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).     

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.     

Modified oscillating gradient pulses for direct sampling of the diffusion spectrum suitable for imaging sequences

A variation of the oscillating gradient spin echo method had been developed, which isolates temporal frequencies of the dephasing spectrum. This allows sampling of the diffusion spectrum, the Fourier transform of the velocity correlation function (VCF). It has been shown that restriction and flow alter this function in ways that can be mathematically characterized, yielding quantitative information on restriction geometry and flow parameters. It is demonstrated that in many systems of interest, dispersion of velocity will produce a peak in the VCF spectrum near omega=0, while restricted diffusion will manifest itself in the spectrum at higher frequencies. The method, therefore, may be useful for decoupling their effects on the apparent diffusion coefficient (ADC), as well as in revealing the physics of both phenomena. This method has been implemented in model systems of packed beads, yielding data consistent with theoretical models of restricted diffusion spectra and data from one previous study. The method may have significant application to biology and medicine, as well as the study of transport phenomena in porous media and complex flow.     

直接相位调制产生周期性线性啁啾脉冲特性研究

提出一种利用周期性抛物线调制信号对光脉冲进行相位调制以获得周期性线性啁啾脉冲的方法, 并对其进行了数值模拟与实验研究. 数值模拟结果表明: 增益饱和效应、群速度色散以及同步误差对啁啾脉冲的时间-光谱特性影响较大; 自相位调制对啁啾脉冲的影响较小. 实验获得了0.52 nm带宽的周期性线性啁啾脉冲, 与模拟结果符合较好. 实验结果同时表明装置中存在较大的偏振模色散, 导致幅频效应较大, 后续的研究中需加入对此的考虑. 模拟及实验研究表明: 直接相位调制是一种新型的可方便地获得周期性线性啁啾脉冲的方法, 其在光谱色散平滑中具有潜在应用. 关键词： 直接相位调制 周期性线性啁啾脉冲 幅频效应     

Multiple echo diffusion tensor acquisition technique

The standard method of diffusion tensor imaging (DTI) involves one diffusion-sensitizing gradient direction per acquired signal. This paper describes an alternative method in which the entire direction set required for calculating the diffusion tensor is captured in a few scans. In this method, a series of radiofrequency (RF) pulses are applied, resulting in a train of spin echoes. A pattern of applied magnetic field gradients between the RF pulses generates a different diffusion weighting in both magnitude and direction for each echo, resulting in a dataset sufficient to determine the tensor. This significantly reduces the time required for a full DTI scan and potentially allows a tradeoff of this time for image quality. In the present work, this method is demonstrated in an anisotropic diffusion phantom (asparagus).     

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.     

Diffusion pore imaging with generalized temporal gradient profiles

In porous material research, one main interest of nuclear magnetic resonance diffusion (NMR) experiments is the determination of the shape of pores. While it has been a longstanding question if this is in principle achievable, it has been shown recently that it is indeed possible to perform NMR-based diffusion pore imaging. In this work we present a generalization of these previous results. We show that the specific temporal gradient profiles that were used so far are not unique as more general temporal diffusion gradient profiles may be used. These temporal gradient profiles may consist of any number of “short” gradient pulses, which fulfil the short-gradient approximation. Additionally, “long” gradient pulses of small amplitude may be present, which can be used to fulfil the rephasing condition for the complete profile. Some exceptions exist. For example, classical q-space gradients consisting of two short gradient pulses of opposite sign cannot be used as the phase information is lost due to the temporal antisymmetry of this profile.     

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.     

Measurement of hyperpolarized gas diffusion at very short time scales

We present a new pulse sequence for measuring very-short-time-scale restricted diffusion of hyperpolarized noble gases. The pulse sequence is based on concatenating a large number of bipolar diffusion-sensitizing gradients to increase the diffusion attenuation of the MR signal while maintaining a fundamentally short diffusion time. However, it differs in several respects from existing methods that use oscillating diffusion gradients for this purpose. First, a wait time is inserted between neighboring pairs of gradient pulses; second, consecutive pulse pairs may be applied along orthogonal axes; and finally, the diffusion-attenuated signal is not simply read out at the end of the gradient train but is periodically sampled during the wait times between neighboring pulse pairs. The first two features minimize systematic differences between the measured (apparent) diffusion coefficient and the actual time-dependent diffusivity, while the third feature optimizes the use of the available MR signal to improve the precision of the diffusivity measurement in the face of noise. The benefits of this technique are demonstrated using theoretical calculations, Monte-Carlo simulations of gas diffusion in simple geometries, and experimental phantom measurements in a glass sphere containing hyperpolarized (3)He gas. The advantages over the conventional single-bipolar approach were found to increase with decreasing diffusion time, and thus represent a significant step toward making accurate surface-to-volume measurements in the lung airspaces.     

Dispersion compensation by microstructured optical devices in ultrafast optics

Dispersion compensation is a ubiquitous problem for the generation and application of ultrashort optical pulses. Early approaches to compensate for the spectral group-delay dependence in materials used prism and grating sequences for this purpose, but are limited in bandwidth. Microstructuring dielectric optical materials on the scale of the optical wavelength have developed as an alternative for inducing a desired spectral group-delay dependence. With this approach a nearly arbitrary dependence of group delay vs. wavelength can be compensated for. We will discuss different approaches to microstructured dispersion compensation, namely chirped Bragg gratings, different generations of chirped mirrors, quasi-phase-matching gratings, and arrayed-waveguide gratings. We will outline common limitations and discuss ideas to expand further the utility of these approaches. PACS 42.65 Re; 42.79 Wc; 42.81 Wg     

The effect of impermeable boundaries of arbitrary geometry on the apparent diffusion coefficient

The apparent diffusion coefficient (ADC) obtained from NMR measurements is modelled for diffusion in a compartment restricted by an impermeable boundary. For a given pulse sequence, the ADC can be determined from the connected velocity autocorrelation function (the second-order velocity cumulant), which we show can be expressed as a double surface integral over the boundary, involving the probability for molecules to diffuse from one boundary point to another. There is no restriction on the geometry of the boundary. This result allows a fast calculation of the ADC for an arbitrary time course of the diffusion-sensitizing gradient. Explicit examples are given for diffusion within three basic geometries for different pulse sequences. The ADCs measured with the Stejskal-Tanner pulse sequence and a more realistic pulse sequence with slice selection gradient and eddy current compensation are found to yield almost identical results. The application of the results are discussed in relation to determination of the microscopic structure of brain white matter.     

Microscopic imaging of slow flow and diffusion: a pulsed field gradient stimulated echo sequence combined with turbo spin echo imaging.

In this paper we present a pulse sequence that combines a displacement-encoded stimulated echo with rapid sampling of k-space by means of turbo spin echo imaging. The stimulated echo enables the use of long observation times between the two pulsed field gradients that sample q-space completely. Propagators, constructed with long observation times, could discriminate slowly flowing protons from diffusing protons, as shown in a phantom in which a plug flow with linear velocity of 50microm/s could clearly be distinguished from stationary water. As a biological application the apparent diffusion constant in longitudinal direction of a transverse image of a maize plant stem had been measured as a function of observation time. Increasing contrast in the apparent diffusion constant image with increasing observation times were caused by differences in plant tissue: although the plant stem did not take up any water, the vascular bundles, concentrated in the outer ring of the stem, could still be discerned because of their longer unrestricted diffusional pathways for water in the longitudinal direction compared to cells in the parenchymal tissue. In the xylem region of a tomato pedicel flowing water could be distinguished from a large amount of stationary water. Linear flow velocities up to 0.67 mm/s were measured with an observation time of 180 ms.     

色散介质中啁啾高斯脉冲的时间和光谱特性

对啁啾高斯脉冲光束在色散介质中的时间和光谱特性作了研究.给出了远场光谱蓝移和脉冲展宽的解析式.结果表明：通过选择适当的啁啾参量,啁啾高斯脉冲光束沿轴上传输色散长度时,脉冲可恢复到初始值.随啁啾参量增加,谱线宽度展宽,轴上光谱蓝移增加,在远场蓝移趋于一渐近值.随啁啾参量增加,离轴光谱红移增加.     

Feasibility of probing boundary morphology of structured materials by 2D NMR q-space imaging

It is well known that one-dimensional (1D) q-space imaging allows retrieval of structural information at cellular resolution. Here we demonstrate by simulation that boundary morphology of structured materials can be derived from 2D q-space mapping. Based on a finite-difference model for restricted diffusion, 2D q-space maps obtained from water diffusion inside apertures at various levels of asperity were simulated. The results indicate that the observed ring patterns (diffraction minima) reveal the boundary profiles of the apertures but become blurred in the case of significant variation in aperture size. For uniform size distribution of apertures, a quantitative measure of surface roughness can be established by means of spatial autocorrelation analysis. The results suggest that 2D q-space imaging may allow probing of the boundary morphology of structured materials and possibly biological cells.     

Dispersion control over the ultraviolet-visible-near-infrared spectral range with HfO2/SiO2-chirped dielectric multilayers

We report the first realization, to the best of our knowledge, of a chirped multilayer dielectric mirror providing dispersion control over the spectral range of 300-900 nm and the first use of hafnium oxide in a chirped mirror. The technology opens the door to the reliable and reproducible generation of monocycle laser pulses in the blue-violet spectral range, will benefit the development of optical waveform and frequency-comb synthesizers over the ultraviolet-visible-near-infrared spectral range, and permits the development of ultrabroadband-chirped multilayers for high-power applications.     

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.     

Wavelength-tunable spectral compression in a dispersion-increasing fiber

We demonstrate, both numerically and experimentally, adiabatic soliton spectral compression in a dispersion-increasing fiber (DIF). We show that a positively chirped pulse provides better spectral compression in a DIF with a large anomalous dispersion ramp. An experimental spectral compression ratio of 15.5 is obtained using 350 fs positively chirped input pulse centered at 1.5 μm. A 30 nm wavelength tuning ability is experimentally achieved.     

啁啾高斯脉冲光束在正色散介质中的自聚焦特性

 采用分步法结合Hankel变换对修正薛定谔方程进行数值求解,通过数值计算对飞秒脉冲在非线性正色散介质中的自聚焦特性进行了简要分析。在此基础上,针对啁啾脉冲放大系统(CPA)中的啁啾高斯脉冲,对其全光束自聚焦特性进行了计算模拟和分析讨论。研究结果表明,群速度色散(GVD)对大啁啾脉冲的影响很小,谱宽对自聚集的影响可以忽略。因此,具有大啁啾的脉冲在非线性正色散介质中的自聚焦特性不同于飞秒脉冲,而与纳秒脉冲相似。