R1ρ dispersion and sodium imaging in human calf muscle

PurposeTo evaluate the magnitude of chemical exchange effects and R_1ρ dispersion in muscle and their relationship to tissue sodium levels with aging.MethodsSeven healthy volunteers (aged 24 to 87 years, median age 47) underwent MRI to assess tissue sodium levels and water T_1ρ values at different spin-locking frequencies in calf muscles. T_1ρ values at each locking field were computed based on a three-parameter mono-exponential model to fit signals obtained at different locking times, and R_1ρ (= 1/T_1ρ) rates were compared at different locking fields. In particular, the dispersion of R_1ρ (ΔR_1ρ = R_1ρ(0 Hz) − R_1ρ(500 Hz)) was examined as a function of subject age. Muscle sodium content was calculated by comparing signal intensities between tissues and reference standards within the same image. The variations of ΔR_1ρ with age and sodium were analyzed by linear regression.ResultsT_1ρ values and sodium content both increased with age. R_1ρ dispersion also increased with age and showed a strong linear correlation (correlation coefficient r = 0.98, P = 0.000578) with sodium content.ConclusionΔR_1ρ reports on the contribution of labile protons such as hydroxyls which may be associated with macromolecule accumulation in the extracellular matrix (ECM). An increase of sodium signal suggests an enlarged ECM volume fraction and/or an increase in sodium concentration, which occurs during normal aging. The strong correlation between ΔR_1ρ and sodium is likely the consequence of increased ECM and density of total charged sites within the matrix from molecules such as collagens and proteoglycans. The results from this study show the potential use of R_1ρ dispersion and sodium imaging in the assessment of pathological changes in muscle such as fibrosis.     

Functional MRI Using Spin Lock Editing Preparation Pulses

A novel approach for detecting blood oxygenation level-dependent (BOLD) signals in the brain is investigated using spin locking (SL) pulses to selectively edit the effects of extravascular diffusion in field gradients from different sized vascular structures. We show that BOLD effects from diffusion amongst susceptibility gradients will contribute significantly not only to transverse relaxation rates (R₂* and R₂) but also to R_1ρ, the rate of longitudinal relaxation in the rotating frame. Similar to the ability of 180-degree pulses to refocus static dephasing effects in a spin echo, moderately strong SL pulses can also reduce contributions of diffusion in large-scale gradients and the choice of SL amplitude can be used to selectively emphasize smaller scale inhomogeneities (such as microvasculature) and to drastically reduce the influence of larger structures (such as veins). Moreover, measurements over a range of locking fields can be used to derive estimates of the spatial scales of intrinsic gradients. The method was used to detect BOLD activation in human visual cortex. Eight healthy young adults were imaged at 3 T using a single-slice, SL-prepped turbo spin echo (TSE) sequence with spin-lock amplitudes ω₁ = 80 Hz and 400 Hz, along with conventional T₂*-weighted and T₂-prepped sequences. The BOLD signal varied from 1.1 ± 0.4 % (ω₁ = 80 Hz) to 0.7 ± 0.2 % (at 400 Hz), whereas the T₂-weighted sequence measured 1.3 ± 0.3 % and the T₂* sequence measured 1.9 ± 0.3 %. This new R_1ρ functional contrast can be made selectively sensitive to intrinsic gradients of different spatial scales, thereby increasing the spatial specificity of the evoked response.     

Quantitative T(1)(ρ) imaging using phase cycling for B0 and B1 field inhomogeneity compensation

T_1ρ imaging is useful in a number of clinical applications. T_1ρ preparation methods, however, are sensitive to non-uniformities of the B₀ magnetic field and the B₁ RF field. These common system imperfections can result in image artifacts and quantification errors in T_1ρ imaging. We report on a phase-cycling method which can eliminate B₁ RF inhomogeneity effects in T_1ρ imaging. This method does not only correct for image artifacts but also for T_2ρ contamination caused by B₁ RF inhomogeneity. The presence of B₀ magnetic field inhomogeneity can compromise the effectiveness of this method for B₁ RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90-94) with phase cycling, we can simultaneously correct B₀ magnetic field inhomogeneity effects and B₁ RF inhomogeneity effects in T_1ρ imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T_1ρ preparation methods.     

Exchange-mediated contrast in CEST and spin-lock imaging

Purpose

Magnetic resonance images of biological media based on chemical exchange saturation transfer (CEST) show contrast that depends on chemical exchange between water and other protons. In addition, spin–lattice relaxation rates in the rotating frame (R_1ρ) are also affected by exchange, especially at high fields, and can be exploited to provide novel, exchange-dependent contrast. Here, we evaluate and compare the factors that modulate the exchange contrast for these methods using simulations and experiments on simple, biologically relevant samples.

Methods

Simulations and experimental measurements at 9.4 T of rotating frame relaxation rate dispersion and CEST contrast were performed on solutions of macromolecules containing amide and hydroxyl exchanging protons.

Results

The simulations and experimental measurements confirm that both CEST and R_1ρ measurements depend on similar exchange parameters, but they manifest themselves differently in their effects on contrast. CEST contrast may be larger in the slow and intermediate exchange regimes for protons with large resonant frequency offsets (e.g. > 2 ppm). Spin-locking techniques can produce larger contrast enhancement when resonant frequency offsets are small (< 2 ppm) and exchange is in the intermediate-to-fast regime. The image contrasts scale differently with field strength, exchange rate and concentration.

Conclusion

CEST and R_1ρ measurements provide different and somewhat complementary information about exchange in tissues. Whereas CEST can depict exchange of protons with specific chemical shifts, appropriate R_1ρ-dependent acquisitions can be employed to selectively portray protons of specific exchange rates.     

Magnetization-Grid Rotating-Frame Imaging Technique for Diffusion and Flow Measurements

A method for NMR imaging of magnetization patterns generated by a preparation radiofrequency pulse is reported. The technique is suitable for the simultaneous spatially and spectroscopically resolved acquisition of diffusion, flow, and spin-lattice relaxation data. The procedure is based on gradients of the RF amplitude B₁. A first preparation RF pulse produces a z-magnetization grid. After a certain evolution interval, the grid is imaged by a rotating-frame imaging technique using the same RF coil. Neither rotary nor Hahn echoes are intrinsic to the method. Transverse relaxation in the free-evolution intervals is irrelevant. High-power transmitters in combination with suitable probeheads normally produce RF pulses which are short relative to transverse relaxation in the presence of RF, so that spin-lattice relaxation is the only time-limiting factor. Gradients of the main magnetic field induced by variations of the magnetic susceptibility are uncritical. The proposed "real-space detection" method is compared with stimulated or rotary-echo "wave number encoding" procedures for diffusion experiments. It is shown that the imaging procedure presented not only makes visible the spatial (apart from the spectral) distribution of transport properties which otherwise are concealed in the wave-number encoded signal, but also renders the measuring procedure insensitive to inhomogeneities of the B₁ gradient, which needs neither to be constant nor to be uniformly oriented. Extremely inhomogeneous B₁ gradient distributions should even make single-scan diffusion experiments feasible. The magnetization-grid rotating-frame imaging procedure can be employed for the two-dimensional measurement and representation of the probability P(z₁, 0|z₂, t) that a particle is at a position z₁ at a time 0 and at a position z₂ at a time t.     

An average-magnetization analysis of R 1ρ relaxation outside of the fast exchange limit

Approximate expressions for the NMR spin relaxation rate constant in the rotating frame of reference R _1ρ are derived for two-site chemical exchange by consideration of the evolution of the average density operator using the stochastic Liouville equation. R _1ρ is obtained as a linearized approximation to the largest (least negative) eigenvalue of the matrix describing the evolution of the average density operator in the long-term limit. The expressions obtained are more accurate than existing expressions when exchange is not fast and the populations of the exchanging sites are close to equal. The new expressions for R _1ρ facilitate the interpretation of chemical exchange phenomena in proteins and other biological macromolecules.     

混合漫射近似模型的漫反射理论及其模拟实验研究

研究了一个改进的漫射近似模型.该模型将漫射近似中的漫射系数D用描述P₃近似的漫射系数D_asym替代.推导了这个混合的漫射近似模型在单点源近似和外推边界条件下的反射率R_Hybrid(ρ)的解析表达式,比较了有效反照率a′对标准漫射近似R_DA(ρ)和R_Hybrid(ρ关键词： 漫射近似 P₃近似')" href="#">P₃近似 混合漫反射模型 强吸收     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

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.     

Earlier detection of tumor treatment response using magnetic resonance diffusion imaging with oscillating gradients

An improved method for detecting early changes in tumors in response to treatment, based on a modification of diffusion-weighted magnetic resonance imaging, has been demonstrated in an animal model. Early detection of therapeutic response in tumors is important both clinically and in pre-clinical assessments of novel treatments. Noninvasive imaging methods that can detect and assess tumor response early in the course of treatment, and before frank changes in tumor morphology are evident, are of considerable interest as potential biomarkers of treatment efficacy. Diffusion-weighted magnetic resonance imaging is sensitive to changes in water diffusion rates in tissues that result from structural variations in the local cellular environment, but conventional methods mainly reflect changes in tissue cellularity and do not convey information specific to microstructural variations at sub-cellular scales. We implemented a modified imaging technique using oscillating gradients of the magnetic field for evaluating water diffusion rates over very short spatial scales that are more specific for detecting changes in intracellular structure that may precede changes in cellularity. Results from a study of orthotopic 9L gliomas in rat brains indicate that this method can detect changes as early as 24 h following treatment with 1,3-bis(2-chloroethyl)-1-nitrosourea, when conventional approaches do not find significant effects. These studies suggest that diffusion imaging using oscillating gradients may be used to obtain an earlier indication of treatment efficacy than previous magnetic resonance imaging methods.     

Multiple Nonlinear Stimulated Echoes

Three-pulse sequences in the presence of magnetic field gradients at high magnetic fields produce multiple nonlinear stimulated echoes (NOSE) at timesnτ₁after the third pulse, wherenis an integer and τ₁the interval between the first two pulses. These phenomena are due to the demagnetizing field produced by the spatial modulation of the nuclear magnetization arising in the sample after the first two pulses. The theory is presented and compared with experiments. The dependence of the NOSE amplitudes on the flip angles and on the pulse intervals is described. Implications for multidimensional NMR experiments based on sequences of three or more pulses in the presence of field gradients are discussed.     

基于多弛豫信号补偿的快速磁共振T1ρ散布成像

定量磁共振成像（MRI）可量化组织特性,是科学研究和临床研究的重要工具.旋转坐标系下的自旋-晶格弛豫时间（T_1ρ）能反映水与大分子之间的低频交互作用,在3 T及以上的高场环境下,T_1ρ受水和不稳定质子之间化学交换的影响较大,通过测量弛豫率随自旋锁定场强度的变化而得到其分布情况（T_1ρ散布）,可用于分析和量化质子的交换过程,因此T_1ρ散布是一种重要的定量MRI技术.然而,获得不同自旋锁定场强下T_1ρ加权图像的时间过长,限制了其应用范围.针对这一问题,本研究提出一种基于多弛豫信号补偿策略的快速T_1ρ散布成像方法.该方法将不同锁定频率下的T_1ρ加权图像补偿到同一信号强度水平,并结合低秩与稀疏建立重建模型.实验结果表明,该方法在加速倍数高达7倍时仍获得了较好的重建结果.     

Microstructural analysis of foam by use of NMR R2 dispersion

The spin–spin relaxation rate R₂ (=1/T₂) in hydrogel foams measured by use of a multiple spin echo sequence is found to be dependent on the echo time spacing. This property, referred to as R₂-dispersion, originates to a large extent from molecular self-diffusion of water within internal field gradients that result from magnetic susceptibility differences between the gel and air phase. Another contribution to the R₂ relaxation rate is surface relaxation. Numerical simulations are performed to investigate the relation between the foam microstructure (the mean air bubble radius and standard deviation of the air bubble radius) and foam composition properties (such as magnetic susceptibilities, diffusion coefficient and surface relaxivity) at one hand and the R₂-dispersion at the other hand. The simulated R₂-dispersions of gel foam are in agreement with the measured R₂-dispersions. By correlating the R₂-dispersion parameters and simulated microstructure properties a semi-empirical relationship is obtained that enables the mean air bubble size to be derived from measured R₂-dispersion curves. The R₂-derived mean air bubble size of a hydrogel foam is in agreement with the bubble size measured with X-ray micro-CT. This illustrates the feasibility of using ¹H R₂-dispersion measurements to determine the size of air bubbles in hydrogel foams and of alveoli in lung tissue.     

Primordial magnetic fields and dynamos from parity violated torsion

It is well known that torsion induced magnetic fields may seed galactic dynamos, but the price one pays for that is the conformal and gauge invariance breaks and a tiny photon mass. More recently I have shown [L.C. Garcia de Andrade, Phys. Lett. B 468 (2011) 28] that magnetic fields decay in a gauge invariant non-minimal coupling theory of torsion is slow down, which would allow for dynamo action to take place. In this Letter, by adding a parity violation term of the type _Rμνρσ?^μνρσ$R_{\mu \nu \rho \sigma }{?}^{\mu \nu \rho \sigma }$ to the non-coupling term, a magnetic dynamo equation is obtained. From dynamo equation it is shown that torsion terms only appear in the dynamo equation when diffusion in the cosmic plasma is present. Torsion breaks the homogeneity of the magnetic field in the universe. Since Zeldovich anti-dynamo theorem assumes that the spacetime should be totally flat, torsion is responsible for violation of anti-dynamo theorem in 2D spatial dimensions. Contrary to previous results torsion induced primordial magnetic fields cannot seed galactic dynamos since from torsion and diffusion coefficient the decaying time of the magnetic field is 10⁶yrs${10}^{6}yrs$, which is much shorter than the galaxy age.     

A high-sensitivity laser-pumped Mx magnetometer

We discuss the design and performance of a laser-pumped cesium vapor magnetometer in the M_x configuration. The device will be employed in the control and stabilization of fluctuating magnetic fields and gradients in a new experiment searching for a permanent electric dipole moment of the neutron. We have determined the intrinsic sensitivity of the device to be 15 fT in a 1 Hz bandwidth, limited by technical laser noise. In the shot noise limit the magnetometer can reach a sensitivity of 10 fT in a 1 Hz bandwidth. We have used the device to study the fluctuations of a stable magnetic field in a multi-layer magnetic shield for integration times in the range of 2–100 seconds. The residual fluctuations for times up to a few minutes are traced back to the instability of the power supply used to generate the field.     

Antiferromagnetic-resonance spectrum in charge-ordered R<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> manganites (R=La,Pr, Tb): The effect of orbital and charge structures

A theoretical study is made into the effect of the crystal, orbital, and charge structures on the magnetic structure and spin-wave spectra and on the antiferromagnetic resonance (AFMR) for R_0.5Ca_0.5MnO₃ crystals of monoclinic structure. The model assumes fixed crystal, charge, and orbital structures and enables one to determine the orbitally dependent exchange interaction and single-ion anisotropy for R = La, Pr, Tb. A 16-sublattice weakly noncollinear magnetic CE-structure without a ferromagnetic component is obtained. The behavior of magnetic structure in an external magnetic field is simulated, and the values of fields of spin-flop-transition for different Rs are obtained. The law of spin-wave dispersion and the field dependence of the antiferromagnetic-resonance spectrum are calculated.     

生物组织的δ-P1近似漫反射光学模型

本文研究了生物组织的改进的δ-P₁近似漫反射光学模型,推导了含有等效光源一阶矩的双点源近似空间分辨漫反射解R_δ－P1(ρ).研究表明,考虑等效光源一阶矩的光学模型,较好地描述了具有强的前向散射特性和较大吸收系数的生物组织散射特性;与漫射近似下的漫反射率R_SDA(ρ)相比,新的光学模型能较好地描述光源附近的漫辐射强度分布,并且由于解析表达式中含有散射相函数的二阶参量γ,这对 关键词： 组织光学 1近似')" href="#">δ-P₁近似 等效光源 微区漫反射     

Spin relaxation of Mn ions in (CdMn)Te/(CdMg)Te quantum wells under picosecond optical pumping

Spin relaxation of Mn ions in a Cd_0.97Mn_0.03Te/Cd_0.75Mg_0.25Te quantum well with photogenerated quasi-two-dimensional electron-hole plasma at liquid helium temperatures in an external magnetic field has been investigated. Heating of Mn ions by photogenerated carriers due to spin and energy exchange between the hot electron-hole plasma and Mn ions through direct sd-interaction between electron and Mn spins has been detected. This process has a short characteristic time of about 4 ns, which leads to appreciable heating of the Mn spin subsystem in about 0.5 ns. Even under uniform excitation of a dense electron-hole plasma, the Mn heating is spatially nonuniform, and leads to formation of spin domains in the quantum well magnetic subsystem. The relaxation time of spin domains after pulsed excitation is measured to be about 70 ns. Energy relaxation of excitons in the random exchange potential due to spin domains results from exciton diffusion in magnetic field B=14 T with a characteristic time of 1 to 4 ns. The relaxation time decreases with decreasing optical pump power, which indicates smaller dimensions of spin domains. In weak magnetic fields (_B=2 T) a slow down in the exciton diffusion to 15 ns has been detected. This slow down is due to exciton binding to neutral donors (formation of bound excitons) and smaller spin domain amplitudes in low magnetic fields. The optically determined spin-lattice relaxation time of Mn ions in a magnetic field of 14 T is 270±10 and 16±7 ns for Mn concentrations of 3% and 12%, respectively. Zh. éksp. Teor. Fiz. 112, 1440–1463 (October 1997)     

NMR Relaxation and Diffusion Measurements on Iron(III)-Doped Kaolin Clay

Kaolin clay samples were mixed with various amounts of Fe₂O₃ powder. The influence of this magnetic impurity on NMR relaxation and diffusion measurements on the water in this porous material was investigated. The NMR relaxation measurements showed a nearly mono-exponential decay, leading to the conclusion that the pore size distribution of the clay samples is either narrow and/or that the pores are interconnected very well. Both the longitudinal and the transverse relaxation rate depend linearly on the concentration of the Fe₂O₃ impurity. The NMR diffusion measurements revealed that the Fe₂O₃ causes internal magnetic field gradients that largely exceed the maximum external gradient that could be applied by our NMR apparatus (0.3 T/m). Additional SQUID measurements yielded the magnetization and magnetic susceptibility of the samples at the magnetic field strength used in the NMR measurements (0.8 T). A theoretical estimate of the internal magnetic field gradients leads to the conclusion that the water in the porous clay samples cannot be described by the commonly observed motional averaging regime. Probably an intermediate or a localization regime is induced by the large internal gradients, which are estimated to be on the order of 1 to 10 T/m in the pore volume and may exceed 1000 T/m at the pore surface.     

非晶态磁性合金的磁阻和磁击穿现象

在室温下磁场在0—15kOe范围内测量了非晶态磁性合金(Fe_1-xCo_x)₈₂Cu_0.4Si_4.4B_13.2的横向磁阻△ρ/ρ。发现在高磁场下,磁阻与磁场强度有三种函数关系:(1)磁阻趋于饱和;(2)磁阻随磁场平方正比地增加;(3)对x=0.15的合金,在特殊的电流、磁场方向和确定的磁场强度下,有磁阻尖峰出现。情况(3)是一种磁击穿现象。磁击穿发生在自旋向上和向下的两片Fer 关键词：