Pulsed Magnetic Field Gradients Research Articles

Mathematical Modeling and Data Analysis of NMR Experiments using Hyperpolarized (13)C Metabolites.

Rapid-dissolution dynamic nuclear polarization (DNP) has made significant impact in the characterization and understanding of metabolism that occurs on the sub-minute timescale in several diseases. While significant efforts have been made in developing applications, and in designing rapid-imaging radiofrequency (RF) and magnetic field gradient pulse sequences, very few groups have worked on implementing realistic mathematical/kinetic/relaxation models to fit the emergent data.The critical aspects to consider when modeling DNP experiments depend on both nuclear magnetic resonance (NMR) and (bio)chemical kinetics. The former constraints are due to the relaxation of the NMR signal and the application of ‘read’ RF pulses, while the kinetic constraints include the total amount of each molecular species present. We describe the model-design strategy we have used to fit and interpret our DNP results. To our knowledge, this is the first report on a systematic analysis of DNP data.

Stejskal–tanner equation derived in full

AbstractThe pulsed field gradient spin‐echo nuclear magnetic resonance method is used to measure the translational diffusion of solvents and solutes in homogeneous and heterogeneous systems. It is widely used in the characterization of molecules and materials in general, via phenomena such as ‘diffusion interference’. It is also the basis of tissue discrimination in magnetic resonance imaging, via diffusion tensor imaging. The mathematical equation used to analyze data from a simple noninteracting solute (using a pair of magnetic field gradient pulses that are applied in the experiment) was first derived by Stejskal and Tanner. However, in the article and in subsequent presentations the basic derivation, which we call the the “theoretical physics” of the theory, is not presented in extenso. Conversely, many papers in which the exploration of the effects of magnetic field gradient pulses of shapes other than simple rectangles generally begin with the time‐dependent integral that emerges from the original theoretical physics. To fill this “pedagogical gap” we use here a rigorous step‐by‐step approach to the theoretical physics of the Stejskal–Tanner equation and indicate how it was based on earlier theories. We also take the opportunity to indicate a contemporary approach to deriving new relationships between user‐defined magnetic field gradient pulse shapes and the diffusion coefficient; and we show how these can be rapidly and accurately derived using symbolic computation. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40A: 205–214, 2012.

Background and mathematical analysis of diffusion MRI methods

The addition of a pair of magnetic field gradient pulses had initially provided the measurement of spin motion with nuclear magnetic resonance (NMR) techniques. In the adaptation of DW-NMR techniques to magnetic resonance imaging (MRI), the taxonomy of mathematical models is divided in two categories: model matching and spectral methods. In this review, the methods are summarized starting from early diffusion weighted (DW) NMR models followed up with their adaptation to DW MRI. Finally, a newly introduced Fourier analysis based unifying theory, so-called Complete Fourier Direct MRI, is included to explain the mechanisms of existing methods.

NMR Fourier zeugmatography

A new technique of forming two- or three-dimensional images of a macroscopic sample by means of NMR is described. It is based on the application of a sequence of pulsed magnetic field gradients during a series of free induction decays. The image formation can be achieved by a straightforward two- or three-dimensional Fourier transformation. The method has the advantage of high sensitivity combined with experimental and computational simplicity.

Self-diffusion of lithium cations and ionic conductivity in polymer electrolytes based on polyesterdiacrylate

The processes of ionic conductivity are studied in a polymer gel electrolyte synthesized based on polyesterdiacrylate and a low-molecular solvent ethylene carbonate. The self-diffusion coefficients of solvent molecules and Li+ cations are measured by the NMR with the pulsed magnetic field gradient. The Li+ self-diffusion coefficients increase with the increase in the solvent content and are independent of the diffusion time in the interval from 10 to 1600 ms. The latter values imply the absence of limitations for the translational mobility of lithium ions in the spatial range from 10−7 to 10−5 m. Based on the Nernst-Einstein equation, the ionic conductivities are calculated and compared with the experimental conductivities measured by the impedance method. These values coincide for high contents of solvent; for low ethylene carbonate concentrations, the calculated conductivities much exceed the experimental values.

Lipid Lateral Diffusion and Hydrocarbon Chain Order

Recent advances in molecular simulations have stimulated new discussions on the molecular mechanisms of lateral diffusion of lipids in fluid bilayers. To enable a deeper comparison between theory and experiments, we conducted a systematic study of lateral diffusion rates for a series of phosphatidylcholines with 14, 16, 18 and 20 hydrocarbons per chain over the temperature range from 10 to 600C. Bilayers of the pure lipids as well as binary mixtures with 30 mol% cholesterol were investigated. Diffusion coefficients were measured by 1H MAS NMR with application of pulsed magnetic field gradients. All lipids had saturated, perdeuterated sn-1 chains that enabled measurement of chain order parameters by 2H NMR. From the average chain order parameters effective hydrophobic thicknesses of bilayers and lateral areas per lipid molecule were calculated. This enabled a quantitative comparison of experimentally determined and calculated lateral diffusion rates as a function of chain length, cholesterol content and temperature using a free-volume model of lateral diffusion. The implications of this comparison for models of lateral lipid diffusion will be discussed.

Defeating Radiation Damping and Magnetic Field Inhomogeneity with Spatially Encoded Noise

A simple NMR experiment capable of providing well resolved spectra under conditions where either radiation damping or static magnetic field inhomogeneity would broaden otherwise high-resolution NMR spectra is introduced. The approach involves using a strong pulsed magnetic field gradient and a selective radio-frequency pulse to encode a predetermined noise pattern into the spatial distribution of magnetization. Following readout in a much smaller field gradient, the noise sequence may be deconvolved from the acquired data and a high-resolution spectrum is obtained, eliminating the effects of either radiation damping or the static field inhomogeneity. In the presence of field inhomogeneity a field map is also obtained from the same single transient. A quasi-two-dimensional version of the experiment eliminates the need for deconvolution and produces improved results with simplified processing, but without requiring a full two-dimensional experiment. Example spectra are shown for both radiation damping and one-dimensional field inhomogeneity with improvement in linewidths of more than a factor of 40.

Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble

Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holographic techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.

Effects of temperature and concentration factors on the conformational state and reactivity of potassium poly(oxyethylene glycolate)

With the use of pulsed magnetic-field gradient NMR, self-diffusion coefficients of potassium poly(oxyethylene glycolate) macromolecules and solvent molecules (acetone) and the variation in the dimensions of supramolecular structures of potassium poly(oxyethylene glycolate) with temperature and its concentration in acetone are measured. It is discovered that the temperature dependences of change in the rate constants of reactions that proceed during the interaction of potassium poly(oxyethylene glycolate) with 2,4-toluylene diisocyanate do not fit Arrhenius coordinates.

Fast measurements of average flow velocity by Low-Field 1H NMR

In this paper, we describe a method for measuring the average flow velocity of a sample by means of Nuclear Magnetic Resonance. This method is based on the Carr–Purcell–Meiboom–Gill (CPMG) sequence and does not require the application of any additional static or pulsed magnetic field gradients to the background magnetic field. The technique is based on analyzing the early-time behavior of the echo amplitudes of the CPMG sequence. Measurements of average flow velocity of water are presented. The experimental results show a linear relationship between the slope/ y-intercept ratio of a linear fit of the first echoes in the CPMG sequence, and the average flow velocity of the flowing fluid. The proposed method can be implemented in low-cost Low-Field NMR spectrometers allowing a continuous monitoring of the average velocity of a fluid in almost real-time, even if the flow velocity changes rapidly.

Quantifying the transfer and settling in NMR experiments with sample shuttling

Nuclear magnetic resonance (NMR) in combination with pulsed magnetic field gradients has proven very successful for measuring molecular diffusion, where the correlation time of the motion is much shorter than the timescale of the experiment. In this article, it is demonstrated that a single-scan NMR technique to measure molecular diffusion can be employed to also study incoherent random motions over macroscopic length scales that show correlation times similar to the timescale of the experiment. Such motions are observed, for example, after the mixing of two components or after transferring a sample from one container into another. To measure the fluid settling, a series of magnetization helices were encoded onto a sample. Stimulated gradient echo trains were then generated after different mixing times, which enabled the determination of an effective dispersion coefficient for the fluid. This technique was used to optimize the timing of NMR experiments combined with dissolution dynamic nuclear polarization, where a sample was shuttled between two magnets. In addition to the decay of fluid turbulences, the presence of microbubbles in the sample tube at the end of the shuttling step was identified as another contribution to the NMR linewidth. Microbubbles could be indirectly observed through the line broadening effect on the NMR signal due to their different susceptibility compared to the solvent, which induced field gradients near the interfaces. Using these data, the signal attenuation caused by sample motion in single-scan two-dimensional correlation spectroscopy NMR experiments could be predicted with reasonable accuracy.

Effect of temperature on water transport through aquaporins

The mean effective water self-diffusion coefficient in maize root segments under the effect of aquaporin blocker (mercuric chloride, 0.1 mM) was measured using the spin-echo NMR method with pulsed magnetic field gradient within the temperature range from 10 to 35 °C. HgCl2 caused the reduction in water diffusion by 30 % as compared to the control samples. Temperature dependences of water self-diffusion coefficients showed two linear regions with different values of Q10 and activation energy, Ea. As the temperature reduced from 20 to 10 °C, Ea values calculated from the Arrhenius plots were close to those of bulk water (20 ± 3 kJ mol−1) and slightly changed for the sample pretreated HgCl2. Within the temperature range from 25 to 35 °C the slope of temperature dependences became steeper and Ea values were 31 ± 3 kJ mol−1 for the control and 40 ± 4 kJ mol−1 for the treated sample. In the vicinity of 20 °C, the temperature dependence of water diffusion via the mercury-sensitive water channels showed extreme value. In the region, the specific area of the mercury-sensitive aquaporins was 0.004 % of the total cell surface area. The data indicate that water transfer via aquaporins is sensitive to temperature, and the contributions of the transmembrane pathways (aquaporins, lipid bilayer) differ in different temperature ranges.

Self-Diffusion Studies in CuBTC by PFG NMR and MD Simulations

Self-diffusion and relaxation time studies of C3 to C6 hydrocarbons adsorbed in the microporous metal−organic framework CuBTC were performed by nuclear magnetic resonance (NMR) in the temperature range of 193−373 K. The presence of paramagnetic copper species in the solid CuBTC framework leads to short longitudinal (T1) and transverse (T2) relaxation times of the hydrocarbons with typical values of T1 ≲ 10 ms and T2 ≲ 3 ms. Under these conditions, pulsed field gradient (PFG) NMR self-diffusion studies could only be performed at short observation times using the primary spin echo sequence with high-intensity pulsed magnetic field gradients. The obtained temperature dependent self-diffusion coefficients were analyzed using an Arrhenius approach. The activation energies of the alkanes are in the range of 6.5−8.5 kJ/mol, increasing slightly with increasing number of carbon atoms. Significantly higher values were found for propene (13.2 kJ/mol) and 1-butene (15.0 kJ/mol). These tendencies are consistent with corresponding measurements of heats of adsorption and with data obtained in molecular dynamics (MD) simulations. The MD simulations show a strong dependence of the heat of adsorption and diffusion on loading and temperature. This is caused by the preferential adsorption of small alkanes such as propane and butane in the side pockets of the CuBTC structure at low loading and temperature.

Phase‐field dithering for active catheter tracking

A strategy to increase the robustness of active MR tracking of microcoils in low signal-to-noise ratio conditions was developed and tested. The method employs dephasing magnetic field gradient pulses that are applied orthogonal to the frequency-encoding gradient pulse used in conventional point-source MR tracking. In subsequent acquisitions, the orthogonal dephasing gradient pulse is rotated while maintaining a perpendicular orientation with respect to the frequency-encoding gradient. The effect of the dephasing gradient is to apply a spatially dependent phase shift in directions perpendicular to the frequency-encoding gradient. Since the desired MR signal for robust MR tracking comes from the small volume of nuclear spins near the small detection coil, the desired signal is not dramatically altered by the dephasing gradient. Undesired MR signals arising from larger volumes (e.g., due to coupling with the body coil or surface coils), on the other hand, are dephased and reduced in signal intensity. Since the approach requires no a priori knowledge of the microcoil orientation with respect to the main magnetic field, data from several orthogonal dephasing gradients are acquired and analyzed in real time. One of several selection algorithms is employed to identify the "best" data for use in the coil localization algorithm. This approach was tested in flow phantoms and animal models, with several multiplexing schemes, including the Hadamard and zero-phase reference approaches. It was found to provide improved MR tracking of untuned microcoils. It also dramatically improved MR tracking robustness in low signal-to-noise-ratio conditions and permitted tracking of microcoils that were inductively coupled to the body coil.

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Abstract Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.

Location, Structure, and Dynamics of the Synthetic Cannabinoid Ligand CP-55,940 in Lipid Bilayers

The widely used hydrophobic cannabinoid ligand CP-55,940 partitions with high efficiency into biomembranes. We studied the location, orientation, and dynamics of CP-55,940 in POPC bilayers by solid-state NMR. Chemical-shift perturbation of POPC protons from the aromatic ring-current effect, as well as 1H NMR cross-relaxation rates, locate the hydroxyphenyl ring of the ligand near the lipid glycerol, carbonyls, and upper acyl-chain methylenes. Order parameters of the hydroxyphenyl ring determined by the 1H- 13C DIPSHIFT experiment indicate that the bond between the hydroxyphenyl and hydroxycyclohexyl rings is oriented perpendicular to the bilayer normal. 2H NMR order parameters of the nonyl tail are very low, indicating that the hydrophobic chain maintains a high level of conformational flexibility in the membrane. Lateral diffusion rates of CP-55,940 and POPC were measured by 1H magic-angle spinning NMR with pulsed magnetic field gradients. The rate of CP-55,940 diffusion is comparable to the rate of lipid diffusion. The magnitude of cross-relaxation and diffusion rates suggests that associations between CP-55,940 and lipids are with lifetimes of a fraction of a microsecond. With its flexible hydrophobic tail, CP-55,940 may efficiently approach the binding site of the cannabinoid receptor from the lipid-water interface by lateral diffusion.

Multidimensional NMR diffusion studies in microporous materials

The diffusional behavior of selected hydrocarbons adsorbed in NaX zeolites were investigated with pulsed magnetic field gradient (PFG) NMR methods in two different ways. First, the exchange time τ exch of n-pentane between the interior and the exterior of the zeolite crystals was determined by two-dimensional diffusion exchange spectroscopy. The results were compared to the mean life time τ intra as obtained by fast NMR tracer desorption method. Second, the diffusion of a propylene–propane mixture adsorbed in the zeolite was studied by Fourier transform PFG NMR, thus employing the chemical shift of the individual organic constituents as a second dimension for a selective evaluation of the PFG NMR signal decays and the subsequent extraction of corresponding diffusion coefficients. Modifications of NMR pulse sequences necessary for the application of ultra-high pulsed magnetic field gradients of up to ± 35 T m - 1 in microporous materials are briefly discussed for both kind of experiments.

Vacuolar symplast formation is due to highly permeable gap junctions between the tonoplast and endoplasmic reticulum membrane

An NMR method with a pulsed magnetic field gradient was applied to study changes in water permeability of the vacuolar symplast in maize (Zea mays L.) seedling roots treated with various inhibitors of cell metabolism. The results were qualitatively analogous to literature data on conductivity changes of intercellular gap junctions in animal cells exposed to similar treatments. Electron microscopy examination of root cells provided evidence for the existence of membrane contacts between the endoplasmic reticulum and the tonoplast. It is supposed that vacuoles of neighboring plant cells are interconnected through highly dynamical gap junctions between the tonoplast and the endoplasmic reticulum membrane.

Simple modifications to the NMR PGSE technique for investigations in the regime of short diffusion observation times

AbstractSimple modifications to the spin‐echo NMR technique with pulsed magnetic field gradients are proposed. These modifications make it possible to compensate the negative influence of gradient pulse fronts by applying an additional gradient pulse, to eliminate the acoustic effect of gradient pulses on a sample by decoupling the probe and gradient coils, and to simplify the generation of bipolar gradient pulses of the magnetic field using a scheme of two electronic circuits. © 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 33B: 216–219, 2008

The self-diffusion of water and saturated aliphatic alcohols in cation-exchange membranes

The self-diffusion of water, methanol, ethanol, isopropanol, and butanol in membranes based on polyethylene and sulfonated copolymer of styrene and divinylbenzene (MK-100) and membranes based on sulfo-containing aromatic polyamides (PA) and a copolymer of 1,2,4,5-benzenetetracarboxylic acid with 4,4′-diaminodiphenyl oxide (PAK) was investigated by the pulsed magnetic field gradient NMR technique. In MK-100 sulfo cation-exchange membranes and PAK carboxylic membranes, two types of sorbate molecules with translational mobilities differing by an order of magnitude were observed. It was established that, in these membranes, the major diffusant portion was transferred trough transport channels formed by functional groups of membranes, counterions, and diffusant molecules (ionogenic channels). The conclusion was drawn that, in PA membranes, water and alcohol molecules were distributed uniformly and carbonyl croups of the polymeric matrix participated in the formation of transport channels. Relations between the structure of membranes, the character of diffusant-polymeric matrix interaction, and the translational mobility of sorbate molecules were found.