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.     

Water diffusion-exchange effect on the paramagnetic relaxation enhancement in off-resonance rotating frame

The off-resonance rotating frame technique based on the spin relaxation properties of off-resonance T1rho can significantly increase the sensitivity of detecting paramagnetic labeling at high magnetic fields by MRI. However, the in vivo detectable dimension for labeled cell clusters/tissues in T1rho-weighted images is limited by the water diffusion-exchange between mesoscopic scale compartments. An experimental investigation of the effect of water diffusion-exchange between compartments on the paramagnetic relaxation enhancement of paramagnetic agent compartment is presented for in vitro/in vivo models. In these models, the size of paramagnetic agent compartment is comparable to the mean diffusion displacement of water molecules during the long RF pulses that are used to generate the off-resonance rotating frame. The three main objectives of this study were: (1) to qualitatively correlate the effect of water diffusion-exchange with the RF parameters of the long pulse and the rates of water diffusion, (2) to explore the effect of water diffusion-exchange on the paramagnetic relaxation enhancement in vitro, and (3) to demonstrate the paramagnetic relaxation enhancement in vivo. The in vitro models include the water permeable dialysis tubes or water permeable hollow fibers embedded in cross-linked proteins gels. The MWCO of the dialysis tubes was chosen from 0.1 to 15 kDa to control the water diffusion rate. Thin hollow fibers were chosen to provide sub-millimeter scale compartments for the paramagnetic agents. The in vivo model utilized the rat cerebral vasculatures as a paramagnetic agent compartment, and intravascular agents (Gd-DTPA)30-BSA were administrated into the compartment via bolus injections. Both in vitro and in vivo results demonstrate that the paramagnetic relaxation enhancement is predominant in the T1rho-weighted image in the presence of water diffusion-exchange. The T1rho contrast has substantially higher sensitivity than the conventional T1 contrast in detecting paramagnetic agents, especially at low paramagnetic agent volumetric fractions, low paramagnetic agent concentrations, and low RF amplitudes. Short pulse duration, short pulse recycle delay and efficient paramagnetic relaxation can reduce the influence of water diffusion-exchange on the paramagnetic enhancement. This study paves the way for the design of off-resonance rotating experiments to detect labeled cell clusters/tissue compartments in vivo at a sub-millimeter scale.     

Comparison of agarose and cross-linked protein gels as magnetic resonance imaging phantoms

Measurements of the magnetic field dependence of spin-lattice relaxation rates and the response of the water-proton signal intensity to off-resonance radio frequency fields show that the commonly used agarose phantom provides a less faithful representation for the magnetic response of tissue than does a cross-linked protein system. The origin of these differences lies in the structure and intramolecular dynamics of the macromolecular system used to make the gel. These distinctions will also cause differences in the magnetic response of the water spin system when paramagnetic relaxation agents or contrast agents are incorporated. Use of a thermally cross-linked bovine serum albumin phantom is suggested.     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

Relaxation dispersion in MRI induced by fictitious magnetic fields

A new method entitled Relaxation Along a Fictitious Field (RAFF) was recently introduced for investigating relaxations in rotating frames of rank ≥ 2. RAFF generates a fictitious field (E) by applying frequency-swept pulses with sine and cosine amplitude and frequency modulation operating in a sub-adiabatic regime. In the present work, MRI contrast is created by varying the orientation of E, i.e. the angle ε between E and the z″ axis of the second rotating frame. When ε > 45°, the amplitude of the fictitious field E generated during RAFF is significantly larger than the RF field amplitude used for transmitting the sine/cosine pulses. Relaxation during RAFF was investigated using an invariant-trajectory approach and the Bloch-McConnell formalism. Dipole-dipole interactions between identical (like) spins and anisochronous exchange (e.g., exchange between spins with different chemical shifts) in the fast exchange regime were considered. Experimental verifications were performed in vivo in human and mouse brain. Theoretical and experimental results demonstrated that changes in ε induced a dispersion of the relaxation rate constants. The fastest relaxation was achieved at ε ≈ 56°, where the averaged contributions from transverse components during the pulse are maximal and the contribution from longitudinal components are minimal. RAFF relaxation dispersion was compared with the relaxation dispersion achieved with off-resonance spin lock T(?ρ) experiments. As compared with the off-resonance spin lock T(?ρ) method, a slower rotating frame relaxation rate was observed with RAFF, which under certain experimental conditions is desirable.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Proton longitudinal NMR relaxation of poly(p-phenylene sulfide) in the laboratory and the rotating frames reference

Spin-lattice NMR relaxation times T1 in the laboratory frame and T1rho(off) as well as T1rho(off) in the rotating frame off-resonance were employed to the study of molecular dynamics of both pristine PPS and thermally treated poly(p-phenylene sulfide) (PPS). The temperature dependence of T1 was exponential in the whole temperature range studied, whereas T1rho only in low temperatures. In the high temperature range the distribution of relaxation times T1rho and correlation times tau(c) as well as activation energy Ea was observed. The distribution of activation energy determined from T1 minima at 15 and 30 MHz and from low temperature slopes of T1rho dependence as well as from spectral density functions (estimated from proton off-resonance technique) was attributed to the reorientation of phenylene groups around the sulfur-phenyl-sulfur axis in amorphous and crystalline phases of PPS. Furthermore, it is suggested that an additional relaxation mechanism related to interactions of protons with paramagnetic centers is operative in a low temperature range. After thermal treatment of PPS the low temperature minima disappeared and the relaxation times shortened in the low temperature regime. Both these facts were attributed to an increased contribution of spin diffusion in the relaxation process.     

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.     

Rotating frame relaxation during adiabatic pulses vs. conventional spin lock: simulations and experimental results at 4 T

Spin relaxation taking place during radiofrequency (RF) irradiation can be assessed by measuring the longitudinal and transverse rotating frame relaxation rate constants (R_1ρ and R_2ρ). These relaxation parameters can be altered by utilizing different settings of the RF irradiation, thus providing a useful tool to generate contrast in MRI. In this work, we investigate the dependencies of R_1ρ and R_2ρ due to dipolar interactions and anisochronous exchange (i.e., exchange between spins with different chemical shift δω≠0) on the properties of conventional spin-lock and adiabatic pulses, with particular emphasis on the latter ones which were not fully described previously. The results of simulations based on relaxation theory provide a foundation for formulating practical considerations for in vivo applications of rotating frame relaxation methods. Rotating frame relaxation measurements obtained from phantoms and from the human brain at 4 T are presented to confirm the theoretical predictions.     

Molecular oxygen spin-lattice relaxation in solutions measured by proton magnetic relaxation dispersion

Proton spin-lattice relaxation rate constants have been measured as a function of magnetic field strength for water, water-glycerol solution, cyclohexane, methanol, benzene, acetone, acetonitrile, and dimethyl sulfoxide. The magnetic relaxation dispersion is well approximated by a Lorentzian shape. The origin of the relaxation dispersion is identified with the paramagnetic contribution from molecular oxygen. In the small molecule cases studied here, the effective correlation time for the electron-nuclear coupling may include contributions from both translational diffusion and the electron T(1). The electron T(1) for molecular oxygen dissolved in several solvents was found to be approximately 7.5 ps and nearly independent of solvent or viscosity.     

Mechanism of relaxation enhancement of spin labels in membranes by paramagnetic ion salts: dependence on 3d and 4f ions and on the anions

Progressive saturation EPR measurements and EPR linewidth determinations have been performed on spin-labeled lipids in fluid phospholipid bilayer membranes to elucidate the mechanisms of relaxation enhancement by different paramagnetic ion salts. Such paramagnetic relaxation agents are widely used for structural EPR studies in biological systems, particularly with membranes. Metal ions of the 3d and 4f series were used as their chloride, sulfate, and perchlorate salts. For a given anion, the efficiency of relaxation enhancement is in the order Mn(2+) > or = Cu(2+) > Ni(2+) > Co(2+) approximately Dy(3+). A pronounced dependence of the paramagnetic relaxation enhancement on the anion is found in the order ClO(-)(4) > Cl(-) > SO(2-)(4). This is in the order of the octanol partition coefficients multiplied by spin exchange rate constants that were determined for the different paramagnetic salts in methanol. Detailed studies coupled with theoretical estimates reveal that, for the chlorides and perchlorates of Ni(2+) (and Co(2+)), the relaxation enhancements are dominated by Heisenberg spin exchange interactions with paramagnetic ions dissolved in fluid membranes. The dependence on membrane composition of the relaxation enhancement by intramembrane Heisenberg exchange indicates that the diffusion of the ions within the membrane takes place via water-filled defects. For the corresponding Cu(2+) salts, additional relaxation enhancements arise from dipolar interactions with ions within the membrane. For the case of Mn(2+) salts, static dipolar interactions with paramagnetic ions in the aqueous phase also make a further appreciable contribution to the spin-label relaxation enhancement. On this basis, different paramagnetic agents may be chosen to optimize sensitivity to different structurally correlated interactions. These results therefore will aid further spin-label EPR studies in structural biology.     

High-frequency dynamic nuclear polarization in the nuclear rotating frame

A proton dynamic nuclear polarization (DNP) NMR signal enhancement (epsilon) close to thermal equilibrium, epsilon = 0.89, has been obtained at high field (B(0) = 5 T, nu(epr) = 139.5 GHz) using 15 mM trityl radical in a 40:60 water/glycerol frozen solution at 11 K. The electron-nuclear polarization transfer is performed in the nuclear rotating frame with microwave irradiation during a nuclear spin-lock pulse. The growth of the signal enhancement is governed by the rotating frame nuclear spin-lattice relaxation time (T(1rho)), which is four orders of magnitude shorter than the nuclear spin-lattice relaxation time (T(1n)). Due to the rapid polarization transfer in the nuclear rotating frame the experiment can be recycled at a rate of 1/T(1rho) and is not limited by the much slower lab frame nuclear spin-lattice relaxation rate (1/T(1n)). The increased repetition rate allowed in the nuclear rotating frame provides an effective enhancement per unit time(1/2) of epsilon(t) = 197. The nuclear rotating frame-DNP experiment does not require high microwave power; significant signal enhancements were obtained with a low-power (20 mW) Gunn diode microwave source and no microwave resonant structure. The symmetric trityl radical used as the polarization source is water-soluble and has a narrow EPR linewidth of 10 G at 139.5 GHz making it an ideal polarization source for high-field DNP/NMR studies of biological systems.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique in the presence of magnetization transfer effect

The simple method for measuring the rotational correlation time of paramagnetic ion chelates via off-resonance rotating frame technique is challenged in vivo by the magnetization transfer effect. A theoretical model for the spin relaxation of water protons in the presence of paramagnetic ion chelates and magnetization transfer effect is described. This model considers the competitive relaxations of water protons by the paramagnetic relaxation pathway and the magnetization transfer pathway. The influence of magnetization transfer on the total residual z-magnetization has been quantitatively evaluated in the context of the magnetization map and various difference magnetization profiles for the macromolecule conjugated Gd-DTPA in cross-linked protein gels. The numerical simulations and experimental validations confirm that the rotational correlation time for the paramagnetic ion chelates can be measured even in the presence of strong magnetization transfer. This spin relaxation model also provides novel approaches to enhance the detection sensitivity for paramagnetic labeling by suppressing the spin relaxations caused by the magnetization transfer. The inclusion of the magnetization transfer effect allows us to use the magnetization map as a simulation tool to design efficient paramagnetic labeling targeting at specific tissues, to design experiments running at low RF power depositions, and to optimize the sensitivity for detecting paramagnetic labeling. Thus, the presented method will be a very useful tool for the in vivo applications such as molecular imaging via paramagnetic labeling.     

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.     

Nuclear spin relaxation in solution of paramagnetic complexes with large transient zero-field splitting

A theory for paramagnetic relaxation enhancement (PRE) in systems with S> 1 at low magnetic field is developed for the case when the fluctuations of zero-field splitting (ZFS) in the molecular frame are larger than the averaged ZFS. The validity limits of the new theory are discussed, and its performance is evaluated by comparisons with the general slow-motion approach. The relevance of the new approach for the proton PRE in aqueous solution of Ni(II) is discussed.     

Theoretical prediction and experimental measurement of the field dependence of the apparent transverse relaxation of hyperpolarized noble gases in lungs

In this work, computer modeling based on a finite element method is used to simulate the T2* relaxation of hyperpolarized noble gases (HNG) in the lungs. A physical model of lung airways consisting of a phantom constructed from micro-capillary fibers of diameters similar to the size of lung airways with semi-permeable walls is also presented. The fibers are surrounded by a liquid medium (water) of magnetic susceptibility similar to lung tissue. Theoretical predictions of the field strength dependence of T2* for 129Xe in the phantom and in vivo rat lung are presented. These predictions are in good agreement with experimental T2* values obtained from the phantoms and in vivo rat lungs (160, 19 and 8 ms) at three different field strengths (0.074, 1.89 and 3T, respectively) using hyperpolarized 129Xe. The strong dependence of T2* on field strength is consistent with the theoretical prediction that low fields may be optimal for HNG MR imaging of the lungs as the decreased T2* at high fields necessitates an increase in bandwidth for conventional MR imaging.     

Low-frequency proton NMR relaxometry of a polymer dispersed liquid crystal above TNI

Using proton NMR relaxometry in the kilohertz frequency range, we study dynamics of 5CB liquid crystal molecules dispersed in the form of spherical microdroplets in a PDLC material. The focus of the study is the spin-lattice relaxation in the rotating frame, T1rho(-1), measured above the nematic-isotropic transition TNI. We show that the relaxation rate T1rho(-1)--when induced by uniform molecular translational diffusion in a spherical cavity--depends on the strength of the rotating magnetic field as T1rho(-1) proportional to omega1(-alpha) where alpha varies between 0.7 and 1, depending on the thickness of the ordered surface layer. This relaxation mechanism governs mainly the transverse spin relaxation, whereas the measurements of the frequency and temperature dependence of T1rho(-1) indicate a strong effect of slowing-down of molecular translational diffusion in contact with the polymer surface and yield the average dwell-time of molecules at the surface of the order 10(-5) s.     

Low-frequency molecular dynamics studied by spin-lock field cycling imaging

Spin-lock adiabatic field cycling imaging (SLOAFI) relaxometry was shown to be a useful technique for obtaining a fast study of spin-lattice relaxation dispersion in the rotating frame. The aim of the present article is to describe some technical aspects of the experiment in more detail, while showing simple examples that can be compared with laboratory frame relaxation. We also present here a general discussion of the equations for an off-resonance experiment used to analyze low-frequency molecular dynamics.     

Nuclear spin relaxation in paramagnetic systems (S>/=1) under fast rotation conditions

A new theoretical model for nuclear spin relaxation in paramagnetic systems in solution has been developed. Fast rotational motion is included in the model, both as a source of modulation of the static zero-field splitting, which provides a mechanism for electron spin relaxation, and as an origin of the stochastic variation of the electron spin-nuclear spin dipole-dipole interaction leading to nuclear spin relaxation. At the limit of low magnetic field, the model is essentially identical to the earlier formulations from our laboratory, but new closed-form expressions are given for the inner- and outer-sphere relaxation at the high-field limit. Numerical comparisons with a general theory are reported for the inner-sphere case. In addition, some nuclear magnetic relaxation dispersion (NMRD) profiles from the literature are considered for systems where experiments have been done with both low-molecular weight paramagnetic complexes and their adducts with proteins. Previously developed theories are used to interpret data for the slowly rotating protein adducts, and good fits of the fast-rotating counterparts are obtained by further adjustment of one or two additional parameters.     

Four complementary theoretical approaches for the analysis of NMR paramagnetic relaxation

Four theoretical and computational approaches used at the University of Michigan to analyze NMR paramagnetic relaxation enhancement (NMR-PRE) are described. The primary objective of the theory is to describe the relationship of the NMR-PRE phenomenon to the electron spin hamiltonian and the spin energy level structure when zero field splitting interactions are significant. Four formulations of theory are discussed: (1) spin dynamics simulation; (2) the laboratory frame "constant H(S)" formulation; (3) the Molecular Frame "constant H(S)" formulation; and (4) the zfs-limit "constant H(S)" formulation. No single theoretical approach describes all important aspects of the relaxation mechanism in a fully satisfactory way. We use the four formulations in a complementary manner to provide as complete a picture of the relaxation mechanism as possible. We also discuss the integration of NMR-PRE theory and recently developed theory of electron spin relaxation which accounts for effects of the permanent zfs hamiltonian.