Solving the problem of concomitant gradients in ultra-low-field MRI

In ultra-low-field magnetic resonance imaging (ULF MRI), spin precession is detected typically in magnetic fields of the order of 10-100 μT. As in conventional high-field MRI, the spatial origin of the signals can be encoded by superposing gradient fields on a homogeneous main field. However, because the main field is weak, gradient field amplitudes become comparable to it. In this case, the concomitant gradients forced by Maxwell's equations cause the assumption of linearly varying field gradients to fail. Thus, image reconstruction with Fourier transformation would produce severe image artifacts. We propose a direct linear inversion (DLI) method to reconstruct images without limiting assumptions about the gradient fields. We compare the quality of the images obtained using the proposed reconstruction method and the Fourier reconstruction. With simulations, we show how the reconstruction errors of the methods depend on the strengths of the concomitant gradients. The proposed approach produces nearly distortion-free images even when the main field reaches zero.     

On low-field electron emission mechanisms

It is established by direct experiments that the main component of the stationary field-emission current in fields E<10⁵ V/cm is due to piezogeometric intensification (by a factor of 10³) of the electricfield at the end faces of piezoelectrically active films. An emission mechanism governed by electrons supplied by tunneling from the valence band of the piezoelectric is proposed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 823–827 (10 June 1997)     

Optimization of spoiler gradients in flash MRI

The FLASH technique for fast magnetic resonance (MR) imaging often employs strong magnetic field gradients, called spoiler gradients, to dephase the transverse magnetization after it has been measured. Otherwise, image artifacts can develop. The effectiveness of spoiler gradients at suppressing these artifacts was evaluated experimentally on two-dimensional MR images of a uniform phantom and patients. It was informative to compare the magnetization immediately before the RF excitation in each phase encoding step. Only spoiler gradients in the slice selection direction were effective. Spoiler gradients that decreased steadily from a large amplitude in the first phase encoding step to zero in the last minimized the transverse magnetization and suppressed the image artifact, without changing the image contrast.     

Correction of concomitant gradient artifacts in experimental microtesla MRI

Magnetic resonance imaging (MRI) suffers from artifacts caused by concomitant gradients when the product of the magnetic field gradient and the dimension of the sample becomes comparable to the static magnetic field. To investigate and correct for these artifacts at very low magnetic fields, we have acquired MR images of a 165-mm phantom in a 66-microT field using gradients up to 350 microT/m. We prepolarize the protons in a field of about 100 mT, apply a spin-echo pulse sequence, and detect the precessing spins using a superconducting gradiometer coupled to a superconducting quantum interference device (SQUID). Distortion and blurring are readily apparent at the edges of the images; by comparing the experimental images to computer simulations, we show that concomitant gradients cause these artifacts. We develop a non-perturbative, post-acquisition phase correction algorithm that eliminates the effects of concomitant gradients in both the simulated and the experimental images. This algorithm assumes that the switching time of the phase-encoding gradient is long compared to the spin precession period. In a second technique, we demonstrate that raising the precession field during phase encoding can also eliminate blurring caused by concomitant phase-encoding gradients; this technique enables one to correct concomitant gradient artifacts even when the detector has a restricted bandwidth that sets an upper limit on the precession frequency. In particular, the combination of phase correction and precession field cycling should allow one to add MRI capabilities to existing 300-channel SQUID systems used to detect neuronal currents in the brain because frequency encoding could be performed within the 1-2 kHz bandwidth of the readout system.     

MRI of the lung gas-space at very low-field using hyperpolarized noble gases

In hyperpolarized (HP) noble-gas magnetic resonance imaging, large nuclear spin polarizations, about 100,000 times that ordinarily obtainable at thermal equilibrium, are created in 3He and 129Xe. The enhanced signal that results can be employed in high-resolution MRI studies of void spaces such as in the lungs. In HP gas MRI the signal-to-noise ratio (SNR) depends only weakly on the static magnetic field (B(0)), making very low-field (VLF) MRI possible; indeed, it is possible to contemplate portable MRI using light-weight solenoids or permanent magnets. This article reports the first in vivo VLF MR images of the lungs in humans and in rats, obtained at a field of only 15 millitesla (150 Gauss).     

Simulating magnetic nanoparticle behavior in low-field MRI under transverse rotating fields and imposed fluid flow

In the presence of alternating-sinusoidal or rotating magnetic fields, magnetic nanoparticles will act to realign their magnetic moment with the applied magnetic field. The realignment is characterized by the nanoparticle's time constant, τ. As the magnetic field frequency is increased, the nanoparticle's magnetic moment lags the applied magnetic field at a constant angle for a given frequency, Ω, in rad s⁻¹. Associated with this misalignment is a power dissipation that increases the bulk magnetic fluid's temperature which has been utilized as a method of magnetic nanoparticle hyperthermia, particularly suited for cancer in low-perfusion tissue (e.g., breast) where temperature increases of between 4 and 7 °C above the ambient in vivo temperature cause tumor hyperthermia. This work examines the rise in the magnetic fluid's temperature in the MRI environment which is characterized by a large DC field, B₀. Theoretical analysis and simulation is used to predict the effect of both alternating-sinusoidal and rotating magnetic fields transverse to B₀. Results are presented for the expected temperature increase in small tumors ( radius) over an appropriate range of magnetic fluid concentrations (0.002-0.01 solid volume fraction) and nanoparticle radii (1-10 nm). The results indicate that significant heating can take place, even in low-field MRI systems where magnetic fluid saturation is not significant, with careful the goal of this work is to examine, by means of analysis and simulation, the concept of interactive fluid magnetization using the dynamic behavior of superparamagnetic iron oxide nanoparticle suspensions in the MRI environment. In addition to the usual magnetic fields associated with MRI, a rotating magnetic field is applied transverse to the main B₀ field of the MRI. Additional or modified magnetic fields have been previously proposed for hyperthermia and targeted drug delivery within MRI. Analytical predictions and numerical simulations of the transverse rotating magnetic field in the presence of B₀ are investigated to demonstrate the effect of Ω, the rotating field frequency, and the magnetic field amplitude on the fluid suspension magnetization. The transverse magnetization due to the rotating transverse field shows strong dependence on the characteristic time constant of the fluid suspension, τ. The analysis shows that as the rotating field frequency increases so that Ωτ approaches unity, the transverse fluid magnetization vector is significantly non-aligned with the applied rotating field and the magnetization's magnitude is a strong function of the field frequency. In this frequency range, the fluid's transverse magnetization is controlled by the applied field which is determined by the operator. The phenomenon, which is due to the physical rotation of the magnetic nanoparticles in the suspension, is demonstrated analytically when the nanoparticles are present in high concentrations (1-3% solid volume fractions) more typical of hyperthermia rather than in clinical imaging applications, and in low MRI field strengths (such as open MRI systems), where the magnetic nanoparticles are not magnetically saturated. The effect of imposed Poiseuille flow in a planar channel geometry and changing nanoparticle concentration is examined. The work represents the first known attempt to analyze the dynamic behavior of magnetic nanoparticles in the MRI environment including the effects of the magnetic nanoparticle spin-velocity. It is shown that the magnitude of the transverse magnetization is a strong function of the rotating transverse field frequency. Interactive fluid magnetization effects are predicted due to non-uniform fluid magnetization in planar Poiseuille flow with high nanoparticle concentrations.     

Intermolecular double-quantum coherence imaging without coherence selection gradients and its application in in vivo MRI

In the COSY Revamped with Asymmetric Z-gradient Echo Detection (CRAZED) experiments, magnetization is modulated by the distant dipolar field (DDF) generated by coherence selection gradient (CSG) commonly in sinusoidal wave-form and results in detectable intermolecular multiple-quantum coherence (iMQC) signal. IMQCs have some attractive features, but their intrinsic weak signal intensity prevents their widespread applications. In this paper, a new phase cycling scheme was applied to obtain intermolecular double-quantum coherence (iDQC) signal. It is found that DDF can arise from nonspherical sample geometry or background inhomogeneous field in the absence of CSGs, which is more efficient than that created from CSGs. The experimental results show that the resulting DDF can refocus the ± iDQC signals simultaneously and thus enhance the signal intensity to about two folds of that from the conventional CRAZED sequence. Theoretical prediction and experiments give coincident results.     

基于高温超导SQUID的低场核磁共振研究

采用一高温超导射频量子干涉器(HTS rf-SQUID)作为信号探测器件,研究了多种液体样品的低场核磁共振信号。通过改变测量场(简称Bm)的大小,可以探测到质子拉莫频率(简称fL)从2Hz到40kHz的信号。由于在低场核磁共振中,Bm的均匀性能很好的得到满足,因而可能得到很窄的谱线宽度。实验发现,对自来水样品,在7μT以下均可接近谱线的自然宽度。同时,在低场核磁共振条件下,样品的化学位移很小以至于消失,因而可以研究"纯"的异核间的自旋耦合谱。作者研究了低场下2,2,2-三氟乙醇的低场自旋耦合谱。另外,作者首次采用SQUID在户外探测到地球磁场下的核磁共振现象,并研究了地球磁场的涨落对测量的影响,为SQUID的低场核磁共振研究开辟了一个新的研究方向。     

Anomalous low-field classical magnetoresistance in two dimensions

The magnetoresistance of classical two-dimensional electrons scattered by randomly distributed impurities is investigated by numerical simulation. At low magnetic fields, we find for the first time a negative magnetoresistance proportional to |B|. This unexpected behavior is shown to be due to a memory effect specific for backscattering events, which was not considered previously.     

The design of a body RF coil for low-field open MRI using pseudo electric dipole radiation and simulated annealing

The paper presents a new body RF coil design scheme for a low-field open MRI system. The RF coil is composed of four rectangular loops which are made of wide copper strips located near the surfaces of the bottom and top pole faces of the permanent magnet. The body RF coil has been designed by using the pseudo electric dipole radiation (PEDPR) method with the Metropolis algorithm. In the calculation of the RF fields via the finite difference time domain (FDTD) method, the computational time increases as the RF frequency becomes lower. Moreover, the computational process using the FDTD method takes a very long time when the RF coil is optimized. The optimization requires varying the configuration of the RF coil system and performing successive calculations of field strength and field homogeneity. When we perform these successive calculations, the computational time can be reduced by using the PEDPR method, where the segmented current elements of the RF coil are treated as pseudo electric dipole radiation sources. Because the RF coil is made of wide strips, the variation of the current density on the strip has been considered in the B₁-field calculation. For each configuration of the RF coil system, the current distribution is calculated via circuit analysis, where each copper strip is considered as a parallel combination of current element lines. The preliminary field calculation study by the FDTD method verifies both the circuit analysis method for the current distribution and the PEDPR method for the radiation field strength. The optimization of the RF coil configuration is performed by the Simulated Annealing (SA) process using the Metropolis algorithm. Simulations have been performed for a 10 MHz RF frequency. The optimized RF coil has four rectangular loops of 37 cm × 100 cm with 6.5 cm wide strips which are separated vertically 49 cm and horizontally center-to-center 63 cm. In the 25 cm diameter of spherical volume (DSV), the design results show a good field inhomogeneity of the B₁-field below 0.49 dB (5.8%).     

On MRI turbulence quantification

Turbulent flow, characterized by velocity fluctuations, accompanies many forms of cardiovascular disease and may contribute to their progression and hemodynamic consequences. Several studies have investigated the effects of turbulence on the magnetic resonance imaging (MRI) signal. Quantitative MRI turbulence measurements have recently been shown to have great potential for application both in human cardiovascular flow and in engineering flow. In this article, potential pitfalls and sources of error in MRI turbulence measurements are theoretically and numerically investigated. Data acquisition strategies suitable for turbulence quantification are outlined. The results show that the sensitivity of MRI turbulence measurements to intravoxel mean velocity variations is negligible, but that noise may degrade the estimates if the turbulence encoding parameter is set improperly. Different approaches for utilizing a given amount of scan time were shown to influence the dynamic range and the uncertainty in the turbulence estimates due to noise. The findings reported in this work may be valuable for both in vitro and in vivo studies employing MRI methods for turbulence quantification.     

Frequency shifts in parametrically enhanced low-field MR detection

A high-amplitude, high-frequency readout field has previously been proposed for use with low-field MR. Because the resulting modulation sidebands are at higher frequencies than the low-field steady precession, improved detection sensitivity results. However, if the ac readout field is inhomogeneous, it will necessarily have transverse components resulting in frequency shifts and broadening of the MR signal. Numerical solutions of Bloch's equations are compared to the Bloch-Siegert result to assess the size of the frequency shifts. A formula is derived by the average Hamiltonian method and provides an excellent fit to the numerically obtained shifts.     

Third-derivative modulation spectroscopy with low-field electroreflectance

The theoretical basis and experimental procedures are reviewed for third-derivative modulation spectroscopy, which is the same as low-field electroreflectance. The physical origin of the third-derivative behavior is discussed in terms of the effect of a uniform electric field on the translational symmetry of the unperturbed crystal. The relationship between the low-field and the Franz-Keldysh electroreflectance theories is discussed. In the lowfield range, both intraband and interband electric-field effects can be treated by first-order perturbation techniques, leading to great simplifications in the more general theory. By formulating the expression for the experimentally measured relative reflectivity change, $\text{ΔR}\text{R}$, in complex-variable form, effects due to experimental field inhomogeneities, the electron-hole interaction, and the optical constants of the material can be described by complex coefficients multiplying a theoretically calculated complex lineshape, thereby simplifying the analysis of experimental spectra. We also review the commonly used experimental configurations, and discuss procedures for determining experimentally the low-field range in a given experimental situation. The linearized third-derivative (LTD) technique, which makes use of specific properties of fully depleted space-charge regions, is discussed in detail. Finally, the application of third-derivative spectroscopy in the measurement of weak spectroscopic features and the determination of band structure parameters is demonstrated with specific examples.     

Theory of MRI in the presence of zero to low magnetic fields and tensor imaging field gradients

Today, all commonly practiced magnetic resonance imaging (MRI) reconstruction methods assume that the magnetic field created by the gradient coils is everywhere truncated by a dominant static uniform magnetic field. However, with the advent of SQUID detected MRI at microtesla fields, the opposite limit attracts attention, i.e., image formation in the unperturbed tensor field of the gradient coils. Here, we show by numerical simulations that, in principle, it is possible to reconstruct the image of an object in the absence of a uniform static field, working with the same gradient field setup as used in conventional MRI. Our calculations show that this approach could increase the image resolution limit attainable at low fields with a minimal incorporation of additional hardware and pulse sequences.     

High-field vs. low-field magneto-transport in a percolating medium

Recent theoretical and numerical work on high-field magneto-transport in a percolating medium is described and compared to earlier work on weak-field magneto-transport in such systems. While the weak-field behavior is well described by the simple nodes-links picture, which ignores blobs and loops on a scale smaller than the percolation correlation length ξ_p, the strong-field behavior is extremely sensitive to those features. The critical behavior at strong magnetic fields H near the percolation threshold is governed by competition between the usual H=0 fixed point and a new H=∞ fixed point. Which of those fixed points dominates the behavior is determined by the relative sizes of two characteristic lenghts: the percolation correlation length ξ_p and a new, magnetic field dependent length ξ_H.     

Ferromagnetism of 3He films in the low-field limit

We provide evidence for a finite-temperature ferromagnetic transition in two dimensions as H -->0 in thin films of 3He on graphite, a model system for the study of two-dimensional magnetism. We perform pulsed and cw NMR experiments at fields of 0.03-0.48 mT on 3He at areal densities of 20.5-24.2 atoms/nm(2). At these densities, the second layer of 3He has a strongly ferromagnetic tendency. With decreasing temperature, we find a rapid onset of magnetization that becomes independent of the applied field at temperatures in the vicinity of 1 mK. Both the dipolar field and the NMR linewidth grow rapidly as well, which is consistent with a large (order unity) polarization of the 3He spins.     

Enhanced low-field magnetoresistance in LSMO/SFO composite system

The granular composites of (1−x)La_0.7Sr_0.3MnO₃/xSrFe₁₂O₁₉ [(1−x)LSMO/xSFO] were prepared. The magnetic, electrical, and magnetoresistive properties of the composites were investigated systematically. Two magnetic transitions originating from LSMO and SFO are observed for x=0.05, 0.10, and 0.20. The addition of hard-magnetic SFO ferrite leads to the increased substantially resistivity of the composites and the shift of insulating-metallic transition temperature T_IM correlated with LSMO. Enhanced low-field magnetoresistance (LFMR) in the composites can be mainly attributed to the enhanced spin disorder and spin-dependent tunneling at LSMO grain boundaries induced by the interaction between LSMO and SFO ferrite. The transport mechanisms in detail are analyzed in LSMO/SFO composite system.     

On NUFFT-based gridding for non-Cartesian MRI

For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [L. Sha, H. Guo, A.W. Song, An improved gridding method for spiral MRI using nonuniform fast Fourier transform, J. Magn. Reson. 162(2) (2003) 250-258] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.