Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.     

Exploring the limits of broadband excitation and inversion pulses

The design of broadband excitation and inversion pulses with compensation of B(1)-field inhomogeneity is a long standing goal in high resolution NMR spectroscopy. Most optimization procedures used so far have been restricted to particular pulse families to keep the scale of the problem within manageable limits. This restriction is unnecessary using efficient numerical algorithms based on optimal control theory. A systematic study of rf-limited broadband excitation by optimized pulses and broadband inversion by optimized pulses with respect to bandwidth and B(1)-field is presented. Upper limits on minimum pulse lengths are set for different degrees of pulse performance.     

Optimal experiments for maximizing coherence transfer between coupled spins

Hyperpolarized noble gases (HNGs) provide exciting possibilities for MR imaging at ultra-low magnetic field strengths (<0.15 T) due to the extremely high polarizations available from optical pumping. The fringe field of many superconductive magnets used in clinical MR imaging can provide a stable magnetic field for this purpose. In addition to offering the benefit of HNG MR imaging alongside conventional high field proton MRI, this approach offers the other useful advantage of providing different field strengths at different distances from the magnet. However, the extremely strong field gradients associated with the fringe field present a major challenge for imaging since impractically high active shim currents would be required to achieve the necessary homogeneity. In this work, a simple passive shimming method based on the placement of a small number of ferromagnetic pieces is proposed to reduce the fringe field inhomogeneities to a level that can be corrected using standard active shims. The method explicitly takes into account the strong variations of the field over the volume of the ferromagnetic pieces used to shim. The method is used to obtain spectra in the fringe field of a high-field (1.89 T) superconducting magnet from hyperpolarized 129Xe gas samples at two different ultra-low field strengths (8.5 and 17 mT). The linewidths of spectra measured from imaging phantoms (30 Hz) indicate a homogeneity sufficient for MRI of the rat lung.     

Homonuclear decoupling for liquid-state NMR

We present a solution to the problem of decoupling of a homonuclear two-spin system having weak isotropic scalar coupling. We describe non-selective pulse sequences that create an effective field perpendicular to the coupling interaction over a broad range of chemical shifts, with a magnitude proportional to the chemical shifts. Effective decoupling is achieved when the difference in chemical shifts imprinted on the perpendicular field is sufficiently larger than the coupling between the spins. The proposed methods scale down the chemical shifts. The pulse sequences may be useful in various applications in nuclear magnetic resonance spectroscopy.     

Fourier synthesis techniques for NMR spectroscopy in inhomogeneous fields

This paper describes a method for synthesizing spin rotations with arbitrary space dependence on a sample of noninteracting spin 12 by using nonselective radio frequency pulses and pulsed field gradients. This method is used to map out spatial distribution of inhomogeneous B(0) field and to engineer a space dependent evolution of spins that cancels the space dependent phase spins acquire when precessing in an inhomogeneous magnetic field. The technique allows one to record high resolution spectra in inhomogeneous magnetic field by using only time varying linear gradients and rf fields and is expected to find applications in ex situ NMR.     

Optimal control design of constant amplitude phase-modulated pulses: application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform Iz to greater than 0.99 Ix over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3 degrees over almost the entire range, with sporadic deviations of 6-9 degrees at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.     

Sensitivity enhanced recoupling experiments in solid-state NMR by gamma preparation

In this paper, we introduce a class of dipolar recoupling experiments under magic angle spinning (MAS), which use gamma dependent antiphase polarization during the t1 evolution period. We show that this helps us to design dipolar recoupling experiments that transfer both components of the transverse magnetization of spin S to a coupled spin I in the mixing step of a 2D NMR experiment. We show that it is possible to design such transfer schemes and make them insensitive to the orientation dependency of the couplings in powders. This helps us to develop sensitivity enhanced 2D NMR experiments of powder samples under MAS.     

Heteronuclear decoupling by optimal tracking

The problem to design efficient heteronuclear decoupling sequences is studied using optimal control methods. A generalized version of the gradient ascent engineering (GRAPE) algorithm is presented that makes it possible to design complex non-periodic decoupling sequences which are characterized by tens of thousands of pulse sequence parameters. In contrast to conventional approaches based on average Hamiltonian theory, the concept of optimal tracking is used: a pulse sequence is designed that steers the evolution of an ensemble of spin systems such that at a series of time points, a specified trajectory of the density operator is tracked as closely as possible. The approach is demonstrated for the case of low-power heteronuclear decoupling in the liquid state for in vivo applications. Compared to conventional sequences, significant gains in decoupling efficiency and robustness with respect to offset and inhomogeneity of the radio-frequency field were found in simulations and experiments.