Vector Flow Field Research Articles

Swirling Flow Quantification in Helical Stents Using Ultrasound Velocimetry.

Helical stents have been developed to treat peripheral arterial disease (PAD) in the superficial femoral artery (SFA), with the premise that their particular geometry could promote swirling flow in the blood. The aim of this work is to provide evidence on the existence of this swirling flow by quantifying its signatures. This study consists of in vitro and in vivo parts. For the in vitro part, 3 helical stent models of different helicity degrees and 1 straight model were fabricated, and the flow was assessed at the inlet and outlet of each model. For the in vivo part, only 1 patient, treated with the helical stent, was eligible to participate in the study. The stent implanted in the SFA of the patient was evaluated in 2 leg postures (straight and flexed), and flow was assessed in 12 locations along the SFA. The in vivo study was approved by an ethical board (NL80130.091.21) in the Netherlands. High-frame-rate ultrasound was used to acquire data from the regions of interest (ROIs), using microbubbles as contrast agents. After processing the data via a correlation-based algorithm (echo particle image velocimetry or echoPIV), the velocity vector field within each ROI was extracted and analyzed for parameters such as vector complexity and velocity profile skewedness. The results show that in the outlet of the helical stents, when compared with the inlet, the flow vector field is more complex and the velocity profile is more skewed. For the in vivo case, the outcomes demonstrate more complexity and higher variability in the sign of skewedness inside the stent when compared with the flow in the proximal to the stent. Helical stents make the vector field of the flow more complex and the velocity profile more skewed, both of which are signatures of swirling flow. Further studies are needed to evaluate whether these features can benefit patients in terms of patency rates. This study demonstrates that helical stent models alter the blood flow when compared with straight stent models. Particularly, the flow grows more complex and its velocity profile becomes more skewed, both of which hint at the existence of swirling flow inside the helical stent. These observations, alongside with population-based studies that are currently being carriet out, may provide the evidence that helical stents have some advantages over straight stents for the patients.

Analysis and prediction of mesoscale eddy kinetic energy variations in the Kuroshio extension

The Kuroshio Extension (KE) region, a crucial area in the Northwest Pacific Ocean, exhibits eddy kinetic energy with various scales of periodicity. Understanding how to extract its characteristic features and analyze and predict their periodic correlations has become vital for studying the regulatory mechanisms of eddy kinetic energy in the KE region. This paper first introduces a mesoscale eddy hybrid identification algorithm based on the flow field vector and the closed flow field. Using this algorithm, we gather mesoscale eddy identification data from the KE region to extract the monthly average series of five typical features of the KE region. Subsequently, wavelet theory is applied to analyze the cycles of these main features, identifying the common cycles of the KE region as the primary focus for analyzing the vorticity kinetic energy. This analysis includes cycle correlations with globally recognized indices, and it predicts these correlations. Further analysis of the main characteristic cycles through wavelet theory reveals that the KE region's eddy kinetic energy is significantly influenced by solar activity over long periods and by the North Pacific ocean-atmosphere interaction over shorter, interannual periods. Finally, this paper introduces a W-LSTM (Wavelet Decomposition based Long Short-term Memory Networks) prediction model based on wavelet decomposition for the KE region, covering January 2023–December 2023. The model demonstrates its effectiveness, achieving a Root Mean Square Error (RMSE) of 0.2530 and a correlation coefficient of 0.8259 between the predicted data and the actual observations.

Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice

The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable vector fields on this surface are linear. Finally, using the formal Laurent solutions of the system, we provide a detailed geometric description of these abelian surfaces and the divisor at infinity.

Local Path Planning of Unmanned Surface Vehicles’ Formation Based on Vector Field and Flow Field Traction

Local Path Planning of Unmanned Surface Vehicles’ Formation Based on Vector Field and Flow Field Traction

A parametric investigation of Dual-throat nozzle bypass channel configurations for advanced Aviation applications

The Bypass Dual-Throat Nozzle (BDTN) has garnered growing attention due to its remarkable thrust vectoring capabilities. This type of nozzle boasts broad application prospects as it achieves deflection control of the jet stream merely through regulating the opening and closing of bypass channels. Our comprehensive study delves deeply into the intricate parameterization of the bypass channel within the BDTN. Research has demonstrated that utilizing Fluent software in conjunction with the Realizable k-epsilon turbulence model, standard wall functions, and the Sutherland formula for viscosity coefficient approximation can yield a relatively accurate representation of the vector flow field structure within the BDTN. Following the validation of the numerical computation methodology employed in this study, we have investigated the influence of factors such as bypass channel radius, precise valve positioning, and actuation direction on the nozzle's vectoring performance. Key findings indicate that, due to the relatively small proportion of secondary flow, the radius of the bypass channel has minimal impact on the thrust vector angle. The positioning of the valve and its opening direction are critical in determining the thrust vector angle, requiring careful consideration during the design and optimization process. Fully opening the bypass channel does not necessarily yield the maximum thrust vector angle. Moreover, the total pressure, velocity, position, and direction of the secondary flow within the bypass channel exert a more profound influence on the nozzle's vector performance compared to the mere presence of the secondary flow itself. Notably, the forward opening method of the valve emerges as the preferred choice, as it facilitates more precise later vector control.

KF-PEV: a causal Kalman filter-based particle event velocimetry

Event-based pixel sensors asynchronously report changes in log-intensity in microsecond-order resolution. Its exceptional speed, cost effectiveness, and sparse event stream make it an attractive imaging modality for particle tracking velocimetry. In this work, we propose a causal Kalman filter-based particle event velocimetry (KF-PEV). Using the Kalman filter model to track the events generated by the particles seeded in the flow medium, KF-PEV yields the linear least squares estimate of the particle track velocities corresponding to the flow vector field. KF-PEV processes events in a computationally efficient and streaming manner (i.e., causal and iteratively updating). Our simulation-based benchmarking study with synthetic particle event data confirms that the proposed KF-PEV outperforms the conventional frame-based particle image/tracking velocimetry as well as the state-of-the-art event-based particle velocimetry methods. In a real-world water tunnel event-based sensor data experiment performed on what we believe to be the widest field view ever reported, KF-PEV accurately predicted the expected flow field of the SD7003 wing, including details such as the lower velocity in the wake and the flow separation around the underside of an angled wing.

Relating ciliary propulsion morphology and flow to particle acquisition in marine planktonic ciliates I: the tintinnid ciliateAmphorides quadrilineata

AbstractThe marine tintinnid ciliate Amphorides quadrilineata is a feeding-current feeder, creating flows for particle encounter, capture and rejection. Individual-level behaviors were observed using high-speed, high-magnification digital imaging. Cells beat their cilia backward to swim forward, simultaneously generating a feeding current that brings in particles. These particles are then individually captured through localized ciliary reversals. When swimming backward, cells beat their cilia forward (=ciliary reversals involving the entire ring of cilia), actively rejecting unwanted particles. Cells achieve path-averaged speeds averaging 3–4 total lengths per second. Both micro-particle image velocimetry and computational fluid dynamics were employed to characterize the cell-scale flows. Forward swimming generates a feeding current, a saddle flow vector field in front of the cell, whereas backward swimming creates an inverse saddle flow vector field behind the cell; these ciliary flows facilitate particle encounter, capture and rejection. The model-tintinnid with a full-length lorica achieves an encounter rate Q ~29% higher than that without a lorica, albeit at a ~142% increase in mechanical power and a decrease in quasi-propulsive efficiency (~0.24 vs. ~ 0.38). It is also suggested that Q can be approximated by π(W/2 + l)2U, where W, l and U represent the lorica oral diameter, ciliary length and swimming speed, respectively.

Hemodynamic factors of spontaneous vertebral artery dissecting aneurysms assessed with numerical and deep learning algorithms: Role of blood pressure and asymmetry

Background and ObjectivesThe pathophysiology of spontaneous vertebral artery dissecting aneurysms (SVADA) is poorly understood. Our goal is to investigate the hemodynamic factors contributing to their formation using computational fluid dynamics (CFD) and deep learning algorithms. MethodsWe have developed software that can use patient imagery as input to recreate the vertebrobasilar arterial system, both with and without SVADA, which we used in a series of three patients. To obtain the kinematic blood flow data before and after the aneurysm forms, we utilized numerical methods to solve the complex Navier-Stokes partial differential equations. This was accomplished through the application of a finite volume solver (OpenFoam/Helyx OS). Additionally, we trained a neural ordinary differential equation (NODE) to learn and replicate the dynamical streamlines obtained from the computational fluid dynamics (CFD) simulations. ResultsIn all three cases, we observed that the equilibrium of blood pressure distributions across the VAs, at a specific vertical level, accurately predicted the future SVADA location. In the two cases where there was a dominant VA, the dissection occurred on the dominant artery where blood pressure was lower compared to the contralateral side. The SVADA sac was characterized by reduced wall shear stress (WSS) and decreased velocity magnitude related to increased turbulence. The presence of a high WSS gradient at the boundary of the SVADA may explain its extension. Streamlines generated by CFD were learned with a neural ordinary differential equation (NODE) capable of capturing the system’s dynamics to output meaningful predictions of the flow vector field upon aneurysm formation. ConclusionIn our series, asymmetry in the vertebrobasilar blood pressure distributions at and proximal to the site of the future SVADA accurately predicted its location in all patients. Deep learning algorithms can be trained to model blood flow patterns within biological systems, offering an alternative to the computationally intensive CFD. This technology has the potential to find practical applications in clinical settings.

On the regularity of the flow of analytic vector fields

The flow of vector field X is the solution to the system of linear partial differential equations ∂_t u(t,z)=X(u(t,z)) with initial condition u(0,z)=z. It is known that for an analytic vector field, its flow is given by a convergent Lie series. Recently, Carillo gave a quick and elementary proof of this fact by introducing a special family of norms. This paper gives an even more concise proof by directly estimating the formal series expansion and using a family of majorant functions studied by Lax.

Study of fluidized bed freeboard for effect of Geldart A particles shape using particle image velocimetry (PIV)

A study was carried out using Particle Image Velocimetry (PIV) to reveal velocity vector flow fields in the freeboard region of a Geldart A fluidized bed. For the first time the effect of particle shape, was studied for three powder types, namely China clay (platelet-like), Diatomite (spherical) and Quartz (irregular). A bench-scale fluidized bed set-up of perspex glass was used for direct PIV imagining over a substantial inlet gas velocity range. Interestingly the freeboard was not found to be highly turbulent as has been reported in the case of Geldart B particles. Rather a transition regime was observed which was dominated by laminar streamlines and punctuated by short-lived eddies with life span even less than 400 μs. Bed expansion was significantly affected by particle shape. This was explained by an ‘effective cluster size’ hypothesis for the three powder types. The ‘uniformity’ of the velocity field was also quantified for each powder.

Extracting the gradient component of the gamma index using the Lie derivative method

Objective. The gamma index (γ) has been extensively investigated in the medical physics and applied in clinical practice. However, γ has a significant limitation when used to evaluate the dose-gradient region, leading to inconveniences, particularly in stereotactic radiotherapy (SRT). This study proposes a novel evaluation method combined with γ to extract clinically problematic dose-gradient regions caused by irradiation including certain errors. Approach. A flow-vector field in the dose distribution is obtained when the dose is considered a scalar potential. Using the Lie derivative from differential geometry, we defined L, S, and U to evaluate the intensity, vorticity, and flow amount of deviation between two dose distributions, respectively. These metrics multiplied by γ (γL, γS, γU), along with the threshold value σ, were verified in the ideal SRT case and in a clinical case of irradiation near the brainstem region using radiochromic films. Moreover, Moran’s gradient index (MGI), Bakai’s χ factor, and the structural similarity index (SSIM) were investigated for comparisons. Main results. A high L-metric value mainly extracted high-dose-gradient induced deviations, which was supported by high S and U metrics observed as a robust deviation and an influence of the dose-gradient, respectively. The S-metric also denotes the measured similarity between the compared dose distributions. In the γ distribution, γL sensitively detected the dose-gradient region in the film measurement, despite the presence of noise. The threshold σ successfully extracted the gradient-error region where γ > 1 analysis underestimated, and σ = 0.1 (plan) and σ = 0.001 (film measurement) were obtained according to the compared resolutions. However, the MGI, χ, and SSIM failed to detect the clinically interested region. Significance. Although further studies are required to clarify the error details, this study demonstrated that the Lie derivative method provided a novel perspective for the identifying gradient-induced error regions and enabled enhanced and clinically significant evaluations of γ.

Developing and testing a web-based platform for visualizing flow in a watershed

Abstract Thanks to the rapid development of internet technology and computer hardware, it is now possible to use web services to provide visual simulations of flow field calculation results. Visualization technology can display complex water flow data and the laws that govern water flow through graphical means, and can be used to solve scientific and engineering problems related to water conservancy. In this study, we developed a platform for visualizing flow in a watershed based on a Cesium rendering framework with Browser/Server (B/S) architecture that used isosurface, particles, texture-based, and dynamic flow visualization techniques to visualize scalar field, vector field, and dynamic flow field data. Furthermore, our performance test results indicate that the rendering performance meets the practical application requirements for visualizing large-scale flow fields by employing frame interpolation and viewpoint-based dynamic rendering techniques. The results from testing the water flow visualization platform in the Beijiang River Basin, Guangdong Province, China, demonstrated that the platform performed well on different devices and that the running frame rate reached 50–60 fps. These findings can be used to guide further development and applications of web-side flow field visualization technology.

Wave propagation in periodic nano structures through second strain gradient elasticity

The study of wave propagation in the periodic nano-waveguides is of importance to advance the development of energy and wave controlling systems. In this paper, firstly, the element discretization of nano structures is introduced based on the second strain gradient theory. The displacement field is determined through the utilization of six quintic Hermite polynomial interpolating functions. By applying Hamilton’s principle, the weak form, which incorporates the element matrices, is determined and the global dynamic stiffness matrix of a unit cell is assembled. Then, the wave finite element method, based on the inverse form, direct form and contour integral solution, is used to analyze the two-dimensional free wave propagation properties of complex nano structures by solving the eigenvalue problems. The interpretation of the frequency spectrum is confined to the irreducible first Brillouin zone, encompassing both the dispersion relation and band structure. Furthermore, the slowness surfaces and energy flow vector fields are discussed via the second strain gradient theory. The novel work, which utilizes the second strain gradient theory equipped with the wave finite element method to investigate two-dimensional complex nano structures, has revealed significant potential in elucidating the two-dimensional wave propagation characteristics of the complex nano-waveguides.

Classical flows of vector fields with exponential or sub-exponential summability

We show that vector fields b whose spatial derivative Dxb satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin (N) condition in a quantitative form, too. Furthermore, we prove that if Dxb satisfies a suitable exponential summability condition then the flow associated to b has Sobolev regularity, without assuming boundedness of divxb. We then apply these results to the representation and Sobolev regularity of weak solutions of the Cauchy problem for the transport and continuity equations.

Comparison of the Measurement Results of PIV with Different Tracer

Particle Image Velocimetry (PIV) was used to measure the solenoidal vector field of the Taylor-Couette flow with different tracers. It can be seen that both of them, the polyamide and flocs can be a suitable performance tracer particles for PIV in flow field measurement. The results indicated that the instantaneous velocity vector maps obtained with different tracer particles which could denote the characteristics of the flow structure, the size and the vortex centers of the vortex. At the meantime, the experimental results demonstrated that the velocity vector obtained by the flocs generated in real-time as tracer particles was similar with suitable performance to those obtained by polyamide.

Indoor and outdoor in-flight odometry based solely on optic flows with oscillatory trajectories

Estimating distance traveled is a frequently arising problem in robotic applications designed for use in environments where GPS is only intermittently or not at all available. In UAVs, the presence of weight and computational power constraints makes it necessary to develop odometric strategies based on minimilastic equipment. In this study, a hexarotor was made to perform up-and-down oscillatory movements while flying forward in order to test a self-scaled optic flow based odometer. The resulting self-oscillatory trajectory generated series of contractions and expansions in the optic flow vector field, from which the flight height of the hexarotor could be estimated using an Extended Kalman Filter. For the odometry, the downward translational optic flow was scaled by this current visually estimated flight height before being mathematically integrated to obtain the distance traveled. Here we present three strategies based on sensor fusion requiring no, precise or rough prior knowledge of the optic flow variations generated by the sinusoidal trajectory. The “rough prior knowledge” strategy is based on the shape and timing of the variations in the optic flow. Tests were performed first in a flight arena, where the hexarotor followed a circular trajectory while oscillating up and down over a distance of about [Formula: see text] m under illuminances of [Formula: see text] lux and [Formula: see text] lux. Preliminary field tests were then performed, in which the hexarotor followed a longitudinal bouncing [Formula: see text]-long trajectory over an irregular pattern of grass.

Medical Image Segmentation with active contour and optimization Techniques: Survey

The principal aim is to improve medical diagnosis through segmented images. Thus, medical image segmentation become one of the key technologies in computer-aided diagnosis. Active contours, or snakes, have been widely used for image segmentation purposes. However, high noise sensitivity and poor performance over weak edges are the most acute issues that hinder the segmentation accuracy of these curves, particularly in medical images. To overcome these issues, a novel external force that integrates gradient vector flow (GVF) field forces and the traditional snake function is proposed in this research. In addition, a novel technique is applied to limit the boundary of the initial contour by set four initial points around the medical issue and then connecting them by polynomial curves. Moreover, the positive effect of Particle Swarm Optimization (PSO) on calculating the final active contour area and its percentage to the entire image area is proved in this work.

Time-Resolved Wall Shear Rate Mapping Using High-Frame-Rate Ultrasound Imaging.

In atherosclerosis, low wall shear stress (WSS) is known to favor plaque development, while high WSS increases plaque rupture risk. To improve plaque diagnostics, WSS monitoring is crucial. Here, we propose wall shear imaging (WASHI), a noninvasive contrast-free framework that leverages high-frame-rate ultrasound (HiFRUS) to map the wall shear rate (WSR) that relates to WSS by the blood viscosity coefficient. Our method measures WSR as the tangential flow velocity gradient along the arterial wall from the flow vector field derived using a multi-angle vector Doppler technique. To improve the WSR estimation performance, WASHI semiautomatically tracks the wall position throughout the cardiac cycle. WASHI was first evaluated with an in vitro linear WSR gradient model; the estimated WSR was consistent with theoretical values (an average error of 4.6% ± 12.4 %). The framework was then tested on healthy and diseased carotid bifurcation models. In both scenarios, key spatiotemporal dynamics of WSR were noted: 1) oscillating shear patterns were present in the carotid bulb and downstream to the internal carotid artery (ICA) where retrograde flow occurs; and 2) high WSR was observed particularly in the diseased model where the measured WSR peaked at 810 [Formula: see text] due to flow jetting. We also showed that WASHI could consistently track arterial wall motion to map its WSR. Overall, WASHI enables high temporal resolution mapping of WSR that could facilitate investigations on causal effects between WSS and atherosclerosis.

Towards the 2D velocity reconstruction in abdominal aorta from Color-Doppler Ultrasound.

Magnetic resonance imaging (MRI) is the preferred modality to assess hemodynamics in healthy and diseased blood vessels. As an affordable and non-invasive alternative, Color-Doppler imaging is a good candidate. Nevertheless, Color-Doppler acquisitions provide only partial information on the blood velocity within the vessel. We present a framework to reconstruct 2D velocity fields in the aorta. We generated 2D Color-Doppler-like images from patient-specific Computational Fluid Dynamics (CFD) models of abdominal aortas and evaluated the framework's performance. The 2D velocity field reconstruction is based on the minimization of a cost function, in which the reconstructed velocities are constrained to satisfy fluid dynamics principles. The numerical evaluations show that the reconstructed vector flow fields agree with ground-truth velocities, with an average magnitude error of less than 4% and an average angular error of less than 2∘. We lastly illustrate the 2D velocity field reconstructed from in-vivo Color-Doppler data. Observing the hemodynamics in patients is expected to have a clinical impact in assessing disease development and progression, such as abdominal aortic aneurysms.

Regular Flow Field Sparse Processing and Blue Finance of Ocean City Research Based on GIS System

In order to explore the development path of blue finance in ocean cities, this paper combines GIS to conduct blue finance research in ocean cities, draws on the traditional direct visualization method of point icons, and uses arrow symbols to render vector flow field data. Moreover, this paper uses GIS means to perform statistical analysis on flow field data, studies the adaptive sparse algorithm of flow field data spatial structure based on GIS, and proposes a program implementation method for regular flow field sparse processing suitable for the general flow of the sparse algorithm. The experimental research shows that the GIS technology proposed in this paper can play an important role in the research of blue finance in ocean cities and has a certain role in promoting the development of ocean blue finance.