Bone is porous and has a complex microstructure. This study considers the effect of microstructural morphology on the macrolevel mechanical properties of bone. Improved incorporation of such properties is required to advance current finite element approximations of bone behaviour. A technique to computationally generate realistic trabecular bone microstructures is developed. This provides the possibility of examining the effect of different microstructures on the macrolevel mechanical behaviour of bone. They would also permit direct incorporation of bone microstructure in macroscale finite element analyses without the prohibitive computational and experimental costs of donor-image based mesh generation. Micro- finite-element analyses are used for the first time to evaluate the macrolevel orthotropic elastic constants of cortical bone resulting from variations of microstructural morphology. It is concluded that the ratio of canal volume to tissue volume is the most powerful predictor of cortical bone elastic constants and that considerable periosteal-endosteal variations in these constants can develop with bone loss. The role of microstructure in cortical bone toughness is investigated using nano- finite-element analyses of murine cortical bone samples to simulate the initiation and propagation of microcracks. Results confirm the experimentally observed ability of canal and lacuna pores to act as stress raisers, thereby guiding the growth of microcracks. A novel and numerically efficient strain-based plasticity algorithm is presented which permits easy incorporation of strength anisotropy in finite element analyses of bone. The previously evaluated elastic properties of cortical bone are combined with the developed plasticity algorithm to conduct a detailed macro-finite-element investigation of external fixation of tibial midshaft fractures. Old patients are found to be at considerably higher risk of implant loosening under both unilateral and Ilizarov fixation, compared to younger patients.

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No / Age estimations based on conventional multifactorial methods were compared with trends observed in the internal morphology of bones obtained from high-resolution µCT. Specifically, average trabecular thickness and number of trabeculae/mm transect were determined in the non-load-bearing capitate (hand) and the load-bearing navicular (foot). The µCT findings reveal age-related trends but - surprisingly - these correspond only loosely with the ages assigned by conventional ageing methods, and are also not in accordance with what would be predicted from biomechanical considerations: trabeculae tend to be thinner in the (habitually) load-bearing navicular than in the (habitually) non-load-bearing capitate. While the statistically significant correlation between trabecular thickness and number of trabeculae would suggest a compensatory mechanism between these two aspects of microanatomy, they are not correlated with the assigned ages and, importantly, may differ between sexes. Only in females is there an unequivocal trend towards trabecular thickness increase with age. These findings, although unexpected, can be reconciled with recent histological evidence and assumed average activity levels in historical populations. Conversely, changes in trabecular number are less clear-cut and may be due to the lack of very old individuals in the sample. Nevertheless, the trends observed for trabecular thickness, as well as for trabecular number, seem to imply that the higher incidence of osteoporosis in women could be explained from a structural point of view alone.

Consensus in scientific literature is that hyperglycemia, which is a condition that manifests in individuals with uncontrolled diabetes, causes compromised bone growth, but the exact mechanisms of are unknown. It has been estimated that 5% of dental implant failures that have previously been linked to unknown causes may be associated with undiagnosed diabetes. It is important to study the early stages of bone growth as it is accepted that they are critical in the long-term success rate of endosseous implants. This study aimed to investigate the bone healing seen in the hyperglycemic group compared to the normal (i.e. control) group, at an early time point, using high-resolution microscopy techniques. Ten young (200-250gram) male Wistar rats were used for this study with five rats assigned to the control group and the other five rats intravenously injected with 65 mg/kg of streptozotocin (STZ) to induce diabetes. An osteotomy model was used to make a 1.3mm defect in the diaphysis of the rat femurs. After five days, the femurs were removed, fixed in glutaraldehyde, dehydrated, and embedded in resin. Structural and chemical analyses were conducted on the samples using a variety of microscopy techniques to examine various factors of bone quality including: bone porosity, relative mineralization level, and the arrangement of collagen and mineral. When analyzing the micro-structure, the hyperglycemic group showed increased porosity in the newly formed bone as compared to the control group. However, no significant differences were found in the nano-structure when analyzing the arrangement of collagen and mineral.Therefore, the results in this thesis suggest that alterations in micro-architecture rather than nano-architecture may play a pivotal role in the compromised bone healing in uncontrolled diabetes at this five-day time point. Future work should investigate additional time points in the bone healing process. / Thesis / Master of Applied Science (MASc) / According to the International Diabetes Federation, 387 million people worldwide are living with diabetes of which 46.3% are undiagnosed. Uncontrolled diabetes results in hyperglycemia, which is a condition where there is an increased level of glucose in the blood. When diabetes is not regulated correctly with medication, it leads to problems in the long-term success rate of dental implants. The objective of this thesis was to investigate the early stages of bone formation, which are accepted to be critical in the long-term success rate of dental implants, in hyperglycemic animal models compared to control groups using various microscopy techniques. The different techniques used allowed for the structural and elemental compositions of bone to be studied on the micro-scale and nano-scale. It was shown that at the 5-day healing time point studied, the micro-structure, rather than the nano-structure, was negatively altered in the hyperglycemic group compared to the control group.

[EN] Cortical bone tissue is the responsible of giving support and structure to vertebrates. For that reason, understanding and analyzing its behavior is needed from each different hierarchical level that composes it. The lower the structural scale is, the greater the complexity and scarcity of studies in literature. These studies are relevant for understanding, preventing and solving important health problems that affect human beings. From a mechanical point of view is interesting to evaluate and apply engineering numerical tools to analyze complex materials as biological tissues, increasing the state of the art in different disciplines that can be applied in numerous fields as material science, biomechanics, numerical methods, medicine and more. In this Thesis the mechanical behavior of cortical bone at microstructural level is analyzed, with finite element models of its basic structure, the osteon. The microstructure of osteons, composed of mineralized collagen fibrils in layers with different orientations disposed concentrically around blood vessels is considered in the models for the calculation of elastic properties and failure criteria definition. For obtaining elastic properties, the use of micromechanical finite element models is considered, with heterogeneous composition for both mineralized collagen fibrils (at nanostructural level) and lamellar level (at sub-microstructural level). The failure analysis for realistic geometries is applied after comparing different models that involve, on one hand the growth of microcracks with contact conditions and on the other, degradation of elastic material properties by user subroutines of the finite element code, the latter being the one that brings better results from a computational cost viewpoint. Therefore an interesting alternative is here presented that can be used to evaluate the damage propagation at three-dimensional level, which with other methods as X-FEM can be computationally unaffordable. Composite materials failure criteria are applied to osteon analysis and the results are related with experimental tests from bibliography, showing the relevance of shear stresses between lamellae for failure initiation and propagation. In a two-dimensional study it is also shown the important role of osteocyte lacunae in the failure initiation, what is interesting from a cellular mechanotransduction approach. / [ES] El tejido óseo cortical es el encargado de dar soporte y estructura a los vertebrados. Existe por tanto una necesidad de conocer y analizar mecánicamente su comportamiento desde los distintos niveles jerárquicos que lo componen, siendo mayor la complejidad y más escasos los estudios disponibles en la literatura cuanto más pequeña es la escala estructural que se analiza. Estos estudios son relevantes para comprender, prevenir y solucionar problemas de salud importantes que afectan al ser humano. Desde el punto de vista mecánico es interesante evaluar y aplicar herramientas numéricas ingenieriles para el análisis de materiales más complejos como son los biológicos, incrementando el estado del arte en distintas disciplinas que pueden ser aplicadas en numerosos campos como la ciencia de los materiales, la biomecánica, los métodos numéricos o la medicina, entre otras. En esta Tesis se analiza el comportamiento mecánico del hueso cortical a nivel microestructural, donde se modela mediante el método de los elementos finitos su unidad básica, la osteona. Para la obtención de las propiedades elásticas se considera en los modelos la microestructura compuesta por capas de colágeno mineralizado con diferentes orientaciones, dispuestas de manera concéntrica alrededor de los canales vasculares. Se incluye además la utilización de modelos micromecánicos de elementos finitos que tienen en cuenta la composición heterogénea tanto para el nivel del fibrilo de colágeno mineralizado (nivel nanoestructural) como para el nivel de lamela (nivel sub microestructural). El análisis del fallo para geometrías realistas se aplica tras comparar varios modelos que involucran por un lado el crecimiento de grietas mediante condiciones de contacto y por otro, degradación de las propiedades elásticas del material mediante subrutinas de usuario del código de elementos finitos, siendo este último el que mejores resultados presenta desde el punto de vista del coste computacional. De esta manera se presenta una alternativa interesante que permite evaluar la propagación del daño a nivel tridimensional, lo que con otros métodos como el X-FEM puede ser computacionalmente inabordable. Se aplican criterios de fallo utilizados para materiales compuestos en ingeniería estructural a las osteonas y los resultados se relacionan con los de los ensayos experimentales disponibles en la bibliografía, mostrando la relevancia de las tensiones de cortadura entre lamelas para la iniciación y propagación del daño. En un estudio bidimensional, también se muestra la participación importante en la fase de inicio de daño de las lagunas de osteocitos lo que es interesante desde un enfoque de mecanotransducción celular. / [CA] El teixit ossi cortical és l'encarregat de donar suport i estructura als vertebrats. Existeix per tant una necessitat de conèixer i analitzar mecànicament el seu comportament des dels diferents nivells jeràrquics que ho componen, sent major la complexitat i més escassos els estudis disponibles en la literatura com més xicoteta és l'escala estructural que s'analitza. Aquests estudis són rellevants per a comprendre, prevenir i solucionar problemes de salut importants que afecten a l'ésser humà. Des del punt de vista mecànic és interessant avaluar i aplicar eines numèriques ingenieriles per a l'anàlisi de materials més complexos com són els biològics, incrementant l'estat de l'art en diferents disciplines que poden ser aplicades en nombrosos camps com la ciència dels materials, la biomecànica, els mètodes numèrics o la medicina, entre altres. En aquesta Tesi s'analitza el comportament mecànic de l'os cortical a nivell microestructural, on es modela mitjançant el mètode dels elements finits la seua unitat bàsica, la osteona. Per a l'obtenció de les propietats elàstiques es considera en els models la microestructura composta per capes de col·làgen mineralitzat amb diferents orientacions, disposades de manera concèntrica al voltant dels canals vasculars. S'inclou a més la utilització de models micromecànics d'elements finits que tenen en compte la composició heterogènia tant per al nivell del fibril de col·làgen mineralitzat (nivell nanoestructural) com per al nivell de lamela (nivell submicroestructural). L'anàlisi de la fallada per a geometries realistes s'aplica després de comparar diversos models que involucren d'una banda el creixement de clavills mitjançant condicions de contacte i per un altre, degradació de les propietats elàstiques del material mitjançant subrutines d'usuari del codi d'elements finits, sent aquest últim el que millors resultats presenta des del punt de vista del cost computacional. D'aquesta manera es presenta una alternativa interessant que permet avaluar la propagació del dany a nivell tridimensional, la qual cosa amb altres mètodes com el X-FEM pot ser computacionalment inabordable. S'apliquen criteris de fallada utilitzats per a materials compostos en enginyeria estructural a les osteones i els resultats es relacionen amb els de els assajos experimentals disponibles en la bibliografia, mostrant la rellevància de les tensions de cisallament entre lameles per a la iniciació i propagació del dany. En un estudi bidimensional, també es mostra la participació important en la fase d'inici de dany de les llacunes d'osteòcits el que és interessant des d'un enfocament de mecanotransducción cel·lular. / Arango Villegas, C. (2016). Study of the mechanical behavior of cortical bone microstructure by the finite element method [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/67570

L’ostéoporose est une maladie fréquente et généralisée du squelette qui se caractérise par une perte de masse osseuse et des altérations de la structure des os. Ces variations des propriétés osseuses, observées à diverses échelles et associées à une augmentation du contenu adipeux de la moelle, témoignent d’une plus grande fragilité du squelette. Ces modifications sont cependant différentes en fonction du site. Cette variation du contenu adipeux médullaire, rapportée notamment dans les os longs du squelette appendiculaire, semble jouer un rôle crucial dans la survenue de l’ostéoporose. Néanmoins, ces altérations ostéo-médullaires, aussi bien quantitatives que qualitatives, sont controversées et peu documentées au niveau des maxillaires, la mandibule en particulier. Le but de notre étude est d’évaluer, au cours du vieillissement et dans un modèle d’ostéoporose (ratte adulte ovariectomisée), les relations entre les variations du contenu adipeux médullaire et la microarchitecture osseuse en site mandibulaire en comparaison avec un site de référence, le tibia. La microarchitecture osseuse, la quantité et la répartition du contenu adipeux médullaire après marquage au tétroxyde d’osmium ont été analysées par microtomographie à rayons X dans la mandibule dentée (os alvéolaire) et non dentée (condyle). Au cours du vieillissement, aucune altération des paramètres osseux et médullaires n’a été mise en évidence. En revanche, le déficit hormonal en oestrogènes induit par ovariectomie conduit à une perte osseuse plus marquée (+35%) dans le tibia que dans la mandibule, associée à des modifications microarchitecturales et adipeuses médullaires site-spécifiques. En effet, en comparaison avec le tibia, un faible contenu adipeux (<10% de moelle) est retrouvé dans le secteur denté (alvéolaire) ainsi que non denté (condyle). A la différence du tibia, au sein duquel un effet de « clustering » des adipocytes est observé à la surface osseuse trabéculaire, le contenu adipeux mandibulaire est réparti de manière homogène dans les espaces médullaires avec très peu de contact avec la surface osseuse trabéculaire. En conclusion, nos résultats indiquent une perte osseuse modérée dans la mandibule par rapport au tibia associée à une augmentation du contenu adipeux médullaire tardive dont la répartition au sein des espaces médullaires n’est pas modifiée à la différence du tibia. Nous émettons l’hypothèse qu’une activité de remodelage et des sollicitations biomécaniques différentes puissent expliquer les spécificités physiopathologiques observées en site mandibulaire. D’autres études seront nécessaires pour préciser l’impact de telles modifications sur la qualité osseuse à l’échelle moléculaire et élémentaire, ainsi que pour préciser les mécanismes de dialogues entre les ostéoblastes et les adipocytes. / Osteoporosis is a common disease of the skeleton characterized by a loss of bone mass and changes in bone structure. These variations in bone properties, observed at various scales and associated with an increase in the bone marrow adipose tissue (BMAT) content, indicate a greater fragility of the skeleton in a site-specific manner. This variation in the BMAT content, reported in some skeletal sites, seems to play a crucial role in the occurrence of osteoporosis. Nevertheless, these bone and marrow alterations, both quantitative and qualitative, are controversial and still poorly documented in the jaw bones, the mandible in particular.The aim of our study was to investigate, during aging and in a rodent model of osteoporosis (adult ovariectomized rat), the relationships between the changes in the bone microstructure, the marrow fat content and its distribution in the mandibular site in comparison with a reference site, the tibia. The bone microstructure, the bone marrow fat content and its distribution after osmium tetroxide staining were analyzed by a specific X-ray microfocus tomography approach in the mandible in the teeth-bearing area (alveolar bone) and in the condyle. During aging, neither bone nor bone marrow alterations have been observed. In contrast, estrogen deficiency did lead to more important bone loss (+35%) in the tibia than in the mandible associated with site-specific microstructural and BMAT modifications. Indeed, in comparison with the tibia, a low BMAT content (<10% of marrow volume) was found in the alveolar bone as well as in the condyle. Compared to tibia which reveals a clustering of the marrow adipocytes at the trabecular bone surface, the mandibular BMAT content was homogeneously distributed and located further away with almost no contact with the trabecular bone surface. In conclusion, our results indicate a moderate bone loss in the mandible compared to the tibia associated with an increase in the BMAT content whose distribution within the marrow spaces is not modified in contrast to tibia. We hypothesize that a differential bone turn-over rate, biomechanical stress may explain in part the mandibular physiopathological specificities reported. Further studies will be needed to precise the impact of such alterations on bone quality at the molecular and elemental level, as well as to depict the mechanisms of dialog between osteoblasts and adipocytes.

The content of the presented dissertation work is the study of the histological structure of the burned and unburned compact bone of the human rib. The aim was to evaluate the effects of the differently high cremation temperatures on the structure of the bone tissue, and, on the basis of these findings, to design an applicable methodology for the estimation of the age-at-death of an unknown individual. As the research material the recent human ribs were used, belonging to the individuals of known age-at-death, sex and cause of death. The skeletal samples were experimentally burned under the beforehand set conditions. Every bone was divided into several pieces; one of them remained unburned, and the other were burned at the temperatures of 600, 700, 800 and 1000řC. From burned and unburned bone samples the undecalcified and unstained cross- sections were made, which were microscopically analysed under the magnification of 100×. The histological analysis was performed in the digital microphotographs using the SigmaScan Pro 5 image analysis programme. In each cross-section in total 28 variables were studied, and obtained histomorphometric data were statistically processed using the Statistica 6 programme. The result of the research is the description of the changes of histological structures caused by...

La reconstruction en tomographie discrète de la microstructure de l’os joue un role très important pour le diagnostic de l’ostéoporse, une maladie des os très fréquente. Le diagnostic clinique est basé sur l’absortiométrie duale de rayons X. Avec la tomographie de rayons X, une résolution spatiale élevée avec des images reconstruites in vivo requiert une dose d’irradiation élevée et un temps de balayage long, ce qui est dangereux pour le patient. Une des méthodes pour résoudre ce problème est de limiter le nombre de projections. Cependant, avec cette méthode le problème de reconstruction devient mal posé. Deux types de régularisation par Variation Totale minimisées avec la méthode Alternate Direction of Minimization Method (ADMM) et deux schémas basés sur les méthodes de régularisation Level-set sont appliquées à deux images d’os expérimentales acquises avec un synchrotron (pixel size: 15 μm). Des images de tailles variées et avec différents niveaux de bruit Gaussien additifs ajoutés aux projections sont utlisées pour étudier l’efficacité des méthodes de régularisation. Des minima locaux sont obtenus avec ces méthodes déterministes. Une approche globale d’optimisation est nécessaire pour améliorer les résultats. Des perturbations stochastiques peuvent être un moyen très utile pour échapper aux minima locaux. Dans une première approche, une équation différentielle stochastique basée sur la régularisation level-set est étudiée. Cette méthode améliore les résultats de reconstruction mais ne modifie que les frontières entre les régions 0 et 1. Ensuite une équation aux dérivées partielles stochastique est obtenue avec la régularisation TV pour améliorer la méthode stochastique level-set. A la fin de notre travail, nous avons étendu la méthode de régularisation à des images 3D avec des données réelles. Cette algorithme a été implémenté avec RTK. Nous avons aussi étendu l’approche level-set utilisée pour la tomographie binaire au cas multi-level. / Discrete tomography reconstruction of bone microstructure is important in diagnosis of osteoporosis. One way to reduce the radiation dose and scanning time in CT imaging is to limit the number of projections. This method makes the reconstruction problem highly ill-posed. A common solution is to reconstruct only a finite number of intensity levels. In this work, we investigate only binary tomography reconstruction problem. First, we consider variational regularization methods. Two types of Total Variation (TV) regularization approaches minimized with the Alternate Direction of Minimization Method (ADMM) and two schemes based on Level-set (LS) regularization methods are applied to two experimental bone cross-section images acquired with synchrotron micro-CT. The numerical experiments have shown that good reconstruction results were obtained with TV regularization methods and that level-set regularization outperforms the TV regularization for large bone image with complex structures. Yet, for both methods, some reconstruction errors are still located on the boundaries and some regions are lost when the projection number is low. Local minima were obtained with these deterministic methods. Stochastic perturbations is a useful way to escape the local minima. As a first approach, a stochastic differential equation based on level-set regularization was studied. This method improves the reconstruction results but only modifies the boundaries between the 0 and 1 regions. Then partial stochastic differential equation obtained with the TV regularization semi-norm were studied to improve the stochastic level-set method. The random change of the boundary are performed in a new way with the gradient or wavelet decomposition of the reconstructed image. Random topological changes are included to find the lost regions in the reconstructed images. At the end of our work, we extended the TV regularization method to 3D images with real data on RTK (Reconstruction Toolkit). And we also extended the level-set to the multi-level cases.