Nuclear magnetic resonance T1-T2 inversion with double objective functions

Simple MATLAB and Python scripts for multi-exponential analysis

Multi-exponential decay is prevalent in magnetic resonance spectroscopy, relaxation, and imaging. This paper describes simple MATLAB and Python functions and scripts for regularized multi-exponential analysis methods for 1D and 2D data and example test problems and experiments. Regularized least-squares solutions provide production-quality outputs with robust stopping rules in ~5 and ~20 lines of code for 1D and 2D inversions, respectively. The software provides an open-architecture simple solution for transforming exponential decay data to the distribution of their decay lifetimes. Examples from magnetic resonance relaxation of a complex fluid, a Danish North Sea crude oil, and fluid mixtures in porous materials-brine/crude oil mixture in North Sea reservoir chalk-are presented. Developed codes may be incorporated in other software or directly used by other researchers, in magnetic resonance relaxation, diffusion, and imaging or other physical phenomena that require multi-exponential analysis.

Rapid measurement of T1*-T2* relaxation correlation with a Look-Locker sequence

Measurement of longitudinal-transverse (T₁-T₂*) relaxation may be time-consuming for samples with a long T₁ lifetime. In this work, a fast measurement method of T₁*-T₂* relaxation correlation was presented based on a saturation recovery Look-Locker sequence. T₁* is the effective T₁ lifetime. The T₁ lifetime can be calculated from the measured T₁* lifetime and acquisition parameters. The new measurement method was verified by numerical simulation. Three representative samples, corn starch, Advil caplets, and shale in the fields of food, pharmaceutics, and energy, were employed as test samples. Comparisons of T₁*-T₂* and T₁-T₂* relaxation correlations show that the new two-dimensional magnetic resonance pulse sequence works well, with a high collection efficiency and good accuracy.

3D Relaxation-Assisted Separation of Wideline Solid-State NMR Patterns for Achieving Site Resolution

There are currently no methods for the acquisition of ultra-wideline (UW) solid-state NMR spectra under static conditions that enable reliable separation and resolution of overlapping powder patterns arising from magnetically...

Magnetic resonance T1-T2* and T1ρ-T2* relaxation correlation measurements in solid-like materials with non-exponential decays

Magnetic resonance T₁-T₂* relaxation correlation is a newly emerging and powerful tool to study the structure and dynamics of materials. However, the T₁-T₂* of solid-like materials may consist of a linear combination of exponential decays and non-exponential decays, and the traditional methods for processing T₁-T₂ data would be not applicable. In this paper, a method of processing T₁-T₂* data with non-exponential decays was proposed. The critical idea is to decompose the data into two sub-datasets, exponential decays and non-exponential decays, employing a non-linear fitting method, and then to invert the sub-datasets and to combine the inversion results. We also introduce a related relaxation correlation measurement, T_1ρ-T₂*, for examination of solid-like materials. The same data processing strategy as for T₁-T₂* was implemented. The effectiveness of the proposed method for processing non-exponential data, Sinc Gaussian and Gaussian decay, was validated with simulation and experiment. The results showed that the proposed method recovers T₁-T₂* and T_1ρ-T₂* spectra with accurate relative signal intensities. The proposed method provides a platform for further development of MR methods applied to solid-like materials. These relaxation correlations are well suited to measuring composition of mixtures, with solid components in the mixture.