, novel optimal control pulses and pulse sequences were designed for coherence transfer and heteronuclear decoupling. Relaxation-optimized pulses help to minimize relaxation losses and relaxation-selective pulses provide a new approach to maximize contrast in medical imaging. Pulses were designed taking into account experimental limitations (such as bounds on the maximum pulse amplitudes or on the maximum pulse power) and imperfections (such as amplitude and phase transients.) In addition to novel pulses of practical interest in magnetic resonance spectroscopy and imaging, more flexible and powerful optimal control algorithms were developed and also the the non-linear effects of radiation damping have been implemented. In the case of excitation pulses, it was unexpected to find that prefocussed pulses with a negative effective evolution period during the pulses can be designed more efficiently than excitation pulses that produce transverse magnetization with offset-independent phase. This finding was applied in experiments with a relatively long receiver dead time in pulsed electron-spin resonance. In the case of broadband universal rotation pulses, it was found that the optimization can be made more efficient not only by exploiting pulse symmetry properties but also by specifying the global phase of the target propagators, which helps to avoid local maxima in the optimization landscape. Finally, the geometric analysis of optimal saturation pulses led to the surprising discovery of a previously unknown structure in the Bloch sphere, the so-called ”magic plane”, which represents the location, where the magnetization vector shrinks most rapidly and which is crucial for the understanding of the optimal pulses and of the corresponding trajectories of the spins.

Publications

• ”Exploring the Limits of Excitation and Inversion Pulses II. RF-Power Optimized Pulses”, J. Magn. Reson. 194, 58-66 (2008)
  K. Kobzar, T. E. Skinner, N. Khaneja, S. J. Glaser, B. Luy
  
• ”Linear Phase Slope in Pulse Design: Application to Coherence Transfer”, J. Magn. Reson. 192, 235-243 (2008)
  N. I. Gershenzon, T. E. Skinner, B. Brutscher, N. Khaneja, M. Nimbalkar, B. Luy, S. J. Glaser
  
• ”Heteronuclear Decoupling by Optimal Tracking”, J. Magn. Reson. 201, 7-17 (2009)
  J. L. Neves, B. Heitmann, N. Khaneja, S. J. Glaser
  
• ”Optimal Control in NMR Spectroscopy: Numerical Implementation in SIMPSON”, J. Magn. Reson. 197, 120-134 (2009)
  Z. Tošner, T. Vosegaard, C. T. Kehlet, N. Khaneja, S. J. Glaser, N. C. Nielsen
  
• ”Simultaneous Time-Optimal Control of the Inversion of Two Spin 1/2 Particles”, Phys. Rev. A 82, 013415 (2010)
  E. Assémat, M. Lapert, Y. Zhang, M. Braun, S. J. Glaser, D. Sugny
  
• ”Design and Application of Robust RF Pulses for Toroid Cavity NMR Spectroscopy”, J. Magn. Reson. 209, 282-290 (2011)
  T. E. Skinner, M. Braun, K. Woelk, N. I. Gershenzon, S. J. Glaser
  
• ”Exploring the Limits of Broadband 90◦ and 180◦ Universal Rotation Pulses”, J. Magn. Reson. 225, 142-160 (2012)
  K. Kobzar, S. Ehni, T. E. Skinner, S. J. Glaser, B. Luy
  
• ”Optimal Control Design of Band-Selective Excitation Pulses that Accommodate Relaxation and RF Inhomogeneity”, J. Magn. Reson. 217, 53-60 (2012)
  T. E. Skinner, N. I. Gershenzon, M. Nimbalkar, S. J. Glaser
  
• ”Tailored Real-Time Scaling of Heteronuclear Couplings”, J. Magn. Reson. 223, 207-218 (2012)
  F. Schilling, S. J. Glaser
  
• ”The Fantastic Four: A Plug ’n’ Play Set of Optimal Control Pulses for Enhancing NMR Spectroscopy”, J. Magn. Reson. 228, 16-31 (2013)
  M. Nimbalkar, B. Luy, T. E. Skinner, J. L. Neves, N. I. Gershenzon, K. Kobzar, W. Bermel, S. J. Glaser