Lagrangian Visualization of Flow‐Embedded Surface Structures

The notions of Finite‐Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures provide a strong framework for the analysis and visualization of complex technical flows. Their definition is simple and intuitive, and they are built on a deep theoretical foundation. We apply these concepts to enable the analysis of flows in the immediate vicinity of the boundaries of flow‐embedded objects by limiting the Lagrangian analysis to surfaces closely neighboring these boundaries. To this purpose, we present an approach to approximate FTLE fields over such surfaces. Furthermore, we achieve an effective depiction of boundary‐related flow structures such as separation and attachment over object boundaries and specific insight into the surrounding flow using several specifically chosen visualization techniques. We document the applicability of our methods by presenting a number of application examples.     

Adaptive Surface Visualization of Vessels with Animated Blood Flow

The investigation of hemodynamic information for the assessment of cardiovascular diseases (CVDs) gained importance in recent years. Improved flow measuring modalities and computational fluid dynamics (CFD) simulations yield in reliable blood flow information. For a visual exploration of the flow information, domain experts are used to investigate the flow information combined with its enclosed vessel anatomy. Since the flow is spatially embedded in the surrounding vessel surface, occlusion problems have to be resolved. A visual reduction of the vessel surface that still provides important anatomical features is required. We accomplish this by applying an adaptive surface visualization inspired by the suggestive contour measure. Furthermore, an illustration is employed to highlight the animated pathlines and to emphasize nearby surface regions. Our approach combines several visualization techniques to improve the perception of surface shape and depth. Thereby, we ensure appropriate visibility of the embedded flow information, which can be depicted with established or advanced flow visualization techniques. We apply our approach to cerebral aneurysms and aortas with simulated and measured blood flow. An informal user feedback with nine domain experts, we confirm the advantages of our approach compared with existing methods, e.g. semi‐transparent surface rendering. Additionally, we assessed the applicability and usefulness of the pathline animation with highlighting nearby surface regions.     

Interactive computation and rendering of Finite-time Lyapunov Exponent fields

In this paper, we present a novel technique that allows for the coupled computation and visualization of salient flow structures at interactive frame rates. Our approach is built upon a hierarchical representation of the Finite-time Lyapunov Exponent (FTLE) field, which is adaptively sampled and rendered to meet the need of the current visual setting. The performance of our method allows the user to explore large and complex data sets across scales and to inspect their features at arbitrary resolution. The paper discusses an efficient implementation of this strategy on graphics hardware and provides results for an analytical flow and several CFD simulation data sets.     

Straightening tubular flow for side-by-side visualization

Flows through tubular structures are common in many fields, including blood flow in medicine and tubular fluid flows in engineering. The analysis of such flows is often done with a strong reference to the main flow direction along the tubular boundary. In this paper we present an approach for straightening the visualization of tubular flow. By aligning the main reference direction of the flow, i.e., the center line of the bounding tubular structure, with one axis of the screen, we are able to natively juxtapose (1.) different visualizations of the same flow, either utilizing different flow visualization techniques, or by varying parameters of a chosen approach such as the choice of seeding locations for integration-based flow visualization, (2.) the different time steps of a time-dependent flow, (3.) different projections around the center line , and (4.) quantitative flow visualizations in immediate spatial relation to the more qualitative classical flow visualization. We describe how to utilize this approach for an informative interactive visual analysis. We demonstrate the potential of our approach by visualizing two datasets from two different fields: an arterial blood flow measurement and a tubular gas flow simulation from the automotive industry.     

Comparative Blood Flow Visualization for Cerebral Aneurysm Treatment Assessment

A pathological vessel dilation in the brain, termed cerebral aneurysm, bears a high risk of rupture, and is associated with a high mortality. In recent years, incidental findings of unruptured aneurysms have become more frequent, mainly due to advances in medical imaging. The pathological condition is often treated with a stent that diverts the blood flow from the aneurysm sac back to the original vessel. Prior to treatment, neuroradiologists need to decide on the optimal stent configuration and judge the long‐term rupture risk, for which blood flow information is essential. Modern patient‐specific simulations can model the hemodynamics for various stent configurations, providing important indicators to support the decision‐making process. However, the necessary visual analysis of these data becomes tedious and time‐consuming, because of the abundance of information. We introduce a comprehensive comparative visualization that integrates morphology with blood flow indicators to facilitate treatment assessment. To deal with the visual complexity, we propose a details‐on‐demand approach, combining established medical visualization techniques with innovative glyphs inspired by information visualization concepts. In an evaluation we have obtained informal feedback from domain experts, gauging the value of our visualization.     

Visualization of fibrous and thread-like data

Thread-like structures are becoming more common in modern volumetric data sets as our ability to image vascular and neural tissue at higher resolutions improves. The thread-like structures of neurons and micro-vessels pose a unique problem in visualization since they tend to be densely packed in small volumes of tissue. This makes it difficult for an observer to interpret useful patterns from the data or trace individual fibers. In this paper we describe several methods for dealing with large amounts of thread-like data, such as data sets collected using Knife-Edge Scanning Microscopy (KESM) and Serial Block-Face Scanning Electron Microscopy (SBF-SEM). These methods allow us to collect volumetric data from embedded samples of whole-brain tissue. The neuronal and microvascular data that we acquire consists of thin, branching structures extending over very large regions. Traditional visualization schemes are not sufficient to make sense of the large, dense, complex structures encountered. In this paper, we address three methods to allow a user to explore a fiber network effectively. We describe interactive techniques for rendering large sets of neurons using self-orienting surfaces implemented on the GPU. We also present techniques for rendering fiber networks in a way that provides useful information about flow and orientation. Third, a global illumination framework is used to create high-quality visualizations that emphasize the underlying fiber structure. Implementation details, performance, and advantages and disadvantages of each approach are discussed.     

An Improved Eulerian Approach for the Finite Time Lyapunov Exponent

We propose a new Eulerian numerical approach to compute the Jacobian of flow maps in continuous dynamical systems and subsequently the so-called finite time Lyapunov exponent (FTLE) for Lagrangian coherent structure extraction. The original approach computes the flow map and then numerically determines the Jacobian of the map using finite differences. The new algorithm improves the original Eulerian formulation so that we first obtain partial differential equations for each component of the Jacobian and then solve these equations to obtain the required Jacobian. For periodic dynamical systems, based on the time doubling technique developed for computing the longtime flow map, we also propose a new efficient iterative method to compute the Jacobian of the longtime flow map. Numerical examples will demonstrate that our new proposed approach is more accurate than the original one in computing the Jacobian and thus the FTLE field, especially near the FTLE ridges.     

Flow-inspector: a framework for visualizing network flow data using current web technologies

New web technologies led to the development of browser applications for data analysis. Modern browser engines allow for building interactive real-time visualization applications that enable efficient ways to understand complex data. We present Flow-Inspector, a highly interactive open-source web framework for visualizing network flow data using latest web technologies. Flow-Inspector includes a backend for processing and storing large-scale network flow data, as well as a JavaScript-based web application capable to display and manipulate traffic information in real-time. This work provides operators with a toolkit to analyze their networks and enables the scientific community to create new and innovative visualizations of traffic data with an extensible framework. We demonstrate the applicability of our approach by implementing several different visualization components that help to identify topological characteristics in network flows.     

Lagrangian Coherent Structures with Guaranteed Material Separation

Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they converge to exact material structures. However, due to the finite integration time in FTLE, they are generally not exact material structures. In this paper we introduce a modification of the FTLE method which is guaranteed to produce separating material structures as features of a scalar field. We achieve this by incorporating the complete available integration time both in forward and backward direction, and by choosing an appropriate definition for separating structures. We apply our method to two test data sets and show the differences to classical FTLE.     

MCFTLE: Monte Carlo Rendering of Finite‐Time Lyapunov Exponent Fields

Traditionally, Lagrangian fields such as finite‐time Lyapunov exponents (FTLE) are precomputed on a discrete grid and are ray casted afterwards. This, however, introduces both grid discretization errors and sampling errors during ray marching. In this work, we apply a progressive, view‐dependent Monte Carlo‐based approach for the visualization of such Lagrangian fields in time‐dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high‐quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high‐quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real‐world numerical simulations.     

ChronoCorrelator: Enriching Events with Time Series

Event sequences and time series are widely recorded in many application domains; examples are stock market prices, electronic health records, server operation and performance logs. Common goals for recording are monitoring, root cause analysis and predictive analytics. Current analysis methods generally focus on the exploration of either event sequences or time series. However, deeper insights are gained by combining both. We present a visual analytics approach where users can explore both time series and event data simultaneously, combining visualization, automated methods and human interaction. We enable users to iteratively refine the visualization. Correlations between event sequences and time series can be found by means of an interactive algorithm, which also computes the presence of monotonic effects. We illustrate the effectiveness of our method by applying it to real world and synthetic data sets.     

Parallelized fusion visualization system

The speed-up of supercomputers has increased the complexity of simulations. To analyze such kind of data, we believe that new types of visualization software are needed. Therefore, we have been developing a visualization system called “Fusion Visualization”, and the progresses were reported in the AROB 18th and 19th International Symposiums. We introduced the overall concept at the AROB 18th International Symposium, and then demonstrated a sample of flow visualization in a blood vessel in the AROB 19th International Symposium. To extend our system to enable the handling of larger data, we have implemented the proposed system on a parallelized visualization system; AVS/Express PCE (Parallel Cluster Edition). This paper describes the implementation and the benchmark results.     

Visualizing Strain Anisotropy in Mantle Flow Fields

The evolution of strain and development of material anisotropy in models of the Earth’s mantle flow convey important information about how to interpret the geometric relationship between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time‐varying strain vector fields that build the foundation for a number of feature extraction and visualization techniques. The proposed field segmentation, clustering, histograms and multi‐volume visualization techniques facilitate an intuitive understanding of three‐dimensional strain in such flow fields, overcoming limitations of previous methods such as 2‐D line plots and slicing. We present applications of our approach to an artificial time varying flow data set and a real world example of stationary flow in a subduction zone and discuss the challenges of processing these geophysical data sets as well as the insights gained.     

GPU‐assisted real‐time coupling of blood flow and vessel wall

The vessel wall and the blood flow interact and influence each other, and real‐time coupling between them is of great importance to the virtual surgery as well as the research and diagnosis of vascular disease. On the basis of smoothed particle hydrodynamics (SPH), we present a new approach to solve non‐Newtonian viscous force of blood and a parallel mixed particles‐based coupling method for blood flow and vessel wall. Meanwhile, we also design a proxy particle‐based vessel wall force visualization method. Our method is as follows. Firstly, we solve the non‐Newtonian viscous forces of blood through the SPH method to discretize the Casson equation. Secondly, in each time step, we combine blood particles and sampling proxy particles on the blood vessel wall to form mixed particles and calculate the interaction forces through the SPH method between every pair of the neighboring mixed particles inside the graphics processing unit. Thirdly, the forces of the proxy particles will be mapped to the color display of the proxy particle. Experimental results demonstrate that our method is able to implement real‐time sizeable coupling of blood flow and vessel wall while mainly ensuring physical authenticity and it can also provide real‐time and obvious information about vessel wall force distribution. Copyright © 2015 John Wiley & Sons, Ltd.     

Supervised vessel delineation in retinal fundus images with the automatic selection of <Emphasis Type="Italic">B</Emphasis>-COSFIRE filters

The inspection of retinal fundus images allows medical doctors to diagnose various pathologies. Computer-aided diagnosis systems can be used to assist in this process. As a first step, such systems delineate the vessel tree from the background. We propose a method for the delineation of blood vessels in retinal images that is effective for vessels of different thickness. In the proposed method, we employ a set of B-COSFIRE filters selective for vessels and vessel-endings. Such a set is determined in an automatic selection process and can adapt to different applications. We compare the performance of different selection methods based upon machine learning and information theory. The results that we achieve by performing experiments on two public benchmark data sets, namely DRIVE and STARE, demonstrate the effectiveness of the proposed approach.     

Vortex visualization for practical engineering applications

In order to understand complex vortical flows in large data sets, we must be able to detect and visualize vortices in an automated fashion. In this paper, we present a feature-based vortex detection and visualization technique that is appropriate for large computational fluid dynamics data sets computed on unstructured meshes. In particular, we focus on the application of this technique to visualization of the flow over a serrated wing and the flow field around a spinning missile with dithering canards. We have developed a core line extraction technique based on the observation that vortex cores coincide with local extrema in certain scalar fields. We also have developed a novel technique to handle complex vortex topology that is based on k-means clustering. These techniques facilitate visualization of vortices in simulation data that may not be optimally resolved or sampled. Results are included that highlight the strengths and weaknesses of our approach. We conclude by describing how our approach can be improved to enhance robustness and expand its range of applicability.     

Pairwise ranking component analysis

Uncovering the latent structure of the data is an active research topic in data mining. However, in the distance metric learning framework, previous studies have mainly focused on the classification performance. In this work, we consider the distance metric learning problem in the ranking setting, where predicting the order between the data vectors is more important than predicting the class labels. We focus on two problems: improving the ranking prediction accuracy and identifying the latent structure of the data. The core of our model consists of ranking the data using a Mahalanobis distance function. The additional use of non-negativity constraints and an entropy-based cost function allows us to simultaneously minimize the ranking error while identifying useful meta-features. To demonstrate its usefulness for information retrieval applications, we compare the performance of our method with four other methods on four UCI data sets, three text data sets, and four image data sets. Our approach shows good ranking accuracies, especially when few training data are available. We also use our model to extract and interpret the latent structure of the data sets. In addition, our approach is simple to implement and computationally efficient and can be used for data embedding and visualization.     

Explorative Blood Flow Visualization using Dynamic Line Filtering based on Surface Features

Rupture risk assessment is a key to devise patient‐specific treatment plans of cerebral aneurysms. To understand and predict the development of aneurysms and other vascular diseases over time, both hemodynamic flow patterns and their effect on the vessel surface need to be analyzed. Flow structures close to the vessel wall often correlate directly with local changes in surface parameters, such as pressure or wall shear stress. Yet, in many existing applications, the analyses of flow and surface features are either somewhat detached from one another or only globally available. Especially for the identification of specific blood flow characteristics that cause local startling parameters on the vessel surface, like elevated pressure values, an interactive analysis tool is missing. The explorative visualization of flow data is challenging due to the complexity of the underlying data. In order to find meaningful structures in the entirety of the flow, the data has to be filtered based on the respective explorative aim. In this paper, we present a combination of visualization, filtering and interaction techniques for explorative analysis of blood flow with a focus on the relation of local surface parameters and underlying flow structures. Coherent bundles of pathlines can be interactively selected based on their relation to features of the vessel wall and further refined based on their own hemodynamic features. This allows the user to interactively select and explore flow structures locally affecting a certain region on the vessel wall and therefore to understand the cause and effect relationship between these entities. Additionally, multiple selected flow structures can be compared with respect to their quantitative parameters, such as flow speed. We confirmed the usefulness of our approach by conducting an informal interview with two expert neuroradiologists and an expert in flow simulation. In addition, we recorded several insights the neuroradiologists were able to gain with the help of our tool.     

面向血液循环系统仿真的全身血管重建

血管的点云数据表示在医疗中有着重要的作用,可以帮助医护人员直观地了解血管的几何信息.对于医疗辅助技术、放射学模拟等应用中,除了对局部的血管系统几何信息进行可视之外,也需要对全身血管进行准确的仿真建模,从而对整体血管系统的拓扑及几何信息都需要进行系统性的重建.传统骨架提取技术无法保证血管模型正确的连接拓扑,提出了一种基于点云数据的交互式全身血管模型重建方法,通过对血管数据分段和拟合,并分析各段血管端点连接情况,重建了一种带有血管截面半径信息的全身血管一维骨架模型,且该模型能直接用于血流血压等仿真.与已有方法相比,其优势在于能应用于大规模的复杂的全身血管点云数据,且重建的模型可以直接用于仿真.BodyParts3D数据集下实验结果表明,与已有方法相比,文中方法重建的全身血管一维骨架模型具有准确的拓扑连接,能够生成更好的仿真效果.     

Robust Cardiac Function Assessment in 4D PC‐MRI Data of the Aorta and Pulmonary Artery

Four‐dimensional phase‐contrast magnetic resonance imaging (4D PC‐MRI) allows the non‐invasive acquisition of time‐resolved, 3D blood flow information. Stroke volumes (SVs) and regurgitation fractions (RFs) are two of the main measures to assess the cardiac function and severity of valvular pathologies. The flow rates in forward and backward direction through a plane above the aortic or pulmonary valve are required for their quantification. Unfortunately, the calculations are highly sensitive towards the plane's angulation since orthogonally passing flow is considered. This often leads to physiologically implausible results. In this work, a robust quantification method is introduced to overcome this problem. Collaborating radiologists and cardiologists were carefully observed while estimating SVs and RFs in various healthy volunteer and patient 4D PC‐MRI data sets with conventional quantification methods, that is, using a single plane above the valve that is freely movable along the centerline. By default it is aligned perpendicular to the vessel's centerline, but free angulation (rotation) is possible. This facilitated the automation of their approach which, in turn, allows to derive statistical information about the plane angulation sensitivity. Moreover, the experts expect a continuous decrease of the blood flow volume along the vessel course. Conventional methods are often unable to produce this behaviour. Thus, we present a procedure to fit a monotonous function that ensures such physiologically plausible results. In addition, this technique was adapted for the usage in branching vessels such as the pulmonary artery. The performed informal evaluation shows the capability of our method to support diagnosis; a parameter evaluation confirms the robustness. Vortex flow was identified as one of the main causes for quantification uncertainties.