Improved excitation schemes for multiple-quantum magic-angle spinning for quadrupolar nuclei designed using optimal control theory

We have investigated the use of optimal control theory for the design of improved multiple-quantum excitation schemes for the popular multiple-quantum magic-angle spinning NMR experiment for quadrupolar nuclei with half-integer quadrupolar spin. The advantage of the new low-power experiments, termed OCFASTER, is demonstrated by sensitivity improvements approaching 50% for 87Rb in RbClO4 and RbNO3 as compared to FASTER and standard strong-pulse excitation schemes.     

Chemical and Structural Changes in Blood Undergoing Laser Photocoagulation¶

The treatment of cutaneous vascular lesions (port wine stains etc.) using lasers has been guided by theories based on the “cold” or room‐temperature optical properties of the hemoglobin target chromophore. We have recently presented evidence showing that under the influence of laser irradiation, the optical properties of blood in vitro are time and temperature dependent. Such complications are not currently subsumed into the in vivo theory. Here, we study the time‐domain optical properties of blood undergoing photocoagulation in vitro using two newly developed time‐resolved techniques. We also study the asymptotic effect of laser photocoagulation on the chemical and structural properties of the components of the blood matrix. We present evidence showing that the photocoagulation process involves significant changes in the optical absorption and scattering properties of blood, coupled with photothermally induced chemical and structural changes. We demonstrate the first use of a laser to deliberately generate magnetic resonance imaging contrast in vitro. We show that this technique offers significant potential advantages to in vivo intravenous chemical contrast agent injection.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations

We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretization errors with a new term accounting for the propagation of numerical round-off errors, showing that the accumulated round-off error is inversely proportional to the square root of the step size. As a consequence, the numeric precision eventually sets the limit for the pointwise computability of accurate solutions of any ODE. The theoretical results are supported by numerically computed solutions and error estimates for the Lorenz system and the van der Pol oscillator.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.     

Composite dipolar recoupling: anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.     

Profiles of paint layer samples obtained in the fringe field of a high field magnet by means of very short broadband frequency-modulated pulses

In this article, we describe the acquisition of depth profiles, in particular of paint layers, in the static gradient of a high field magnet, providing a superior sensitivity. The main objective are reference profiles that help to understand scans made with noninvasive unilateral nuclear magnetic resonance (NMR), which often suffers from poor signal-to-noise ratio when working with real samples. Various technical aspects like the coil geometry and the limit of resolution are investigated. A major advancement is the use of frequency-modulated pulses that are very broadband and at the same time very short (25 μs). The latter is necessary to allow the acquisition of a CPMG echo train of old, rigid paint material. Despite being far from adiabatic, they provide uniform excitation and refocusing over 1 MHz, which corresponds to about 400 μm with the used gradient. We show that the uniformity is even sufficient to obtain biexponential relaxation profiles. With these tools, a paint sample from a restoration campaign is analyzed with different contrast criteria: The original and two layers from former restoration attempts can be visualized, and furthermore, the relaxation profiles allow to study the migration of plasticizing molecules.     

Unilateral NMR applied to the conservation of works of art

In conventional NMR, samples from works of art in sizes above those considered acceptable in the field of art conservation would have to be removed to place them into the bore of large superconducting magnets. The portable permanent-magnet-based systems, by contrast, can be used in situ to study works of art, in a noninvasive manner. One of these portable NMR systems, NMR-MOUSE®, measures the information contained in one pixel in an NMR image from a region of about 1 cm², which can be as thin as 2–3 µm. With such a high depth resolution, profiles through the structures of art objects can be measured to characterize the materials, the artists’ techniques, and the deterioration processes. A novel application of the technique to study a deterioration process and to follow up a conservation treatment is presented in which micrometer-thick oil stains on paper are differentiated and characterized. In this example, the spin–spin relaxation T ₂ of the stain is correlated to the iodine number and to the degree of cross-linking of the oil, parameters that are crucial in choosing an appropriate conservation treatment to remove them. It is also shown that the variation of T ₂ over the course of treatments with organic solvents can be used to monitor the progress of the conservation interventions. It is expected that unilateral NMR in combination with multivariate data analysis will fill a gap within the set of high-spatial-resolution techniques currently available for the noninvasive analysis of materials in works of art, where procedures to study the inorganic components are currently far more developed than those suitable for the study of the organic components.