Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Errors in the Measurement of Cross-Correlated Relaxation Rates and How to Avoid Them

Cross-correlated relaxation rates Γ are commonly obtained from constant time experiments by measuring the effect of the desired cross-correlated relaxation on an appropriate coherence during the constant time T. These measurements are affected by systematic errors, which derive from undesired cross-correlated relaxation effects taking place before and after the constant time period T. In this paper we discuss the sources and the size of these errors in an example of two pulse sequences. Higher accuracy of the measured data can be obtained by recording a set of experiments with different T values. Cross-correlated relaxation rates are measured in constant time experiments either from the differential relaxation of multiplet components (J-resolved Γ experiments) or from the efficiency of magnetization transfer between two coherences (quantitative Γ experiments). In this paper we calculate analytically the statistical errors in both J-resolved and quantitative Γ experiments. These formulae provide the basis for the choice of the most efficient experimental approach and parameters for a given measurement time and size of the rate. The optimal constant time T for each method can be calculated and depends on the relaxation properties of the molecule under investigation. Moreover, we will show how to optimize the relative duration of cross and reference experiments in a quantitative Γ approach.     

Improvement of duty-cycle heating compensation in NMR spin relaxation experiments

To reliably measure NMR relaxation properties of macromolecules is a prerequisite for precise experiments that identify subtle variations in relaxation rates, as required for the determination of rotational diffusion anisotropy, CSA tensor determination, advanced motional modeling or entropy difference estimations. An underlying problem with current NMR relaxation measurement protocols is maintaining constant sample temperature throughout the execution of the relaxation series especially when rapid data acquisition is required. Here, it is proposed to use a combination of a heating compensation and a proton saturation sequence at the beginning of the NMR relaxation pulse scheme. This simple extension allows reproducible, robust and rapid acquisition of NMR spin relaxation data sets. The method is verified with (15)N spin relaxation measurements for human ubiquitin.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Hydration water dynamics in biopolymers from NMR relaxation in the rotating frame

Assuming dipole-dipole interaction as the dominant relaxation mechanism of protons of water molecules adsorbed onto macromolecule (biopolymer) surfaces we have been able to model the dependences of relaxation rates on temperature and frequency. For adsorbed water molecules the correlation times are of the order of 10(-5)s, for which the dispersion region of spin-lattice relaxation rates in the rotating frame R(1)(ρ)=1/T(1)(ρ) appears over a range of easily accessible B(1) values. Measurements of T(1)(ρ) at constant temperature and different B(1) values then give the "dispersion profiles" for biopolymers. Fitting a theoretical relaxation model to these profiles allows for the estimation of correlation times. This way of obtaining the correlation time is easier and faster than approaches involving measurements of the temperature dependence of R(1)=1/T(1). The T(1)(ρ) dispersion approach, as a tool for molecular dynamics study, has been demonstrated for several hydrated biopolymer systems including crystalline cellulose, starch of different origins (potato, corn, oat, wheat), paper (modern, old) and lyophilized proteins (albumin, lysozyme).     

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.     

Enhanced superradiance effect in a system of interacting two-level atoms and crossover from coherent to many-atom multiphoton relaxation regime

We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction can promote cooperative radiative relaxation. For small number of atoms this results in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation. Above superradiance threshold increase in delay time and enhancement of superradiance is occurred. In the case of strong interaction (as compared to excitation energy of an atom) transition to the regime of multiphoton relaxation occurs, which we discuss using a simple model of two atoms in a high-Q single mode cavity. It is shown that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed as well.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

13C- and 1H-NMR Relaxation Investigation of a Polyciclic Nitrogen Compound: 3,3-Dimethyl-1,5-diphenyl-9-hydroxy-bispidinium Iodide

The rigid polycyclic nitrogen compound was considered as a test for the reliability of internuclear distances calculated by ¹H-NMR spin-lattice relaxation rates. The ‘isotropic’ motional correlation time was calculated from ¹³C relaxation rates (τ_C = 0.11 ns at 298 K). Dipolar cross-relaxation rates were calculated by measuring non-, mono- and double-selective proton spin-lattice relaxation rates. All the experimental relaxation rates were thoroughly accounted for by dipolar pairwise interactions. Only at high temperatures a certain contribution from the spin rotational mechanism was apparent.     

Selection of pulse sequences producing maximum tissue contrast in magnetic resonance imaging

The importance of spin density [N(H)] and spin-lattice (T₁) and spin-spin (T₂) relaxation in the characterization of tissue by nuclear magnetic resonance (NMR) is clearly recognized. This work considers which optimized pulse sequences provide the best tissue discrimination between a given pair of tissues. The effects of tissue spin density and machine-imposed minimum rephasing echo times (TE_MIN) for achieving maximum signal tissue contrast are discussed. A long TE_MIN sacrifices T₁-dependent contrast in saturation recovery (SR) and inversion recovery (IR) pulse sequences so that spin-echo (SE) becomes the optimum sequence to provide tissue contrast, due to T₂ relaxation. Pulse sequences providing superior performance may be selected based on spin density and T₁ and T₂ ratios for a given pair of tissues. Selection of the preferred pulse sequence and interpulse delay times to produce maximum tissue contrast is strongly dependent on knowledge of tissue spin densities as well as T₁ and T₂ characteristics. As the spin density ratio increases, IR replaces SR as the preferred sequence and SE replaces IR and SR as the pulse sequence providing superior contrast. To select the optimal pulse sequence and interpulse delay times, an accurate knowledge of tissue spin density, T₁ and T₂ must be known for each tissue.     

Osmotic and aging effects in caviar oocytes throughout water and lipid changes assessed by 1H NMR T1 and T2 relaxation and MRI

By combining NMR relaxation spectroscopy and magnetic resonance imaging techniques, unsalted (us) and salted (s) caviar (Acipenser transmontanus) oocytes were characterized over a storage period of up to 90 days. The aging and the salting effects on the two major cell constituents, water and lipids, were separately assessed. T1 and T2 decays were interpreted by assuming a two-site exchange model. At Day 0, two water compartments that were not in fast exchange were identified by the T1 relaxation measurements on the us oocytes. In the s samples, T1 decay was monoexponential. During the time of storage, an increment of the free water amount was found for the us oocytes, ascribed to an increased metabolism. T1 and T2 of the s oocytes shortened as a consequence of the osmotic stress produced by salting. Selective images showed the presence of water endowed with different regional mobility that severely changed during the storage. Lipid T1 relaxation decays collected on us and s samples were found to be biexponential, and the T1 values lengthened during storage. In us and s oocytes, the increased lipid mobility with the storage was ascribed to lipolysis. Selective images of us samples showed lipids that were confined to the cytoplasm for up to 60 days of storage.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Single-scan longitudinal relaxation measurements in high-resolution NMR spectroscopy

Several single-scan experiments for the measurement of the longitudinal relaxation time (T1) are proposed. These experiments result in fast and accurate determinations of the relaxation rate, are relatively robust to pulse imperfections, and preserve information about the chemical shift. The method used in these experiments is to first encode the T1 values as a spatial variation of the magnetization and then to read out this variation either by applying a weak gradient during acquisition or by sequentially observing different slices of the sample. As a result, it is possible to reduce the time necessary to determine the T1 values by one or two orders of magnitude. This time saving comes at the expense of the signal-to-noise level of the resulting spectrum and some chemical shift resolution.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Time-optimal coherence-order-selective transfer of in-phase coherence in heteronuclear IS spin systems

Based on principles of geometric optimal control theory, coherence transfer building blocks can be derived which achieve optimal sensitivity. Here, experimental pulse sequences are presented that achieve the best possible coherence-order-selective in-phase transfer (S(-)-->I(-)) for a heteronuclear 2-spin system for any given mixing time in the absence of relaxation. For short mixing times, the optimal experiment improves the sensitivity of isotropic mixing by up to 12.5%.     

1H and 13C NMR Conformational Analysis of Adrenergic Drugs. III. Dichloroisoproterenol,A Nonselective β-Blocking Agent

¹³C and ¹H NMR parameters were measured for dichloroisoproterenol in solution. Spin-lattice relaxation rates, nuclear Overhauser effects and J couplings were determined and compared to those obtained from isoproterenol. The t rotamer was shown to occur with a much higher probability than the two g rotamers. Dynamics in solution were interpreted in terms of a nearly isotropic motion of an extended molecular backbone. Some interesting differences were given evidence between the ‘preferred’ conformations in solution of dichloroisoproterenol and isoproterenol.     

Improved Estimation of CSA–Dipolar Coupling Cross-Correlation Rates from Laboratory-Frame Relaxation Experiments

We have investigated the underlying assumptions in estimating cross-correlation rates between chemical shift anisotropy (CSA) and dipolar coupling mechanisms in a scalar-coupled two-spin IS system, from laboratory frame relaxation experiments. It has been shown that for an arbitrary relaxation delay, the difference in relaxation rates of the individual components of an in-phase (or antiphase) doublet is not related to the CSA–dipolar coupling cross-correlation rate in a simple way. This is especially true in the case where the difference in the decay rates of the in-phase and antiphase terms of the density matrix becomes comparable to the magnitude of the scalar coupling between the two spins. Improved means of extracting cross-correlation rates in these cases are presented.     

Selection of dipolar interaction by the “2 + 1” pulse train ESE

The new kind of electron spin echo (ESE), the “2 + 1” pulse train, is described. This method allows the measurement of dipole-dipole interactions between paramagnetic centers which are substantially weaker than those that can be measured by the ordinary two-pulse train. The dead time of ESE spectrometer response in this method is decreased to the duration of the first two pulses. The theory of dipole-dipole interaction in the ESE signal decay in the “2 + 1” pulse train is developed for different Flip rates and for different cases of spin spatial distribution. The theoretical data fit the experiment, carried out with model systems of H and D atoms, randomly distributed in the frozen solutions of sulfuric acid, and of biradicals. New data concerning the spatial distribution of radical clusters, resulting from y irradiation of the methanol, are given.     

Spin-State-Selective TPPI: A New Method for Suppression of Heteronuclear Coupling Constants in Multidimensional NMR Experiments

A novel multidimensional NMR pulse sequence tool, spin-state-selective time-proportional phase incrementation (S(3) TPPI), is introduced. It amounts to application of different TPPIs on the two components of doublets so that their frequencies can be manipulated independently. The chief application is for suppression of large heteronuclear one-bond coupling constants in indirect dimensions of multidimensional experiments without interchanging the two transverse magnetization components of doublets as conventional decoupling does, which is advantageous when they relax at different rates such as by partial compensation of dipolar and CSA relaxation contributions. For experimental confirmation we use a sample of (15)N-labeled neural cell adhesion molecule modules 1 and 2, a protein with a molecular weight of about 20 kDa. The new tool is general and can be combined with many multidimensional NMR experiments for proteins.