A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

Multi-angle valve seat machining: experimental analysis and numerical modelling

Modern automotive manufacturers operate in highly competitive markets, heavily influenced by Government regulation and ever more environmentally conscious consumers. Modern high-temperature, high-pressure engines that use high hardness multi-angle valve seats are an attractive environmental option, but one that manufacturers find requires more advanced materials and tighter geometric tolerances to maintain engine performance.Tool manufacturers meet these increasingly tougher demands by using, higher hardness cutting materials such as polycrystalline cubic boron nitride (pcBN), that on paper, promise to wear at a lower rate, require less coolant and deliver tighter tolerances than their carbide counterparts.The low brittle fracture toughness of pcBN makes tools that use it vulnerable to minute chipping. A review of literature for this work pointed to no clear answer to this problem, although suggestions range from manufacturing defects, dynamic and flexibility problems with the production line machinery and fixtures, and radial imbalances in the cutting loads.This work set about experimentally investigating those potential explanations, coming to the conclusion that the high radial imbalance of the cutting loads is responsible for pcBN cutting insert failure during multi-angle valve seat machining, and that by simply relocating the cutting inserts around the multi angle cutting tool, the imbalance can be reduced, thus extending the life of the cutting inserts.It is not always easy to predict the imbalance due to the multiple flexibilities in the system, and simulating such a system in 3D with all its associated cutting phenomena such as friction, thermal expansion, chip flow and shearing, would call upon extraordinary computational power and extremely precise experimental inputs to reduce cumulative error.This thesis proves that such a 3D simulation can be made, that runs in exceptionally short durations compared to traditional methods, by making a number of simplifications.MSC Marc was used to host the simulation, with a parametric script written in Python responsible for generating the model geometry and cutter layout. A Fortran program was developed that is called upon by Marc to calculate the required cutting load outputs and generate new workpiece meshes as material is removed.</div

Analysis and Generation of Quality Polytopal Meshes with Applications to the Virtual Element Method

This thesis explores the concept of the quality of a mesh, the latter being intended as the discretization of a two- or three- dimensional domain. The topic is interdisciplinary in nature, as meshes are massively used in several fields from both the geometry processing and the numerical analysis communities. The goal is to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. In other words, a good quality mesh that is also cheap to handle, overcoming the typical trade-off between quality and computational cost. To reach this goal, we first need to answer the question: ''How, and how much, does the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depend on the particular mesh adopted to model the problem? And which geometrical features of the mesh most influence the result?'' We present a comparative study of the different mesh types, mesh generation techniques, and mesh quality measures currently available in the literature related to both engineering and computer graphics applications. This analysis leads to the precise definition of the notion of quality for a mesh, in the particular context of numerical simulations of partial differential equations with the virtual element method, and the consequent construction of criteria to determine and optimize the quality of a given mesh. Our main contribution consists in a new mesh quality indicator for polytopal meshes, able to predict the performance of the virtual element method over a particular mesh before running the simulation. Strictly related to this, we also define a quality agglomeration algorithm that optimizes the quality of a mesh by wisely agglomerating groups of neighboring elements. The accuracy and the reliability of both tools are thoroughly verified in a series of tests in different scenarios

Constrained deformation for evolutionary optimization

Sieger D. Constrained deformation for evolutionary optimization. Bielefeld: Universität Bielefeld; 2017.This thesis investigates shape deformation techniques for their use in design optimization tasks. In the first part, we introduce state-of-the-art deformation methods and evaluate them in a set of representative benchmarks. Based on these benchmarking results, we derive essential criteria and features a deformation technique should satisfy in order to be successfully applicable within design optimization. In the second part, we concentrate on the application and improvement of deformation techniques based on radial basis functions. We present and evaluate a unified framework for surface and volume mesh deformation and investigate questions of performance and scalability. In the final third part, we concentrate on the integration of additional constraints into the deformation, thereby improving the overall effectiveness of the design optimization process and fostering the creation of more feasible and producible design variations. We present a novel shape deformation technique that effectively maintains different types of geometric constraints such as planarity, circularity, or characteristic feature lines during deformation. At the same time, our method provides a unique level of modeling flexibility, quality, robustness, and scalability. Finally, we integrate techniques for automatic constraint detection directly into our deformation framework, thereby making our method more easily applicable within complex design optimization scenarios

Knee joint biomechanics after anterior cruciate ligament reconstruction

Anterior cruciate ligament (ACL) is an important stabilizer of the knee joint. After ACL rupture, the knee joint has difficulty maintaining its stability; thus the patient often has to receive an ACL-reconstructive surgery to regain the knee joint functions. Unfortunately, traditional transtibial surgical techniques could not fully restore the normal knee joint kinematics during daily activities. Moreover, a higher rate of osteoarthritis was found from the ACL-reconstructed knees compared to the knees without a history of ACL-injuries. The reason for the increased risk of knee osteoarthritis is still unclear, and the pathologies due to abnormal knee joint kinematics remain controversial. The dissertation was to delineate the knee joint motion and loading after ACL-reconstruction. Thirty patients who received ACL-reconstructive surgeries using the traditional transtibial technique and 14 using the recently developed anteromedial portal technique were recruited from the same center (OrthoCarolina). Twenty healthy subjects without history of knee injuries were recruited as the control group. Human motion data and ground reaction force data were collected during level walking and downstairs pivoting using an optical motion capture system. Three-dimensional (3D) knee joint motions were determined from redundant markers using an optimization approach. The 3D knee joint moments and forces were calculated from motion data, ground reaction data by using an inverse dynamics model of the lower extremity. A finite element model was created, and the distributions of stress/strain within articular cartilage under physiological loading were estimated. The results from two groups of patients using different reconstruction techniques were compared. In the transtibial group, excessive internal tibial rotation (2° on average during stance phase), varus rotation and anterior femur translation (swing phase) were observed in the ACL-reconstructed knees when compared to the control group during level walking. The 3D knee joint motion following ACL-reconstruction was found to be influenced by the leg dominance. The motion and load in the uninjured contralateral knee were also affected. During downstairs pivoting, the normal varus rotation and adduction moment were not fully restored by the transtibial technique. Overall, the anteromedial portal technique improved the postsurgical knee joint kinematics by reducing the offsets in the internal tibial rotation, varus rotation and anterior femur translation during level walking. It also improved the adduction moment during downstairs pivoting. At the same time, the anteromedial portal technique may cause a flexion/extension deficit during the stance phase of walking. Results of finite element analysis demonstrated higher pressures within the medial femoral cartilage during the stance phase of walking; it also demonstrated that there is an increased knee joint laxity after ACL-reconstruction. The anteromedial portal technique was overall better than the traditional transtibial technique in respect to postsurgical knee joint compressive loading and contact pressure. The study provides evidence of the possibility by using anatomical single-bundle ACL-reconstruction technique to fight the knee joint osteoarthritis after ligament injury

Frame Fields for Hexahedral Mesh Generation

As a discretized representation of the volumetric domain, hexahedral meshes have been a popular choice in computational engineering science and serve as one of the main mesh types in leading industrial software of relevance. The generation of high quality hexahedral meshes is extremely challenging because it is essentially an optimization problem involving multiple (conflicting) objectives, such as fidelity, element quality, and structural regularity. Various hexahedral meshing methods have been proposed in past decades, attempting to solve the problem from different perspectives. Unfortunately, algorithmic hexahedral meshing with guarantees of robustness and quality remains unsolved. The frame field based hexahedral meshing method is the most promising approach that is capable of automatically generating hexahedral meshes of high quality, but unfortunately, it suffers from several robustness issues. Field based hexahedral meshing follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a feature-aligned frame field and (2) generation of an integer-grid map that best aligns with the frame field. The main robustness issue stems from the fact that smooth frame fields frequently exhibit singularity graphs that are inappropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The thesis aims at analyzing the gap between the topologies of frame fields and hexahedral meshes and developing algorithms to realize a more robust field based hexahedral mesh generation. The first contribution of this work is an enumeration of all local configurations that exist in hexahedral meshes with bounded edge valence and a generalization of the Hopf-Poincaré formula to octahedral (orthonormal frame) fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field. In the collaboration work with colleagues [BRK+22], the dataset HexMe consisting of practically relevant models with feature tags is set up, allowing a fair evaluation for practical hexahedral mesh generation algorithms. The extendable and mutable dataset remains valuable as hexahedral meshing algorithms develop. The results of the standard field based hexahedral meshing algorithms on the HexMesh dataset expose the fragility of the automatic pipeline. The major contribution of this thesis improves the robustness of the automatic field based hexahedral meshing by guaranteeing local meshability of general feature aligned smooth frame fields. We derive conditions on the meshability of frame fields when feature constraints are considered, and describe an algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite the fact that local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 57%, when compared on the challenging HexMe dataset