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.     

R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions

Analytic expressions for the nuclear magnetic spin relaxation rate constant for magnetization spin-locked in the rotating reference frame under an applied radiofrequency field, R(1rho), are obtained for two-site chemical exchange. The theoretical approach is motivated by Laguerre's method and obtains R(1rho) as the root of a (p1,q1) Padé approximant. The general formula for R(1rho) obtained by this approach is substantially simpler than existing expressions and is equally or slightly more accurate, in most cases. In addition, particular solutions for the R(1rho) rate constant are presented for two special cases: equal populations of the two exchanging sites, or placement of the radiofrequency carrier at the average resonance frequency of the two sites. The solutions are exact when the R1 and R2 relaxation rate constants are identical, and nearly exact under realistic experimental conditions.     

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.     

Transverse relaxation mechanisms in articular cartilage

Relaxation rates in the rotating frame (R1rho) and spin-spin relaxation rates (R2) were measured in articular cartilage at various orientations of cartilage layer to the static magnetic field (B0), at various spin locking field strengths and at two different static magnetic field strengths. It was found that R1rho in the deep radial zone depended on the orientation of specimens in the magnet and decreased with increasing the spin locking field strength. In contrast, R1rho values in the transitional zone were nearly independent of the specimen orientation and the spin locking field strength. Measurements of the same specimens at 2.95 and 7.05 T showed an increase of R1rho and most R2 values with increasing B0. The inverse B0 dependence of some R2 values was probably due to a multicomponent character of the transverse magnetization decay. The experiments revealed that the dominant T1rho and T2 relaxation mechanism at B0 < or = 3 T is a dipolar interaction due to slow anisotropic motion of water molecules in the collagen matrix. On average, the contribution of scalar relaxation due to rapid proton exchange in femoral head cartilage at 2.95 T is about 6% or less of the total R1rho at the spin locking field of 1000 Hz.     

Fast proton spin-lattice relaxation time in the rotating frame during the application of time averaged precession frequency

A relatively rapid phase alternation of the effective field in the time averaged precession frequency (TAPF) sequence results in averaging of the proton RF spin-lock field. The spin-locking of the proton magnetization becomes less efficient and thus shortens T(1rho)(H), the proton spin-lattice relaxation time in the rotating frame. The relaxation time also depends on the ratio of tau(1) and tau(2) intervals i.e. tau(1)/tau(2) and not only on the number of tau(c)=tau(1)+tau(2) blocks, i.e. the number of the phase transients. Experiments are performed on solid samples of ferrocene and glycine and for some time intervals, T(1rho)(H) is shortened by factors of 9-100 compared to the relaxation times obtained in the standard experiment.     

Rotating frame analog of spin-locking and spin-lattice relaxation in the doubly rotating frame

The present paper reports the achievement of the rotating-frame analog of spin-locking and its application to the precise measurements of the spin-lattice relaxation time T(1DR) in the doubly rotating frame. After the magnetization is aligned along the resonant RF field H(1), a pulse sequence of a low-frequency oscillating magnetic field at exact resonance is applied perpendicular to H(1). We have overcome several technical difficulties arising from the fact that the rotating-wave approximation is not valid for the low-frequency field. We have theoretically derived an expression of T(-1)(1DR) due to fluctuating magnetic dipole interactions in the weak collision case and found an important relation among the spin-lattice relaxation rates T(-1)(1), T(-1)(1rho), and T(-1)(1DR). This relation can be used to ascertain whether the relaxation is only due to the fluctuating magnetic dipole interactions between like spins. The experiment was carried out on (1)H nuclei in tetramethylammonium iodide (CH(3))(4)NI and the temperature dependence of T(-1)(1DR) was measured together with that of T(-1)(1) and T(-1)(1rho). The activation energies and the preexponential factors of Arrhenius expressions of the correlation times are newly determined.     

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.     

Anisotropic spin relaxation in graphene

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.     

T1rho Dispersion profile of rat tissues in vitro at very low locking fields

The purpose of this study was to show the T(1rho) dispersion profile in various rat tissues (liver, brain, spleen, kidney, heart and skeletal muscle) at low (0.1 T) B(0) field at very low locking field B1, starting from 10 microT. The T(1rho) dispersion profile showed a quite similar pattern in all tissues. The highest R(1rho) relaxation rates were seen in the liver and muscle followed by the heart, whereas the values for spleen, kidney and brain were rather similar. The greatest difference between R2 relaxation rate and R(1rho) relaxation rate at B1=10 microT was seen in the liver and muscle. The steepest slope for a dispersion curve was seen in the muscle. The value of T(1rho) approximately approached the value of T2 when the locking field B1 approached 0. Except for the liver, the calculated apparent relaxation rate R2' was slightly larger than the calculated one. The potential value of T(1rho) imaging is to combine high R1 contrast of low-field imaging with the high signal-to-noise ratio (SNR) of high static field imaging. T(1rho) relaxation and dispersion data presented in the current study help to optimize the rotating-frame MR imaging.     

T1rho dispersion of rat tissues in vitro.

The purpose of this study was to demonstrate T1rho dispersion in different rat tissues (liver, brain, spleen, kidney, heart, and skeletal muscle), and to compare the 1/T1rho data to previous 1/T1 data and magnetization transfer of rat tissues at low (0.1 T) B0 field. The 1/T1rho dispersion showed a fairly similar pattern in all tissues. The highest 1/T1rho relaxation rates were seen in liver and muscle followed by heart, whereas the values for spleen, kidney, and brain were quite similar. Compared to 1/T2 relaxation rate, the greatest difference was seen in liver and muscle. The rank order 1/T1rho value at each locking field B1 was the same as the transfer rate of magnetization from the water to the macromolecular pool (Rwm) for liver, muscle, heart, and brain. The potential value T1rho imaging is to combine high T1 contrast of low field imaging with the high signal to noise ratio of high static field imaging. When the T1rho value for a given tissue is known, the contrast between different tissues can be optimized by adjusting the locking time TL. Further studies are encouraged to fully exploit this. Targets for more detailed research include brain infarct, brain and liver tumors.     

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.     

Microsecond time-scale dynamics from relaxation in the rotating frame: experiments using spin lock with alternating phase

A spin lock comprised of radiofrequency pulses with alternating phase, (x) (-x)(x) (-x) , is proposed as a new technique to probe microsecond time-scale dynamics. A series of R1rho measurements using different pulse duration tp allows one to determine exchange rate, kex, the product p(a)p(b)(Delta omega(ab))2 involving populations of the exchanging species, p(a) and p(b), together with chemical shift difference, (Delta omega(ab)), and the strength of the spin-lock field, B1. The interpretation is based on simple analytical expression for R1rho derived on the basis of Redfield theory. The application of the method is demonstrated for partially deuterated molecule of cyclohexane undergoing chair-to-chair interconversion at -9 degrees C.     

Spinning-frequency-dependent narrowband RF-driven dipolar recoupling

Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.     

Measuring T₂ and T₁, and imaging T₂ without spin echoes

During adiabatic excitation, the nuclear magnetization in the transverse plane is subject to T(2) (spin-spin) relaxation, depending on the pulse length τ. Here, this property is exploited in a method of measuring T(2) using the ratio of NMR signals acquired with short and long-duration self-refocusing adiabatic pulses, without spin-echoes. This Dual-τ method is implemented with B(1)-insensitive rotation (BIR-4) pulses. It is validated theoretically with Bloch equation simulations independent of flip-angle, and experimentally in phantoms. Dual-τT(2) measurements are most accurate at short T(2) where results agree with standard spin-echo measures to within 10% for T(2) ≤ 100 ms. Dual-τ MRI performed with a long 0° BIR-4 pre-pulse provides quantitative T(2) imaging of phantoms and the human foot while preserving desired contrast and functional properties of the rest of the MRI sequence. A single 0° BIR-4 pre-pulse can provide T(2) contrast-weighted MRI and serve as a "T(2)-prep" sequence with a lower B(1) requirement than prior approaches. Finally, a Tri-τ experiment is introduced in which both τ and flip-angle are varied, enabling measurement of T(2), T(1) and signal intensity in just three acquisitions if flip-angles are well-characterized. These new methods can potentially save time and simplify relaxation measurements and/or contrast-weighted NMR and MRI.     

Spin-lock MRI with amplitude- and phase-modulated adiabatic waveforms: an MR simulation study

INTRODUCTION: Image contrast between tissue types can be generated based on their T1/T2 ratio using spin-lock MRI techniques. An interesting application of such a concept would be to generate contrast in tissue with tissue relaxation times modified using exogenous contrast agents. An amplitude-modulated adiabatic waveform has been shown in the past to perform spin-lock MRI. However, implementation of this waveform may not prove to be efficient and practical in research or a clinical setup due to high radiofrequency power deposition. Recent advancement in software and hardware MR technology allows implementation of amplitude- and phase-modulated adiabatic waveforms on MR systems. The aim of this work was to explore role of adiabatic waveforms in performing rho imaging and demonstrate that amplitude- and phase-modulated waveforms [e.g., hyperbolic secant, B1 independent rotation-4 (BIR-4) waveforms] can be used to distinguish materials that differ in T1/T2 ratio. METHODS AND RESULTS: MR simulation was performed using computer routines implemented in MATLAB environment (Mathworks, Natick, MA). Modified Bloch equations with trapezoidal, hyperbolic secant and BIR-4 waveforms were used to perform MR simulation. Trapezoidal waveforms were only used for comparison to other waveforms. Gadolinium DTPA (Gad-DTPA) (T1/T2 approximately 1) and manganese chloride (MnCl(2)) (T1/T2 approximately 10) were used as examples of contrast agents due to their routine use in clinical and research setups and more importantly because they provide good examples of materials differing in T1/T2 ratios. Results of spin locking using trapezoidal waveform agree very well with the previously published results, thereby validating the computer routines used in this MR simulation. Plots of M(rho) (magnetization vector in rho domain) vs. offset frequency show distinct curves for these materials differing in T1/T2 for the three waveforms. BIR-4 waveform demonstrated a 40% difference in M(rho) ( approximately 150 Hz) for the materials. Rate of spin lock with hyperbolic secant waveform was rapid compared to other waveforms. DISCUSSION: MR simulation using contrast agents Gad-DTPA and MnCl(2) provided a useful way to demonstrate that amplitude- and phase-modulated adiabatic waveforms can be used to perform spin-lock imaging. Future work involves implementation of these waveforms on MR scanners and performing in vivo imaging to generate tissue contrast based on relaxation times ratio.     

Temperature dependence of nuclear magnetization and relaxation

The temperature dependences of nuclear magnetization and relaxation rates are reviewed theoretically and experimentally in order to quantify the effects of temperature on NMR signals acquired by common imaging techniques. Using common sequences, the temperature dependences of the equilibrium nuclear magnetization and relaxation times must each be considered to fully understand the effects of temperature on NMR images. The temperature dependence of the equilibrium nuclear magnetization is negative because of Boltzmann's distribution for all substances at all temperatures, but the combined temperature dependences of the equilibrium magnetization and relaxation can be negative, weak or positive depending on the temperature (T), echo time (T(E)), repetition time (T(R)), and the temperature dependences of the relaxation times T(1)(T) and T(2)(T) in a pulse sequence. As a result, the magnitude of the NMR signal from a given substance can decrease, increase or stay somewhat constant with increasing temperature. Nuclear thermal coefficients are defined and predictions for spin echo and other simple sequences are verified experimentally using a number of substances representing various thermal and NMR properties.     

Low-power water suppression by hyperbolic secant pulses with controlled offsets and delays (WASHCODE)

A class of chemical-shift-selective (CHESS) water suppression (WS) schemes is presented in which the characteristic frequency-domain excitation profiles of "adiabatic" full-passage (AFP) RF pulses are utilized for frequency-selective excitation of the water resonance. In the proposed WS schemes, dubbed WASHCODE, hyperbolic secant (HS) pulses were used as the AFP pulses. Besides the high immunity of WS efficiency toward B(1) inhomogeneity, these sequences also exhibit extraordinary insensitivity to the dispersion of the water T(1) relaxation times. The actual performance of the proposed WS schemes was achieved in particular by optimizing the frequency offsets of WS HS pulses and the time intervals between them. To reduce the RF power requirements of these WS sequences for in vivo applications, HS pulses with the minimum possible frequency bandwidths were employed, which also substantially reduced the adverse effects on the observed proton MR spectra. The proposed WS schemes were evaluated by simulations based on the Bloch equations. Several WS sequences which looked particularly promising were verified experimentally on the human brain on a 3 T MR scanner using very short echo-time STEAM for volume selection and a standard single-loop surface coil for both signal transmission and reception. Routinely, water-suppression factors ranging from 2000 to 4000 were achieved in vivo without additional adjustment of parameters for individual subjects and without violating legal safety limits.