An evaluation of the contributions of diffusion and exchange in relaxation enhancement by MRI contrast agents

Magnetic compounds are known to enhance water proton relaxation, either by diffusion or by proton exchange. An experimental procedure to distinguish both mechanisms is proposed and validated by relaxation measurements made in water-methanol solutions of Dy(3+), Ni(2+), Gd(3+), Tempo, and AMI-25. The test discriminates according to the character of the transverse relaxation in water-methanol solutions: a mono-exponential decay corresponds to diffusion, while a bi-exponential decay indicates the contribution of a proton exchange. The study of ferritin and akaganeite particle solutions confirms the occurrence of a proton exchange between protons belonging to hydroxyl groups of the particle surface and free water protons.     

The interpretation of multi-exponential water proton transverse relaxation in the human and porcine eye lens

We report results of 1H NMR transverse relaxation experiments on human and porcine eye lenses. Several authors have reported that transverse relaxation is not mono-exponential when observed by the Carr-Purcell-Meiboom-Gill (CPMG) sequence and have interpreted the results by postulating the presence of "pools" of water molecules in different binding environments that do not exchange rapidly on the NMR timescale. We have compared CPMG data for intact lenses with results for lens homogenates and have combined a CPMG spectroscopic pulse train with NMR micro-imaging to study the nature of the transverse relaxation process in human and porcine lenses. Fast exchange of water protons with the lens proteins (crystallins) leads to an enhanced transverse relaxation rate that varies linearly with protein concentration. At the resolution of NMR micro-imaging the transverse relaxation process is mono-exponential. The results show that the multi-exponential CPMG data observed spectroscopically for whole lenses reflect spatial variations in crystallin content through the lens rather than the presence of distinct "bound" and "free" water pools.     

NMR relaxation of protons in tissues and other macromolecular water solutions

Nuclear magnetic resonance (NMR) longitudinal (T₁) and transverse (T₂) relaxation parameters have been evaluated for protein solutions, cellular suspensions and tissues using both data from our laboratory and the extensive literature. It is found that this data can be generalized and explained in terms of three water phases: free water, hydration water, and crystalline water. The proposed model which we refer to as the FPD model differs from similar models in that it assumes that free and hydration water are two phases with distinct relaxation times but that T₁ = T₂ in each phase. In addition there is a single correlation time for each rather than a distribution as assumed in most other models. Longitudinal decay is predicted to be single exponent in character resulting from a fast exchange between the free and hydration compartments. Transverse decay is predicted to be multiphasic with crystalline (T₂ 10 μsec), hydration (T₂ 10 sec) and free (T₂ 100 sec) water normally visible. The observed or effective transverse relaxation times for both the hydration and free water phases are greatly affected by the crystalline phase and are much shorter than the inherent relaxation times.     

Two-Dimensional Transferred Nuclear-Overhauser Effects with Incomplete Averaging of Free- and Bound-Ligand Resonances

Two distinct time scales prevail in the study of conformational exchange in general and specifically in deriving the protein-bound conformations of ligands by two-dimensional transferred-NOE experiments. Fast-exchange compared to the chemical-shift difference leads to a complete averaging of the free and bound resonances of the ligands, while fast exchange compared to the longitudinal relaxation rate 1/T₁ and cross relaxation results in an average of the relaxation matrices in the free and bound states. Slower chemical exchange leads to incomplete averaging of the free and bound resonances, giving rise to a reduction of transferred NOEs compared to fast-exchange conditions, Theoretical analysis and simulation results indicated that, in the absence of information on the chemical-shift time scale, transferred NOEs may be quantitated only to an accuracy with average NOE intensities and transferred NOEs to the free ligands as upper and lower bounds, respectively. Regardless of the exchange conditions, NOE intensities can be approximated by the NOEs transferred to the free ligands when a large excess of the free ligands (α_b < 0.1) is used to amplify the NOE transfers between the bound protons, These results suggest that two-dimensional transferred-NOE experiments (transferred NOESY) can be applied in situations of intermediate and slow exchange as long as the fraction of bound ligands is small and the exchange rates are fast enough to transfer the cross-relaxation pathways in the protein-ligand complex to the easily detected resonances of the free ligands,     

Effects of thermal denaturation on the longitudinal relaxation time (T1) of water protons in protein solutions: study of the factors determining the T1 of water protons

The factors determining the longitudinal relaxation time (T1) of water protons in protein solutions were investigated by analyzing the effects of thermal denaturation on the T1 of the water protons. We treated the water protons and the protein protons "on a protein surface" as a dipole-dipole coupled two-spin system where relative translational diffusion is the dominant mechanism, and measured the change in the time development of the nuclear Overhauser effect (NOE) factors of the water protons. The T1 of the water protons was shortened markedly when the proteins were thermally denatured. Our analysis indicates that this relaxation enhancement is due to an increase in the value of the translational correlation time as well as the fraction of hydration water molecules, though the influence of "proton exchange" between the water protons and the labile protein protons cannot be completely neglected.     

Surface-NMR relaxation and echo of aquifers in geomagnetic field

Macroscopic samples of near-surface water in pores or fractures of rocks down to 100 m and deeper are studied by the measurement of proton relaxation and echo in the Earth’s magnetic field. The excitation and reception of the surface nuclear magnetic resonance (SNMR) signal is accomplished with the help of an antenna, circle or 8-shaped (for the minimization of the outer electromagnetic jamming influence), placed at the surface. The frequency of magnetic resonance in the case considered amounts to several kilohertz, the dead time of the instrumentation to several milliseconds. Water in extremely small pores of water-resisting rocks (e.g., in argillaceous grounds), is chemically bound, crystallization or frozen water has smaller times of spin relaxation and is not registered. The distribution of water concentration with depth is determined by inversion of an integral equation, including the model and measured dependences of the SNMR signal against the intensity of excitation. The current state of the art of the SNMR sounding and perspectives of this method on the basis of free induction decay and spin echo detection and relaxation times measurement are presented. Free induction decayT ₂ ^* equal to 60 ms, spin-echoT ₂ equal to 220 ms, and inversion-recoveryT ₁ equal to 700 ms relaxation times have been measured for medium-to coarse-grained sand aquifer. Microscopic characteristics of the aquifer — longitudinal relaxivity (7·10^?3 cm/s), transverse relaxivity (3.5·10^?2 cm/s), and local magnetic field gradient (2·10^?2 G/cm) — have been estimated from experimental data. The importance of spin relaxation and echo measurements for obtaining the information about the microstructure of pores and fractures, as well as filtration, properties of aquifers and diamagnetic, paramagnetic and hydrocarbon contamination, is emphasized.     

Concentration Dependence of NMR T1 in Agar Solutions

In this study, in order to explain solvent proton relaxation mechanism, the spin-lattice relaxation time (T1) of agar solutions was measured as a function of agar concentration. Relaxation measurements were carried out by a FT-NMR spectrometer operating at 60 MHz and inversion recovery pulse squence was used. Relaxation rate(1/T1a) was linearly proportional to concentration of agar solution (C), and the T1 mechanism of solvent water protons in agar solutions should be caused by the chemical exchange of water protons between free and bound water.     

Concentration Dependence of NMR T1 in Agar Solutions

In this study, in order to explain solvent proton relaxation mechanism, the spin-lattice relaxation time (T1) of agar solutions was measured as a function of agar concentration. Relaxation measurements were carried out by a FT-NMR spectrometer operating at 60 MHz and inversion recovery pulse squence was used. Relaxation rate(1/T1a) was linearly proportional to concentration of agar solution (C), and the T1 mechanism of solvent water protons in agar solutions should be caused by the chemical exchange of water protons between free and bound water.     

NMR Study of Water Distribution inside Tomato Cells: Effects of Water Stress

Tomato pericarp tissue was studied by low-field nuclear magnetic resonance (NMR) relaxometry. Two kinds of experiments were performed to investigate the correlation between multi-exponential NMR relaxation and the subcellular compartments. The longitudinal (T ₁) versus transverse (T ₂) relaxation times were first measured on fresh samples and then the transverse relaxation time was measured on samples exposed to water stress. Four signal components were found in all experiments. The results showed that all signal components corresponded to the water in different cell compartments, and that no signal from non-exchangeable protons was present. Moreover, we demonstrated that NMR relaxation is suitable for the continuous monitoring of water rebalancing between subcellular compartments of plant tissues.     

表面活性剂CTAB水溶液中的T2弛豫分散研究

用CPMG脉冲序列测定了表面活性剂十六烷基三甲基溴化铵（CTAB）分子中的氮甲基(N-CH₃)质子的横向弛豫时间（T₂表观）,并发现测得的T₂表观\}与序列中的重聚脉冲间隔时间的一半τ _cp有关,说明存在横向弛豫分散现象. 当在τ_cp≤1 ms时,T₂表观与τ²_cp}呈线性关系;而当τ_cp≥4.6 ms时,T₂表观变得与τ_cp无关. 利用Luz-Meiboom两体化学交换模型计算了不同浓度的CTAB溶液中的N-CH₃质子的本征横向弛豫时间（T₂本征）和化学交换速率k_ex,发现k_ex与T₂本征和自扩散系数D一样,在临界胶束浓度（CMC）附近发生突变. 这个突变反映了CTAB分子在从单体到胶束的转变过程中其动力学特性发生了改变.      

Cooling overall spin temperature: protein NMR experiments optimized for longitudinal relaxation effects

In experiments performed on protonated proteins at high fields, 80% of the NMR spectrometer time is spent waiting for the ¹H atoms to recover their polarization after recording the free induction decay. Selective excitation of a fraction of the protons in a large molecule has previously been shown to lead to faster longitudinal relaxation for the selected protons [K. Pervushin, B. Vögeli, A. Eletsky, Longitudinal ¹H relaxation optimization in TROSY NMR spectroscopy, J. Am. Chem. Soc. 124 (2002) 12898–12902; P. Schanda, B. Brutscher, Very fast two-dimensional NMR spectroscopy for real-time investigation of dynamic events in proteins on the time scale of seconds, J. Am. Chem. Soc. 127 (2005) 8014–8015; H.S. Attreya, T. Szyperski, G-matrix Fourier transform NMR spectroscopy for complete protein resonance assignment, Proc. Natl. Acad. Sci. USA 101 (2004) 9642–9647]. The pool of non-selected protons acts as a “thermal bath” and spin-diffusion processes (“flip-flop” transitions) channel the excess energy from the excited pool to the non-selected protons in regions of the molecule where other relaxation processes can dissipate the excess energy. We present here a sensitivity enhanced HSQC sequence (COST-HSQC), based on one selective E-BURP pulse, which can be used on protonated ¹⁵N enriched proteins (with or without ¹³C isotopic enrichment). This experiment is compared to a gradient sensitivity enhanced HSQC with a water flip-back pulse (the water flip-back pulse quenches the spin diffusion between ¹H^N and ¹H^α spins). This experiment is shown to have significant advantages in some circumstances. Some observed limitations, namely sample overheating with short recovery delays and complex longitudinal relaxation behaviour are discussed and analysed.     

Rotating-Frame Proton Cross Relaxation in the Presence of Paramagnetic Metal Ions

Rotating-frame cross relaxation for a pair of protons rotating in a spherical molecule with external relaxation is examined theoretically. The results of this study allow us to model intensities in 1D ROE and 2D ROESY spectra of protons in the presence of a paramagnetic metal ion. External relaxation moves the threshold correlation time for spin diffusion to longer times. In contrast to the effect of external relaxation on longitudinal cross relaxation (NOESY), the range of observable transverse cross relaxation (ROESY) expands with increasing external relaxation. At the same time, external relaxation compresses the overall time scale for cross-peak evolution. The initial slopes of cross-peak evolution are unaffected by external relaxation, but are sensitive to the rotational correlation time of the proton pair. Very short mixing times are necessary for accurate estimation of the initial Slopes.     

Manifestations of Slow Site Exchange Processes in Solution NMR: A Continuous Gaussian Exchange Model

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.     

Another approach to protons with constricted mobility in white matter: pilot studies using wideline and high-resolution NMR spectroscopy

We report a new approach for the identification of an independent method of studying the semi-solid pool of protons, i.e., protons with constrained motion as a result of being bound to lipid and protein matrices. These protons cannot be observed using conventional imaging techniques since their transverse relaxation times are much shorter than the minimum echo times that are currently available on clinical scanners. In this pilot study, in vitro multicomponent transverse relaxation experiments were made on human white matter slices, fixed in formalin (7 normal and 5 with multiple sclerosis). The transverse relaxation decay curves were multiexponential and were decomposed to yield three primary components. The shortest T(2) component that we obtained (a component too short to be seen by in vivo methods) was of the order of microseconds. We hypothesize that this might correspond to the macromolecular pool of lipid protons trapped within the myelin sheaths. To our knowledge, this is the first attempt at extracting this ultra short T(2) component from human white matter. Subsequently, an attempt was made to directly detect the lipid protons in a proton NMR spectrum and, if possible, measure their concentration in some of the tissues, using the technique of magic angle spinning.     

Chemical exchange of hydroxyl protons in quercetin measured by pulsed field gradient NMR

The diffusion behavior of hydroxyl protons (OH) in quercetin in 100% DMSO-d₆ (deuterium dimethylsulfoxide) and a 90% DMSO-d₆ solution containing 10% H₂O was investigated with 600 MHz ¹H pulsed field gradient (PFG) nuclear magnetic resonance (NMR). Only resonances of the 5-hydroxyl protons (OH5) were well resolved in NMR spectra of quercetin for all solutions under study. This phenomenon is explained by the intramolecular hydrogen bonding between OH5 protons and the 4-carbonyl oxygen (CO4). During diffusion experiments, the OH5 protons showed a biexponential diffusion decay, indicating an exchange process with water. As water content in the solvents increased, the lifetime (τ _q) of the OH5 protons decreased from 96.7±10.0 ms in 100% DMSO-d₆ to 14.3±1.4 ms in the 90% DMSO-d₆ solution containing 10% H₂O, indicating an increase in the exchange rate (k _q = l/τ _q) of the OH5 protons. This study demonstrates that the diffusion approach with PFG-NMR is much faster and easier for estimating the short lifetime or fast exchange rate of hydroxyl protons in quercetin.     

The effects of morphology and exchange on proton N.M.R. relaxation in agarose gels

The effects of morphology and exchange on N.M.R. relaxation times in agarose gels are interpreted within a unified theoretical framework based on the generalized Bloch equations. By acknowledging the spacial dependence of the N.M.R. parameters it is shown how the relaxation behaviour depends on the distance scale characterizing the heterogeneity of the gel. If this distance scale is sufficiently small to allow complete diffusive averaging we recover the traditional results based on the Bloch-McConnell equations describing relaxation in a homogeneous system. This is the case for fresh agarose gels which show monoexponential relaxation and has been widely interpreted in terms of the rapid exchange of protons between populations of ‘free’ and ‘bound’ water. Conversely, if the distance scale characterizing the heterogeneity is sufficiently large to prevent complete diffusive averaging our model predicts multiexponential relaxation. This is the case with the transverse magnetization in agarose gels that have been slowly frozen then thawed. These results show how it is possible to probe the degree of microheterogeneity in gel samples using N.M.R. For the purpose of deriving simple analytical expressions for the N.M.R. relaxation times we only consider one-dimensional solutions to our model. More realistic morphologies can be treated using numerical methods.     

Characterization of Porous Materials by Magnetic Relaxometry in the Earth’s Field

In this paper, it is shown how free induction decay signals recorded in the Earth’s magnetic field from water protons confined in porous media can be used to derive transversal relaxation times (T ₂) and their distributions. After T ₂ determination of six sintered glass samples with various pore sizes, the common theoretical model can be fitted to the data set. The T ₂ distribution of water protons in a bimodal porous system is analyzed and compared to mercury porosimetry results. The implications for the calculation of pore sizes and pore size distributions of porous media by this method are discussed.     

The influence of chemical and diffusive exchange on water proton transverse relaxation in plant tissues

Transverse water proton relaxation in parenchyma tissue of courgette, onion and apple shows a dependence on CPMG pulse spacing characteristic of each tissue. An analysis of this dependence suggests that transverse relaxation in these tissues is caused by various combinations of fast proton exchange between water and cell biopolymers (or solutes) and diffusion through internally generated magnetic field gradients. Diffusion between intra- and extracellular water compartments also averages the water proton signal to an extent that depends on cell morphology and membrane permeability and this is calculated using a two-compartment model. No recourse need be made to popular concepts such as exchange between free and "bound" water. The implications of our results for NMR image contrast are discussed.     

The Effect of Curing Temperature on Early Hydration of Gray Cement Via Fast Field Cycling-NMR Relaxometry

In the present work, we use fast field cycling (FFC) nuclear magnetic resonance relaxometry to evaluate the influence introduced by the curing temperature on the hydration process of gray cement. The main advantage of FFC relaxometry as compared with other relaxation studies performed at a specific frequency is that it is sensitive to a wider range of molecular motions and better separates the surface and bulk contributions from the global measured relaxation rate. In the case of cement hydration, the relaxation process is dominated by the interaction of water protons with the paramagnetic centers located on the surface of cement grains. This allows us in the frame of a two-phase exchange model to monitor the temperature dependence of the transverse diffusional correlation time at the surface of cement grains. An increase of the surface diffusion coefficient of water molecules with the temperature was revealed. Another outcome is that the surface-to-volume ratio of capillary pores continuously increases during the early hydration and this process is strongly enhanced by rising the temperature.