Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

Origin of the asymmetric magnetization reversal behavior in exchange-biased systems: competing anisotropies

The magnetization reversal in exchange-biased ferromagnetic-antiferromagnetic (FM-AFM) bilayers is investigated. Different reversal pathways on each branch of the hysteresis loop, i.e., asymmetry, are obtained both experimentally and theoretically when the magnetic field is applied at certain angles from the anisotropy direction. The range of angles and the magnitude of this asymmetry are determined by the ratio between the FM anisotropy and the interfacial FM-AFM exchange anisotropy. The occurrence of asymmetry is linked with the appearance of irreversibility, i.e., finite coercivity, as well as with the maximum of exchange bias, increasing for larger anisotropy ratios. Our results indicate that asymmetric hysteresis loops are intrinsic to exchange-biased systems and the competition between anisotropies determines the asymmetric behavior of the magnetization reversal.     

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.     

An Off-resonance Rotating Frame Relaxation Experiment for the Investigation of Macromolecular Dynamics Using Adiabatic Rotations

¹⁵N off-resonance rotating frame relaxation can be applied to the study of internal dynamics in proteins in the millisecond to microsecond regime. We show that the performance of existing methods can be improved by application of simultaneous amplitude and phase-modulated adiabatic RF pulses to align the nuclear spin magnetization with the off-resonance spin-lock field for all the spins under investigation. Application of this technique to the 269-residue serine protease PB92 allowed the measurement of¹⁵N off-resonance rotating frame relaxation rates for all nonoverlapping residues in the protein, including the arginine side chains, encompassing a chemical shift range of 50 ppm. Simulations indicate that by use of the proposed adiabatic RF pulses rotating frame relaxation rates can be obtained for magnetization vectors aligned at arbitrary angles with the static field.     

Spin-locking in one pulse NMR experiment

The response of a spin system to a long (in comparison to spin–spin relaxation time T₂) radiofrequency pulse has been studied. We observed that the magnetization after the long pulse does not fall to zero at time tT₂ for both on-resonance and off-resonance conditions. The dependencies of the magnetization on frequency offset, linewidth and radiofrequency power are investigated, both theoretically and experimentally. The question of the effective field direction is also discussed.     

纵向弛豫对核磁共振线型的影响

根据经典 Bloch方程的解析解以及考虑辐射阻尼效应的Bloch方程的数值解,通过解析分析和数值模拟,从理论上研究了在射频场扰动下以及在辐射阻尼效应的作用下纵向弛豫对核磁共振线型的影响.结果表明:①射频场的扰动和辐射阻尼效应将导致纵向磁化与横向磁化的耦合,从而使纵向弛豫对线型产生了一定的影响.②在射频场的扰动下,峰强和线宽分别为2M0sin(θ)T1T2/(T1+T2)和(T1+T2)/(2πT1T2),即纵向弛豫将使谱线的峰强增大、线宽变窄,且影响程度随着比值T2/T1的减小而增大,峰强最大可增加1倍而线宽最多可减小1/2.③在强辐射阻尼效应的作用下,纵向弛豫会使谱线的峰强降低,降低的幅度与扳转角θ以及比值T2/T1密切相关.当θ从0到3π/4时,降低的幅度均较小,只有当θ＞3π/4时,降低的幅度才开始逐渐变大,且当 θ接近π时,降低的幅度急剧增大.谱线峰强降低的幅度与T2/T1呈较严格的正比关系,即T1越接近T2,峰强下降得越显著.     

Magnetization transfer using inversion recovery during off-resonance irradiation

Estimation of magnetization transfer (MT) parameters in vivo can be compromised by an inability to drive the magnetization to a steady state using allowable levels of radiofrequency (RF) irradiation, due to safety concerns (tissue heating and specific absorption rate (SAR)). Rather than increasing the RF duration or amplitude, here we propose to circumvent the SAR limitation by sampling the formation of the steady state in separate measurements made with the magnetization initially along the -z and +z axis of the laboratory frame, i.e. with or without an on-resonance inversion pulse prior to the off-resonance irradiation. Results from human brain imaging demonstrate that this choice provides a tremendous benefit in the fitting procedure used to estimate MT parameters. The resulting parametric maps are characterized by notably increased tissue specificity as compared to those obtained with the standard MT acquisition in which magnetization is initially along the +z axis only.     

Magnetization Transfer Imaging of Rat Brain under Non-steady-state Conditions. Contrast Prediction Using a Binary Spin–Bath Model and a Super-Lorentzian Lineshape

Magnetization transfer contrast imaging using turbo spin echo and continuous wave off-resonance irradiation was carried out on rat brainin vivoat 4.7 T. By systematically varying the off-resonance irradiation power and the offset-frequency, the signal intensities obtained under steady-state for both transverse and longitudinal magnetization were successfully analyzed with a simple binary spin–bath model taking into account a free water compartment and a pool of protons with restricted motions bearing a super-Lorentzian lineshape. Due to important RF power deposition, such experimental conditions are not practical for routine imaging on humans. An extension of the model was derived to describe the system for shorter off-resonance pulse duration, i.e., when the longitudinal magnetization of the free protons has not reached a steady-state. Data sets obtained for three regions of interest, namely thecorpus callosum,the basal ganglia, and the temporal lobe, were correctly interpreted for off-resonance pulse durations varying from 0.3 to 3 s. The parameter sets obtained from the calculations made it possible to predict the contrast between the different regions as a function of the pulse power, the offset frequency, and pulse duration. Such an approach could be extended to contrast prediction for human brain at 1.5 T.     

One- and two-dimensional 15N exchange CP/MAS NMR studies of the structure and electronic properties of the intermolecular N-H...N hydrogen bond in imidazole crystal

The hydrogen bond of the type N-H...N in imidazole crystal has been studied by one and two-dimensional 15N exchange CP/MAS NMR measurements as well as the powder NMR spectrum. The chemical shift anisotropies for -N= and -N< were determined from the powder 1D spectrum. In 2D exchange CP/MAS NMR spectrum, the cross peaks between the 15N main resonance peaks for -N= and -N< were observed, implying that magnetization exchange between -N= and -N< takes place. The 1D exchange CP/MAS NMR measurements determined the exchange rate of magnetization at 289 K to be 1.3 and 1.5 s(-1) for -N= and -N<, respectively. The proton-driven spin-diffusion model interprets the experimental values, and the exchange rate depends strongly on the RF power of the proton decoupling field, suggesting that the magnetization transfer between -N= and -N< takes place by the 1H-driven spin-diffusion mechanism.     

Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems under Selective Saturation. IV. Reformulation of the Spin-Bath-Model Equations by the Redfield-Provotorov Theory

Alternative formulations to the conventional Bloch equations for the RF saturation of the solid component in heterogeneous spin systems according to a spin-bath model are derived using the concept of spin temperature as suggested by Redfield and Provotorov. These formulations and the resulting equations derived by the projection-operator technique provide an analytical and explicit solution to the general problem of solid saturation under continuous RF irradiation. Using the Provotorov theory, a set of generalized (non-Markovian) equations of motions is derived. The solutions to these generalized equations approach those of the conventional Bloch formulation at one extreme when the applied RF is weak and the Redfield formulation at another when the applied RF is strong. In short, this development provides a simple alternative which removes the restriction of the lineshape function used to represent the solid component; the latter is well known to be non-Lorentzian, contrary to the tacit assumption made in the conventional Bloch formulation. Experimental verification of the generalized theory is provided by transient and steady-state longitudinal magnetization data acquired from cross-linked bovine serum albumin under selective saturation by continuous off-resonance RF irradiation.     

Restricted diffusion in grossly inhomogeneous fields

We analyze the effects of geometrical restriction on the nuclear magnetization of spins diffusing in grossly inhomogeneous fields where radio-frequency (RF) pulses are weak relative to the total field inhomogeneity, making the rotation angle space-dependent and thus exciting multiple coherence pathways. We show how to separate the effects of restricted diffusion from the effects of the pulses in the case when the change in the field experienced by a diffusing spin in the course of the experiment is small compared to the RF magnitude. We then derive explicit formulas for the contribution of individual coherence pathways to the total magnetization in arbitrary pulse sequences. We find that, for long diffusion times, restriction can dramatically alter the spectrum and the shape of a particular echo, while for short times, the correction will be proportional to the pore space surface-to-volume ratio. We demonstrate these results on the example of the early echoes of the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

Large RF susceptibility of transverse domain walls

Changes in domain wall resistance under radio-frequency (RF) irradiation are experimentally studied for transverse walls. An original experimental technique is applied to the measurement in a permalloy nano-stripe with a notch, where the walls are found to provide a largely enhanced resistive response as compared to saturated domains. Their susceptibility is found to be an order of magnitude larger than that of the domains in a frequency range between 5 and 20 GHz. We argue that the RF fields induce an internal distortion of the magnetization profile that depends on the shape of the domain wall.     

Exchange bias and asymmetric hysteresis loops from a microscopic model of core/shell nanoparticles

We present Monte Carlo simulations of hysteresis loops of a model of a magnetic nanoparticle with a ferromagnetic core and an antiferromagnetic shell with varying values of the core/shell interface exchange coupling which aim to clarify the microscopic origin of exchange bias observed experimentally. We have found loop shifts in the field direction as well as displacements along the magnetization axis that increase in magnitude when increasing the interfacial exchange coupling. Overlap functions computed from the spin configurations along the loops have been obtained to explain the origin and magnitude of these features microscopically.     

Broadband phase modulation by adiabatic pulses

The use of inhomogeneous but spatially correlated static and radiofrequency (RF) magnetic fields offers a potential methodology for performing magnetic resonance spectroscopy of samples placed outside the bore of the magnet. However, its practical implementation still presents challenging problems, among them the control of nuclear spins over broad frequency offset intervals. The present study introduces an efficient method of encoding the phase of the magnetization when the variation of the static field along the sample is much larger than the RF amplitude. The procedure is based on the use of consecutively applied full-passage adiabatic pulses. The induced phase modulation is broadband and selective because it does not depend on the offset relative to the central frequency and the limits can be sharply defined. Finally, the encoded phase depends almost linearly on the local RF amplitude. All these features enable the recovery of an inhomogeneity-free spectrum with amplitudes close to the theoretically attainable maximum.     

Two-dimensional on- and off-resonance nutation FFT/MEM NQR spectroscopy

The new two-dimensional nuclear quadrupole resonance experiments based on the principle of nutation spectroscopy, which can be used to determine the asymmetry parameter, and thus the full quadrupolar tensor of spin-3/2 nuclei at zero applied magnetic field are discussed. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. Use of the MEM in 2D-NQR spectroscopy can lead to sensitivity improvement, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. The possibilities of off-resonance irradiation in nutation experiments are demonstrated experimentally and theoretically. It is shown that the off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments thus facilitating the determination of asymmetry parameters in multiple spectrum. The methods have been successfully demonstrated for the³⁵Cl on-and off-resonance 2D-nutation spectra in polycrystalline 2,4,6-trichloro-1,3,5-triazine.     

Tagging of the magnetization with the transition zones of 360 degrees rotations generated by a tandem of two adiabatic DANTE inversion sequences

A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0 degrees and 360 degrees rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0 degrees or 360 degrees rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B(1) inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B(1) field magnitude.     

Optimization of the irradiation power in chemical exchange dependent saturation transfer experiments

In chemical exchange dependent saturation transfer imaging experiments, exchangeable solute protons are saturated and the transfer of saturation to water is subsequently detected. When the applied irradiation power is comparable to the resonance frequency difference between the water protons and saturated solute protons, the proton transfer (PT) efficiency is reduced due to concomitant direct saturation effects. In this study, the PT process is modeled using a two-pool system. An empirical general proton transfer ratio (PTR) equation for arbitrary RF irradiation power is derived, and its optimal power to maximize the PTR is analyzed. The results are confirmed experimentally on 4.7 T using a poly-L-lysine solution. The theory provides a useful tool for optimizing the irradiation power of the PT sequences in the presence of direct saturation effects.     

Lifetimes of the singlet-states under coherent off-resonance irradiation in NMR spectroscopy

Singlet-states |S=(|alphabeta> - |betaalpha>)/sq.rt.2 can be excited in pairs of coupled spins I and S, first by preparing either a non-vanishing zero-quantum coherence I(+)S(-) or a state of longitudinal two-spin order I(z)S(z) and then by applying a coherent radio-frequency (RF) irradiation with a carrier frequency omega(rf) = (Omega(I) + Omega(S))/2 that lies half-way between the chemical shifts of the two spins involved. The life-times T(S) can be much longer than the spin-lattice relaxation time T(1) of longitudinal magnetization, but singlet-states are ultimately relaxed, not only by dipolar interactions between the active spins or with the external spins, but also as a result of a non-vanishing offset Deltaomega = omega(rf) - (Omega(I) + Omega(S))/2 or an insufficient amplitude of the RF irradiation that fails to fulfill the condition omega(1) > DeltaOmega = (Omega(I) - Omega(S)). In this work, the effect of off-resonance irradiation is explored and an approximate formula for the effective relaxation rate of the singlet population is provided on the basis of perturbation theory. The qualitative features of the dependence of the relaxation rate of the singlet population on the offset Deltaomega and on the difference DeltaOmega of the chemical shifts of the two spins are illustrated by comparison with numerical simulations.