White matter changes in multiple sclerosis: correlation of q-space diffusion MRI and 1H MRS

OBJECTIVE: To explore the diagnostic usefulness of high b-value diffusion magnetic resonance brain imaging ("q-space" imaging) in multiple sclerosis (MS). More specifically, we aimed at evaluating the ability of this methodology to identify tissue damage in the so-called normal-appearing white matter (NAWM). DESIGN: In this study we examined the correlation between q-space diffusion imaging and magnetic resonance spectroscopy (MRS)-based two-dimensional 1H chemical shift imaging. Eight MS patients with different degree of disease severity and seven healthy subjects were scanned in a 1.5-T magnetic resonance imaging (MRI) scanner. The MRI protocol included diffusion tensor imaging (DTI) (with bmax of 1000 s/mm2), high b-value diffusion-weighted imaging (with bmax of 14,000 s/mm2) and 2D chemical shift imaging. The high b-value data set was analyzed using the q-space methodology to produce apparent displacement and probability maps. RESULTS: We found that the q-space diffusion displacement and probability image intensities correlated well with N-acetylaspartate levels (r=.61 and .54, respectively). Furthermore, NAWM that was abnormal on MRS was also found to be abnormal using q-space diffusion imaging. In these areas, the q-space displacement values increased from 3.8+/-0.2 to 4.6+/-0.6 microm (P<.02), the q-space probability values decreased from 7.4+/-0.3 to 6.8+/-0.3 (P<.002), while DTI revealed only a small, but still significant, reduction in fractional anisotropy values from 0.40+/-0.02 to 0.37+/-0.02 (P<.05). CONCLUSION: High b-value diffusion imaging can detect tissue damage in the NAWM of MS patients. Despite the theoretical limitation of this method, in practice it provides additional information which is clinically relevant for detection of tissue damage not seen in conventional imaging techniques.     

Definition of displacement probability and diffusion time in q-space magnetic resonance measurements that use finite-duration diffusion-encoding gradients

In q-space diffusion NMR, the probability P(r,td) of a molecule having a displacement r in a diffusion time td is obtained under the assumption that the diffusion-encoding gradient g has an infinitesimal duration. However, this assumption may not always hold, particularly in human MRI where the diffusion-encoding gradient duration delta is typically of the same order of magnitude as the time offset Delta between encoding gradients. In this case, finite-delta effects complicate the interpretation of displacement probabilities measured in q-space MRI, and the form by which the signal intensity relates to them. By considering the displacement-specific dephasing, , of a set of spins accumulating a constant displacement vector r in the total time Delta+delta during which diffusion is encoded, the probability recovered by a finite-delta q-space experiment can be interpreted. It is shown theoretically that a data analysis using a modified q-space index q=gammadeltaetag, with gamma the gyromagnetic ratio and eta=square root (Delta-delta/3)/(Delta+delta), recovers the correct displacement probability distribution if diffusion is multi-Gaussian free diffusion. With this analysis, we show that the displacement distribution P(r,texp) is measured at the experimental diffusion-encoding time texp=Delta+delta, and not at the reduced diffusion time tr=Delta-delta/3 as is generally assumed in the NMR and MRI literature. It is also shown that, by defining a probability P(y,Delta) that a time tdeltac then eta is not equal to square root (Delta-delta/3)/(Delta+delta) which implies that we can no longer obtain the correct displacement probability from the displacement distribution. In the case that /g/=18 mT/m and Delta-delta=5 ms, the parameter deltac in ms is given by "deltac=0.49a2+0.24" where a is the sphere's radius expressed in microm. Simulation of q-space restricted diffusion MRI experiments indicate that if eta=square root (Delta-delta/3)/(Delta+delta), the recovered displacement probability is always better than the Gaussian approximation, and the measured diffusion coefficient matches the diffusion coefficient at time texp=Delta+delta better than it matches the diffusion coefficient at time tr=Delta-delta/3. These results indicate that q-space MRI measurements of displacement probability distributions are theoretically possible in biological tissues using finite-duration diffusion-encoding gradients provided certain compartment size and diffusion encoding gradient duration constraints are met.     

In vivo visualization of displacement-distribution-derived parameters in q-space imaging

OBJECTIVE: This study aimed to explore the potential of in vivo q-space imaging in the differentiation between different cerebral water components. MATERIALS AND METHODS: Diffusion-weighted imaging was performed in six directions with 32 equally spaced q values and a maximum b value of 6600 s/mm(2). The shape of the signal-attenuation curve and the displacement propagator were examined and compared with a normal distribution using the kurtosis parameter. Maps displaying kurtosis, fast and slow components of the apparent diffusion coefficients, fractional anisotropy and directional diffusion were calculated. The displacement propagator was further described by the full width at half and at tenth maximum and by the probability density of zero displacement P(0). Three healthy volunteers and three patients with previously diagnosed multiple sclerosis (MS) were examined. RESULTS: Simulations indicated that the kurtosis of a signal-attenuation curve can determine if more than one water component is present and that care must be taken to select an appropriate threshold. It was possible to distinguish MS plaques in both signal and diffusional kurtosis maps, and in one patient, plaques of different degree of demyelinization showed different behavior. DISCUSSION: Our results indicate that in vivo q-space analysis is a potential tool for the assessment of different cerebral water components, and it might extend the diagnostic interpretation of data from diffusion magnetic resonance imaging.     

Probing restrictive diffusion dynamics at short time scales

Diffusion imaging gradients serve to spectrally filter the temporally evolving diffusion tensor. In this framework, the design of diffusion sensitizing gradients is reduced to the problem of adequately sampling q-space in the spectral domain. The practical limitations imposed by the requirement for delta-function type diffusion-sensitizing gradients to adequately sample q-space, can be relaxed if these impulse gradients are replaced with chirped oscillatory gradients. It is well known that in many systems of interest, dispersion of velocity will itself produce a peak in the velocity correlation function near w=0, while restricted diffusion will manifest itself in the dispersion spectrum at higher frequencies. In this paper, chirped diffusion-sensitizing gradients are proposed and analytically shown to yield an efficient sampling of q-space in a manner that asymptotically approaches that using delta-function diffusion-sensitizing gradient. The challenge is the consequent reduction in diffusion sensitivity as one probes higher frequency dynamics. This problem is addressed by restricting the gradient power to a spectral bandwidth corresponding to the diffusion spectral range of the underlying restrictive geometry. Simultaneous imaging of diffusion and flow at microscopic resolution and at temporally resolvable diffusion time scales thus becomes possible in vivo. Simulations and experiments validate the proposed approach.     

Measurement of pulsatile flow using MRI and a Bayesian technique of probability analysis

This work shows that complete spatial information of periodic pulsatile fluid flows can be rapidly obtained by Bayesian probability analysis of flow encoded magnetic resonance imaging data. These data were acquired as a set of two-dimensional images (complete two-dimensional sampling of k-space or reciprocal position space) but with a sparse (six point) and nonuniform sampling of q-space or reciprocal displacement space. This approach enables more precise calculation of fluid velocity to be achieved than by conventional two q-sample phase encoding of velocities, without the significant time disadvantage associated with the complete flow measurement required for Fourier velocity imaging. For experimental comparison with the Bayesian analysis applied to nonuniformly sampled q-space data, a Fourier velocity imaging technique was used with one-dimensional spatial encoding within a selected slice and a uniform sampling of q-space using 64 values of the pulsed gradients to encode fluid flow. Because the pulsatile flows were axially symmetric within the resolution of the experiment, the radial variation of fluid velocity, in the direction of the pulsed gradients, was reconstructed from one-dimensional spatial projections of the velocity by exploiting the central slice theorem. Data were analysed for internal consistency using linearised flow theories. The results show that nonuniform q-space sampling followed by Bayesian probability analysis is at least as accurate as the combined uniform q-space sampling with Fourier velocity imaging and projection reconstruction method. Both techniques give smaller errors than a two-point sampling of q-space (the conventional flow encoding experiment).     

q-Space high b value diffusion MRI of hemi-crush in rat spinal cord: evidence for spontaneous regeneration

The development of the damage following hemi-crush trauma in rat spinal cord was studied ex vivo using high b value (bmax = 1 x 10(7) s cm(-2)) q-space diffusion weighted MRI (DWI) at five days, ten days and six weeks post-trauma. Rat spinal cord trauma, produced by hemi-crush of 15s and 60s duration, was studied. The water signal decay in these diffusion experiments was found to be non mono-exponential and was analyzed using the q-space approach. The q-space MRI parameters were compared with T1 and T2 MR images, behavioral tests and histopathological osmium staining. A very good anatomical correlation was found between the q-space MRI parameters and the osmium staining. Interestingly, we found that in the 15s hemi-crush model significant recovery was observed in both the q-space MR images and the osmium staining six weeks post-trauma. However, in the 60s hemi-crush trauma model very little recovery was observed. These results paralleled those obtained from behavioral tests demonstrating that partial spontaneous recovery seems to occur in the 15s hemi-crush spinal cord model, which should be taken in consideration when using it to evaluate new therapies.     

Quantitative measurement and imaging of transport processes in plants and porous media by 1H NMR.

NMR and MRI have been applied to transport processes, that is, net flow and diffusion/perfusion, of water in whole plants, cells, and porous materials. By choosing proper time windows and pulse sequences, magnetic resonance imaging can be made selective for each of the two transport processes. For porous media and plant cells the evolution of the spatial distribution of excited spins has been determined by q-space imaging, using a 20 MHz pulsed 1H NMR imager. The results of these experiments are explained by including spin-relaxation and exchange at boundaries. A 10 MHz portable 1H NMR spectrometer is described, particularly suitable to study the response of net flow in plants and canopies to changing external conditions.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

High b-value q-space diffusion MRI in myelin-deficient rat spinal cords

In this study, we explore the effect of the lack of myelin on the diffusion characteristics and diffusion anisotropy obtained from high b-value q-space diffusion-weighted MRI (q-space DWI) in excised rat spinal cords. Twenty-one-day-old myelin-deficient (md) mutant (N=6) and control rats (N=6) were used in this study. The MRI protocol included multi-slice T(1), T(2), proton density (PD) MR images and high b-value q-space diffusion MRI measured perpendicular and parallel to the fibers of the spine. q-Space displacement and probability maps, in both directions, as well as displacement anisotropy maps, were computed from the diffusion data. At the end of the MRI protocol, representative spinal cords from both groups were subjected to electron microscopy (EM). The md spinal cords show different gray/white matter contrast in the T(1), T(2) and PD MR images as compared with controls. In addition, the mean displacement extracted from the high b-value q-space diffusion data was found to be dramatically higher in the white matter (WM) of the md spinal cords than the controls when diffusion was measured perpendicular and parallel to the fibers of the spine. However, interestingly, at the diffusion time used in the present study, the difference in the WM displacement anisotropies of the two groups was not found to be statistically significant. Myelin was found to have a pronounced effect on the diffusion characteristics of water in WM but less so on the diffusion anisotropy observed at the diffusion time used in the present study.     

The effect of rotational angle and experimental parameters on the diffraction patterns and micro-structural information obtained from q-space diffusion NMR: implication for diffusion in white matter fibers

Diffusion NMR may provide, under certain experimental conditions, micro-structural information about confined compartments totally non-invasively. The influence of the rotational angle, the pulse gradient length and the diffusion time on the diffusion diffraction patterns and q-space displacement distribution profiles was evaluated for ensembles of long cylinders having a diameter of 9 and 20 microm. It was found that the diffraction patterns are sensitive to the rotational angle (alpha) and are observed only when diffusion is measured nearly perpendicular to the long axis of the cylinders i.e., when alpha= 90 degrees +/- 5 degrees under our experimental conditions. More importantly, we also found that the structural information extracted from the displacement distribution profiles and from the diffraction patterns are very similar and in good agreement with the experimental values for cylinders of 20 microm or even 9 microm, when data is acquired with parameters that satisfy the short gradient pulse (SGP) approximation (i.e., delta -->0) and the long diffusion time limit. Since these experimental conditions are hardly met in in vitro diffusion MRI of excised organs, and cannot be met in clinical MRI scanners, we evaluated the effect of the pulse gradient duration and the diffusion time on the structural information extracted from q-space diffusion MR experiments. Indeed it was found that, as expected, accurate structural information, and diffraction patterns are observed when Delta is large enough so that the spins reach the cylinders' boundaries. In addition, it was found that large delta results in extraction of a compartment size, which is smaller than the real one. The relevance of these results to q-space MRI of neuronal tissues and fiber tracking is discussed.     

Mapping the intracellular fraction of water by varying the gradient pulse length in q-space diffusion MRI

Finite gradient pulse lengths are traditionally considered a nuisance in q-space diffusion NMR and MRI, since the simple Fourier relation between the acquired signal and the displacement probability is invalidated. Increasing the value of the pulse length leads to an apparently smaller value of the estimated compartment size. We propose that q-space data at different gradient pulse lengths, but with the same effective diffusion time, can be used to identify and quantify components with free or restricted diffusion from multiexponential echo decay curves obtained on cellular systems. The method is demonstrated with experiments on excised human brain white matter and a series of model systems with well-defined free, restricted, and combined free and restricted diffusion behavior. Time-resolved diffusion MRI experiments are used to map the spatial distribution of the intracellular fraction in a yeast cell suspension during sedimentation, and observe the disappearance of this fraction after a heat treatment.     

Construction and calibration of a 50 T/m z-gradient coil for quantitative diffusion microimaging

q-Space imaging is capable of providing quantitative geometrical information of structures at cellular resolution. However, the size of restrictions that can be probed hinges on available gradient amplitude and places very high demands on gradient performance. In this work we describe the design and construction of a small, high-amplitude (50 T/m) z-gradient coil, interfaced with a commercial 9.4 T microimaging system. We also describe a method to calibrate the coil for quantitative measurements of molecular diffusion at very high-gradient amplitudes. Calibration showed linear current response up to 50 T/m, with a gain=1.255 T/m/A. The z-gradient coil was combined with the commercial x- and y-gradients for tri-axial imaging, and its performance was demonstrated by ADC maps of free water and by q-space experiments on water sequestered around polystyrene microspheres (4.5 microm diameter), which showed the expected diffraction peak. In addition, diffusion-weighted images of a fixed mouse spinal cord illustrated the capability of this coil for quantitative imaging of tissue microstructure.     

闪烁体衰减常数对辐射源边界测量影响数值模拟

在辐射成像系统测量辐射源边界中,有闪烁体时间弥散效应得到的边界值与没有闪烁体时的真实边界值存在差别,影响辐射源尺寸变化计算。研究构建了一类辐射源强时间宽度、半径扩散速率与边界相对强度不同的辐射源,应用卷积和图像强度梯度法,对选用BC408,LaBr3和LSO闪烁体得到的边界与真实边界的偏差进行了数值模拟计算。结果表明,拍摄时间为20 ns时,由BC408闪烁体得到的边界值偏差最小;若偏差小于1 mm认为闪烁体适合测量,BC408,LaBr3和LSO测量的强度时间宽度最小值分别为33 ns,133 ns和266 ns; 拍摄全积分图像时偏差大小不受闪烁体不同的影响;最终得出的偏差计算公式较好地反映了真实偏差的变化趋势。     

Thickness dependence of grain size and surface roughness for dc magnetron sputtered Au films

<正>The grain size and surface morphology of sputtered Au films are studied by x-ray diffraction and atomic force microscope.For as-deposited samples the grain growth mechanism is consistent with the two-dimensional(2D) theory, which gives relatively low diffusion coefficient during deposition.The annealing process demonstrates the secondary grain growth mechanism in which the thickness dependence of grain boundary energy plays a key role.The surface roughness increases with the increase of grain size.     

Structural changes in glutamate cell swelling followed by multiparametric q-space diffusion MR of excised rat spinal cord

Diffusion in the extracellular and intracellular spaces (ECS and ICS, respectively) was evaluated in excised spinal cords, before and after cell swelling induced by glutamate, by high b-value q-space diffusion MR of specific markers and water. The signal decays of deuterated tetramethylammonium (TMA-d(12)) chloride, an exogenous marker of the ECS, and N-acetyl aspartate (NAA), an endogenous marker of the ICS, were found to be non-mono-exponential at all diffusion times. The signal decays of these markers were found to depend on the diffusion time and the cell swelling induced by the glutamate. It was found, for example, that the mean displacements of the apparent fast and slow diffusion components of TMA-d(12) are 7.21 +/- 0.11 and 1.16 +/- 0.05 microm, respectively at a diffusion time of 496 ms. After exposure of the spinal cords to 10 mM of glutamate, these values decreased to 6.62 +/- 0.13 and 1.01 +/- 0.05 microm, respectively. The mean displacement of NAA, however, showed a less pronounced opposite trend and increased after cell swelling induced by exposure to glutamate. q-Space diffusion MR of water was found to be sensitive to exposure to glutamate, and q-space diffusion MRI showed that a more pronounced decrease in the apparent diffusion coefficient and the mean displacement of water is observed in the gray matter (GM) of the spinal cord. All these changes demonstrate that diffusion MR is indeed sensitive to structural changes caused by cell swelling induced by glutamate. Multiparametric high b-value q-space diffusion MR is useful for obtaining microstructural information in neuronal tissues.     

以q空间法研究水分子在水晶体中之扩散及其结构

在核磁共振中的脉冲梯度自旋回响法(pulsed gradient spin echo,PGSE)常用来测量溶液中分子或离子的扩散现象,近年来利用PGSE q空间法对多孔隙物质的系统扩散研究。观察到类似绕射效应,在此工作中我们尝试以q空间法直接观察眼球水晶体中的纤维细胞组织和水分子扩散间的关系,实验结果显示,从类似绕射纹图可了解纤维细胞蜂巢式排列结构。     

How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI

The q-space imaging techniques and high angular resolution diffusion (HARD) imaging have shown promise to identify intravoxel multiple fibers. The measured orientation distribution function (ODF) and apparent diffusion coefficient (ADC) profiles can be used to identify the orientations of the actual intravoxel fibers. The present study aims to examine the accuracy of these profile-based orientation methods by comparing the angular deviations between the estimated local maxima of the profiles and the real fiber orientation for a fiber crossing simulated with various intersection angles under different b values in diffusion-weighted MRI experiments. Both noisy and noise-free environments were investigated. The diffusion spectrum imaging (DSI), q-ball imaging (QBI), and HARD techniques were used to generate ODF and ADC profiles. To provide a better comparison between ODF and ADC techniques, the phase-corrected angular deviations were also presented for the ADC method based on a circular spectrum mapping method. The results indicate that systematic angular deviations exist between the actual fiber orientations and the corresponding local maxima of either the ADC or ODF profiles. All methods are apt to underestimation of acute intersection and overestimation of obtuse intersection angle. For a typical slow-exchange fiber crossing, the ODF methods have a non-deviation zone around the 90 degrees intersection. Before the phase-correction, the deviation of ADC profiles approaches a peak at the 90 degrees intersection, while after the correction the ADC deviations are significantly reduced. When the b factor is larger than 1000 s/mm2, the ODF methods have smaller angular deviations than the ADC methods for the intersections close to 90 degrees . QBI method demonstrates a slight yet consistent advantage over the DSI method under the same conditions. In the noisy environment, the mean value of the deviation angles shows a high consistency with the corresponding deviation in the nose-free condition.     

The effect of the rotational angle on MR diffusion indices in nerves: is the rms displacement of the slow-diffusing component a good measure of fiber orientation?

In recent years, much effort has been made to increase our ability to infer nerve fiber direction through the use of diffusion MR. The present study examines the effect of the rotational angle (alpha), i.e. the angle between the diffusion sensitizing gradients and the main axis of the fibers in the nerves, on different NMR indices. The indices examined were the apparent diffusion coefficient (ADC), extracted from low b-values (b(max) approximately 1200 s/mm(2)), and the root mean square (rms) displacement of the fast and the slow-diffusing components extracted from high b-value q-space diffusion MR data. In addition, the effect of both the diffusion time and myelination was evaluated. We found that the most sensitive index to the rotational angle is the rms displacement of the slow-diffusing component extracted from the high b-value q-space diffusion MR experiment. For this component the rms displacement was nearly constant for alpha values ranging from -10 degrees to +80 degrees (where alpha=0 degrees is the z direction), but it changed dramatically when diffusion was measured nearly perpendicular to the nerve fiber direction, i.e., for alpha=90+/-10 degrees. The ADC and the rms displacement of the fast-diffusing component exhibited only gradual changes, with a maximal change at alpha=45+/-15 degrees. The sensitivity of the rms displacement of the slow-diffusing component to the rotational angle was found to be higher at longer diffusion times and in mature fully myelinated nerves. The relevance of these observations for determining the fiber direction is briefly discussed.     

Fabrication of three-dimensional ZnO with hierarchical structure via an electrodeposition process

A novel three-dimensional (3D) hierarchical structured ZnO was prepared on TiO₂ nanoparticles film by electrodeposition process from aqueous ZnCl₂ solution. The hierarchical structured ZnO was observed by scanning electron microscopy. The results showed that the deposition time had an obvious effect on the morphology of the ZnO structures. Accordingly, a possible growth mechanism was proposed. Furthermore, the room-temperature optical properties of hierarchical structured ZnO were investigated by photoluminescence spectrum, indicating that a strong green emission peak centered at 542 nm.     

3D beamforming with ultrasonic divided-ring arrays

Conventional 2D arrays have a set of squared elements whose inter-element spacing is around lambda/2. This arrangement requires an excessive amount of electronic resources for the generation and processing of ultrasonic signals. In this work, the beam properties of a single divided-ring array are analysed theoretically with the goal of producing volumetric images. Divided-ring arrays are based on a circular pattern, which has a lower periodicity than square arrays, and this property allows increasing the element size while keeping the amplitude of the grating lobes at a reasonably low level. The paper emphasises several advantages of ring arrays, suggesting that these apertures are useful for 3D ultrasonic imaging. First, as the element size may increase, the number of elements can be reduced with little loss of emitting area. Second, ring arrays produce beams of large depth of field in both transmission and reception. This can be used to avoid the complexity associated with dynamic focusing.