Reconstruction of 3D ultrasound images based on Cyclic Regularized Savitzky-Golay filters

This paper presents a new three-dimensional (3D) ultrasound reconstruction algorithm for generation of 3D images from a series of two-dimensional (2D) B-scans acquired in the mechanical linear scanning framework. Unlike most existing 3D ultrasound reconstruction algorithms, which have been developed and evaluated in the freehand scanning framework, the new algorithm has been designed to capitalize the regularity pattern of the mechanical linear scanning, where all the B-scan slices are precisely parallel and evenly spaced. The new reconstruction algorithm, referred to as the Cyclic Regularized Savitzky-Golay (CRSG) filter, is a new variant of the Savitzky-Golay (SG) smoothing filter. The CRSG filter has been improved upon the original SG filter in two respects: First, the cyclic indicator function has been incorporated into the least square cost function to enable the CRSG filter to approximate nonuniformly spaced data of the unobserved image intensities contained in unfilled voxels and reduce speckle noise of the observed image intensities contained in filled voxels. Second, the regularization function has been augmented to the least squares cost function as a mechanism to balance between the degree of speckle reduction and the degree of detail preservation. The CRSG filter has been evaluated and compared with the Voxel Nearest-Neighbor (VNN) interpolation post-processed by the Adaptive Speckle Reduction (ASR) filter, the VNN interpolation post-processed by the Adaptive Weighted Median (AWM) filter, the Distance-Weighted (DW) interpolation, and the Adaptive Distance-Weighted (ADW) interpolation, on reconstructing a synthetic 3D spherical image and a clinical 3D carotid artery bifurcation in the mechanical linear scanning framework. This preliminary evaluation indicates that the CRSG filter is more effective in both speckle reduction and geometric reconstruction of 3D ultrasound images than the other methods.     

Fluoroscopically triggered contrast-enhanced 3D MR DSA and 3D time-of-flight turbo MRA of the carotid arteries: first clinical experiences in correlation with ultrasound, x-ray angiography, and endarterectomy findings

The aim of this article was to obtain initial experiences with fluoroscopically triggered contrast-enhanced (CE) 3D MR DSA with elliptical centric k-space order and 3D time-of-flight (TOF) turbo MRA of the carotid arteries. In this prospective study we examined 16 consecutive patients with suspicion of atherosclerotic disease involving the carotid arteries. Ultrasound was available in all, x-ray angiography in 12, surgical correlation in 9, and intraoperative x-ray angiography in 4 patients. All examinations were done on a 1.5 T unit applying: transverse plain 3D TOF turbo MRA and coronal CE MRA with fluoroscopic triggering. Combining head and neck array coils allowed the visualization of supraaortic arteries from the aortic arch to the circle of Willis. MRA results (maximum intensity projections) were compared with x-ray angiography, ultrasound, and inspection of endarterectomy specimens. Volume rendering was performed in selected cases additionally. Agreement between CE MRA, 3D TOF turbo MRA and x-ray angiography regarding stenoses of the internal and external carotid artery was very good. CE MRA was able to detect correctly intracranial stenoses, but delineation of the aortic arch and proximal common carotid arteries was sometimes reduced. Volume rendering was suited for visualization of MRA images providing a realistic three-dimensional impression. In conclusion, high-resolution fluoroscopically triggered CE MRA as non-invasive technique is another important step on the way to replace invasive x-ray angiography for the evaluation of atherosclerotic carotid artery disease. High resolution 3D TOF turbo MRA might be a helpful adjunct to increase the diagnostic reliability for the carotid bifurcation.     

Novel methodology for 3D reconstruction of carotid arteries and plaque characterization based upon magnetic resonance imaging carotid angiography data

In this study, we present a novel methodology that allows reliable segmentation of the magnetic resonance images (MRIs) for accurate fully automated three-dimensional (3D) reconstruction of the carotid arteries and semiautomated characterization of plaque type. Our approach uses active contours to detect the luminal borders in the time-of-flight images and the outer vessel wall borders in the T(1)-weighted images. The methodology incorporates the connecting components theory for the automated identification of the bifurcation region and a knowledge-based algorithm for the accurate characterization of the plaque components. The proposed segmentation method was validated in randomly selected MRI frames analyzed offline by two expert observers. The interobserver variability of the method for the lumen and outer vessel wall was -1.60%±6.70% and 0.56%±6.28%, respectively, while the Williams Index for all metrics was close to unity. The methodology implemented to identify the composition of the plaque was also validated in 591 images acquired from 24 patients. The obtained Cohen's k was 0.68 (0.60-0.76) for lipid plaques, while the time needed to process an MRI sequence for 3D reconstruction was only 30 s. The obtained results indicate that the proposed methodology allows reliable and automated detection of the luminal and vessel wall borders and fast and accurate characterization of plaque type in carotid MRI sequences. These features render the currently presented methodology a useful tool in the clinical and research arena.     

Fast carotid artery MR angiography with compressed sensing based three-dimensional time-of-flight sequence

ObjectiveIn this study, we sought to investigate the feasibility of fast carotid artery MR angiography (MRA) by combining three-dimensional time-of-flight (3D TOF) with compressed sensing method (CS-3D TOF).Materials and methodsA pseudo-sequential phase encoding order was developed for CS-3D TOF to generate hyper-intense vessel and suppress background tissues in under-sampled 3D k-space. Seven healthy volunteers and one patient with carotid artery stenosis were recruited for this study. Five sequential CS-3D TOF scans were implemented at 1, 2, 3, 4 and 5-fold acceleration factors for carotid artery MRA. Blood signal-to-tissue ratio (BTR) values for fully-sampled and under-sampled acquisitions were calculated and compared in seven subjects. Blood area (BA) was measured and compared between fully sampled acquisition and each under-sampled one.ResultsThere were no significant differences between the fully-sampled dataset and each under-sampled in BTR comparisons (P > 0.05 for all comparisons). The carotid vessel BAs measured from the images of CS-3D TOF sequences with 2, 3, 4 and 5-fold acceleration scans were all highly correlated with that of the fully-sampled acquisition. The contrast between blood vessels and background tissues of the images at 2 to 5-fold acceleration is comparable to that of fully sampled images. The images at 2 × to 5 × exhibit the comparable lumen definition to the corresponding images at 1 ×.ConclusionBy combining the pseudo-sequential phase encoding order, CS reconstruction, and 3D TOF sequence, this technique provides excellent visualizations for carotid vessel and calcifications in a short scan time. It has the potential to be integrated into current multiple blood contrast imaging protocol.     

An optimized 3D inversion recovery prepared fast spoiled gradient recalled sequence for carotid plaque hemorrhage imaging at 3.0 T

An optimized 3D inversion recovery prepared fast spoiled gradient recalled sequence (IR FSPGR) on a 3-T scanner for carotid plaque imaging is described. It offers clear blood and fat signal suppression at the carotid artery bifurcation and highlights the regions of carotid plaque affected by hemorrhage at 3 T with high contrast and contrast-to-noise ratio compared with other sequences. It can potentially be used to replace the more traditional noncontrast T₁-weighted 2D black-blood imaging for hemorrhage detection and offers additional benefits of high-resolution 3D volumetric visualization.     

三层膜管壁结构的颈动脉超生仿真

颈动脉超声仿真 有助于血管壁超声检测及信号处理方法的性能评价。提出三层膜管壁结构的颈动脉超声仿真方法。根据组织散射点分布的形状和密度与超声回声斑点分布的变化规律,对临床图像统计分析,确定对应组织散射点分布、密度及强度等特征参数,利用FIELD II产生超声射频回波信号并得到B超图像。30 例仿真试验结果表明,血管壁内、中、外膜及血流回声的统计分布与临床B超图像的一致;与中心频率为8 MHz的结果相比,12 MHz仿真的内、中、外膜厚度及管腔直径测量均值与预设值相等,最大相对误差分别为4.01%, 1.25%, 0.04%及0.15%,仿真效果更为逼真。      

Study of the Wada fractal boundary and indeterminate crisis

By using the generalized cell mapping digraph (GCMD)method,we study bifurcations governing the escape of periodically forced oscillators in a potential well,in which a chaotic saddle plays an extremely important role.Int this paper,we find the chaotic saddle,and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property,that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins.The chaotic saddle in the Wada fractal boundary,by colliding with a chaotic attractor,leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system.We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary particularly concentrating on its discontinuous bifurcations(metamorphoses),We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries.After a final escape bifurcation,there only exists the attractor at infinity;a chaotic saddle with a beautiful pattern is left behind in phase space.     

An ultrasound simulation method for carotid arteries with a wall structure of three membranes

Ultrasound simulation for carotid arteries is helpful to the performance assessments of vessel wall detection and signal processing methods by using ultrasound techniques.An ultrasound simulation method of carotid artery wall with a three-membrane structure is proposed in present study.According to the ultrasound speckle distributions varying with the shapes and densities of scatterer distributions,as well as the statistic results of the clinical images,the parameters of distributions,densities and intensities of scatterers for different kinds of tissues in the carotid artery phantoms are determined.Each region is acoustically characterized using FIELD II software to produce the radio frequency echo signals,from which ultrasound images are derived.The results based on 30 simulations show that the echo distributions of the intimae,mediae,adventitias and blood are consistent with the clinical ones.Moreover,compared with the results from the central frequency of 8 MHz,the mean measurements for thicknesses of the intima,media and adventitia membranes,as well as the lumen diameter from the simulation images based on 12 MHz are the same as the preset ones,and the maximum relative errors are the 4.01%,1.25%,0.04%and 0.15%,respectively.The simulation under this condition is more realistic.     

3D reconstruction of the brain from magnetic resonance images using a connectivity algorithm

We present high resolution three dimensional (3D) connectivity, surface construction and display algorithms that detect, extract, and display the surface of a brain from contiguous magnetic resonance (MR) images. The algorithms identify the external brain surface and create a 3D image, showing the fissures and surface convolutions of the cerebral hemispheres, cerebellum, and brain stem. Images produced by these algorithms also show the morphology of other soft tissue boundaries such as the cerebral ventricular system and the skin of the patient. For the purposes of 3D reconstruction, our experiments show that T1 weighted images give better contrast between the surface of the brain and the cerebral spinal fluid than T2 weighted images. 3D reconstruction of MR data provides a non-invasive procedure for examination of the brain surface and other anatomical features.     

Wada bifurcations and partially Wada basin boundaries in a two-dimensional cubic map

The partially Wada basin boundaries are referred to the coexistence of Wada points and non-Wada points in the same basin boundary. We demonstrate two types of Wada bifurcations and analyze the transitions from totally Wada basins to partially Wada basins and from totally Wada basins to totally Wada basins in a two-dimensional cubic map. We describe some numerical experiments giving the evidence of partially Wada basin boundaries. Our results show that the basin cell erosion and the basin cell bifurcation can induce the Wada basin boundary metamorphoses.     

MRI angiography of the carotid artery

Spin echo images of the carotid arteries in longitudinal view have been obtained by selection of oblique imaging planes. Blood flow within the lumen in the region of the carotid bifurcation has been visualized through the use of cardiac gating during end diastole. Using a surface coil placed about the mandible, high resolution images [(0.75 mm)² per pixel) were obtained with scan times typically equal to 9 min and image data matrix equal to 256 × 256. Images obtained with this technique of MRI carotid angiography demonstrate blood flow phenomenon as well as vascular anatomy.     

Asymmetric radial expansion and contraction of rat carotid artery observed using a high-resolution ultrasound imaging system

The geometry of carotid artery bifurcation is of high clinical interest because it determines the characteristics of blood flow that is closely related to the formation and development of atherosclerotic plaque. However, information on the dynamic changes in the vessel wall of carotid artery bifurcation during a pulsatile cycle is limited. This pilot study investigated the cyclic changes in carotid artery geometry caused by blood flow pulsation in rats. A high-resolution ultrasound imaging system with a broadband scanhead centered at 40 MHz was used to obtain longitudinal images of the rat carotid artery. A high frame rate retrospective B-scan imaging technique based on the use of electrocardiogram to trigger signal acquisition was used to examine precisely the fast arterial wall motion. Two-dimensional geometry data obtained from nine rats showed that the rat carotid artery asymmetrically contracts and dilates during each cardiac cycle. Systolic/diastolic vessel diameters near the upstream and downstream regions from the bifurcation were 0.976 ± 0.011/0.825 ± 0.015 mm and 0.766 ± 0.015/0.650 ± 0.016 mm, respectively. Their posterior/anterior wall displacement ratios in the radial direction were 41.0 ± 14.9% and 2.9 ± 1.6%, respectively. These results indicate that in the vicinity of bifurcation, the carotid artery favorably expands to the anterior side during the systolic phase. This phenomenon was observed to be more prominent in the downstream region near the bifurcation. The cyclic variation pattern in wall movement varies depending on the measurement site, which shows different patterns at far upstream and downstream of the bifurcation. The asymmetric radial expansion and contraction of the rat carotid artery observed in this study may be useful in studying the hemodynamic etiology of cardiovascular diseases because the pulsatile changes in vessel geometry may affect the local hemodynamics that determines the spatial distribution of wall shear stress, one of important cardiovascular risk factors. Further systematic study is needed to clarify the effects of wall elasticity, branch angle and vessel diameter ratio on the asymmetric wall motion of carotid artery bifurcation.     

3D ultrasound reconstruction algorithms from analog and digital data

Freehand 3D ultrasound is increasingly being introduced in the clinic for diagnostics and image-assisted interventions. Various algorithms exist for combining 2D images of regular ultrasound probes to 3D volumes, being either voxel-, pixel- or function-based. Previously, the most commonly used input to 3D ultrasound reconstruction has been digitized analog video. However, recent scanners that offer access to digital image frames exist, either as processed or unprocessed data. To our knowledge, no comparison has been performed to determine which data source gives the best reconstruction quality. In the present study we compared both reconstruction algorithms and data sources using novel comparison methods for detecting potential differences in image quality of the reconstructed volumes. The ultrasound scanner used in this study was the Sonix RP from Ultrasonix Medical Corp (Richmond, Canada), a scanner that allow third party access to unprocessed and processed digital data. The ultrasound probe used was the L14-5/38 linear probe. The assessment is based on a number of image criteria: detectability of wire targets, spatial resolution, detectability of small barely visible structures, subjective tissue image quality, and volume geometry. In addition we have also performed the more “traditional” comparison of reconstructed volumes by removing a percentage of the input data. By using these evaluation methods and data from the specific scanner, the results showed that the processed video performed better than the digital scan-line data, digital video being better than analog video. Furthermore, the results showed that the choice of video source was more important than the choice of tested reconstruction algorithms.     

耦合发电机系统的分岔和双参数特性

在综合分析系统基本动力学特性的基础上,通过数值计算Lyapunov指数谱、分岔图等,讨论了耦合发电机系统的混沌分岔行为和周期窗口的性态变化;计算和分析了系统在二维参数空间的双参数特性.结果显示系统在倍周期分岔中会出现缺边现象,在双参数空间系统出现复杂的分岔结构,两个控制参数对系统动力学行为的影响特性有所差别. 关键词： 耦合发电机系统 分岔 周期窗口 双参数特性     

3DSEM++: Adaptive and intelligent 3D SEM surface reconstruction

Structural analysis of microscopic objects is a longstanding topic in several scientific disciplines, such as biological, mechanical, and materials sciences. The scanning electron microscope (SEM), as a promising imaging equipment has been around for decades to determine the surface properties (e.g., compositions or geometries) of specimens by achieving increased magnification, contrast, and resolution greater than one nanometer. Whereas SEM micrographs still remain two-dimensional (2D), many research and educational questions truly require knowledge and facts about their three-dimensional (3D) structures. 3D surface reconstruction from SEM images leads to remarkable understanding of microscopic surfaces, allowing informative and qualitative visualization of the samples being investigated. In this contribution, we integrate several computational technologies including machine learning, contrario methodology, and epipolar geometry to design and develop a novel and efficient method called 3DSEM++ for multi-view 3D SEM surface reconstruction in an adaptive and intelligent fashion. The experiments which have been performed on real and synthetic data assert the approach is able to reach a significant precision to both SEM extrinsic calibration and its 3D surface modeling.     

一类可变禁区的不连续系统的加周期分岔

研究了一类可变禁区不连续系统的加周期分岔行为, 发现由可变禁区导致不同类型的加周期分岔. 研究表明, 系统的迭代轨道和禁区的上下两个边界均可发生边界碰撞, 从而产生加周期分岔. 基于边界碰撞分岔理论, 定义基本的迭代单元, 解析推导出了相应的分岔曲线, 在全参数空间中给出了不同加周期所出现的范围. 与数值模拟结果比较, 理论分析结果与数值结果高度一致.     

Optimising image quality in 2D and 3D confocal Raman mapping

This article compares the quality of Raman images obtained using metallurgical and oil immersion objectives to map complex structures in two and three dimensions. While the performance of these objectives for depth profiling planar structures has been discussed at length in the literature, the same comparison has not yet been made for 3D mapping of complex objects, where additional complications are introduced by non‐planar geometries. Studying samples with increasing complexity shows that the oil immersion objective is strongly preferred because it yields brighter images with better contrast, and eliminates some new and confusing artefacts that do not arise with simple planar objects. Copyright © 2013 John Wiley & Sons, Ltd.     

Boundary intersection crossing bifurcation in the presence of sliding

Piecewise smooth systems are known to present a richer set of bifurcations than their smooth counterparts. An interesting family of bifurcations that is present in this type of systems are the so called boundary intersection crossing bifurcations, that take place when a periodic orbit crosses the intersection between two or more discontinuity boundaries. Such bifurcations have been observed in many different models, and have been studied in a number of papers over the past few years. Nonetheless, the particular case in which sliding solutions (as defined by Filippov) are involved, has been left out in previous analyses. This paper addresses this particular case, carrying out a complete analysis and deriving the discontinuity mappings that can be used to characterise such bifurcations. Then, in the second part of the paper, the results are applied to the study of a model of a common electronic device, showing how the mappings can be used systematically to determine the dynamics around the bifurcation.     

Development of a portable 3D ultrasound imaging system for musculoskeletal tissues

3D ultrasound is a promising imaging modality for clinical diagnosis and treatment monitoring. Its cost is relatively low in comparison with CT and MRI, no intensive training and radiation protection is required for its operation, and its hardware is movable and can potentially be portable. In this study, we developed a portable freehand 3D ultrasound imaging system for the assessment of musculoskeletal body parts. A portable ultrasound scanner was used to obtain real-time B-mode ultrasound images of musculoskeletal tissues and an electromagnetic spatial sensor was fixed on the ultrasound probe to acquire the position and orientation of the images. The images were digitized with a video digitization device and displayed with its orientation and position synchronized in real-time with the data obtained by the spatial sensor. A program was developed for volume reconstruction, visualization, segmentation and measurement using Visual C++ and Visualization toolkits (VTK) software. A 2D Gaussian filter and a Median filter were implemented to improve the quality of the B-scan images collected by the portable ultrasound scanner. An improved distance-weighted grid-mapping algorithm was proposed for volume reconstruction. Temporal calibrations were conducted to correct the delay between the collections of images and spatial data. Spatial calibrations were performed using a cross-wire phantom. The system accuracy was validated by one cylinder and two cuboid phantoms made of silicone. The average errors for distance measurement in three orthogonal directions in comparison with micrometer measurement were 0.06 ± 0.39, −0.27 ± 0.27, and 0.33 ± 0.39 mm, respectively. The average error for volume measurement was −0.18% ± 5.44% for the three phantoms. The system has been successfully used to obtain the volume images of a fetus phantom, the fingers and forearms of human subjects. For a typical volume with 126 × 103 × 109 voxels, the 3D image could be reconstructed from 258 B-scans (640 × 480 pixels) within one minute using a portable PC with Pentium IV 2.4 GHz CPU and 512 MB memories. It is believed that such a portable volume imaging system will have many applications in the assessment of musculoskeletal tissues because of its easy accessibility.