This thesis presents research that was conducted to develop anatomically realistic finite element models of breast deformation under a variety of gravity loading conditions to assist clinicians in tracking suspicious tissues across multiple imaging modalities. Firstly, the accuracy of the modelling framework in predicting deformations of a homogeneous body was measured using custom designed silicon gel phantoms. The model predicted surface deformations with an average RMS error of 1.5 mm +/- 0.2 mm and tracked internal marker locations with an average RMS error of 1.4 mm +/- 0.7 mm. A novel method was then developed to determine the reference configuration of a body, when given its mechanical properties, boundary conditions and a deformed configuration. The theoretical validity of the technique was confirmed with an analytic solution. The accuracy of the method was also measured using silicon gel experiments, predicting the reference configuration surface with an average RMS error of 1.3 mm +/- 0.1 mm, and tracking internal marker locations with an average error of 1.5 mm +/- 0.8 mm. Silicon gel composites were then created to measure the accuracy of standard techniques to model heterogeneity. The models did not match the experimentally recorded deformations. This highlighted the need for further validation exercises on modelling heterogeneity before modelling them in the breast. A semi-automated algorithm was developed to fit finite element models to the skin and muscle surfaces of each individual, which were segmented from breast MR images. The code represented the skin with an average RMS error of 1.46 mm +/- 0.32 mm and the muscle with an average RMS error of 1.52 mm +/- 0.3 mm. The framework was then tested using images of the breast obtained under different gravity loading conditions and neutral buoyancy. A homogeneous model was first developed using the neutral buoyancy images as a representation of the reference configuration. The model did not accurately capture the regional deformations of the breast under gravity loading. However, the gross shape of the breast was reproduced, indicating that a biomechanical model of the breast could be useful to reliably track tissues across multiple images for cancer diagnosis. / This research was sponsored by the Top Achiever Doctoral Scholarship and the University of Auckland Doctoral Scholarship. Extra funding for travel was provided by the Graduate Research Fund and the John Logan Campbell Trust Fund.

Um tema relevante de pesquisa em pneumologia atualmente é a contratilidade de via aérea, e como a mesma é modulada por estímulos mecânicos e farmacológicos. De modo a contribuir com este campo de pesquisa, este projeto tem por objetivo a execução de medições de grandezas associadas à mecânica respiratória de vias aéreas isoladas in vitro para avaliar sua resposta a estímulos externos como alterações de pressão transmural, estiramento, poluentes e drogas. Para tal finalidade, foi integrada uma nova instrumentação de processamento de imagens e condicionamento/estimulação de tecidos aos equipamentos já em uso em diversas pesquisas pelo Laboratório de Engenharia Biomédica da Escola Politécnica da Universidade de São Paulo. Este ambiente foi testado em corpos de prova; foi avaliado o efeito da pressão transmural na mecânica de traqueias e o ambiente foi utilizado na análise do efeito de bronco-constritores na mecânica respiratória de traqueias decelularizadas (utilizadas em transplante traqueal). Os testes em corpos de prova demonstraram a capacidade do ambiente em executar as medidas de interesse; os estudos com pressão transmural quantificaram a expansão das paredes da traqueia com o incremento da pressão interna e os estudos com traqueias decelularizadas mostram que as mesmas não respondem a broncoconstritores, ao contrário de traqueias normais que apresentaram indícios de contração. Desta forma, o ambiente foi capaz de realizar pesquisas de contratilidade de via aérea, demonstrando indícios da insensibilidade de traqueias decelularizadas a bronco-constritores. / Currently, a relevant field in the research of pulmonology is the contractibility of airways, and their modulation through mechanical and pharmacological stimuli. In order to contribute to this research, the goal of this project is to execute measurements of respiratory mechanic indicators to assess the behavior of isolated airways in vitro to external stimuli such as modifications in transmural pressure, dynamic stretching, pollution and drugs. For this purpose a new image processing and tissue conditioning/stimulation environment was integrated with the existing instrumentation already in use by the Biomedical Engineering Laboratory in the Escola Politécnica da Universidade de São Paulo. The environment was tested in tubular structures mimicking airways, the effect of transmural pressure in the respiratory mechanics of trachea was assessed and the environment was used in the research of the effect that bronchoconstrictor drugs have on the respiratory mechanics of decellularized tracheas (used in tracheal transplants). The tests in tubular structures proved the environments capacity to execute the desired measurements; the expansion of the tracheal walls with the rise of internal pressure was quantified and the experiments with decellularized tracheas show that they are not responsive to bronchoconstrictor durgs, opposite to normal tracheas that presented evidences of contraction. The environment succeeded in the execution of research of airway contractibility and demonstrated evidences of insensitivity of decellularized trachea to bronchoconstrictor drugs.

The development and maintenance of tissues and organs depend on the careful regulation and coordinated motion of large numbers of cells. There is substantial evidence that many complex tissue functions, such as cell division, collective cell migration and gene expression, are directly regulated by mechanical forces. However, relatively little is known about how mechanical stress is distributed within a tissue and how this may guide biochemical signalling. Working in the framework of a popular vertex-based model, we derive expressions for stress tensors at the cell and tissue level to build analytic relationships between cell shape and mechanical stress. The discrete vertex model is upscaled, providing exact expressions for the bulk and shear moduli of disordered cellular networks, which bridges the gap to traditional continuum-level descriptions of tissues. Combining this theoretical work with new experimental techniques for whole-tissue stretching of Xenopus laevis tissue, we separate the roles of mechanical stress and cell shape in orienting and cueing epithelial mitosis. We find that the orientation of division is best predicted by the shape of tricellular junctions, while there appears to be a more direct role for mechanical stress as a mitotic cue.

abstract: This dissertation features a compilation of studies concerning the biophysics of multicellular systems. I explore eukaryotic systems across length scales of the cell cytoskeleton to macroscopic scales of tissues. I begin with a general overview of the natural phenomena of life and a philosophy of investigating developmental systems in biology. The topics covered throughout this dissertation require a background in eukaryotic cell physiology, viscoelasticity, and processes of embryonic tissue morphogenesis. Following a brief background on these topics, I present an overview of the Subcellular Element Model (ScEM). This is a modeling framework which allows one to compute the dynamics of large numbers of three-dimensional deformable cells in multi-cellular systems. A primary focus of the work presented here is implementing cellular function within the framework of this model to produce biologically meaningful phenotypes. In this way, it is hoped that this modeling may inform biological understanding of the underlying mechanisms which manifest into a given cell or tissue scale phenomenon. Thus, all theoretical investigations presented here are motivated by and compared to experimental observations. With the ScEM modeling framework I first explore the passive properties of viscoelastic networks. Then as a direct extension of this work, I consider the active properties of cells, which result in biological behavior and the emergence of non-trivial biological phenotypes in cells and tissues. I then explore the possible role of chemotaxis as a mechanism of orchestrating large scale tissue morphogenesis in the early embryonic stages of amniotes. Finally I discuss the cross-sectional topology of proliferating epithelial tissues. I show how the Subcellular Element Model (ScEM) is a phenomenological model of finite elements whose interactions can be calibrated to describe the viscoelastic properties of biological materials. I further show that implementing mechanisms of cytoskeletal remodeling yields cellular and tissue phenotypes that are more and more biologically realistic. Particularly I show that structural remodeling of the cell cytoskeleton is crucial for large scale cell deformations. I provide supporting evidence that a chemotactic dipole mechanism is able to orchestrate the type of large scale collective cell movement observed in the chick epiblast during gastrulation and primitive streak formation. Finally, I show that cell neighbor histograms provide a potentially unique signature measurement of tissue topology; such measurements may find use in identifying cellular level phenotypes from a single snapshot micrograph. / Dissertation/Thesis / Ph.D. Physics 2011

Developing tissues are out-of-equilibrium systems that grow and reshape to form organs in adult animals. They are typically composed of a large number of cells. The constitutive cells of a tissue perform different roles in tissue development and contribute to the overall tissue shape changes. In this thesis, we construct a hydrodynamic theory of developing epithelial tissues. We use it to investigate the developing wing of the fruit fly Drosophila melanogaster. This theory relates the coarse-grained cell scale properties to the large-scale tissue flows. We explicitly account for the active cellular processes in the tissue that drive tissue flows. In our description of the tissue, we also include the memory effects that are necessary to account for the experimental observations. These memory effects have a significant influence on the tissue rheology. Using this hydrodynamic theory we analyze shear flow in a developing fruit fly wing tissue. We find that the active cellular processes contribute to overall tissue flows and that memory effects are present in the wing tissue. We investigate consequences of these findings on the rheology of tissue shear flow. We find that the memory effects give rise to an inertial response that leads to oscillations in the tissue but it does not stem from the wing mass. Finally, we describe how the tissue rheology is affected by different boundary conditions. We then investigate the area changes during the pupal wing development and we construct a mechanosensitive model for the cell extrusion rate in the pupal wing. Analysis of cell extrusions in the context of this model also allows us to extract information about the cell division properties. Boundary connections between the wing tissue and surrounding cuticle are crucial for the proper development of the pupal wing. A dumpy mutant wing is strongly misshaped during the pupal wing morphogenesis. We use a simple model for the wing to show that the dumpy mutant wing can be described as a wild type wing with compromised boundary conditions. Finally, we analyze cell properties and tissue flows in a developing wing disc epithelium. Motivated by the observation of radially oriented active T1 transitions in the wing disc epithelium, we use the hydrodynamic theory to investigate the influence of such T1 transitions on stresses in the tissue. We show that sufficiently strong radially oriented active T1 transitions can contribute to the control of the tissue size. Results obtained in this thesis extend our understanding of the fly wing tissue rheology and the role of internal and external forces in the proper shaping of the wing epithelium. The hydrodynamic theory we use to describe the fly wing development provides a set of phenomenological parameters that characterize the tissue mechanics and can be experimentally measured. Therefore, we expect that future research will include and extend the hydrodynamic theory presented in this thesis.

Die Tumorprogression wird von Veränderungen der Gewebemorphologie begleitet. In 2D-Zellkulturen wurden verschiedene Gewebezustände gefunden, z.B. flüssigar- tige, 'gejammete' sowie nematische Zustände, die mit den Zellformen zusammen- hingen. Obwohl man diese Resultate nicht einfach auf dreidimensionale Gewebe wie Tumore übertragen kann, legen sie nahe, den Zusammenhang von Zellformen, Gewebemorphologie und Aggregatzustand von 3D-Geweben zu untersuchen. Ich untersuche Zellbeweglichkeit in 3D-Sphäroiden, wobei ich einen krebsartigen (ma- lignen) und einen nicht-krebsartigen Zelltyp miteinander vergleiche. Ich analysiere sowohl das Gesamtverhalten des Gewebes durch Sphäroid-Fusionsexperimente als auch Einzel-Zell-Bewegungen, und zeige damit dass das maligne Gewebe durch aktive, bewegliche Zellen verflüssigt wird, wohingegen das epitheliale (gesunde) Gewebe sich eher verhält wie ein Festkörper. Eine komplette 3D-Segmentation der Proben zeigt, dass sich im flüssigen Gewebe mehr elongierte Zellen befinden, was Zellformen mit Zellmotilität verbindet. Ich finde somit zwei aktive Zustände in 3D- Geweben: einen amorphen, glas-artigen, der Züge von Zell-Jamming trägt; sowie einen ungeordneten, flüssigen Zustand. Darüber hinaus demonstriere ich einen en- gen Zusammenhang zwischen Zellformen und Kernformen in beiden Gewebearten. Zum ersten Mal kann damit eine Verbindung von Krebs-Grading in histologischen Schnitten mit der Physik des Jamming hergestellt werden, womit sich die Tür zu klinischen Anwendungen im diagnostischen Bereich öffnet.

Reverse shoulder arthroplasty (RSA) is a common treatment for individuals with arthritis of the glenohumeral joint in the presence of a massive rotator cuff tear. Though this procedure has been effective in restoring function to these individuals, it has also been associated with high early to mid-term complications, such as scapular notching and instability. A finite element (FE) modeling approach has previously been used to study the range of motion an individual with RSA could adduct their arm the polyethylene liner impinged on the inferior scapular bone and the contact stress at the impingement site. This model was then validated in a physical experiment using cadaveric tissue. In this document, I introduce modifications to that FE model to further study instability and scapular notching risk. First, modern RSA implant geometries were introduced into the model, and the effect of polyethylene liner rotation and glenoid version on impingement-free range of motion and instability risk was assessed. Then, a physical material property characterization of rotator cuff tissues present after RSA was performed. Finally, those material properties and continuum elements representative of the rotator cuff tendons were introduced into the FE model. Throughout all of these studies, greater complexity and fidelity was added to improve the ability to model both contact at the impingement site and potential dislocation events through more accurate loadings and boundary conditions.

Developing tissues are out-of-equilibrium systems that grow and reshape to form organs in adult animals. They are typically composed of a large number of cells. The constitutive cells of a tissue perform different roles in tissue development and contribute to the overall tissue shape changes. In this thesis, we construct a hydrodynamic theory of developing epithelial tissues. We use it to investigate the developing wing of the fruit fly Drosophila melanogaster. This theory relates the coarse-grained cell scale properties to the large-scale tissue flows. We explicitly account for the active cellular processes in the tissue that drive tissue flows. In our description of the tissue, we also include the memory effects that are necessary to account for the experimental observations. These memory effects have a significant influence on the tissue rheology. Using this hydrodynamic theory we analyze shear flow in a developing fruit fly wing tissue. We find that the active cellular processes contribute to overall tissue flows and that memory effects are present in the wing tissue. We investigate consequences of these findings on the rheology of tissue shear flow. We find that the memory effects give rise to an inertial response that leads to oscillations in the tissue but it does not stem from the wing mass. Finally, we describe how the tissue rheology is affected by different boundary conditions. We then investigate the area changes during the pupal wing development and we construct a mechanosensitive model for the cell extrusion rate in the pupal wing. Analysis of cell extrusions in the context of this model also allows us to extract information about the cell division properties. Boundary connections between the wing tissue and surrounding cuticle are crucial for the proper development of the pupal wing. A dumpy mutant wing is strongly misshaped during the pupal wing morphogenesis. We use a simple model for the wing to show that the dumpy mutant wing can be described as a wild type wing with compromised boundary conditions. Finally, we analyze cell properties and tissue flows in a developing wing disc epithelium. Motivated by the observation of radially oriented active T1 transitions in the wing disc epithelium, we use the hydrodynamic theory to investigate the influence of such T1 transitions on stresses in the tissue. We show that sufficiently strong radially oriented active T1 transitions can contribute to the control of the tissue size. Results obtained in this thesis extend our understanding of the fly wing tissue rheology and the role of internal and external forces in the proper shaping of the wing epithelium. The hydrodynamic theory we use to describe the fly wing development provides a set of phenomenological parameters that characterize the tissue mechanics and can be experimentally measured. Therefore, we expect that future research will include and extend the hydrodynamic theory presented in this thesis.

Indiana University-Purdue University Indianapolis (IUPUI) / Finite element analysis (FEA) in implantology is performed in design applications concerning the complex topology of an implant, according to theoretical assumptions about and clinical data concerning the biomechanical nature of skeletal tissue. Implants are placed in topologically and physiologically complex sites, and major disagreement exists in literature about various aspects concerning their modeling and analysis. Current research seeks to improve the implementation of an implant by the use of short implants, which negate the necessity of additional surgical procedures in regions of limited bone height. However, short implants with large crown heights introduce biomechanical complications associated with increased stress and strain distributions in skeletal tissue, which may cause bone loss and implant failure. The short implant is characterized by the geometric ratio of the crown height to the implant length, called the crown-to-implant (C/I) ratio. In this work nonlinear FEA was performed to investigate the effects and significance of the C/I ratio on long-term implant stability. A finite element model was developed according to literature, and emulation of previous research and comparison of reported results were performed. Comparison of results demonstrated significant sources of error in previous research, which are argued to be caused by mesh-dependency from common model idealizations in literature. A convergence test was then performed, which verified the mesh-dependency of results and challenged the reliability of some common model assumptions and methods of analysis in literature. A 16-point design of experiments was then performed to evaluate the significance and influence of the C/I ratio, considering a proposed novel method for evaluating results and predicting long-term stability. Analysis of results demonstrated that the C/I ratio augments the inherent biomechanical effects of an implant design, particularly overloading strain concentrations at implant interface features. The use of short implants with high C/I ratios is determined to be inadvisable, considering the physiological response of tissue to strain distributions and biological context. A novel, multiscale material model is then proposed to describe the short-term accumulation of damage and biomechanical remodeling response in orthotropic skeletal tissue, as a potential solution to the mesh-dependency of results.

Osteoarthritis (OA) is a chronic, painful, and currently incurable disease characterized by structural deterioration and loss of function of synovial joints. OA is known to involve profound changes in bone density and microstructure near to, and even distal to, the joint. The prevailing view is that these changes in density and microstructure serve to stiffen the subchondral region thereby altering the mechanical environment (stresses and strains) within the epiphyseal and metaphyseal bone, and that these alterations trigger the aberrant cellular signaling and tissue damage characteristic of the progression of OA. Critically, however, these alterations in mechanical environment have never been well documented in a quantitative fashion in hip OA. Separately, although OA is generally thought to be inversely associated with fragility fracture, recent data challenge this idea and suggest that OA may actually modulate which regions of the proximal femur are at risk of fracture. Therefore, the goal of this work was to provide a spatial assessment of bone density and microstructure in hip OA and then examine the mechanical consequences of these OA-related abnormalities throughout the proximal femur. First, micro-computed tomography and data-driven computational anatomy were used to examine 3-D maps of the distribution of bone density and microstructure in human femoral neck samples with increasing severity of radiographic OA, providing evidence of the heterogeneous and multi-faceted changes in hip OA and discussion of the implications for OA progression and fracture risk. Second, the feasibility of proton density-weighted MRI in image-based finite element (FE) modeling, to examine stress, strain, and risk of failure in the proximal femur under sideways fall, was assessed by comparison to the current standard of CT-based FE modeling. Third, phantom-less calibration for CT-based FE modeling was used with clinically available pre-operative patient scans to assess bone strength and failure risk of the proximal femur in hip OA. Overall, the results of this work provide a rich, quantitative definition of the ways in which the bone mechanical environment under traumatic loading differ in association with hip OA, and then highlight the potential for clinical image-based FE methods to be used opportunistically to assess bone strength and failure risk at the hip. This work is significant because it directly tests the long-standing premise that OA is associated with changes in the mechanical environment of the bone tissue in ways that are impactful for OA progression; further, this work examines how these changes may influence risk of hip fracture. The results can be used to identify mechanistic predictors of OA progression, to inform development of bone-targeting treatments for OA, and to more broadly understand bone damage and fracture in this population.