Detection and modelling of contacts in explicit finite-element simulation of soft tissue biomechanics

Realistic modelling of soft-tissue biomechanics and mechanical interactions between tissues is an important part of surgical simulation, and may become a valuable asset in surgical image-guidance. Unfortunately, it is also computationally very demanding. Explicit matrix-free FEM solvers have been shown to be a good choice for fast tissue simulation, however little work has been done on contact algorithms for such FEM solvers. This work introduces such an algorithm that is capable of handling the scenarios typically encountered in image-guidance. The responses are computed with an evolution of the Lagrange-multiplier method first used by Taylor and Flanagan in PRONTO 3D with spatio-temporal smoothing heuristics for improved stability with coarser meshes and larger time steps. For contact search, a bounding-volume hierarchy (BVH) capable of identifying self collisions, and which is optimised for the small time steps by reducing the number of bounding-volume refittings between iterations through identification of geometry areas with mostly rigid motion and negligible deformation, is introduced. Further optimisation is achieved by integrating the self-collision criterion in the BVH creation and updating algorithms. The effectiveness of the algorithm is demonstrated on a number of artificial test cases and meshes derived from medical image data

Robust, Efficient, and Accurate Contact Algorithms

Robust, efficient, and accurate contact response remains a challenging problem in the simulation of deformable materials. Contact models should robustly handle contact between geometry by preventing interpenetrations. This should be accomplished while respecting natural laws in order to maintain physical correctness. We simultaneously desire to achieve these criteria as efficiently as possible to minimize simulation runtimes. Many methods exist that partially achieve these properties, but none yet fully attain all three. This thesis investigates existing methodologies with respect to these attributes, and proposes a novel algorithm for the simulation of deformable materials that demonstrate them all. This new method is analyzed and optimized, paving the way for future work in this simplified but powerful manner of simulation

View space linking, solid node compression and binary space partitioning for visibility determination in 3D walk-throughs

Today\u27s 3D games consumers are expecting more and more quality in their games. To enable high quality graphics at interactive rates, games programmers employ a technique known as hidden surface removal (HSR) or polygon culling. HSR is not just applicable to games; it may also be applied to any application that requires quality and interactive rates, including medical, military and building applications. One such commonly used technique for HSR is the binary space partition (BSP) tree, which is used for 3D ‘walk-throughs’, otherwise known as 3D static environments or first person shooters. Recent developments in 3D accelerated hardware technology do not mean that HSR is becoming redundant; in fact, HSR is increasingly becoming more important to the graphics pipeline. The well established potentially visible sets (PSV) BSP tree algorithm is used as a platform for exploring three enhanced algorithms; View Space Lighting, Solid Node Compression and hardware accelerated occlusion are shown to reducing the amounts of nodes that are traversed in a BSP tree, improving tree travel efficiency. These algorithms are proven (in cases) to improve overall efficiency

Discrete Differential Geometry of Thin Materials for Computational Mechanics

Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation

Discrete Element Modeling Of Railroad Ballast Under Simulated Train Loading

Ballasted tracks have been widely used in many countries around the world. Ballast layer is the main element in ballasted track. After service, ballast aggregates degrade and deform. Periodical maintenance for ballast layer is required; which is a cost and time expensive activity. Researchers used numerical approaches to understand the behavior of railroad ballast that leads to efficient design and maintenance. The Discrete Element Method (DEM) has been used increasingly to understand the mechanical behavior of railroad ballast, more frequently through box test. Most researches in the literature simulate the train loading as a pure continuous sinusoid based on train speed and axle spacing; unlike the actual loading induced by trains. This study aims to show the influence of simulated train loadings on ballast mechanical behavior using DEM via box test. The study utilizes the theory of Beam on Elastic Foundation to simulate a more realistic train load. The results from the more realistic simulated train load are compared with those from a sinusoidal load. The compared results highlight the influence of the simulated train load on the mechanical behavior of railroad ballast.Author: " I would like to acknowledge Qatar Rail for their sponsorship to this research under a project entitled “Framework for Research on Railway Engineering” with a grant reference number: QUEX-CENG-Rail 17/18.

Technologies for Biomechanically-Informed Image Guidance of Laparoscopic Liver Surgery

Laparoscopic surgery for liver resection has a number medical advantages over open surgery, but also comes with inherent technical challenges. The surgeon only has a very limited field of view through the imaging modalities routinely employed intra-operatively, laparoscopic video and ultrasound, and the pneumoperitoneum required to create the operating space and gaining access to the organ can significantly deform and displace the liver from its pre-operative configuration. This can make relating what is visible intra-operatively to the pre-operative plan and inferring the location of sub-surface anatomy a very challenging task. Image guidance systems can help overcome these challenges by updating the pre-operative plan to the situation in theatre and visualising it in relation to the position of surgical instruments. In this thesis, I present a series of contributions to a biomechanically-informed image-guidance system made during my PhD. The most recent one is work on a pipeline for the estimation of the post-insufflation configuration of the liver by means of an algorithm that uses a database of segmented training images of patient abdomens where the post-insufflation configuration of the liver is known. The pipeline comprises an algorithm for inter and intra-subject registration of liver meshes by means of non-rigid spectral point-correspondence finding. My other contributions are more fundamental and less application specific, and are all contained and made available to the public in the NiftySim open-source finite element modelling package. Two of my contributions to NiftySim are of particular interest with regards to image guidance of laparoscopic liver surgery: 1) a novel general purpose contact modelling algorithm that can be used to simulate contact interactions between, e.g., the liver and surrounding anatomy; 2) membrane and shell elements that can be used to, e.g., simulate the Glisson capsule that has been shown to significantly influence the organ’s measured stiffness

Algorithms for fat objects : decompositions and applications

Computational geometry is the branch of theoretical computer science that deals with algorithms and data structures for geometric objects. The most basic geometric objects include points, lines, polygons, and polyhedra. Computational geometry has applications in many areas of computer science, including computer graphics, robotics, and geographic information systems. In many computational-geometry problems, the theoretical worst case is achieved by input that is in some way "unrealistic". This causes situations where the theoretical running time is not a good predictor of the running time in practice. In addition, algorithms must also be designed with the worst-case examples in mind, which causes them to be needlessly complicated. In recent years, realistic input models have been proposed in an attempt to deal with this problem. The usual form such solutions take is to limit some geometric property of the input to a constant. We examine a specific realistic input model in this thesis: the model where objects are restricted to be fat. Intuitively, objects that are more like a ball are more fat, and objects that are more like a long pole are less fat. We look at fat objects in the context of five different problems—two related to decompositions of input objects and three problems suggested by computer graphics. Decompositions of geometric objects are important because they are often used as a preliminary step in other algorithms, since many algorithms can only handle geometric objects that are convex and preferably of low complexity. The two main issues in developing decomposition algorithms are to keep the number of pieces produced by the decomposition small and to compute the decomposition quickly. The main question we address is the following: is it possible to obtain better decompositions for fat objects than for general objects, and/or is it possible to obtain decompositions quickly? These questions are also interesting because most research into fat objects has concerned objects that are convex. We begin by triangulating fat polygons. The problem of triangulating polygons—that is, partitioning them into triangles without adding any vertices—has been solved already, but the only linear-time algorithm is so complicated that it has never been implemented. We propose two algorithms for triangulating fat polygons in linear time that are much simpler. They make use of the observation that a small set of guards placed at points inside a (certain type of) fat polygon is sufficient to see the boundary of such a polygon. We then look at decompositions of fat polyhedra in three dimensions. We show that polyhedra can be decomposed into a linear number of convex pieces if certain fatness restrictions aremet. We also show that if these restrictions are notmet, a quadratic number of pieces may be needed. We also show that if we wish the output to be fat and convex, the restrictions must be much tighter. We then study three computational-geometry problems inspired by computer graphics. First, we study ray-shooting amidst fat objects from two perspectives. This is the problem of preprocessing data into a data structure that can answer which object is first hit by a query ray in a given direction from a given point. We present a new data structure for answering vertical ray-shooting queries—that is, queries where the ray’s direction is fixed—as well as a data structure for answering ray-shooting queries for rays with arbitrary direction. Both structures improve the best known results on these problems. Another problem that is studied in the field of computer graphics is the depth-order problem. We study it in the context of computational geometry. This is the problem of finding an ordering of the objects in the scene from "top" to "bottom", where one object is above the other if they share a point in the projection to the xy-plane and the first object has a higher z-value at that point. We give an algorithm for finding the depth order of a group of fat objects and an algorithm for verifying if a depth order of a group of fat objects is correct. The latter algorithm is useful because the former can return an incorrect order if the objects do not have a depth order (this can happen if the above/below relationship has a cycle in it). The first algorithm improves on the results previously known for fat objects; the second is the first algorithm for verifying depth orders of fat objects. The final problem that we study is the hidden-surface removal problem. In this problem, we wish to find and report the visible portions of a scene from a given viewpoint—this is called the visibility map. The main difficulty in this problem is to find an algorithm whose running time depends in part on the complexity of the output. For example, if all but one of the objects in the input scene are hidden behind one large object, then our algorithm should have a faster running time than if all of the objects are visible and have borders that overlap. We give such an algorithm that improves on the running time of previous algorithms for fat objects. Furthermore, our algorithm is able to handle curved objects and situations where the objects do not have a depth order—two features missing from most other algorithms that perform hidden surface removal