Three dimensional k-space trajectory design using genetic algorithms

Image quality and total scan time in MRI are determined in large part by the trajectory employed to sample the Fourier space. Each trajectory has different properties like coverage of k-space, scan time, sensitivity to off-resonance conditions, etc. These properties are often contradictory, therefore a universal optimal trajectory does not exist and ultimately, it will depend on the image characteristics sought. Most trajectories used today are designed based on intuition and k-space analysis more than with optimization methods. This work presents a 3D k-space trajectory design method based on Genetic Algorithm optimization. Genetic Algorithms have been chosen because they are particularly good for searching large solution spaces. They emulate the natural evolutionary process allowing better offsprings to survive. The objective function searches the maximum of the trajectory's k-space coverage subject to hardware constraints for a fixed scanning time using the trajectory's torsion as its optimization variable.The method proved to be effective for generating k-space trajectories. They are compared with well-established trajectories. The results of simulated experiments show that they can be appropriate for image acquisition under certain special conditions, like off-resonance and undersampling. This design method can be extended to include other objective functions for different behaviors.     

A 3D trajectory for undersampling k-space in MRSI applications

Magnetic resonance spectroscopic imaging (MRSI) is a noninvasive technique for producing spatially localized spectra. MRSI presents the important challenge of reducing the scan time while maintaining the spatial resolution. The preferred approach for this is to use time-varying readout gradients to collect the spatial and chemical-shift information. Fast, three-dimensional (3D) spatial encoded methods also reduce the scan time. Despite the existence of several new and faster 3D encoded methods, or k-space trajectories, for magnetic resonance imaging (MRI), only stack of spirals and echo planar have been studied in 3D MRSI. A novel formulation for designing fast, 3D k-space trajectory applicable to 3D MRSI is presented. This approach is simple and consists of rays expanding from the origin of k-space into a revolving sphere, collecting spectral data of all 3D spatial k-space at different times in the same scan. This article describes this new method and presents some results of its application to 3D MRSI. This technique allows some degree of undersampling; hence, it is possible to reconstruct high-quality undersampled spectroscopic imaging in order to recognize different compounds in short scan times. Additionally, the method is tested in regular 3D MRI. This proposed method can also be used for dynamic undersampled imaging.     

MRI with TRELLIS: a novel approach to motion correction

A motion-correcting pulse sequence and reconstruction algorithm, termed TRELLIS, is presented. k-Space is filled using orthogonal overlapping strips and the directions for phase- and frequency-encoding are alternated such that the frequency-encode direction always runs lengthwise along each strip. The overlap between strips is used both for signal averaging and to produce a system of equations that, when solved, quantifies the rotational and translational motion of the object. Results obtained from simulations with computer-generated phantoms, a purpose-built moving phantom, and in human subjects show the method is effective. TRELLIS offers some advantages over existing techniques in that k-space is sampled uniformly and all acquired data are used for both motion detection and image reconstruction.     

刀锋伪影校正技术在精神疾病患者海马MRI检查中的应用

为探讨磁共振刀锋伪影校正（BLADE）技术提升精神疾病患者海马磁共振图像质量的效果，本文分别使用结合了BLADE技术的BLADE T₂WI TSE、BLADE T₂WI FLAIR及传统T₂WI TSE、T₂WI FLAIR四种序列，对47例精神疾病患者和美国放射学院（ACR）标准模体在3.0 T磁共振成像（MRI）设备上分别进行常规海马斜冠状位扫描和ACR标准检测.患者的磁共振图像由2名放射科医师采用5分法对运动伪影、搏动伪影、颗粒度、海马磁共振图像质量进行评价，并应用Wilcoxon符号秩检验进行数据分析.模体图像通过识别图像的钻孔阵列和轮辐的数目，半定量评价各序列的高对比空间分辨力（HCSR）和低对比物体探测能力（LCD）.结果表明相比传统序列，结合BLADE技术的序列能够明显改善海马磁共振图像的运动伪影、搏动伪影（p<0.001），提高图像质量（p<0.05）；但在图像颗粒度方面，传统序列表现更优（p<0.001）.ACR模体半定量分析显示，结合BLADE技术序列与传统序列相比，在LCD检测方面结果更优、在HCSR检测方面结果相同或略逊.本文推荐将BLADE技术应用于不合作的精神疾病患者海马的MRI检查.     

Volumetric q-space imaging by 3D diffusion-weighted MRI

High b-value diffusion magnetic resonance imaging (MRI) enables us to detect far smaller architectures, by using q-space analysis, than the resolution in conventional MRI. Average displacement, one of the q-space parameters, quantitatively reflects architecture size and is very useful in observing small changes in microstructures in vivo (e.g., neurodegeneration, tumor heterogeneity, and others). Diffusion-weighted imaging (DWI) is performed by a two-dimensional (2D) multislice method; however, due to finite slice thickness and slice gap, there is a partial-volume effect that makes it difficult to detect the net q-space signal. On the other hand, three-dimensional (3D) MRI, having the advantages of very thin slice thickness and no slice gap (contiguous slices), allows volumetric evaluation acquired in a small isotropic voxel, as compared to 2D multislice imaging. Little is known about the isotropic high-resolution 3D DWI application to q-space analysis. In this study, we have developed and implemented a high b-value 3D DWI sequence, applied q-space analysis to study the reliability of high b-value 3D DWI and obtained a microscopic analytical map with isotropic high resolution and less contamination.     

Influence of flow on the structure and dynamics of clusters in complex plasma systems

The influence of flow with different strengths, positions, and widths on the structure and dynamics of clusters is studied by two-dimensional (2D) Langevin molecular dynamics simulations. The particles are confined by a quadratic confining potential. The horizontal position of the system centre, average inter-particle distance, and coupling parameter are calculated to characterize the effect of changing the strength, position, and width of the flow on the cluster structure. The trajectories, the velocity autocorrelation function, and the mean square displacement are obtained to further uncover the dynamic properties of the 2D dusty plasma system.     

不同管口浸没方式下气泡运动特性实验研究

为了对比研究不同管口浸没方式下气泡的运动特性,通过可视化实验揭示了顶部、侧部和底部三种管口浸没方式下的气泡上升运动过程,得到了气泡形状、等效直径、位移、速度以及高宽比的变化规律,通过获得相邻气泡质心间垂直距离定量表征了气泡在上升过程中的紊乱程度.研究结果表明,顶部管口浸没方式下的气泡形态明显区别于侧部和底部管口浸没方式...     

Resonance cone formation in a curved cylindrically anisotropic metamaterial film

Resonance cones, the regions where major power and high-intensity fields are concentrated, form with cylindrically anisotropic media when the permittivity tensor elements have opposite signs. The resonance cones inside a circular layer of cylindrically anisotropic material is shown to experience multiple internal reflections from the layer boundaries. We introduce a spectrometer class by exploiting the dispersive properties of a metal-insulator stack metamaterial. The cones can exhibit negative refraction at the interface of two such circular layers, leading to a far-field bilayer subwavelength imaging system with more flexibility in the material parameter and operating wavelength spaces.     

Accelerated free-breathing 3D whole-heart magnetic resonance angiography with a radial phyllotaxis trajectory,compressed sensing,and curvelet transform

PurposeTo develop and validate an accelerated free-breathing 3D whole-heart magnetic resonance angiography (MRA) technique using a radial k-space trajectory with compressed sensing and curvelet transform.MethodA 3D radial phyllotaxis trajectory was implemented to traverse the centerline of k-space immediately before the segmented whole-heart MRA data acquisition at each cardiac cycle. The k-space centerlines were used to correct the respiratory-induced heart motion in the acquired MRA data. The corrected MRA data were then reconstructed by a novel compressed sensing algorithm using curvelets as the sparsifying domain. The proposed 3D whole-heart MRA technique (radial CS curvelet) was then prospectively validated against compressed sensing with a conventional wavelet transform (radial CS wavelet) and a standard Cartesian acquisition in terms of scan time and border sharpness.ResultsFifteen patients (females 10, median age 34-year-old) underwent 3D whole-heart MRA imaging using a standard Cartesian trajectory and our proposed radial phyllotaxis trajectory. Scan time for radial phyllotaxis was significantly shorter than Cartesian (4.88 ± 0.86 min. vs. 6.84 ± 1.79 min., P-value = 0.004). Radial CS curvelet border sharpness was slightly lower than Cartesian and, for the majority of vessels, was significantly better than radial CS wavelet (P-value < 0.050).ConclusionThe proposed technique of 3D whole-heart MRA acquisition with a radial CS curvelet has a shorter scan time and slightly lower vessel sharpness compared to the Cartesian acquisition with radial profile ordering, and has slightly better sharpness than radial CS wavelet. Future work on this technique includes additional clinical trials and extending this technique to 3D cine imaging.     

SNR phase order k-space encoding (SPOKE)

A method of determining the phase-encode order for MR Fourier-encoded imaging is described, which provides an additional option for optimizing images from samples with signals that change during data acquisition. Examples are in hyperpolarized helium gas imaging of the lungs where polarization is lost with each RF pulse or the signal changes observed in rapid dynamic studies with T₁ or T₂* contrast agents when mixing is taking place. The method uses a single frequency-encoded projection in the proposed phase-encoding direction. The projection is subsequently sorted into signal-to-noise ratio (SNR) order. The indices of the sorted array are then used to create the phase-encode table to be used for the scan. This phase table is sorted in descending SNR order for signals that decrease during data acquisition and in ascending order for signals that increase during data acquisition. Simulations suggest that this technique can produce higher resolution than centric-ordered phase encoding at the expense of increased modulation (ghosting) artifact for dynamically changing signals. Initial practical implementation of the technique has been carried out on a dedicated 0.2-T Niche MR system, and the test object results agree well with simulations. Hyperpolarized 3-He lung images have also been acquired and postprocessed using the SNR phase order k-space encoding (SPOKE) methodology and show potential for improved imaging with high flip angles where polarization is rapidly lost. Applications may also be found for 3D volumetric acquisitions where two dimensions can be SPOKE encoded.     

Quantile motion and tunneling

The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial parameters. In quantum mechanics the quantile trajectories are mathematically identical to Bohm's trajectories. A generalization to three dimensions is given.     

Flow of a two-fluid plasma carrying a pulsed current in a steady-state magnetic field

The problem of the motion of plasma carrying a pulsed current in a steady-state magnetic field is solved in terms of two-fluid magnetohydrodynamics. The initial directions of the force and current vectors are determined, and the relations that determine their time evolution are obtained. The time dependences of the slope of the two-fluid plasma flow trajectory with respect to the one-fluid plasma motion direction are calculated. The smaller the ion mass in the plasma, the faster the decrease in the slope of the trajectory with time. The calculation results agree well with the data of our experiments [1–7] on studying the current sheets in 3D magnetic fields with an X line and support the necessity of taking into account the two-fluid properties of plasma when current sheets form in heavy inert gases.     

Lagrangian dynamics and statistical geometric structure of turbulence

The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Experimental investigation on flow boiling bubble motion under ultrasonic field in vertical minichannel by using bubble tracking algorithm

Bubble dynamics is important in flow boiling of minichannel, and ultrasonic field effects bubble behaviors. However, flow boiling bubble movements in minichannels under ultrasonic field have received little research attention and are still poorly understood. In this paper, the effects of ultrasonic field on bubble dynamics are experimentally studied by capturing the bubble motion behaviors of the flow boiling bubbles. The ultrasonic frequencies are set to 23, 28, 32, and 40 kHz. Bubble tracking algorithm, which studies the growth, trajectories, velocities, and traveled distances for bubbles, is created to qualitatively describe bubble motion behavior of flow boiling in minichannel. It is found that after the application of ultrasound, the detachment frequency, velocity, and travel distance of the bubbles significantly increases, and the growth behavior and trajectory are extremely complex, the two-phase gas-liquid flow is extremely unstable. The bubbles gain kinetic energy as the ultrasound frequency increases. Finally, numerical simulations are used to quantitatively investigate the mechanism of bubble motion in microchannels under ultrasonic fields.     

Truncation effects in SENSE reconstruction

Finite sampling is an important practical issue in Fourier imaging systems. Although data truncation effects are well understood in conventional Fourier imaging where a single uniform receiver channel is used for data acquisition, this issue is not yet fully addressed in parallel imaging where an array of nonuniform receiver channels is used for sensitivity encoding to enable sub-Nyquist sampling of k-space. This article presents a systematic analysis of the problem by comparing the truncation effects in parallel imaging with those in conventional Fourier imaging. Specifically, it derives a convolution kernel function to characterize the truncation effects, which is shown to be approximately equal to that associated with the conventional Fourier imaging scheme. This article also describes a set of conditions under which significant differences between the truncation effects in parallel imaging and conventional Fourier imaging occur. The results should provide useful insight into interpreting and reducing data truncation effects in parallel imaging.     

Wide dynamic range detection of bidirectional flow in Doppler optical coherence tomography using a two-dimensional Kasai estimator

We demonstrate extended axial flow velocity detection range in a time-domain Doppler optical coherence tomography (DOCT) system using a modified Kasai velocity estimator with computations in both the axial and transverse directions. For a DOCT system with an 8 kHz rapid-scanning optical delay line, bidirectional flow experiments showed a maximum detectable speed of >56 cm/s using the axial Kasai estimator without the occurrence of aliasing, while the transverse Kasai estimator preserved the approximately 7 microm/s minimum detectable velocity to slow flow. By using a combination of transverse Kasai and axial Kasai estimators, the velocity detection dynamic range was over 100 dB. Through a fiber-optic endoscopic catheter, in vivoM-mode transesophageal imaging of the pulsatile blood flow in rat aorta was demonstrated, for what is for the first time to our knowledge, with measured peak systolic blood flow velocity of >1 m/s, while maintaining good sensitivity to detect aortic wall motion at <2 mm/s, using this 2D Kasai technique.     

Rapid 3D whole-heart cine imaging using golden ratio stack of spirals

Three-dimensional cine imaging provides a wealth of information about cardiac anatomy and function, but its use in the clinical environment is limited because data acquisition is very time consuming. In this work, a free-breathing 3D whole-heart cine imaging framework was developed using a time-efficient stack of spirals trajectory and accelerated reconstruction. Two suitable view ordering methods are considered with different spacing between k-space readouts in the partition dimension: uniform and tiny golden ratio based. A simulation study suggested the latter did not present any benefits in terms of similarity to the true image. The proposed method was subsequently tested on 10 prospective subjects and compared with conventional multi-slice breath-hold imaging. Image quality was evaluated using objective and subjective scores and ventricular measurements were compared to assess clinical accuracy. Image quality was lower in the proposed technique than in breath-hold images but good agreement was found in clinically relevant ventricular measurements. In addition, the proposed method was fast to acquire, required minimal planning and provided full anatomical coverage with isotropic resolution.     

Evaluation of intracranial stenoses and aneurysms with accelerated 4D flow

The aim of this study was to evaluate intracranial arterial stenoses and aneurysms with accelerated time-resolved three-dimensional (3D) phase-contrast MRI or 4D flow. The 4D flow technique was utilized to image four normal volunteers, two patients with intracranial stenoses and two patients with intracranial aneurysms. In order to reduce scan time, parallel imaging was combined with an acquisition strategy that eliminates the corners of k-space. In the two patients with intracranial stenoses, 4D flow velocity measurements showed that one patient had normal velocity profiles in agreement with a previous magnetic resonance angiogram (MRA), while the second showed increased velocities that indicated a less significant narrowing than suspected on a previous MRA, as confirmed by catheter angiography. This result may have prevented an invasive angiogram. In the two patients with 4-mm intracranial aneurysm, one had a stable helical flow pattern with a large jet, while the other had a temporally unstable flow pattern with a more focal jet possibly indicating that the second aneurysm may have a higher likelihood of rupture. Accelerated 4D flow provides time-resolved 3D velocity data in an 8- to 10-min scan. In the stenosis patients, the addition of 4D flow to a traditional MRA adds the velocity data provided from transcranial Doppler ultrasound (TCD) possibly allowing for more accurate grading of stenoses. In the aneurysm patients, visualization of flow patterns may help to provide prognostic information about future risk of rupture.     

Itinerant to relocalized transition of f electrons in the Kondo insulator CeRu4Sn6

The three-dimensional electronic structure and the nature of Ce 4f electrons of the Kondo insulator CeRu₄Sn₆ are investigated by angle-resolved photoemission spectroscopy, utilizing tunable photon energies. Our results reveal (i) the three-dimensional k-space nature of the Fermi surface, (ii) the localized-to-itinerant transition of f electrons occurs at a much high temperature than the hybridization gap opening temperature, and (iii) the “relocalization” of itinerant f-electrons below 25 K, which could be the precursor to the establishment of magnetic order.