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Description: Diese Bachelorarbeit beschäftigt sich mit der Entwicklung eines allgemeinen Verfahrens, welches die Dicke der mineralisierten Schicht von Haikieferelementen automatisch bestimmt. Dabei soll das Verfahren die Dicke näherungsweise im zweidimensionalen (2D) Raum sowie im dreidimensionalen (3D) Raum anhand von Computertomografie-Scans berechnen (im Folgenden als zweidimensionaler bzw. dreidimensionaler Fall bezeichnet). Es werden drei mögliche Verfahren eingeführt und im Anschluss auf ihre Verwendbarkeit analysiert. Für die Implementierung zur Dickenbestimmung wird der Kern der Rayburst Sampling Methode verwendet und im Weiteren für den 2D-Raum durch kleinere Optimierungen verbessert. Die Überprüfung der Genauigkeit des für den zweidimensionalen Fall entwickelten Programms erfolgt manuell. Für einen Vergleich im 3D-Raum wird ein zweites Verfahren programmiert, das auf der Berechnung der Isoflächen basiert. Diese Arbeit ist in den Bereich der angewandten Mathematik mit dem Schwerpunkt Informatik einzuordnen. Das entwickelte Programm wird im Anschluss Anwendung im Bereich der Biologie am Max-Planck-Institut für Grenzflächen- und Kolloidforschung Potsdam-Golm finden.

Description: Haie und Rochen sind die einzigen Wirbeltiere, die sich durch ein Knorpelskelett auszeichnen, das mit winzigen mineralisierten Elementen bedeckt ist, die sogenannten Tesserae. Obwohl dieser mineralisierte Knorpel seit hunderten von Millionen Jahren ein charakteristisches Merkmal dieser Tiere ist, ist der funktionelle Vorteil dieses Gewebestruktur bisher unklar geblieben. In dieser Masterarbeit wird diese Struktur mithilfe der Finite-Elemente-Methode(FEM) untersucht, wobei biologische Informationen zu den Muskeln und der geometrischen Gegebenheiten aus einem hochaufgelösten, kontrastgefärbten μCT-Scan einer Stechrochenhyomandibula verwendet werden. Für die Analyse werden Computer-Aided-Design(CAD)-Modelle und FE-Modelle konstruiert sowie vorhandene Methoden erweitert, um bei den Berechnungen die Charakteristika des biologischen Objektes bestmöglich zu berücksichtigen. Die Modelle bauen auf einer Segmentierung der Hyomandibula auf, wobei die mehreren tausend Tesserae in diesem Datensatz bereits voneinander isoliert sind. Für die Modellierung der Hyomandibula wird als erstes ein CAD-Modell konstruiert. Bei dieser Konstruktion wird eine Tesserae-Mittelfläche erstellt und im Anschluss nach innen und außen verschoben. Der nächste Schritt basiert auf dem Einbau von Zwischenwänden, die die Tesserae voneinander separieren. Auf Grundlage dieses Modells wird ein Tetraedergitter generiert, das die Basis für den zweiten Teil dieser Arbeit darstellt - die Berechnungen mit der FEM. Die wesentliche Aufgabe des zweiten Teils beinhaltet die Konstruktion eines FE-Modells, das in die lineare FEM einzuordnen ist. In dieses fließen die Randbedingungen und die Materialeigenschaften des Skelettelements ein. Mithilfe der FEM lassen sich die durch Krafteinwirkung auftretenden Verschiebungen und Spannungen der Hyomandibula ermitteln. Die Ergebnisse geben Rückschlüsse über das Verhalten des Materials, die Besonderheiten der Geometrie und damit über die Stabilität des Objektes. Der dritte Teil der Abschlussarbeit beschäftigt sich mit zusätzlichen Anpassungen und Änderungen der Modelle (CAD-Modell und FE-Modell), um diese Resultate mit dem Modell zu vergleichen, das der Biologie am nächsten kommt. Diese Anpassungen beinhalten das Variieren der Dicke der mineralisierten Schicht, die Konstellation des Materials und den Abstand zwischen den Tesserae. Die Ergebnisse zeigen, dass sowohl die Tesserae-Struktur als auch die zwischen den Tesserae liegenden Kollagenfasern vermutlich keinen Einfluss auf die Mechanik und dementsprechend die Stabilität haben. Jedoch lassen die unterschiedlichen Resultate im Fall verschieden gewählter Tesserae-Dicken annehmen, dass diese sehr wohl einen Einfluss besitzen.

Description: Sharks and rays are the only vertebrates characterized by a peculiar cartilage skeleton covered with minute mineralized tiles called tesserae. Although this tessellated cartilage has been a defining feature of this lineage for hundreds of millions of years, the functional advantage of this tissue design has remained obscure. In this Master’s thesis, the finite element method (FEM) is used to investigate the role of tiling in the skeleton, using biological information on the muscles and shape from a high-resolution, contrast-stained μCT-scan of a stingray hyomandibula. For this purpose, computer aided design (CAD) models and FE models are constructed and existing methods will be extended to take the best possible account of the characteristics of the biological object. The analysis builds from a segmentation of the hyomandibula, with the dataset’s several thousand tesserae pre-isolated from one another. For the modeling of the hyomandibula a CAD model is constructed. In this construction, a medial surface is created using the tesserae which is subsequently moved to the inside and outside. The next step is to integrate partition walls separating the tesserae elements. Based on this model, a tetrahedral grid is then generated, which is the content of the second part of this thesis, the calculation with the FEM. A finite element model is constructed including boundary conditions and material properties of the skeletal element to compute the results using the linear FEM theory. The FEM is used to determine the displacements and stresses resulting from biological forces acting on the hyomandibula. The results allow conclusions of the material behavior, geometric characteristics (tesselation) and therefore the object stability. Important contributions of this thesis are additional adjustments and changes to the models (CAD model and FE model) to make it more appropriate to study the biological data at hand. The tesserae thickness, the length of the collagenious fibres and the constellation of the material are the parameters, which are changed. In contrast to the tesserae thicknesses, the results suggest that both the arrangement of the tesserae and its interposed collagen fibers have no substantial influence on the mechanics.

Description: A prerequisite for many analysis tasks in modern comparative biology is the segmentation of 3-dimensional (3D) images of the specimens being investigated (e.g. from microCT data). Depending on the specific imaging technique that was used to acquire the images and on the image resolution, different segmentation tools will be required. While some standard tools exist that can often be applied for specific subtasks, building whole processing pipelines solely from standard tools is often difficult. Some tasks may even necessitate the implementation of manual interaction tools to achieve a quality that is sufficient for the subsequent analysis. In this work, we present a pipeline of segmentation tools that can be used for the semi-automatic segmentation and quantitative analysis of voids in tissue (i.e. internal structural porosity). We use this pipeline to analyze lacuno-canalicular networks in stingray tesserae from 3D images acquired with synchrotron microCT. * The first step of this processing pipeline, the segmentation of the tesserae, was performed using standard marker-based watershed segmentation. The efficient processing of the next two steps, that is, the segmentation of all lacunae spaces belonging to a specific tessera and the separation of these spaces into individual lacunae required modern, recently developed tools. * For proofreading, we developed a graph-based interactive method that allowed us to quickly split lacunae that were accidentally merged, and to merge lacunae that were wrongly split. * Finally, the tesserae and their corresponding lacunae were subdivided into anatomical regions of interest (structural wedges) using a semi- manual approach.

Description: In most vertebrates the embryonic cartilaginous skeleton is replaced by bone during development. During this process, cartilage cells (chondrocytes) mineralize the extracellular matrix and undergo apoptosis, giving way to bone cells (osteocytes). In contrast, sharks and rays (elasmobranchs) have cartilaginous skeletons throughout life, where only the surface mineralizes, forming a layer of tiles (tesserae). Elasmobranch chondrocytes, unlike those of other vertebrates, survive cartilage mineralization and are maintained alive in spaces (lacunae) within tesserae. However, the function(s) of the chondrocytes in the mineralized tissue remain unknown. Applying a custom analysis workflow to high-resolution synchrotron microCT scans of tesserae, we characterize the morphologies and arrangements of stingray chondrocyte lacunae, using lacunar morphology as a proxy for chondrocyte morphology. We show that the cell density is comparable in unmineralized and mineralized tissue from our study species and that cells maintain the similar volume even when they have been incorporated into tesserae. This discovery supports previous hypotheses that elasmobranch chondrocytes, unlike those of other taxa, do not proliferate, hypertrophy or undergo apoptosis during mineralization. Tessera lacunae show zonal variation in their shapes—being flatter further from and more spherical closer to the unmineralized cartilage matrix and larger in the center of tesserae— and show pronounced organization into parallel layers and strong orientation toward neighboring tesserae. Tesserae also exhibit local variation in lacunar density, with the density considerably higher near pores passing through the tesseral layer, suggesting pores and cells interact (e.g. that pores contain a nutrient source). We hypothesize that the different lacunar types reflect the stages of the tesserae formation process, while also representing local variation in tissue architecture and cell function. Lacunae are linked by small passages (canaliculi) in the matrix to form elongate series at the tesseral periphery and tight clusters in the center of tesserae, creating a rich connectivity among cells. The network arrangement and the shape variation of chondrocytes in tesserae indicate that cells may interact within and between tesserae and manage mineralization differently from chondrocytes in other vertebrates, perhaps performing analogous roles to osteocytes in bone.

Description: In most vertebrates the embryonic cartilaginous skeleton is replaced by bone during development. During this process, cartilage cells (chondrocytes) mineralize the extracellular matrix and undergo apoptosis, giving way to bone cells (osteocytes). In contrast, sharks and rays (elasmobranchs) have cartilaginous skeletons throughout life, where only the surface mineralizes, forming a layer of tiles (tesserae). Elasmobranch chondrocytes, unlike those of other vertebrates, survive cartilage mineralization and are maintained alive in spaces (lacunae) within tesserae. However, the function(s) of the chondrocytes in the mineralized tissue remain unknown. Applying a custom analysis workflow to high-resolution synchrotron microCT scans of tesserae, we characterize the morphologies and arrangements of stingray chondrocyte lacunae, using lacunar morphology as a proxy for chondrocyte morphology. We show that the cell density is comparable in unmineralized and mineralized tissue from our study species and that cells maintain the similar volume even when they have been incorporated into tesserae. This discovery supports previous hypotheses that elasmobranch chondrocytes, unlike those of other taxa, do not proliferate, hypertrophy or undergo apoptosis during mineralization. Tessera lacunae show zonal variation in their shapes—being flatter further from and more spherical closer to the unmineralized cartilage matrix and larger in the center of tesserae— and show pronounced organization into parallel layers and strong orientation toward neighboring tesserae. Tesserae also exhibit local variation in lacunar density, with the density considerably higher near pores passing through the tesseral layer, suggesting pores and cells interact (e.g. that pores contain a nutrient source). We hypothesize that the different lacunar types reflect the stages of the tesserae formation process, while also representing local variation in tissue architecture and cell function. Lacunae are linked by small passages (canaliculi) in the matrix to form elongate series at the tesseral periphery and tight clusters in the center of tesserae, creating a rich connectivity among cells. The network arrangement and the shape variation of chondrocytes in tesserae indicate that cells may interact within and between tesserae and manage mineralization differently from chondrocytes in other vertebrates, perhaps performing analogous roles to osteocytes in bone.

Description: A prerequisite for many analysis tasks in modern comparative biology is the segmentation of 3-dimensional (3D) images of the specimens being investigated (e.g. from microCT data). Depending on the specific imaging technique that was used to acquire the images and on the image resolution, different segmentation tools will be required. While some standard tools exist that can often be applied for specific subtasks, building whole processing pipelines solely from standard tools is often difficult. Some tasks may even necessitate the implementation of manual interaction tools to achieve a quality that is sufficient for the subsequent analysis. In this work, we present a pipeline of segmentation tools that can be used for the semi-automatic segmentation and quantitative analysis of voids in tissue (i.e. internal structural porosity). We use this pipeline to analyze lacuno-canalicular networks in stingray tesserae from 3D images acquired with synchrotron microCT. * The first step of this processing pipeline, the segmentation of the tesserae, was performed using standard marker-based watershed segmentation. The efficient processing of the next two steps, that is, the segmentation of all lacunae spaces belonging to a specific tessera and the separation of these spaces into individual lacunae required modern, recently developed tools. * For proofreading, we developed a graph-based interactive method that allowed us to quickly split lacunae that were accidentally merged, and to merge lacunae that were wrongly split. * Finally, the tesserae and their corresponding lacunae were subdivided into anatomical regions of interest (structural wedges) using a semi- manual approach.

Description: Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems.

Description: Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPer-Meshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell’s equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.