NMR at very low fields

Although nuclear magnetic resonance in low fields around or below the Earth's magnetic field is almost as old as nuclear magnetic resonance itself, the recent years have experienced a revival of this technique that is opposed to the common trend towards higher and higher fields. The background of this development is the expectation that the low-field domain may open a new window for the study of molecular structure and dynamics. Here, we will give an overview on the specific features in the low-field domain, both from the technical and from the physical point of view. In addition, we present a short passage on the option of magnetic resonance imaging in fields of the micro-Tesla range.     

Optimal echo spacing for multi-echo imaging measurements of Bi-exponential T2 relaxation

Calculations, analytical solutions, and simulations were used to investigate the trade-off of echo spacing and receiver bandwidth for the characterization of bi-exponential transverse relaxation using a multi-echo imaging pulse sequence. The Cramer–Rao lower bound of the standard deviation of the four parameters of a two-pool model was computed for a wide range of component T₂ values and echo spacing. The results demonstrate that optimal echo spacing (TE_opt) is not generally the minimal available given other pulse sequence constraints. The TE_opt increases with increasing value of the short T₂ time constant and decreases as the ratio of the long and short time constant decreases. A simple model of TE_opt as a function of the two T₂ time constants and four empirically derived scalars is presented.     

MSE-MRI sequence optimisation for measurement of bi- and tri-exponential T2 relaxation in a phantom and fruit

The transverse relaxation signal from vegetal cells can be described by multi-exponential behaviour, reflecting different water compartments. This multi-exponential relaxation is rarely measured by conventional MRI imaging protocols; mono-exponential relaxation times are measured instead, thus limiting information about of the microstructure and water status in vegetal cells. In this study, an optimised multiple spin echo (MSE) MRI sequence was evaluated for assessment of multi-exponential transverse relaxation in fruit tissues. The sequence was designed for the acquisition of a maximum of 512 echoes. Non-selective refocusing RF pulses were used in combination with balanced crusher gradients for elimination of spurious echoes. The study was performed on a bi-compartmental phantom with known T₂ values and on apple and tomato fruit. T₂ decays measured in the phantom and fruit were analysed using bi- and tri-exponential fits, respectively. The MRI results were compared with low field non-spatially resolved NMR measurements performed on the same samples.     

Three-dimensional T1, T2 and proton density mapping with inversion recovery balanced SSFP

By combining a balanced steady-state free precession (bSSFP) readout with an initial inversion pulse, all three contrast parameters, T₁, T₂ and proton density (M₀), may be rapidly calculated from the signal progression in time. However, here it is shown that this technique is quite sensitive to variation in the applied transmit RF (B₁) field, leading to pronounced errors in calculated values. Two-dimensional (2D) acquisitions are taxed to accurately quantify the relaxation, as the short RF pulses required by SSFP's rapid TR contain a broad spectrum of excitation angles. A 3D excitation using a large diameter excitation coil was able to correctly quantify the parameters. While the extreme B₁ sensitivity was previously problematic and has precluded use of IR-bSSFP for relaxometry, in this work these obstacles were significantly reduced, allowing the rapid quantification of T₁, T₂ and M₀. The results may further be used to simulate image contrast from common sequences, such as a T₁-weighted or fluid-attenuated inversion recovery (FLAIR) examination.     

Recent Fourier and Laplace perspectives for multidimensional NMR in porous media

Multidimensional NMR techniques used in the measurement of molecular displacements, whether by diffusion or advection, and in the measurement of nuclear spin relaxation times are categorised. Fourier-Fourier, Fourier-Laplace and Laplace-Laplace methods are identified, and recent developments discussed in terms of the separation, correlation and exchange perspective of multidimensional NMR spectroscopy.     

Quantification of superparamagnetic iron oxide using inversion recovery balanced steady-state free precession

Cellular and molecular MRI trafficking studies using superparamagnetic iron oxide (SPIO) have greatly improved non-invasive investigations of disease progression and drug efficacy, but thus far, these studies have largely been restricted to qualitative assessment of hypo- or hyperintense areas near SPIO. In this work, SPIO quantification using inversion recovery balanced steady-state free precession (IR-bSSFP) was demonstrated at 3 T by extracting R₂ values from a monoexponential model (P. Schmitt et al., 2004). A low flip angle was shown to reduce the apparent recovery rate of the IR-bSSFP time course, thus extending the dynamic range of quantification. However, low flip angle acquisitions preclude the use of traditional methods for combining RF phase-cycled images to reduce banding artifacts arising from off-resonance due to B₀ inhomogeneity. To achieve R₂ quantification of SPIO, we present a new algorithm applicable to low flip angle IR-bSSFP acquisitions that is specifically designed to identify on-resonance acquisitions. We demonstrate in this work, using both theoretical and empirical methods, that the smallest estimated R₂ from multiple RF phase-cycled acquisitions correspond well to the on-resonance time course. Using this novel minimum R₂ algorithm, homogeneous R₂ maps and linear R₂ calibration curves were created up to 100 μg(Fe)/mL with 20° flip angles, despite substantial B₀ inhomogeneity. In addition, we have shown this technique to be feasible for pre-clinical research: the minimum R₂ algorithm was resistant to off-resonance in a single slice mouse R₂ map, whereas maximum intensity projection resulted in banding artifacts and overestimated R₂ values. With the application of recent advances in accelerated acquisitions, IR-bSSFP has the potential to quantify SPIO in vivo, thus providing important information for oncology, immunology, and regenerative medicine MRI studies.     

A simulation based method to assess inversion algorithms for transverse relaxation data

NMR relaxometry is a very useful tool for understanding various chemical and physical phenomena in complex multiphase systems. A Carr-Purcell-Meiboom-Gill (CPMG) [P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1991] experiment is an easy and quick way to obtain transverse relaxation constant (T₂) in low field. Most of the samples usually have a distribution of T₂ values. Extraction of this distribution of T₂s from the noisy decay data is essentially an ill-posed inverse problem. Various inversion approaches have been used to solve this problem, to date. A major issue in using an inversion algorithm is determining how accurate the computed distribution is. A systematic analysis of an inversion algorithm, UPEN [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data, Journal of Magnetic Resonance 132 (1998) 65–77; G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data II. Data spacing, T₂ data, systematic data errors, and diagnostics, Journal of Magnetic Resonance 147 (2000) 273–285] was performed by means of simulated CPMG data generation. Through our simulation technique and statistical analyses, the effects of various experimental parameters on the computed distribution were evaluated. We converged to the true distribution by matching up the inversion results from a series of true decay data and a noisy simulated data. In addition to simulation studies, the same approach was also applied on real experimental data to support the simulation results.     

Microstructural analysis of foam by use of NMR R2 dispersion

The spin–spin relaxation rate R₂ (=1/T₂) in hydrogel foams measured by use of a multiple spin echo sequence is found to be dependent on the echo time spacing. This property, referred to as R₂-dispersion, originates to a large extent from molecular self-diffusion of water within internal field gradients that result from magnetic susceptibility differences between the gel and air phase. Another contribution to the R₂ relaxation rate is surface relaxation. Numerical simulations are performed to investigate the relation between the foam microstructure (the mean air bubble radius and standard deviation of the air bubble radius) and foam composition properties (such as magnetic susceptibilities, diffusion coefficient and surface relaxivity) at one hand and the R₂-dispersion at the other hand. The simulated R₂-dispersions of gel foam are in agreement with the measured R₂-dispersions. By correlating the R₂-dispersion parameters and simulated microstructure properties a semi-empirical relationship is obtained that enables the mean air bubble size to be derived from measured R₂-dispersion curves. The R₂-derived mean air bubble size of a hydrogel foam is in agreement with the bubble size measured with X-ray micro-CT. This illustrates the feasibility of using ¹H R₂-dispersion measurements to determine the size of air bubbles in hydrogel foams and of alveoli in lung tissue.     

A simulation-based comparison of two methods for determining relaxation rates from relaxometry images

When assessing liver iron content using relaxometry, an average relaxation rate (R1, R2 or R2*) is usually determined from a region of interest or the entire liver. This is commonly performed by fitting the signal decay in individual voxels to an appropriate relaxation function. The voxel-level parameters resulting from the fits are combined to determine the average relaxation rate, and an empirically derived calibration curve is used to convert this single value to iron content. The goal of this study was to compare the precision and accuracy of this voxel-wise fitting to an alternative method that relies on first averaging the signals from all voxels within the region of interest and then determining the relaxation rate from a single fit. Systematic differences were observed when both methods were applied to clinical images. Mathematical simulations were employed to determine which method provided more robust estimates of the true relaxation rate. The mathematical simulations were then expanded to include a range of conditions expected in typical relaxometry images. The results show that voxel-wise fitting skews the relaxation rate estimates and increases variance, particularly when the true relaxation rate is moderate to fast, as it would be in liver with high iron content. The potential impact of these results on clinical decisions is discussed.