Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.     

多孔介质体元内随机运动的核磁共振成像研究

多孔介质体元内随机运动的核磁共振成像是一种透视流体微观无规则运动的方法.在多孔介质中,存在两种无规则运动.一种是分于扩散.它是由于分子的布朗运动引起的;另一种是弥散,它是由多孔介质中毛管网络的复杂结构造成的.多孔介质中的液体弥散和分子扩散会在成像体无内产生相位分散.这种相位分散致使回波信号发生衰减.采用适当的梯度脉冲.可以从这种信号衰减中获得视扩散系数(ADC)的分布图像.本文作者在4.7T高场超导核磁共振成像系统上.采用特制的高梯度线圈获得了扩散和机扩散系数分布的图像.在水和丙酮模型中获得了扩散系教图像,其扩散系数值与标准值相符.在人体肾结石中获得了扩散系数分布图像,在不同流速下,获得了多孔介质中的视扩散系数分布图像.并分析了视扩散系数与速度的关系.在多孔介质中定量确定扩散系数和机扩散系数及其空间分布将会极大地提高核磁共振成像技术在渗流力学研究中的应用能力.     

Manifestation and post hoc correction of gradient cross-term artifacts in DTI

Cross-terms between imaging and diffusion gradients, unaccounted for during tensor calculations, can lead to erroneous estimation of diffusivity and fractional anisotropy (FA) in regions of isotropic and anisotropic diffusion. Cross-term of magnitude 136.8±1.6 s/mm(2), artificially introduced in the slice-encode direction, caused an increase in FA in isotropic phantom from 0.0546±0.0001 to 0.0996±0.0001, while the change in chimpanzee brain depended on the orientation of the white matter (WM). Mean diffusivity (MD) remained unchanged in isotropic phantom, but increased by ～20% in the WM due to cross-terms. A bias was observed in the principal eigenvectors in both phantom and chimpanzee brain, resulting in significant increase in midline crossing fibers along the bias than perpendicular to it in tractography in chimpanzee brain. Post hoc correction of these artifacts was achieved by estimating the cross-term factors using calibration scans on an isotropic phantom and modifying the b-matrix before tensor calculation. Upon correction, the FA and MD values closely resembled the values obtained from sequence without cross-terms, and the bias in principal eigenvectors was eliminated. Customized sequences involving large b-values, high-resolution imaging, or long diffusion or echo times should therefore be evaluated and any residual cross-terms corrected before implementation.     

Magnetic field anisotropy based MR tractography

Non-invasive measurements of structural orientation provide unique information regarding the connectivity and functionality of fiber materials. In the present study, we use a capillary model to demonstrate that the direction of fiber structure can be obtained from susceptibility-induced magnetic field anisotropy. The interference pattern between internal and external magnetic field gradients carries the signature of the underlying anisotropic structure and can be measured by MRI-based water diffusion measurements. Through both numerical simulation and experiments, we found that this technique can determine the capillary orientation within 3°. Therefore, susceptibility-induced magnetic field anisotropy may be useful for an alternative tractography method when diffusion anisotropy is small at higher magnetic field strength without the need to rotate the subject inside the scanner.     

Diffusion anisotropy indexes are sensitive to selecting the EPI readout-encoding bandwidth at high-field MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) is generally performed using an echo planar imaging (EPI) acquisition to map directional water diffusion. However, the oscillating magnetic field gradients of the EPI acquisition can result in considerable mechanical vibrations, which lead, in turn, to magnetic field fluctuations causing Nyquist ghosting in the EPI data. The objective of this study was to investigate effects of EPI readout gradient modulation frequency, which is directly associated with the EPI readout bandwidth (BW), on the accuracy of DT-MRI measurements in a high magnetic field system. A spherical water phantom was used to study the relationship between the EPI BW and the Nyquist ghost for a spin-echo EPI acquisition with a matrix size of 128x128, complemented by diffusion sensitization gradients of up to b=800 s/mm(2) along six directions for DT-MRI. Nine volunteers (four males and five females) were studied using EPI at different BW acquisitions. Analysis of variance was used to investigate the EPI BW effects. The phantom studies demonstrated a systematic relationship between BWs and the intensities of Nyquist ghosts. In the human brain studies, EPI BW variations substantially corrupted diffusion anisotropy indexes (i.e., fractional anisotropy and relative anisotropy) (F=10.5, P=.0001) but were unrelated to diffusion-encoding directions (F=0.14, P=.98). It was possible to minimize BW dependence (F=1.48, P=.25) by tuning the modulation frequency of the EPI readout gradient. In conclusion, diffusion anisotropic indexes are sensitive to the readout BW of EPI due to associated Nyquist ghosting. However, the effect can be minimized by tuning the modulation frequency of the EPI readout gradient, that is, the EPI BW, to a range outside the harmonics of mechanical gradient vibrations.     

Optical and electronic properties of anisotropic parabolic quantum disks in the presence of tilted magnetic fields

In the present work, the electronic and optical properties of anisotropic parabolic quantum disks are studied in the presence of an applied magnetic field. For this goal, we first obtain the electron energy levels of an anisotropic parabolic quantum disk under axial, tilted, and in-plane magnetic fields. According to the results obtained for the energy levels reveal that there is no degeneracy at zero magnetic field due to symmetry breaking. With increasing the anisotropy, the energy level spacing increases. At a constant anisotropy, the energy levels splitting decreases with increasing tilt angle of magnetic field. The total refractive index changes decrease when the tilt angle of magnetic field and the anisotropy increase. Also, the total absorption coefficients increase as the tilt angle of magnetic field and anisotropy increase.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

Effects of random subject rotation on optimised diffusion gradient sampling schemes in diffusion tensor MRI

The choice of the number (N) and orientation of diffusion sampling gradients required to measure accurately the water diffusion tensor remains contentious. Monte Carlo studies have suggested that between 20 and 30 uniformly distributed sampling orientations are required to provide robust estimates of water diffusions parameters. These simulations have not, however, taken into account what effect random subject motion, specifically rotation, might have on optimised gradient schemes, a problem which is especially relevant to clinical diffusion tensor MRI (DT-MRI). Here this question is investigated using Monte Carlo simulations of icosahedral sampling schemes and in vivo data. These polyhedra-based schemes, which have the advantage that large N can be created from optimised subsets of smaller N, appear to be ideal for the study of restless subjects since if scanning needs to be prematurely terminated it should be possible to identify a subset of images that have been acquired with a near optimised sampling scheme. The simulations and in vivo data show that as N increases, the rotational variance of fractional anisotropy (FA) estimates becomes progressively less dependent on the magnitude of subject rotation (), while higher FA values are progressively underestimated as increases. These data indicate that for large subject rotations the B-matrix should be recalculated to provide accurate diffusion anisotropy information.     

Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

Effective Gradients in Porous Media Due to Susceptibility Differences

In porous media, magnetic susceptibility differences between the solid phase and the fluid filling the pore space lead to field inhomogeneities inside the pore space. In many cases, diffusion of the spins in the fluid phase through these internal inhomogeneities controls the transverse decay rate of the NMR signal. In disordered porous media such as sedimentary rocks, a detailed evaluation of this process is in practice not possible because the field inhomogeneities depend not only on the susceptibility difference but also on the details of the pore geometry. In this report, the major features of diffusion in internal gradients are analyzed with the concept of effective gradients. Effective gradients are related to the field inhomogeneities over the dephasing length, the typical length over which the spins diffuse before they dephase. For the CPMG sequence, the dependence of relaxation rate on echo spacing can be described to first order by a distribution of effective gradients. It is argued that for a given susceptibility difference, there is a maximum value for these effective gradients,g_max, that depends on only the diffusion coefficient, the Larmor frequency, and the susceptibility difference. This analysis is applied to the case of water-saturated sedimentary rocks. From a set of NMR measurements and a compilation of a large number of susceptibility measurements, we conclude that the effective gradients in carbonates are typically smaller than gradients of current NMR well logging tools, whereas in many sandstones, internal gradients can be comparable to or larger than tool gradients.     

Evaluation of diffusional anisotropy and microscopic structure in skeletal muscles using magnetic resonance

The pulsed-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) method is used for detecting the diffusion of water molecules in biological tissues. Because tissues generally have diffusional anisotropy, their diffusion properties are denoted by a tensor. In this study, we evaluated the diffusional anisotropy and microscopic structure in atrophied skeletal muscles using the PGSE NMR method. The left sciatic nerve was severed in twelve 9-week-old rats. Neurotomy caused neurogenic muscular atrophy at the left gastrocnemius. At 2, 4 and 8 weeks after neurotomy, magnetic resonance signals were selectively acquired from a 2 x 2 x 2 mm(3) voxel, which was located on the left gastrocnemius. The diffusion tensor, the mean diffusivity (MD) and the fractional anisotropy (FA) were calculated from the signals. A theoretical model of the diffusion in muscles was derived from Tanner's equation. The muscle fiber diameter was estimated by fitting the model to the measured signals. The measurements were also performed for normal rats as controls. No significant difference was found in the MD and the estimated intracellular diffusion coefficient between the control group and the denervated group. The denervated group had significantly higher FA compared with the control group (P<.05). The estimated muscle fiber diameter of the denervated group was significantly smaller than the estimated value of the control group (P<.05). These differences were found at 8 weeks after neurotomy. The proposed method is effective for evaluating changes in the microscopic structure of skeletal muscles.     

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.     

An in vivo evaluation of the effects of local magnetic susceptibility-induced gradients on water diffusion measurements in human brain.

The effect of possible susceptibility-induced gradients on measurements of water diffusion along the transverse and longitudinal axes of white matter fibers in the brain was investigated in vivo at 1.5 T. Measurements obtained with sequences sensitive and insensitive, respectively, to susceptibility-induced gradients indicated that these gradients do not contribute significantly to diffusion anisotropy in brain white matter. Furthermore, diffusion measurements were unaffected by the presence of known susceptibility-induced gradients at the interface between the petrous bone and brain parenchyma. These results agree with those obtained on in vitro samples and appear to support the hypothesis that interactions between the diffusing water molecules and the cellular environment constitute the principal mechanism for diffusion anisotropy in brain white matter at 1.5 T. This, in turn, simplifies the interpretation of diffusion time-dependent measurements in terms of membrane separation and permeability.     

Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.     

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by ¹H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Dependence of the fractional anisotropy in cervical spine from the number of diffusion gradients,repeated acquisition and voxel size

The aim of this study is to investigate the consequences of using different gradient schemes, number of repeated measurements and voxel size on the fractional anisotropy (FA) value in a diffusion tensor imaging (DTI) sequence on the cervical tract of the spinal cord. Twenty healthy volunteers underwent a total of 86 DTI axial acquisitions performed by using different voxel size and number of diffusion gradient directions (NDGDs). Three different diffusion gradient schemes were applied, named 6, 15 and 32 according to the NDGD. Furthermore, some acquisitions were repeated to investigate the effects of image averaging on FA value.