Contour tree connectivity and analysis of microstructures

The connectivity of microstructures is directly related to the physical properties of materials. Currently, the Euler number is the most popular measure of connectivity. It is an elegant topological invariant, however, it does not provide information about cavities or the proximities and sizes of objects. In this thesis, an alternative measure called contour tree connectivity (CTC) is developed and its applications for the analysis of microstructures are studied. CTC is derived from contour trees that are used in the first publication to represent complex binary images with simple graphs. By analyzing contour trees, CTC produces new connectivity information that is not provided by other approaches described in the literature. Contour tree representation of binary images and CTC can be computed for any dimensions of data and topology as explained in the second publication. Moreover, CTC is designed to be a scalar between 0 and 1, which makes it easy to use and understand. In this thesis, the use of CTC for analyzing microstructures is presented in two studies. In the first study, the microstructure of trabecular bone is analyzed in relation to its mechanical strength. In the second study, the relationship between microstructures and the fluid flow within materials are examined. The results from these studies show that CTC contributes to the understanding of how the structural properties of materials are linked to their physical properties. To conclude, with its unique properties, CTC complements the structural information provided by currently used measures. This makes it an important image analysis tool for the study of the microstructures of materials such as soil, paper, filters and food products as well as biomaterials and biological tissues

REVIEW OF BONE SCAFFOLD DESIGN CONCEPTS AND DESIGN METHODS

The paper brings out a review of existing, state-of-the-art approaches to designing the geometry of the scaffolds that are used for tissue engineering with a special emphasis on the macro scaffolds aimed for bone tissue recovery. Similar concepts of different authors are organized into groups. The focus of the paper is on determining the existing concepts as well as their advantages and disadvantages. Besides the review of scaffolds' geometry solutions, the analysis of the existing designs points to some serious misconceptions regarding the scaffold role within the (bone) tissue recovery. In the last section of the paper, the main requirements regarding geometry, that is, architecture and corresponding mechanical properties and permeability are reconsidered

Simulation of fracture strength improvements of a human proximal femur using finite element analysis.

The most common hip fracture in the elderly occurs as a result of a fall to the side with impact over the greater trochanter resulting in a fracture of the proximal femur. The fracture usually involves the femoral neck or the intertrochanteric region. It has recently been determined that the fracture crack of a hip fracture typically initiates on the superior-lateral cortex of the femoral neck and then propagates across the femoral neck, resulting in a complete fracture. The strength of the superior-lateral cortex of the femoral neck is likely determined by the combined properties of the generally thin cortex (outer layer) and the underlying trabecular bone in this region. The objective of this study was to determine the relative effects of increasing or decreasing the thickness of these bone tissues on the overall failure strength of the proximal femur. The clinical significance of this work relates to hip fracture risk with various potential treatment options to improve either cortical or trabecular bone quality. A human femur obtained from a 68 year old female donor was scanned using computed tomography at 60-micron voxel resolution and a series of high-resolution finite element models were generated. The models were constructed with a base-element dimension of 120 microns and models included a basic model with cortical and trabecular thicknesses representative of the cadaver specimen from the original scan. Other models used a standardized algorithm to either dilate or erode the trabecular and cortical bone compartments of the femoral neck so that a total of nine models were created including the basic model. Each model was used to simulate a fall-to-the-side loading condition with appropriate boundary and loading conditions as used in previous models and experiments. An experimental test of the cadaver femur was also performed with three strain gauges placed on the proximal femur: on the superior-lateral cortex, on the inferior-medial cortex, and on the medial cortex positioned distal to the lesser trochanter. This femur was loaded at a rate of 100 mm/s until fracture of the femoral neck using a standard fall-to-the-side setup and the applied load and gauge strains were recorded. The femur neck fractured at a load of 2140 N. To validate the basic finite element model, the strain gauge strains at the load levels of 1000 N and 2000 N were compared to the calculated strains from the basic model at the same loads and same location as the gauge on the cadaver femur. After the basic model was validated, a failure criterion was determined as the volume percentage of the elements in the model that had exceeded 7000 µε at the failure load corresponding to the load at which the cadaver femur failed. Subsequently, this failure criterion was applied to the other eight models as a parametric analysis to estimate the increase or decrease in failure strength caused by the changes in cortical and trabecular thickness. The validation test results showed that the basic finite element model calculated strain on the superolateral cortex was within 2.1% of the experimentally measured strain at 1000 N loading. The validated basic model was then used to determine that the percentage of finite elements (by volume of the model) in excess of 7000 µε at the failure load was 4.2%. This failure criterion was then used to estimate the failure load for the other eight models with different combinations of either thicker (+120 µm) or thinner (-120 µm) cortex and trabeculae in the femoral neck. The calculated failure loads ranged from 324 N for the model with thinned cortex and thinned trabeculae to 3336 N for the model with thickened cortex and thickened trabeculae. The model with normal cortex and thickened trabeculae had a failure load of 3242 N, which is only 2.8% less than the strongest case. The largest single parameter effect on proximal femoral strength is realized by an increase in trabecular thickness. This is somewhat surprising considering that cortical bone is typically stronger than cancellous bone. However, the spatial arrangement of trabecular bone and the buttress support it provides to the thin cortex apparently plays an important role in the ability of a global increase in thickness to have a significant beneficial effect

Estimating the effective elastic parameters of nodular cast iron from micro-tomographic imaging and multiscale finite elements : comparison between numerical and experimental results

Herein, we describe in detail a methodology to estimate the effective elastic parameters of nodular cast iron, using micro-tomography in conjunction with multiscale finite elements. We discuss the adjustment of the image acquisition parameters, address the issue of the representative-volume choice, and present a brief discussion on image segmentation. In addition, the finite-element computational implementation developed to estimate the effective elastic parameters from segmented microstructural images is described, indicating the corresponding computational costs. We applied the proposed methodology to a nodular cast iron, and estimated the graphite elastic parameters through a comparison between the numerical and experimental results

Constitutive modeling of the finite deformation behavior of membranes possessing a triangulated networked microstructure

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 108-114).Many biological, natural and synthetic materials possess a networked or micro-truss-like microstructure. In this thesis work, a general microstructurally-informed continuum level constitutive model of the large stretch behavior of membranes possessing a triangulated network or truss-like structure is developed. As a specific example, a constitutive model of the stress-strain behavior of the red blood cell membrane is developed. The mechanical behavior of the membrane of the red blood cell is governed by two primary microstructural features: the lipid bilayer and the underlying spectrin network. The lipid bilayer is analogous to a 2D fluid in that it resists changes to its planar area, yet poses little resistance to planar shear. A skeletal network of spectrin molecules is crosslinked to the lipid bilayer and provides the shear stiffness of the membrane. The planar triangulated structure of the spectrin network is used to identify a representative volume element (RVE) for the model. A strain energy density function in terms of an arbitrary planar deformation field is proposed using the RVE. Differentiation of the strain energy density function provides expressions for the general multiaxial stress-stretch behavior of the material.(cont.) The stress-strain behavior of the membrane when subjected to uniaxial and simple shear loading conditions in different directions is given, showing the capabilities of the proposed microstructurally-detailed constitutive modeling approach in capturing the evolving anisotropic nature of the mechanical behavior. The proposed constitutive model also provides a framework to explore the contributions of mechanically-induced unfolding. The force-extension behavior of a single modular macromolecule exhibits a "saw-tooth" pattern due to unfolding giving a sequence of force rise to a peak followed by a load drop. Using the introduced continuum approach together with single molecule force-extension behavior and a transition state model of unfolding, large deformation behavior of two-dimensional networks of biomacromolecules is studied for various loading conditions. The effect of the strain-rate on the mechanical response is investigated.by Melis Arslan.S.M

Análise Biomecânica de Calo Ósseo usando Método Sem Malha

O osso é um tecido fisiologicamente dinâmico e que quando lesionado tem a capacidade de se reparar com o próprio tecido, não envolvendo um tecido cicatrizante, ao contrário de outros tecidos. Esta característica torna-o particularmente interessante para investigar os processos inerentes de fraturas ósseas. A maior parte das fraturas cicatriza através de uma sequência de processos de diferenciação de tecidos, desde os processos iniciais de hematoma, aos tecidos conjuntivos, e através da cartilagem ao osso. No entanto, qualquer falha neste processo pode resultar em uniões tardias, más uniões ou não uniões. A compreensão na totalidade deste processo ainda constitui um desafio. Os mecanismos que envolvem os processos de estimulação mecânica não se encontram bem compreendidos, em consequência da complexidade dos testes experimentais in vivo, que se tornam dependentes de dados in vitro, tornando difícil validar os pressupostos biológicos. Consequentemente, os modelos computacionais têm demonstrado serem bastante úteis e eficazes na investigação sobre a cicatrização óssea. Desta forma, com o presente trabalho foi possível analisar as condições mecânicas de um calo ósseo resultante de uma fratura, assim como compreender as metodologias de análise numérica aplicadas. O modelo teve por base um estudo in vivo de forma a obter uma variação temporal progressiva da forma do calo e das propriedades mecânicas durante a cicatrização óssea. Com este modelo obtiveram-se os campos de tensão e deformação nas diferentes fases do processo de regeneração, obtendo-se resultados que se encontram em conformidade com a literatura. Adicionalmente, foi aplicado um algoritmo de remodelação óssea em combinação com o Radial Point Interpolation Method (RPIM) que foi capaz de reproduzir as condições apresentadas pela respetiva imagem histológica nesta fase. Por último, espera-se que os trabalhos desenvolvidos neste âmbito possibilitem a conceção de estratégias mais precisas e eficazes tanto para o tratamento como para aceleração da cura. De forma complementar, encontram-se em desenvolvimento modelos específicos dos pacientes e que incorporam variabilidade genética.Bone is a physiologically dynamic tissue that, when injured, has the ability to repair itself, not involving scar tissue, unlike other tissues. This characteristic makes it particularly interesting for investigating the inherent processes of bone fractures. Most fractures heal through a sequence of tissue differentiation processes, from the initial hematoma, to connective tissues and through cartilage to bone. However, any failure in this process can result in a delayed union, mal-union or non-union. A complete understanding of this process is still a challenge. The mechanisms surrounding the mechanical stimulation processes are relatively poorly understood as a result of the complexity of in vivo experimental tests, which become dependent on in vitro data, making it difficult to validate the biological assumptions. Consequently, computational models have proven to be very useful and effective in the investigation of bone healing. Therefore, in the present work, it was possible to analyse the mechanical conditions of a bone callus as a consequence of a fracture and to understand the methodologies of numerical analysis applied. The model was based on an in vivo experimental study in order to obtain a progressive temporal variation of the callus shape and mechanical properties during bone healing. With this model, the stress and strain fields in the different phases of the regeneration process were obtained, where the results are in agreement with the literature. Additionally, a bone remodelling algorithm was applied in combination with the Radial Point Interpolation Method (RPIM), which was able to reproduce the conditions presented by the respective histological image at this stage. Finally, it is expected that the work developed in this area will enable the design of more accurate and effective strategies for both treatment and accelerating healing. Complementarily, patient-specific models and the incorporation of genetic variability are being developed