Recent Milestones in Unraveling the Full-Field Structure of Dynamic Shear Cracks and Fault Ruptures in Real-Time: From Photoelasticity to Ultrahigh-Speed Digital Image Correlation

The last few decades have seen great achievements in dynamic fracture mechanics. Yet, it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here, we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key ques- tions of rupture dynamics. Recent milestones include the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, capturing the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the big- gest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simul- taneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on the slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with “supersonic” propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate

Space-Time Transfinite Interpolation of Volumetric Material Properties

The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures

Modeling Interface Motion Of Combustion (MINOC). A computer code for two-dimensional, unsteady turbulent combustion

A computer code for calculating the flow field and flame propagation in a turbulent combustion tunnel is described. The model used in the analysis is the random vortex model, which allows the turbulent field to evolve as a fundamental solution to the Navier-Stokes equations without averaging or closure modeling. The program was used to study the flow field in a model combustor, formed by a rearward-facing step in a channel, in terms of the vorticity field, the turbulent shear stresses, the flame contours, and the concentration field. Results for the vorticity field reveal the formation of large-scale eddy structures in the turbulent flow downstream from the step. The concentration field contours indicate that most burning occurred around the outer edges of the large eddies of the shear layer

Smooth representation of thin shells and volume structures for isogeometric analysis

The purpose of this study is to develop self-contained methods for obtaining smooth meshes which are compatible with isogeometric analysis (IGA). The study contains three main parts. We start by developing a better understanding of shapes and splines through the study of an image-related problem. Then we proceed towards obtaining smooth volumetric meshes of the given voxel-based images. Finally, we treat the smoothness issue on the multi-patch domains with C1 coupling. Following are the highlights of each part. First, we present a B-spline convolution method for boundary representation of voxel-based images. We adopt the filtering technique to compute the B-spline coefficients and gradients of the images effectively. We then implement the B-spline convolution for developing a non-rigid images registration method. The proposed method is in some sense of “isoparametric”, for which all the computation is done within the B-splines framework. Particularly, updating the images by using B-spline composition promote smooth transformation map between the images. We show the possible medical applications of our method by applying it for registration of brain images. Secondly, we develop a self-contained volumetric parametrization method based on the B-splines boundary representation. We aim to convert a given voxel-based data to a matching C1 representation with hierarchical cubic splines. The concept of the osculating circle is employed to enhance the geometric approximation, where it is done by a single template and linear transformations (scaling, translations, and rotations) without the need for solving an optimization problem. Moreover, we use the Laplacian smoothing and refinement techniques to avoid irregular meshes and to improve mesh quality. We show with several examples that the method is capable of handling complex 2D and 3D configurations. In particular, we parametrize the 3D Stanford bunny which contains irregular shapes and voids. Finally, we propose the B´ezier ordinates approach and splines approach for C1 coupling. In the first approach, the new basis functions are defined in terms of the B´ezier Bernstein polynomials. For the second approach, the new basis is defined as a linear combination of C0 basis functions. The methods are not limited to planar or bilinear mappings. They allow the modeling of solutions to fourth order partial differential equations (PDEs) on complex geometric domains, provided that the given patches are G1 continuous. Both methods have their advantages. In particular, the B´ezier approach offer more degree of freedoms, while the spline approach is more computationally efficient. In addition, we proposed partial degree elevation to overcome the C1-locking issue caused by the over constraining of the solution space. We demonstrate the potential of the resulting C1 basis functions for application in IGA which involve fourth order PDEs such as those appearing in Kirchhoff-Love shell models, Cahn-Hilliard phase field application, and biharmonic problems

Cardiac Motion Analysis Based on Optical Flow on Real-Time Three-Dimensional Ultrasound Data

With relatively high frame rates and the ability to acquire volume data sets with a stationary transducer, 3D ultrasound systems, based on matrix phased array transducers, provide valuable three-dimensional information, from which quantitative measures of cardiac function can be extracted. Such analyses require segmentation and visual tracking of the left ventricular endocardial border. Due to the large size of the volumetric data sets, manual tracing of the endocardial border is tedious and impractical for clinical applications. Therefore the development of automatic methods for tracking three-dimensional endocardial motion is essential. In this study, we evaluate a four-dimensional optical flow motion tracking algorithm to determine its capability to follow the endocardial border in three dimensional ultrasound data through time. The four-dimensional optical flow method was implemented using three-dimensional correlation. We tested the algorithm on an experimental open-chest dog data set and a clinical data set acquired with a Philips' iE33 three-dimensional ultrasound machine. Initialized with left ventricular endocardial data points obtained from manual tracing at end-diastole, the algorithm automatically tracked these points frame by frame through the whole cardiac cycle. Finite element surfaces were fitted through the data points obtained by both optical flow tracking and manual tracing by an experienced observer for quantitative comparison of the results. Parameterization of the finite element surfaces was performed and maps displaying relative differences between the manual and semi-automatic methods were compared. The results showed good consistency with less than 10% difference between manual tracing and optical flow estimation on 73% of the entire surface. In addition, the optical flow motion tracking algorithm greatly reduced processing time (about 94% reduction compared to human involvement per cardiac cycle) for analyzing cardiac function in three-dimensional ultrasound data sets. A displacement field was computed from the optical flow output, and a framework for computation of dynamic cardiac information is introduced. The method was applied to a clinical data set from a heart transplant patient and dynamic measurements agreed with known physiology as well as experimental results

4D-CT Lung Registration and its Application for Lung Radiation Therapy

Radiation therapy has been successful in treating lung cancer patients, but its efficacy is limited by the inability to account for the respiratory motion during treatment planning and radiation dose delivery. Physics-based lung deformation models facilitate the motion computation of both tumor and local lung tissue during radiation therapy. In this dissertation, a novel method is discussed to accurately register 3D lungs across the respiratory phases from 4D-CT datasets, which facilitates the estimation of the volumetric lung deformation models. This method uses multi-level and multi-resolution optical flow registration coupled with thin plate splines (TPS), to address registration issue of inconsistent intensity across respiratory phases. It achieves higher accuracy as compared to multi-resolution optical flow registration and other commonly used registration methods. Results of validation show that the lung registration is computed with 3 mm Target Registration Error (TRE) and approximately 3 mm Inverse Consistency Error (ICE). This registration method is further implemented in GPU based real time dose delivery simulation to assist radiation therapy planning

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft