Parameterization of NMR relaxation curves in terms of logarithmic moments of the relaxation time distribution

Hydrogen Diffusion in Hybrid Perovskites from Exchange NMR

Ion migration is an important phenomenon affecting the performance of hybrid perovskite solar cells. It is particularly challenging, however, to disentangle the contribution of H+ diffusion from that of other ions, and the atomic-scale mechanism remains unclear. Here, we use 2H exchange NMR to prove that 2H+ ions exchange between MA+ cations on the time scale of seconds for both MAPbI3 and FA0.7MA0.3PbI3 perovskites. We do this by exploiting 15N-enriched MA+ to label the cations by their 15N spin state. The exchange rates and activation energy are then calculated by performing experiments as functions of mixing time and temperature. By comparing the measured exchange rates to previously measured bulk H+ diffusivities, we demonstrate that, after dissociating, H+ ions travel through the lattice before associating to another cation rather than hopping between adjacent cations.

Joint multi-field T1 quantification for fast field-cycling MRI

Purpose

Recent developments in hardware design enable the use of fast field‐cycling (FFC) techniques in MRI to exploit the different relaxation rates at very low field strength, achieving novel contrast. The method opens new avenues for in vivo characterizations of pathologies but at the expense of longer acquisition times. To mitigate this, we propose a model‐based reconstruction method that fully exploits the high information redundancy offered by FFC methods.

Methods

The proposed model‐based approach uses joint spatial information from all fields by means of a Frobenius ‐ total generalized variation regularization. The algorithm was tested on brain stroke images, both simulated and acquired from FFC patients scans using an FFC spin echo sequences. The results are compared to three non‐linear least squares fits with progressively increasing complexity.

Results

The proposed method shows excellent abilities to remove noise while maintaining sharp image features with large signal‐to‐noise ratio gains at low‐field images, clearly outperforming the reference approach. Especially patient data show huge improvements in visual appearance over all fields.

Conclusion

The proposed reconstruction technique largely improves FFC image quality, further pushing this new technology toward clinical standards.

Regularized inversion of the Laplace transform for series of experiments

Not only in low-field nuclear magnetic resonance, Laplace inversion is a relevant and challenging topic. Considerable conceptual and technical progress has been made, especially for the inversion of data encoding two decay dimensions. Distortion of spectra by overfitting of even moderate noise is counteracted requiring a priori smooth spectra. In this contribution, we treat the case of simple and fast one-dimensional decay experiments that are repeated many times in a series in order to study the evolution of a sample or process. Incorporating the a priori knowledge that also in the series dimension evolution should be smooth, peak position can be stabilized and resolution improved in the decay dimension. It is explained how the standard one-dimensional regularized Laplace inversion can be extended quite simply in order to include regularization in the series dimension. Obvious improvements compared with series of one-dimensional inversions are presented for simulated as well as experimental data. For the latter, comparison with multiexponential fitting is performed.

Multicomponent analysis of T1 relaxation in bovine articular cartilage at low magnetic fields

Purpose

The multi‐exponential character of T₁ relaxation in bovine articular cartilage was investigated at low magnetic fields below 0.5 T. The ultimate aim was to identify a parameter based on the T₁ relaxation time distribution as a biomarker to biochemical features of osteoarthritis.

Methods

Osteoarthritis conditions were simulated by enzymatic digestion of cartilage with trypsin. Fast‐field cycling NMR relaxometry was carried out in the magnetic field range B₀ = 70 μT to 600 mT. The data were analyzed in terms of T₁ distributions on a log‐time scale using inverse Laplace transform, whereas integral properties such as mean T₁s and distribution widths were obtained without data inversion from logarithmic moment analysis and a stretched‐exponential fit to the data. Attempts were also made to differentiate between water dynamic components through multi‐Lorentzian decomposition of average relaxation‐rate dispersions.

Results

T₁ distribution in bovine articular cartilage was found to be bimodal, with the dominating, long component shifting toward larger values following trypsin digestion. The effect is more prominent toward lower magnetic field strength. This shift leads to an overall increase of the distribution width and an equivalently more pronounced deviation from exponential behavior.

Conclusion

The logarithmic width of T₁ distribution functions at fields of 0.5 T and below, and the stretched‐exponential decay fit exponent β, show a significant trend after trypsin digestion of cartilage. These 2 parameters are suggested as possible biomarkers for osteoarthritis in humans and can be acquired entirely in vivo, with increasing significance for lower magnetic field strengths.

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.