Exploring the potential of PCA-based quantitation of NMR signals in T1 relaxometry.

Principal component analysis (PCA) has proved to be a powerful technique for processing NMR data. It is particularly useful in signal quantitation where it often provides better results compared to a direct integration of individual signals. In the present work, we recapitulate the principles and theoretical framework underlying PCA-based quantitation with a special focus on T1 relaxometry. We show that under commonly encountered conditions, this approach can provide up to ~4-fold improvement in scatter of points in magnetization build-up curves compared to direct integration. Best practices to optimize the PCA performance in measuring the total magnetization are discussed, including minimization of the number of signal-related principal components and a proper selection of FT parameters and data quantitation intervals. For signals consisting of distinct relaxation components, formulas are provided for resolving the components relaxation and illustrated on a real-data example. In addition to the problem of quantitation, the use of PCA in denoising of partially relaxed spectra is discussed in connection with such applications as line shape analysis and monitoring relaxation of individual spectral components.

Controlling susceptibility mismatch effects, signal lifetimes, and SNR through variation of B0 in MRI of rock core plugs.

1H relaxometry measurements of petroleum core plugs are commonly performed on low field magnets (<0.5 Tesla) to reduce the influence of magnetic susceptibility mismatch on measurements of the spin-spin relaxation time, T2. The Signal to Noise Ratio (SNR) of the MR signal, however, generally decreases with lower magnetic fields. Higher magnetic fields (>3 Tesla) are typically employed in small animal MRI studies to improve SNR and image resolution. For many rock core plug samples, susceptibility mismatch effects can be severe at these higher fields leading to decreased T2 and T2*. In this work we seek an answer to the general question of what is the best field for MRI of rock core plugs, anticipating that it will be both sample and measurement method dependent. Free Induction Decay (FID) relaxation time measurements were undertaken to investigate the conditions under which the SNR in Centric Scan SPRITE (Single Point Ramped Imaging with T1 Enhancement) MRI measurements is maximized. The image SNR benefits from greater signal at higher fields, but is negatively impacted by the correspondingly shorter signal lifetimes. Depending on the noise regime of the sample, the maximum SNR may be predicted for Centric Scan SPRITE MRI with T2* being B0 field dependent. In this work we describe a series of simple experimental considerations to determine the optimal B0 field for SPRITE MRI. Selection of the best field is aided by a new generation of superconducting magnets which allows the experimentalist to readily vary the field strength. Such magnets allow one to experimentally control sample magnetization for high sensitivity MRI measurements of core plug samples, while controlling the effect of susceptibility mismatch on the signal lifetimes.

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 T1 s 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 ß, 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.

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

This work addresses the problem of a compact and easily comparable representation of multi-exponential relaxation data. It is often convenient to describe such data in a few parameters, all being of physical significance and easy to interpret, and in such a way that enables a model-free comparison between different groups of samples. Logarithmic moments (LMs) of the relaxation time constitute a set of parameters which are related to the characteristic relaxation time on the log-scale, the width and the asymmetry of an underlying distribution of exponentials. On the other hand, the calculation of LMs does not require knowing the actual distribution function and is reduced to a numerical integration of original data. The performance of this method has been tested on both synthetic and experimental NMR relaxation data which differ in a signal-to-noise ratio, the sampling range and the sampling rate. The calculation of two lower-order LMs, the log-mean time and the log-variance, has proved robust against deficiencies of the experiment such as scattered data point and incomplete sampling. One may consider using them as such to monitor formation of a heterogeneous structure, e.g., in phase separation, vitrification, polymerization, hydration, aging, contrast agent propagation processes. It may also assist in interpreting frequency and temperature dependences of relaxation, revealing a crossover from slow to fast exchange between populations. The third LM was found to be a less reliable quantity due to its susceptibility to the noise and must be used with caution.

Lithium ion dynamics in Li2S+GeS2+GeO2 glasses studied using (7)Li NMR field-cycling relaxometry and line-shape analysis.

We use (7)Li NMR to study the ionic jump motion in ternary 0.5Li2S+0.5[(1-x)GeS2+xGeO2] glassy lithium ion conductors. Exploring the "mixed glass former effect" in this system led to the assumption of a homogeneous and random variation of diffusion barriers in this system. We exploit that combining traditional line-shape analysis with novel field-cycling relaxometry, it is possible to measure the spectral density of the ionic jump motion in broad frequency and temperature ranges and, thus, to determine the distribution of activation energies. Two models are employed to parameterize the (7)Li NMR data, namely, the multi-exponential autocorrelation function model and the power-law waiting times model. Careful evaluation of both of these models indicates a broadly inhomogeneous energy landscape for both the single (x=0.0) and the mixed (x=0.1) network former glasses. The multi-exponential autocorrelation function model can be well described by a Gaussian distribution of activation barriers. Applicability of the methods used and their sensitivity to microscopic details of ionic motion are discussed.

Local T2 distribution measurements with DANTE-Z slice selection.

A CPMG pulse sequence incorporated with a DANTE-Z slice selection scheme for measuring spatially-resolved T(2) distributions has been presented. The DANTE-Z pulse train with sinc-modulated pulses selects a single, quasi-rectangular slice of less than 0.8 cm wide at an arbitrary position over a 6-cm long sample. The measured T(2) distributions are of almost the same quality as regular (bulk) CPMG measurements, with the lower T(2) limit being as good as c.a. 0.5 ms. The sequence can be found useful as a supplement or alternative to MRI-based techniques for T(2) mapping in short relaxation time samples (water-saturated rocks, building materials, wood, food products, rubbers, etc.), particularly when T(2) is required to be measured at only few positions along the sample and the resolution of ~1 cm is acceptable.

Two-dimensional T2 distribution mapping in porous solids with phase encode MRI.

Two pure phase encode MRI sequences, CPMG-prepared SPRITE and spin-echo SPI with compressed sensing, for two-dimensional (2-D) T2 distribution mapping have been presented. The sequences are 2-D extensions of their 1-D predecessors previously described and are intended for studying processes in porous solids and other samples with short relaxation times whenever 2-D T2 maps are preferable to simple 1-D profiling. The sequences were tested on model samples and natural water-saturated rocks, in a low field MRI instrument. 2-D spin-echo SPI and CPMG-SPRITE demonstrate a similar performance, enabling measurement of T2 down to 1-2 ms. Both experiments are time consuming (up to 2-2.5 h sample dependent). As such, they can be recommended mostly for measurement during steady state conditions or when studying relatively slow dynamic processes (e.g. enhanced oil recovery, cement paste hydration, curing rubber, infiltration of paramagnetic ions).

T2 distribution mapping profiles with phase-encode MRI.

Two 1-D phase-encode sequences for T2 mapping, namely CPMG-prepared SPRITE and spin-echo SPI, are presented and compared in terms of image quality, accuracy of T2 measurements and the measurement time. The sequences implement two different approaches to acquiring T2-weighted images: in the CPMG-prepared SPRITE, the T2-weighting of magnetization precedes the spatial encoding, while in the spin-echo SPI, the T2-weighting follows the spatial encoding. The sequences are intended primarily for T2 mapping of fluids in porous solids, where using frequency encode techniques may be problematic either due to local gradient distortions or too short T2. Their possible applications include monitoring fluid-flow processes in rocks, cement paste hydration, curing of rubber, filtering paramagnetic impurities and other processes accomplished by changing site-specific T2.

Surface melting of octamethylcyclotetrasiloxane confined in controlled pore glasses: curvature effects observed by 1H NMR.

We have measured the thickness of the pre-molten surface layer that appears at the interface of octamethylcyclotetrasiloxane (OMCTS) to the matrix in controlled pore glasses with pore diameters ranging 7.5-73 nm. Except for the glass with the largest pores, the layer thickness data for different pore diameters fall on a single master curve when plotted versus Tm - T, where Tm is the size-dependent volume melting point of the pore-confined OMCTS. Hence, at a single temperature, the surface layer thickness depends strongly on the curvature of the pore wall and therefore that of the solid-liquid interface. For temperatures where it exceeds two monolayers, the layer thickness depends logarithmically on Tm - T; for the glass with the largest pores, this turns into a power law with the exponent -1/2. The results are interpreted in terms of a continuous model of the solid-liquid interface with an arbitrary curvature. Because OMCTS is a weakly polar molecule with close to spherical shape, our data also lend themselves to Lennard-Jones type simulations.