Planning the Surgical Correction of Spinal Deformities: Toward the Identification of the Biomechanical Principles by Means of Numerical Simulation

The set of surgical devices and techniques to perform spine deformity correction has widened dramatically. Nevertheless, the rate of complications due to mechanical failure remains rather high. Indeed, basic research about the principles of deformity correction and the optimal surgical strategies (i.e. the choice of the fusion length, the most appropriate instrumentation, the degree of tolerable correction) did not progress as much as the techniques. In this work, a software approach for the biomechanical simulation of the correction of patient-specific spinal deformities aimed to the identification of its biomechanical principles is presented. The method is based on three dimensional reconstructions of the spinal anatomy obtained from biplanar radiographic images. A user-friendly graphical interface allows for the planning of the deformity correction and to simulate the instrumentation. Robust meshing of the instrumented spine is provided by using consolidated computational geometry and meshing libraries. Based on finite element simulation, the program predicts the loads acting in the instrumentation as well as in the biological tissues. A simple test case (reduction of a low grade spondylolisthesis at L3-L4) was simulated as a proof-of-concept. Despite the limitations of this approach, the preliminary outcome is promising and encourages a wide effort towards its refinement

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Doctor of Philosophy

dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research

Three-dimensional modeling of natural heterogeneous objects

En la medicina y otros campos relacionados cuando se va a estudiar un objeto natural, se toman imágenes de tomografía computarizada a través de varios cortes paralelos. Estos cortes se apilan en datos de volumen y se reconstruyen en modelos computacionales con el fin de estudiar la estructura de dicho objeto. Para construir con éxito modelos tridimensionales es importante la identificación y extracción precisa de todas las regiones que comprenden el objeto heterogéneo natural. Sin embargo, la construcción de modelos tridimensionales por medio del computador a partir de imágenes médicas sigue siendo un problema difícil y plantea dos problemas relacionados con las inexactitudes que surgen de, y son inherentes al proceso de adquisición de datos. El primer problema es la aparición de artefactos que distorsionan el límite entre las regiones. Este es un problema común en la generación de mallas a partir de imágenes médicas, también conocido como efecto de escalón. El segundo problema es la extracción de mallas suaves 3D que se ajustan a los límites de las región que conforman los objetos heterogéneos naturales descritos en las imágenes médicas. Para resolver estos problemas, se propone el método CAREM y el método RAM. El énfasis de esta investigación está puesto en la exactitud y fidelidad a la forma de las regiones necesaria en las aplicaciones biomédicas. Todas las regiones representadas de forma implícita que componen el objeto heterogéneo natural se utilizan para generar mallas adaptadas a los requisitos de los métodos de elementos finitos a través de un enfoque de modelado de ingeniería reversa, por lo tanto, estas regiones se consideran como un todo en lugar de piezas aisladas ensambladas.In medicine and other related fields when a natural object is going to be studied, computed tomography images are taken through several parallel slices. These slices are then stacked in volume data and reconstructed into 3D computer models. In order to successfully build 3D computer models of natural heterogeneous objects, accurate identification and extraction of all regions comprising the natural heterogeneous object is important. However, building 3D computer models of natural heterogeneous objects from medical images is still a challenging problem, and poses two issues related to the inaccuracies which arise from and are inherent to the data acquisition process. The first issue is the appearance of aliasing artifacts in the boundary between regions, a common issue in mesh generation from medical images, also known as stair-stepped artifacts. The second issue is the extraction of smooth 3D multi-region meshes that conform to the region boundaries of natural heterogeneous objects described in the medical images. To solve these issues, the CAREM method and the RAM method are proposed. The emphasis of this research is placed on accuracy and shape fidelity needed for biomedical applications. All implicitly represented regions composing the natural heterogeneous object are used to generate meshes adapted to the requirements of finite element methods through a reverse engineering modeling approach, thus these regions are considered as whole rather than loosely assembled parts.Doctor en IngenieríaDoctorad

Assisting digital volume correlation with mechanical image-based modeling: application to the measurement of kinematic fields at the architecture scale in cellular materials

La mesure de champs de déplacement et de déformation aux petites échelles dans des microstructures complexes représente encore un défi majeur dans le monde de la mécanique expérimentale. Ceci est en partie dû aux acquisitions d'images et à la pauvreté de la texture à ces échelles. C'est notamment le cas pour les matériaux cellulaires lorsqu'ils sont imagés avec des micro-tomographes conventionnels et qu'ils peuvent être sujets à des mécanismes de déformation complexes. Comme la validation de modèles numériques et l'identification des propriétés mécaniques de matériaux se base sur des mesures précises de déplacements et de déformations, la conception et l'implémentation d'algorithmes robustes et fiables de corrélation d'images semble nécessaire. Lorsque l'on s'intéresse à l'utilisation de la corrélation d'images volumiques (DVC) pour les matériaux cellulaires, on est confronté à un paradoxe: l'absence de texture à l'échelle du constituant conduit à considérer l'architecture comme marqueur pour la corrélation. Ceci conduit à l'échec des techniques ordinaires de DVC à mesurer des cinématiques aux échelles subcellulaires en lien avec des comportements mécaniques locaux complexes tels que la flexion ou le flambement de travées. L'objectif de cette thèse est la conception d'une technique de DVC pour la mesure de champs de déplacement dans des matériaux cellulaires à l'échelle de leurs architectures. Cette technique assiste la corrélation d'images par une régularisation élastique faible en utilisant un modèle mécanique généré automatiquement et basé sur les images. La méthode suggérée introduit une séparation d'échelles au dessus desquelles la DVC est dominante et en dessous desquelles elle est assistée par le modèle mécanique basé sur l'image. Une première étude numérique consistant à comparer différentes techniques de construction de modèles mécaniques basés sur les images est conduite. L'accent est mis sur deux méthodes de calcul particulières: la méthode des éléments finis (FEM) et la méthode des cellules finies (FCM) qui consiste à immerger la géométrie complexe dans une grille régulière de haut ordre sans utiliser de mailleurs. Si la FCM évite une première phase délicate de discrétisation, plusieurs paramètres restent néanmoins délicats à fixer. Dans ce travail, ces paramètres sont ajustés afin d'obtenir (a) la meilleure précision (bornée par les erreurs de pixellisation) tout en (b) assurant une complexité minimale. Pour l'aspect mesure par corrélation d'images régularisée, plusieurs expérimentations virtuelles à partir de différentes simulations numériques (en élasticité, en plasticité et en non-linéarité géométrique) sont d'abord réalisées afin d'analyser l'influence des paramètres de régularisation introduits. Les erreurs de mesures peuvent dans ce cas être quantifiées à l'aide des solutions de référence éléments finis. La capacité de la méthode à mesurer des cinématiques complexes en absence de texture est démontrée pour des régimes non-linéaires tels que le flambement. Finalement, le travail proposé est généralisé à la corrélation volumique des différents états de déformation du matériau et à la construction automatique de la micro-architecture cellulaire en utilisant soit une grille B-spline d'ordre arbitraire (FCM) soit un maillage éléments finis (FEM). Une mise en évidence expérimentale de l'efficacité et de la justesse de l'approche proposée est effectuée à travers de la mesure de cinématiques complexes dans une mousse polyuréthane sollicitée en compression lors d'un essai in situ.Measuring displacement and strain fields at low observable scales in complex microstructures still remains a challenge in experimental mechanics often because of the combination of low definition images with poor texture at this scale. The problem is particularly acute in the case of cellular materials, when imaged by conventional micro-tomographs, for which complex highly non-linear local phenomena can occur. As the validation of numerical models and the identification of mechanical properties of materials must rely on accurate measurements of displacement and strain fields, the design and implementation of robust and faithful image correlation algorithms must be conducted. With cellular materials, the use of digital volume correlation (DVC) faces a paradox: in the absence of markings of exploitable texture on/or in the struts or cell walls, the available speckle will be formed by the material architecture itself. This leads to the inability of classical DVC codes to measure kinematics at the cellular and a fortiori sub-cellular scales, precisely because the interpolation basis of the displacement field cannot account for the complexity of the underlying kinematics, especially when bending or buckling of beams or walls occurs. The objective of the thesis is to develop a DVC technique for the measurement of displacement fields in cellular materials at the scale of their architecture. The proposed solution consists in assisting DVC by a weak elastic regularization using an automatic image-based mechanical model. The proposed method introduces a separation of scales above which DVC is dominant and below which it is assisted by image-based modeling. First, a numerical investigation and comparison of different techniques for building automatically a geometric and mechanical model from tomographic images is conducted. Two particular methods are considered: the finite element method (FEM) and the finite-cell method (FCM). The FCM is a fictitious domain method that consists in immersing the complex geometry in a high order structured grid and does not require meshing. In this context, various discretization parameters appear delicate to choose. In this work, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity. Concerning the ability of the mechanical image-based models to regularize DIC, several virtual experimentations are performed in two-dimensions in order to finely analyze the influence of the introduced regularization lengths for different input mechanical behaviors (elastic, elasto-plastic and geometrically non-linear) and in comparison with ground truth. We show that the method can estimate complex local displacement and strain fields with speckle-free low definition images, even in non-linear regimes such as local buckling. Finally a three-dimensional generalization is performed through the development of a DVC framework. It takes as an input the reconstructed volumes at the different deformation states of the material and constructs automatically the cellular micro-architeture geometry. It considers either an immersed structured B-spline grid of arbitrary order or a finite-element mesh. An experimental evidence is performed by measuring the complex kinematics of a polyurethane foam under compression during an in situ test

IST Austria Thesis

This thesis describes a brittle fracture simulation method for visual effects applications. Building upon a symmetric Galerkin boundary element method, we first compute stress intensity factors following the theory of linear elastic fracture mechanics. We then use these stress intensities to simulate the motion of a propagating crack front at a significantly higher resolution than the overall deformation of the breaking object. Allowing for spatial variations of the material's toughness during crack propagation produces visually realistic, highly-detailed fracture surfaces. Furthermore, we introduce approximations for stress intensities and crack opening displacements, resulting in both practical speed-up and theoretically superior runtime complexity compared to previous methods. While we choose a quasi-static approach to fracture mechanics, ignoring dynamic deformations, we also couple our fracture simulation framework to a standard rigid-body dynamics solver, enabling visual effects artists to simulate both large scale motion, as well as fracturing due to collision forces in a combined system. As fractures inside of an object grow, their geometry must be represented both in the coarse boundary element mesh, as well as at the desired fine output resolution. Using a boundary element method, we avoid complicated volumetric meshing operations. Instead we describe a simple set of surface meshing operations that allow us to progressively add cracks to the mesh of an object and still re-use all previously computed entries of the linear boundary element system matrix. On the high resolution level, we opt for an implicit surface representation. We then describe how to capture fracture surfaces during crack propagation, as well as separate the individual fragments resulting from the fracture process, based on this implicit representation. We show results obtained with our method, either solving the full boundary element system in every time step, or alternatively using our fast approximations. These results demonstrate that both of these methods perform well in basic test cases and produce realistic fracture surfaces. Furthermore we show that our fast approximations substantially out-perform the standard approach in more demanding scenarios. Finally, these two methods naturally combine, using the full solution while the problem size is manageably small and switching to the fast approximations later on. The resulting hybrid method gives the user a direct way to choose between speed and accuracy of the simulation

Surface Reconstruction From 3D Point Clouds

The triangulation of a point cloud of a 3D object is a complex problem, since it depends on the complexity of the shape of such object, as well as on the density of points generated by a specific scanner. In the literature, there are essentially two approaches to the reconstruction of surfaces from point clouds: interpolation and approximation. In general, interpolation approaches are associated with simplicial methods; that is, methods that directly generate a triangle mesh from a point cloud. On the other hand, approximation approaches generate a global implicit function — that represents an implicit surface — from local shape functions, then generating a triangulation of such implicit surface. The simplicial methods are divided into two families: Delaunay and mesh growing. Bearing in mind that the first of the methods presented in this dissertation falls under the category of mesh growing methods, let us focus our attention for now on these methods. One of the biggest problems with these methods is that, in general, they are based on the establishment of dihedral angle bounds between adjacent triangles, as needed to make the decision on which triangle to add to the expansion mesh front. Typically, other bounds are also used for the internal angles of each triangle. In the course of this dissertation, we will see how this problem was solved. The second algorithm introduced in this dissertation is also a simplicial method but does not fit into any of the two families mentioned above, which makes us think that we are in the presence of a new family: triangulation based on the atlas of charts or triangle stars. This algorithm generates an atlas of the surface that consists of overlapping stars of triangles, that is, one produces a total surface coverage, thus solving one of the common problems of this family of direct triangulation methods, which is the appearance of holes or incomplete triangulation of the surface. The third algorithm refers to an implicit method, but, unlike other implicit methods, it uses an interpolation approach. That is, the local shape functions interpolate the points of the cloud. It is, perhaps, one of a few implicit methods that we can find in the literature that interpolates all points of the cloud. Therefore, one of the biggest problems of the implicit methods is solved, which has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function. What is common to the three methods is the interpolation approach, either in simple or implicit methods, that is, the linearization of the surface subject to reconstruction. As will be seen, the linearization of the neighborhood of each point allows us to solve several problems posed to the surface reconstruction algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp features.A triangulação de uma nuvem de pontos de um objeto 3D é um problema complexo, uma vez que depende da complexidade da forma desse objeto, assim como da densidade dos pontos extraídos desse objeto através de um scanner 3D particular. Na literatura, existem essencialmente duas abordagens na reconstrução de superfícies a partir de nuvens de pontos: interpolação e aproximação. Em geral, as abordagens de interpolação estão associadas aos métodos simpliciais, ou seja, a métodos que geram diretamente uma malha de triângulos a partir de uma nuvem de pontos. Por outro lado, as abordagens de aproximação estão habitualmente associadas à geração de uma função implícita global —que representa uma superfície implícita— a partir de funções locais de forma, para em seguida gerar uma triangulação da dita superfície implícita. Os métodos simpliciais dividem‐se em duas famílias: triangulação de Delaunay e triangulação baseada em crescimento progressivo da triangulação (i.e., mesh growing). Tendo em conta que o primeiro dos métodos apresentados nesta dissertação se enquadra na categoria de métodos de crescimento progressivo, foquemos a nossa atenção por ora nestes métodos. Um dos maiores problemas destes métodos é que, em geral, se baseiam no estabelecimento de limites de ângulos diédricos (i.e., dihedral angle bounds) entre triângulos adjacentes, para assim tomar a decisão sobre qual triângulo acrescentar à frente de expansão da malha. Tipicamente, também se usam limites para os ângulos internos de cada triângulo. No decorrer desta dissertação veremos como é que este problema foi resolvido. O segundo algoritmo introduzido nesta dissertação também é um método simplicial, mas não se enquadra em nenhuma das duas famílias acima referidas, o que nos faz pensar que estaremos na presença de uma nova família: triangulação baseada em atlas de vizinhanças sobrepostas (i.e., atlas of charts) ou estrelas de triângulos (i.e., triangle star). Este algoritmo gera um atlas da superfície que é constituído por estrelas sobrepostas de triângulos, ou seja, produz‐se a cobertura total da superfície, resolvendo assim um dos problemas comuns desta família de métodos de triangulação direta que é o do surgimento de furos ou de triangulação incompleta da superfície. O terceiro algoritmo refere‐se a um método implícito, mas, ao invés de grande parte dos métodos implícitos, utiliza uma abordagem de interpolação. Ou seja, as funções locais de forma interpolam os pontos da nuvem. É, talvez, um dos poucos métodos implícitos que podemos encontrar na literatura que interpola todos os pontos da nuvem. Desta forma resolve‐se um dos maiores problemas dos métodos implícitos que é o do arredondamento de forma resultante do blending das funções locais que geram a função global, em particular ao longo dos vincos da superfície (i.e., sharp features). O que é comum aos três métodos é a abordagem de interpolação, quer em métodos simpliciais quer em métodos implícitos, ou seja a linearização da superfície sujeita a reconstrução. Como se verá, a linearização da vizinhança de cada ponto permite‐nos resolver vários problemas colocados aos algoritmos de reconstrução de superfícies, nomeadamente: sub‐amostragem de pontos (point sub‐sampling), amostragem não uniforme (non‐uniform sampling), bem como formas vincadas (sharp features)