Advancements in computational power and micro-imaging has allowed the creation of finite element (FE) models on a microstructural level that can represent complex skeletal structures. These µFE models can analyze the structural integrity of individual trabeculae and may be used to model the impact of complex pathologies on skeletal stability. This thesis aims to: 1) optimize the histological identification of microdamage in healthy and mixed metastatic whole rat vertebrae, 2) quantify trabecular level stress and strain using µFE models and deformable registration generated from µCT data and 3) evaluate stress and strain in µFE models comparing undamaged regions with areas of mechanically induced microdamage. This novel technique allows the histological identification of microdamage in whole vertebrae with accurate alignment to 3D μCT data sets. In the μFE models, significantly higher stresses and strains were found in areas of damaged bone in both healthy and metastatically involved vertebrae.

Advancements in computational power and micro-imaging has allowed the creation of finite element (FE) models on a microstructural level that can represent complex skeletal structures. These µFE models can analyze the structural integrity of individual trabeculae and may be used to model the impact of complex pathologies on skeletal stability. This thesis aims to: 1) optimize the histological identification of microdamage in healthy and mixed metastatic whole rat vertebrae, 2) quantify trabecular level stress and strain using µFE models and deformable registration generated from µCT data and 3) evaluate stress and strain in µFE models comparing undamaged regions with areas of mechanically induced microdamage. This novel technique allows the histological identification of microdamage in whole vertebrae with accurate alignment to 3D μCT data sets. In the μFE models, significantly higher stresses and strains were found in areas of damaged bone in both healthy and metastatically involved vertebrae.

A new three-dimensional finite solid element (3D FE) model for dowel-type wood connections was developed using the concept of a beam on a nonlinear wood foundation, which addresses the intricate wood crushing behaviour under the connector in a dowel type connection. In order to implement the concept of wood foundation with solid elements, a 3D FE wood foundation model was defined within a prescribed foundation zone surrounding the dowel. Based on anisotropic plasticity material theory, the material model for the foundation zone was developed using effective foundation material constants that were defined from dowel-embedment test data. New 3D FE single nail connection models were developed that incorporated the wood foundation model. The 3D wood foundation model was justified and validated using dowel-embedment test data with a range of dowel diameters, from a 2.5-mm nail to a25.4-mm bolt. The connection models provided successful results in simulating the characteristics of load-slip behaviour that were experimentally observed. Based on the success of the single nail connection models, several applications of the3D FE connection models were investigated including statistical wood material models, bolted connection models and a multiple nail connection model. Throughout the application studies, discussion of the benefits and limitations of the new model approach using the 3D FE wood foundation are presented. Also, future areas of study are proposed in order to improve the 3D FE dowel-type wood connections models.

Many soft food materials, including vegetable shortening, exhibit complex rheological behaviour with properties that resemble those of a solid and a liquid simultaneously. The fundamental parameters used to describe the rheological response of vegetable shortening were obtained from uniaxial compression tests, including monotonic and cyclic compression, as well as creep and stress relaxation tests. The fundamental parameters obtained from the various compression tests were then used in two mechanical models (viscoelastic and elasto-visco-plastic) to predict the compression and conical indentation response of vegetable shortening. The accuracy of the two models was studied with the help of the commercially available finite element analysis software package Abaqus. It was determined that the viscoelastic model was not suitable for the prediction of the rheological response of shortening. On the other hand, the proposed elasto-visco-plastic model predicted with reasonable accuracy the uniaxial compression and indentation experimental response of vegetable shortening. / February 2009

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied. <br /><br /> Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.

Cell-cell adhesion is important to understanding the mechanics of cell-cell interactions. A recent study of cell adhesion was conducted by others using an Atomic Force Microscopy to measure forces when two cells are brought together and then pulled apart. When the two cells come in contact, the adhesion molecules of one cell bind to molecules of the other cell throughout the contact region. When the two cells are then pulled apart, some of these bonds break off while others lead to the formation of tethers which also eventually also break. These phenomena create a force-time curve, which is difficult to interpret. In order to model this experiment and understand details of the experiments, a series of modules were added to a 2D finite element model used previously to model cells and their mechanical interactions. These new modules were designed to replicate mechanical processes associated with molecular detachments at the cell-cell interface. The enhanced model includes several new types of elements including an InterfaceTruss, which characterizes individual adhesion bonds between two cells. Parametric studies carried out using the new finite element model showed that cytoplasmic viscosity, actin cortex stiffness, and the lifetime of the molecular attachments at the cell-cell interface all affect one or more portions of the force time curve. The model was able to model virtually all of the significant features of the experimental force-time curve, and when suitable parameter values are chosen, the model closely approximates the observed features of the experimental curves. The new finite element model provides an effective tool for investigating features of the cell-cell interface. It also provides a powerful tool for learning about the mechanical properties of the cells and their bonds and tethers and for the design of new cell adhesion experiments.

In this paper a continuous Galerkin multiscale method (CGMM) and a discontinuous Galerkin multiscale method (DGMM) are proposed, both based on the variational multiscale method for solving partial differential equations numerically. The solution is decoupled into a coarse and a fine scale contribution, where the fine-scale contribution is computed on patches with localized right hand side. Numerical experiments are presented where exponential decay of the error is observed when increasing the size of the patches for both CGMM and DGMM. DGMM gives much better accuracy when the same size of the patches are used.

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied. <br /><br /> Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.

Cell-cell adhesion is important to understanding the mechanics of cell-cell interactions. A recent study of cell adhesion was conducted by others using an Atomic Force Microscopy to measure forces when two cells are brought together and then pulled apart. When the two cells come in contact, the adhesion molecules of one cell bind to molecules of the other cell throughout the contact region. When the two cells are then pulled apart, some of these bonds break off while others lead to the formation of tethers which also eventually also break. These phenomena create a force-time curve, which is difficult to interpret. In order to model this experiment and understand details of the experiments, a series of modules were added to a 2D finite element model used previously to model cells and their mechanical interactions. These new modules were designed to replicate mechanical processes associated with molecular detachments at the cell-cell interface. The enhanced model includes several new types of elements including an InterfaceTruss, which characterizes individual adhesion bonds between two cells. Parametric studies carried out using the new finite element model showed that cytoplasmic viscosity, actin cortex stiffness, and the lifetime of the molecular attachments at the cell-cell interface all affect one or more portions of the force time curve. The model was able to model virtually all of the significant features of the experimental force-time curve, and when suitable parameter values are chosen, the model closely approximates the observed features of the experimental curves. The new finite element model provides an effective tool for investigating features of the cell-cell interface. It also provides a powerful tool for learning about the mechanical properties of the cells and their bonds and tethers and for the design of new cell adhesion experiments.

Ultrasonic is a transport form of sound. There is no mass transportation, only energy transportation occurs in transfer process. Recently, the ultrasonic was widely used in a variety of purposes. For example¡Gsonar, non-destructive testing, washing and emulsification. Due to the effects of mechanical vibration of ultrasonic on the physiological can promote the percutaneous absorption, ultrasonic is widely used in medical cosmetic field. It can get amazing amount of spending and will continue growth every year. The skin is the body's largest organ, which can be divided into epidermis, dermis and hypodermis. There are two main approaches for drugs to be delivered through the skin: directly penetrate the epidermis and penetrate the lipid layer of cell space. The main purpose of this study is to executing numerical simulation through finite element analysis. By constructing the 3D FEM model of the skin, the effects of different level combinations of the three factors, massage time, amplitudes and frequencies of ultrasonic, on the equivalent strain distributions of the epidermis, dermis, hypodermis and muscle layers were studied, while the skin was massaged by using ultrasonic. The simulation results showed that the difference of maximum equivalent strain is nearly one hundred times between different factor¡¦s level combinations. That means the choice of the appropriate factor¡¦s level combination will affect the efficacy of ultrasonic massage seriously. The numerical simulation results also showed that amplitude is the most influential factor on the equivalent strain for every layers of skin except the epidermis.