Robust and objective decomposition and mapping of bifurcating vessels

Computational modeling of human arteries has been broadly employed to investigate the relationships between geometry, hemodynamics and vascular disease. Recent developments in modeling techniques have made it possible to perform such analyses on realistic geometries acquired noninvasively and, thus, have opened up the possibility to extend the investigation to populations of subjects. However, for this to be feasible, novel methods for the comparison of the data obtained from large numbers of realistic models in the presence of anatomic variability must be developed. In this paper, we present an automatic technique for the objective comparison of distributions of geometric and hemodynamic quantities over the surface of bifurcating vessels. The method is based on centerlines and consists of robustly decomposing the surface into its constituent branches and mapping each branch onto a template parametric plane. The application of the technique to realistic data demonstrates how similar results are obtained over similar geometries, allowing for proper model-to-model comparison. Thanks to the computational and differential geometry criteria adopted, the method does not depend on user-defined parameters or user interaction, it is flexible with respect to the bifurcation geometry and it is readily extendible to more complex configurations of interconnecting vessels.     

Fast multiscale modeling of cardiac electrophysiology including Purkinje system

In this paper, we present a modeling methodology to couple the cardiac conduction system to cardiac myocytes through a model of Purkinje-ventricular junctions to yield fast and realistic electrical activation of the ventricles. A patient-specific biventricular geometry is obtained from processing computed tomography scan data. A one-manifold implementation of the fast marching method based on Eikonal-type equations is used for modeling heart electrophysiology, which facilitates the multiscale 1-D-3-D coupling at very low computational costs. The method is illustrated in in-silico experiments where we analyze and compare alternative pacing strategies on the same patient-specific anatomy. We also show very good agreement between the results from the proposed approach and more detailed and comprehensive biophysical models for modeling cardiac electrophysiology. The effect of atrioventricular delay on the distribution of activation time in myocardium is studied with two experiments. Given the reasonable computational times and realistic activation sequences provided by our method, it can have an important clinical impact on the selection of optimal implantation sites of pacing leads or placement of ablation catheter's tip in the context of cardiac rhythm management therapies.     

Cardiovascular modeling of congenital heart disease based on neonatal echocardiographic images

This paper proposes a 3-D cardiovascular modeling system based on neonatal echocardiographic images. With the system, medical doctors can interactively construct patient-specific cardiovascular models, and share the complex topology and the shape information. For the construction of cardiovascular models with a variety of congenital heart diseases, we propose a set of algorithms and interface that enable editing of the topology and shape of the 3-D models. In order to facilitate interactivity, the centerline and radius of the vessels are used to edit the surface of the heart vessels. This forms a skeleton where the centerlines of blood vessel serve as the nodes and edges, while the radius of the blood vessel is given as an attribute value to each node. Moreover, parent-child relationships are given to each skeleton. They are expressed as the directed acyclic graph, where the skeletons are viewed as graph nodes and the connecting points are graph edges. The cardiovascular models generated from some patient data confirmed that the developed technique is capable of constructing cardiovascular disease models in a tolerable timeframe. It is successful in representing the important structures of the patient-specific heart vessels for better understanding in preoperative planning and electric medical recording of the congenital heart disease.     

Computational Patient-Specific Models Based on 3-D Ultrasound Data to Quantify Uterine Arterial Flow During Pregnancy

Information on uterine blood flow rate during pregnancy would widely improve our knowledge on feto-placental patho-physiology. Ultrasonographic flow rate evaluation requires the knowledge of the spatial velocity profiles throughout the investigated vessel; these data may be obtained from hemodynamic simulations with accurate computational models. Recently, computational models of superficial vessels have been created using 3-D ultrasound data; unfortunately, common reconstruction methods are unsuitable for the uterine arteries due to the low quality achievable of imaged deep vessels. In this paper a simplified spline-based technique was applied to create computational models for patient-specific simulations of uterine arterial heamodynamics. Moreover, a novel method to quantify the uterine flow rates was developed based on echo-Doppler measurements and computational data. Preliminary results obtained for four patients indicated a quite narrow range for the blood flow rate through the main uterine artery with large variability in the flow split between corporal and cervical branches. Furthermore, parabolic-like velocity profiles were obtained in the branching region of the different patients, suggesting a clinical use of averaged, not patient-specific, spatial velocity distribution coefficients for the blood flow rate calculation. The developed reconstruction method based on 3-D ultrasound imaging is efficient for creating realistic custom models of the uterine arteries. The results of the fluid dynamic simulations allowed us to quantify the uterine arterial flow and its repartition in normal pregnancies.      

Knee surgery assistance: patient model construction, motion simulation, and biomechanical visualization

We present a new system that integrates computer graphics, physics-based modeling, and interactive visualization to assist knee study and surgical operation. First, we discuss generating patient-specific three-dimensional (3-D) knee models from patient's magnetic resonant images (MRIs). The 3-D model is obtained by deforming a reference model to match the MRI dataset. Second, we present simulating knee motion that visualizes patient-specific motion data on the patient-specific knee model. Third, we introduce visualizing biomechanical information on a patient-specific model. The focus is on visualizing contact area, contact forces, and menisci deformation. Traditional methods have difficulty in visualizing knee contact area without using invasive methods. The approach presented here provides an alternative of visualizing the knee contact area and forces without any risk to the patient. Finally, a virtual surgery can be performed. The constructed 3-D knee model is the basis of motion simulation, biomechanical visualization, and virtual surgery. Knee motion simulation determines the knee rotation angles as well as knee contact points. These parameters are used to solve the biomechanical model. Our results integrate 3-D construction, motion simulation, and biomechanical visualization into one system. Overall, the methodologies here are useful elements for future virtual medical systems where all the components of visualization, automated model generation, and surgery simulation come together.     

A Framework for Geometric Analysis of Vascular Structures: Application to Cerebral Aneurysms

There is well-documented evidence that vascular geometry has a major impact in blood flow dynamics and consequently in the development of vascular diseases, like atherosclerosis and cerebral aneurysmal disease. The study of vascular geometry and the identification of geometric features associated with a specific pathological condition can therefore shed light into the mechanisms involved in the pathogenesis and progression of the disease. Although the development of medical imaging technologies is providing increasing amounts of data on the three-dimensional morphology of the in vivo vasculature, robust and objective tools for quantitative analysis of vascular geometry are still lacking. In this paper, we present a framework for the geometric analysis of vascular structures, in particular for the quantification of the geometric relationships between the elements of a vascular network based on the definition of centerlines. The framework is founded upon solid computational geometry criteria, which confer robustness of the analysis with respect to the high variability of in vivo vascular geometry. The techniques presented are readily available as part of the VMTK, an open source framework for image segmentation, geometric characterization, mesh generation and computational hemodynamics specifically developed for the analysis of vascular structures. As part of the Aneurisk project, we present the application of the present framework to the characterization of the geometric relationships between cerebral aneurysms and their parent vasculature.      

Multiscale-patient-specific artery and atherogenesis models

In this work, we present a platform for the development of multiscale patient-specific artery and atherogenesis models. The platform, called ARTool, integrates technologies of 3-D image reconstruction from various image modalities, blood flow and biological models of mass transfer, plaque characterization, and plaque growth. Patient images are acquired for the development of the 3-D model of the patient specific arteries. Then, blood flow is modeled within the arterial models for the calculation of the wall shear stress distribution (WSS). WSS is combined with other patient-specific parameters for the development of the plaque progression models. Real-time simulation can be performed for same cases in grid environment. The platform is evaluated using both animal and human data.     

Quantifying 3-D vascular structures in MRA images using hybrid PDE and geometric deformable models

The aim of this paper is to present a hybrid approach to accurate quantification of vascular structures from magnetic resonance angiography (MRA) images using level set methods and deformable geometric models constructed with 3-D Delaunay triangulation. Multiple scale filtering based on the analysis of local intensity structure using the Hessian matrix is used to effectively enhance vessel structures with various diameters. The level set method is then applied to automatically segment vessels enhanced by the filtering with a speed function derived from enhanced MRA images. Since the goal of this paper is to obtain highly accurate vessel borders, suitable for use in fluid flow simulations, in a subsequent step, the vessel surface determined by the level set method is triangulated using 3-D Delaunay triangulation and the resulting surface is used as a parametric deformable model. Energy minimization is then performed within a variational setting with a first-order internal energy; the external energy is derived from 3-D image gradients. Using the proposed method, vessels are accurately segmented from MRA data.     

Efficient simulation of blood flow past complex endovascular devices using an adaptive embedding technique

The simulation of blood flow past endovascular devices such as coils and stents is a challenging problem due to the complex geometry of the devices. Traditional unstructured grid computational fluid dynamics relies on the generation of finite element grids that conform to the boundary of the computational domain. However, the generation of such grids for patient-specific modeling of cerebral aneurysm treatment with coils or stents is extremely difficult and time consuming. This paper describes the application of an adaptive grid embedding technique previously developed for complex fluid structure interaction problems to the simulation of endovascular devices. A hybrid approach is used: the vessel walls are treated with body conforming grids and the endovascular devices with an adaptive mesh embedding technique. This methodology fits naturally in the framework of image-based computational fluid dynamics and opens the door for exploration of different therapeutic options and personalization of endovascular procedures.     

Reconstruction and quantification of the carotid artery bifurcation from 3-D ultrasound images

Three-dimensional (3-D) ultrasound is a relatively new technique, which is well suited to imaging superficial blood vessels, and potentially provides a useful, noninvasive method for generating anatomically realistic 3-D models of the peripheral vasculature. Such models are essential for accurate simulation of blood flow using computational fluid dynamics (CFD), but may also be used to quantify atherosclerotic plaque more comprehensively than routine clinical methods. In this paper, we present a spline-based method for reconstructing the normal and diseased carotid artery bifurcation from images acquired using a freehand 3-D ultrasound system. The vessel wall (intima-media interface) and lumen surfaces are represented by a geometric model defined using smoothing splines. Using this coupled wall-lumen model, we demonstrate how plaque may be analyzed automatically to provide a comprehensive set of quantitative measures of size and shape, including established clinical measures, such as degree of (diameter) stenosis. The geometric accuracy of 3-D ultrasound reconstruction is assessed using pulsatile phantoms of the carotid bifurcation, and we conclude by demonstrating the in vivo application of the algorithms outlined to 3-D ultrasound scans from a series of patient carotid arteries.     

Urban object reconstruction using airborne laser elevation image and aerial image

Creating three-dimensional (3-D) models of real urban objects is an important goal in a wide variety of applications. This paper describes a method that utilizes airborne laser elevation images and aerial images for the 3-D reconstruction of urban objects. Our modeling approach uses the vertical geometric pattern analysis of elevation images. These patterns correspond to object contours and, thus, enable the extraction of the object. In addition, to provide realistic textured details, textures are cut from aerial images and mapped onto 3-D models. Our texture-mapping approach can avoid geometry mismatching and enable the automatic registration to determine the most reliable correspondence between projected outlines of 3-D models and contours of real objects shown in aerial images. Edge pairs, which are matched with projected outlines, are detected from aerial images. In order to minimize mismatching, we apply the voting technique based on the generalized Hough transform. Experimental results show that 3-D reconstruction of urban objects is generally successful.     

A closer look at reverberation Chambers - 3-D Simulation and experimental verification

This paper presents three-dimensional (3-D) full-wave simulations of the electromagnetic field inside a medium-sized reverberation chamber. A frequency-domain method-of-moments approach based on the electric field integral equation is used. A synopsis of the computational challenges particular for reverberation chambers is described and a detailed overview on the chamber modeling procedure is given. The electric field inside the chamber is computed and the influence of small geometric details and asymmetries is investigated as well as the effect of different excitations and stirrers. It is demonstrated that a statistics-based validation of reverberation chamber simulations is insufficient. To validate simulation results, therefore extensive near-field measurements inside the prototype reverberation chamber are performed. The complete 3-D reverberation chamber simulation, considering stirrers, door, and various practical excitations, accurately predicts the fields within the chamber in the important lower-to-medium frequency range and thus represents a reliable tool facilitating reverberation chamber optimization.     

Geodesic morphometry with applications to 3-D morpho-functional anatomy

The quantitative analysis of three-dimensional (3-D) shapes in terms of morphology and functionality is one of the most challenging problems in medical image analysis. This paper proposes a general methodology that aims at solving part of this problem. It introduces a nonparametric hierarchical partitioning approach that operates on any arbitrary 3-D shape described as a triangle mesh. It first extends the concept of basin districts to the case of curved spaces through a partitioning process on a valuation representing the main curvatures over a polyhedral support. A hierarchical construction of basin districts is obtained from a watershed transform. The speed of the front propagation on the polyhedral surface is controlled by the local characteristics of the surface geometry. As a prerequisite, a set of co-processing tools has been developed that operates directly on a triangulated domain. This includes classical signal processing tasks (e.g., re-sampling, filtering) on a polyhedral support performing a trade-off between accuracy and efficiency. The ability to provide an intrinsic shape partition from any triangular mesh is useful in a wide range of applications from accurate geometric modeling, and hierarchical shape dissection to robust mesh compression. Examples are presented in the paper to illustrate the principles and methodology.     

基于共形对应的球面图像的计算全息图

研究了基于共形对应的球面图像的计算全息图(CGH)的生成和重现.通常,当用平面波照射全息图时,所重现的图像一般显示在平面上.共形对应在计算机图形学中被广泛应用,它可以将平面图像和任意曲面对应.相对于简单的坐标变换,共形对应关系具有很多优点,如它可以保持变换前后图像之间的几何形状不变性等.将共形对应引入计算机全息图的生成过程中,利用平面与球面的共形对应关系,生成显示于球面的二维图像的计算全息图,并由所生成全息图得到原始图像,从而实现整个全息记录和重现过程的计算机模拟.二维图像重现于球面实际上了产生三维显示,因此上述方法在从计算全息图重现三维图像方面起到重要的作用.     

Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: technique and sensitivity

Hemodynamic factors are thought to be implicated in the progression and rupture of intracranial aneurysms. Current efforts aim to study the possible associations of hemodynamic characteristics such as complexity and stability of intra-aneurysmal flow patterns, size and location of the region of flow impingement with the clinical history of aneurysmal rupture. However, there are no reliable methods for measuring blood flow patterns in vivo. In this paper, an efficient methodology for patient-specific modeling and characterization of the hemodynamics in cerebral aneurysms from medical images is described. A sensitivity analysis of the hemodynamic characteristics with respect to variations of several variables over the expected physiologic range of conditions is also presented. This sensitivity analysis shows that although changes in the velocity fields can be observed, the characterization of the intra-aneurysmal flow patterns is not altered when the mean input flow, the flow division, the viscosity model, or mesh resolution are changed. It was also found that the variable that has the greater impact on the computed flow fields is the geometry of the vascular structures. We conclude that with the proposed modeling pipeline clinical studies involving large numbers cerebral aneurysms are feasible.     

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme     

Personalized tooth shape estimation from radiograph and cast

Three-dimensional geometric information of teeth is usually needed in pre- and postoperative diagnoses of orthodontic dentistry. The computerized tomography can provide comprehensive 3-D teeth geometries. However, there is still a discussion on computed tomography (CT) as a routine in orthodontic dentistry due to radiation dose. Moreover, the CT is useless when a dentist needs to extract 3-D structures from old archive files with only radiographs and casts, where patient's teeth changed ever since. In this paper, we propose a reconstruction framework for patient-specific teeth based on an integration of 2-D radiographs and digitized casts. The reconstruction is under a template-fitting framework. The shape and orientation of teeth templates are tuned in accordance with patient's radiographs. Specially, the tooth root morphology is controlled by 2-D contours in radiographs. With ray tracing and a contour plane assumption, 2-D root contours in radiographs are projected back to 3-D space, and guide tooth root deformations. Moreover, the template's crown is deformed nonrigidly to fit digitized casts that bear patient's crown details. The system allows 3-D tooth reconstruction with patient-specific geometric details from just casts and 2-D radiographs.     

Estimation of dynamically evolving ellipsoids with applications to medical imaging

The estimation of dynamically evolving ellipsoids from noisy lower-dimensional projections is examined. In particular, this work describes a model-based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left-ventricular ejection fraction from a gated set of planar myocardial perfusion images. The proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate. For this work, the left ventricle is modeled as a dynamically evolving three-dimensional (3-D) ellipsoid. The left-ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic, two-dimensional (2-D) ellipsoid, obtained as the projection of the former 3-D ellipsoid. This data is processed in two ways: first, as a 3-D dynamic ellipsoid reconstruction problem; second, each view is considered as a 2-D dynamic ellipse estimation problem and then the 3-D ejection fraction is obtained by combining the effective 2-D ejection fractions of each view. The approximating ellipsoids are reconstructed using a Rauch-Tung-Striebel smoothing filter, which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set; in contrast, traditional ejection fraction estimates are based only on true frames of data. Further, numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented, providing a rational basis for specifying system parameters. This investigation includes estimation of ejection fraction from both simulated and real data.     

Computational studies of transthoracic and transvenousdefibrillation in a detailed 3-D human thorax model

A method for constructing and solving detailed patient-specific 3D finite element models of the human thorax is presented for use in defibrillation studies. The method utilizes the patient's own X-ray CT scan and a simplified meshing scheme to quickly and efficiently generate a model typically composed of approximately 400,000 elements. A parameter sensitivity study on one human thorax model to examine the effects of variation in assigned tissue resistivity values, level of anatomical detail included in the model, and number of CT slices used to produce the model is presented. Of the seven tissue types examined, the average left ventricular (LV) myocardial voltage gradient was most sensitive to the values of myocardial and blood resistivity. Incorrectly simplifying the model, for example modeling the heart as a homogeneous structure by ignoring the blood in the chambers, caused the average LV myocardial voltage gradient to increase by 12%. The sensitivity of the model to variations in electrode size and position was also examined. Small changes (<2.0 cm) in electrode position caused average LV myocardial voltage gradient values to increase by up to 12%. It is concluded that patient-specific 3D finite element modeling of human thoracic electric fields is feasible and may reduce the empiric approach to insertion of implantable defibrillators and improve transthoracic defibrillation techniques     

A Parameterization-Based Numerical Method for Isotropic and Anisotropic Diffusion Smoothing on Non-Flat Surfaces

Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a $p$-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.