RESUMO
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.
RESUMO
Magnetic resonance is an important noninvasive technology across life sciences and industry. Free induction decay is the simplest [Formula: see text]H magnetic resonance measurement method and an important means of probing fast-decaying signals in porous materials such as rocks, lung, and bone. It is commonly assumed that the free induction decay in geological porous materials is single-exponential. We experimentally observed two regimes of free induction decay behavior in geological porous materials: single-exponential and non-exponential decay. Numerical simulations that match experimental data highlight the effect of mass diffusion, especially in the single-exponential behavior. These two regimes of free induction decay in porous materials are associated with a bifurcation point in the solutions of the Bloch-Torrey equation for diffusion of fluids in confined domains in the presence of internal magnetic field gradients. This finding facilitates the extraction of absolute internal magnetic field gradient intensities from simple free induction decay measurements in the laboratory and field. This work also warns against common single-exponential assumptions in surface magnetic resonance methods employed in surveying underground water aquifers.
RESUMO
The majority of low field Magnetic Resonance (MR) analyses rely on T2 lifetime measurements. Modification of the T2 measurement to include a T1 dimension has made the T1-T2 measurement a very powerful analytical technique. The T1-T2 measurement is uniquely well suited to characterization of different spin populations in porous materials, such as fluid bearing reservoir rocks, and in soft biopolymer materials, for example foods. However, the T1-T2 measurement is challenging or impossible if the T2 relaxation lifetime, or a component lifetime, is short-lived and the signal unobservable in an echo measurement. This occurs in many important classes of materials. A short lifetime T2 will not however, in general, preclude observation of a free induction decay with signal decay governed by T2*. As outlined in this paper a T1-T2* measurement is a useful analog to the T1-T2 experiment. T1-T2* measurement enables one to differentiate species as a function of T2* in one dimension and T1 in the other dimension. Monitoring changes of the T1-T2* coordinate, and associated signal intensity changes, has the potential to reveal structural changes in materials evolving in time. These methods may also be employed to discriminate and identify solid-like species present in static samples. The T1-T2* measurement is very general in application, but in this paper we focus on cement-based mortars to develop and illustrate the essential ideas. T1-T2* results show a multi-modal behaviour of the MR signal lifetimes, T1 and T2*, in mortar samples under study, indicating at least two different water populations. The short T2* lifetime was assigned to interlayer water (water between C-S-H layers) where the associated T1 is also short lived. The longer T2* lifetime was assigned to water in the pore space, where T1 is also longer lived. In addition to mortar samples we also show application of the method to a crystalline organic species, o-phenylenediamine, which features Sinc Gaussian and exponential decays of transverse magnetization.
