Pulsed Field Gradient NMR with Sigmoid Shape Gradient Sampling To Produce More Detailed Diffusion Ordered Spectroscopy Maps of Real Complex Mixtures: Examples with Medicine Analysis

Optimising sampling patterns for bi-exponentially decaying signals

A recently reported method, based on the Cramér-Rao Lower Bound theory, for optimising sampling patterns for a wide range of nuclear magnetic resonance (NMR) experiments is applied to the problem of optimising sampling patterns for bi-exponentially decaying signals. Sampling patterns are optimised by minimizing the percentage error in estimating the most difficult to estimate parameter of the bi-exponential model, termed the objective function. The predictions of the method are demonstrated in application to pulsed field gradient NMR data recorded for the two-component diffusion of a binary mixture of methane/ethane in a zeolite. It is shown that the proposed method identifies an optimal sampling pattern with the predicted objective function being within 10% of that calculated from the experiment dataset. The method is used to advise on the number of sampled points and the noise level needed to resolve two-component systems characterised by a range of ratios of populations and diffusion coefficients. It is subsequently illustrated how the method can be used to reduce the experiment acquisition time while still being able to resolve a given two-component system.

Optimising magnetic resonance sampling patterns for parametric characterisation

Sampling strategies are often central to experimental design. Choosing efficiently which data to acquire can improve the estimation of parameters and reduce the acquisition time. This work is focused on designing optimal sampling patterns for Nuclear Magnetic Resonance (NMR) applications, illustrated with respect to the best estimate of the parameters characterising a lognormal distribution. Lognormal distributions are commonly used as fitting models for distributions of spin-lattice relaxation time constants, spin-spin relaxation time constants and diffusion coefficients. A method for optimising the choice of points to be sampled is presented which is based on the Cramér-Rao Lower Bound (CRLB) theory. The method's capabilities are demonstrated experimentally by applying it to the problem of estimating the emulsion droplet size distribution from a pulsed field gradient (PFG) NMR diffusion experiment. A difference of <5% is observed between the predictions of CRLB theory and the PFG NMR experimental results. It is shown that CLRB theory is stable down to signal-to-noise ratios of ∼10. A sensitivity analysis for the CRLB theory is also performed. The method of optimizing sampling patterns is easily adapted to distributions other than lognormal and to other aspects of experimental design; case studies of optimising the sampling scheme for a fixed acquisition time and determining the potential for reduction in acquisition time for a fixed parameter estimation accuracy are presented. The experimental acquisition time is typically reduced by a factor of 3 using the proposed method compared to a constant gradient increment approach that would usually be used.

Reconstructing diffusion ordered NMR spectroscopy by simultaneous inversion of Laplace transform

2D diffusion-ordered NMR spectroscopy (DOSY) has been widely recognized as a powerful tool for analyzing mixtures and probing inter-molecular interactions in situ. But it is difficult to differentiate molecules with similar diffusion coefficients in presence of overlapped spectra. Its performance is susceptible to the number of chemical components, and usually gets worse when the number of components increases. Here, to alleviate the problem, numerical simultaneous inversion of Laplace transform (SILT) of many related variables is proposed for reconstructing DOSY spectrum (SILT-DOSY). The advantage of the proposed method in comparison to other methods is that it is capable of estimating the number of analytes more accurately and deriving corresponding component spectra, which in turn leads to the more reliable identification of the components.

Pulsed-field gradient nuclear magnetic resonance measurements (PFG NMR) for diffusion ordered spectroscopy (DOSY) mapping

The advent of Diffusion Ordered SpectroscopY (DOSY) NMR has enabled diffusion coefficients to be routinely measured and used to characterize chemical systems in solution. Indeed, DOSY NMR allows the separation of the chemical entities present in multicomponent systems and provides information on their intermolecular interactions as well as on their size and shape.