Homeostatic Elastic States and the Stability of Elastic Arteries

Vascular mechanics has undergone significant growth within the last 50 years owing to the rapid development of nonlinear continuum mechanics occurring roughly within the same period and motivated primarily by rubber materials. However, one important distinction of blood vessels, in contrast to typical engineering materials is that, through a variety of physiological mechanisms, they seek to maintain constant a preferred mechanical state (mechanical homeostasis) thereby exhibiting a remarkable mechanical stability in response to temporal evolution and alterations in blood pressure, vessel tethering forces and geometry and material properties. The mechanical state experienced by blood vessels plays a critical role in mechanical homeostasis and mechanical stability, and there remains a pressing need for mechanical/mathematical analysis to i) understand/predict the stretch/stress states within vessels and how they evolve with increasing blood pressure and tethering forces, ii) understand/predict the mechanical stability of arteries in response to diverse stimuli such as inhomogeneities in geometry and material properties. This dissertation seeks to add to this vibrant field by conducting a rigorous analysis of i) the mechanics of the homeostatic states of uniform circumferential stress and uniform stretch in an N-layer cylindrical artery subject to circumferential prestress, axial tethering force and the pressure of blood and ii) the local mechanical stability by imperfection growth in a solid body subject to inhomogeneities in geometry and material properties. In order to make these results relevant to a blood vessel, a micromechanics based constitutive relation is proposed based on the more or less regular architecture of a large elastic artery composed of collagen, elastin and vascular smooth muscle. Although the primary focus of the work is on the healthy artery, the effect on imperfection growth of diseased tissue constituents is accounted for in a simple model of damaged elastin and collagen

Multiscale regulation of cellular mechanical properties

Thesis (Ph.D.)--Boston UniversityIn vivo, cells routinely experience mechanical stresses and strains in the form of circulatory pressure and flow, peristalsis ofthe gut, and airway inflation and deflation. Even on the microscale, all adherent cells apply contractile force to the extracellular matrix and to neighboring cells. Cells respond to these external forces both passively and actively. Passively, cells need to deform in a way that is tissue and function appropriate. Actively, cells use local mechanoreceptors present on their surface to trigger changes in global cell behavior. Dysregulation of cell responses to force are hallmarks of diseases such as atherosclerosis, asthma and cancer. Given the pluripotent role of cell mechanics in both normal cell behavior and disease, cell regulation of mechanical properties has become a major area of focus in biology. In this dissertation, we explore passive mechanical properties and active mechanical responses of cells on the subcellular, single cell and multicellular length scales. In Aim 1, we developed a new tool, called cell biomechanical imaging, for mapping intracellular stiffness and prestress. We have demonstrated a linear relationship between these two quantities, both at the whole cell and subcellular levels, which suggests prestress may be a unifying mechanism by which cells and tissues tune their mechanical properties. In Aim 2, we investigated how coordinated changes in cytoskeletal tension lead to cell reorientation. Previous research has shown that in response to strain applied through focal adhesions, the actin cytoskeleton promptly fluidizes and then slowly resolidifies. Using both experiments and a mathematical model, we found that repeated interplay ofthese phenomena was a driving force behind cytoskeletal reorganization during cell reorientation. It was previously hypothesized that the purpose of cytoskeletal remodeling in response to strain was to minimize changes in intracellular mechanical tension and maintain it at a preferred level. This feedback control mechanism, which balances forces between the cell and its microenvironment, is termed "tensional homeostasis." The dominant paradigm in vascular biology is that tensional homeostasis exists across multiple length and time scales. However, our results from Aim 2 challenged this idea; reoriented cells did not maintain steady levels of contractile force. In Aim 3, we investigated tensional homeostasis and its existence at multiple length scales. We found that cells do not have a preferred level of tension at the subcellular or single cell levels. However, in a cluster of confluent cells, contractile tension is maintained, the more so as cluster size increases. Together, the results of this dissertation emphasize the importance ofa multiscale approach to mechanobiology. Cells and tissue are hierarchically ordered systems that use mechanical stress (prestress) to tune their mechanical properties and responses across lengthscales. Thus, it is important to consider not just the behavior of separate components of each of these systems, but the behaviors that emerge when they interact with one another

Fluctuations in active membranes

Active contributions to fluctuations are a direct consequence of metabolic energy consumption in living cells. Such metabolic processes continuously create active forces, which deform the membrane to control motility, proliferation as well as homeostasis. Membrane fluctuations contain therefore valuable information on the nature of active forces, but classical analysis of membrane fluctuations has been primarily centered on purely thermal driving. This chapter provides an overview of relevant experimental and theoretical approaches to measure, analyze and model active membrane fluctuations. In the focus of the discussion remains the intrinsic problem that the sole fluctuation analysis may not be sufficient to separate active from thermal contributions, since the presence of activity may modify membrane mechanical properties themselves. By combining independent measurements of spontaneous fluctuations and mechanical response, it is possible to directly quantify time and energy-scales of the active contributions, allowing for a refinement of current theoretical descriptions of active membranes.Comment: 38 pages, 9 figures, book chapte

Investigations into the mechanics of connective tissue

This thesis presents work on investigations into the mechanical properties of connective tissue. A model system of hydrogels was used to investigate how volume change through water flow is coupled to relaxation. This was done using digital image correlation (DIC) and a custom built setup. It was found, in hydrogels, that water loss is directly coupled to an increase in tension and water intake is directly coupled to tension relaxation. The experimental setup was tested by investigating the mechanical properties of the well known material polydimethylsiloxane (PDMS) and the novel materials of carbon nanotube (CNT) elastomers, cholesteric liquid crystal elastomers (CLCEs), and 3D polydomain liquid crystal elastomers (3DLCEs). The setup accurately demonstrated the incompressibility of PDMS, even at short time scales, and demonstrated how DIC can map the inhomogeneity of material by locating clusters of CNTs in CNT elastomers by how they deform. Novel results for 3DLCEs were also found, where it was discovered that there is a softening of the bulk modulus at small time scales resulting in a volume increase following deformation, the bulk modulus then recovers and there is over all no volume change. This is in stark contrast to the typical case, where it is the shear modulus that becomes comparable to the bulk modulus, resulting in increased volume. A theoretical investigation was carried out into critical damping in viscoelastic oscillators, where the aim was to apply to the findings to connective tissue. The fractional Maxwell model and zener model where both solved for, where it was found that damping decreases as the material becomes more solid and the peak of critical damping becomes broader. Finally, investigations into how strain relates to the viscoelastic properties of connective tissue were carried out on horse tendon and rat fascia. How relaxation changes was determined through the relaxation constant, where a large constant means it takes the sample longer to relax and it is more solid like. It was found, that in general, the relaxation constant increases quickly with an imposed strain and then either stabilises or increases more slowly. This growth of relaxation constant also occurs during the initial stages of tissue injury, where irreversible deformation occurs

Doctor of Philosophy

dissertationDespite the progress that has been made since the inception of the finite element method, the field of biomechanics has generally relied on software tools that were not specifically designed to target this particular area of application. Software designed specifically for the field of computational biomechanics does not appear to exist. To overcome this limitation, FEBio was developed, an acronym for “Finite Elements for Biomechanics”, which provided an open-source framework for developing finite element software that is tailored to the specific needs of the biomechanics and biophysics communities. The proposed work added an extendible framework to FEBio that greatly facilitates the implementation of novel features and provides an ideal platform for exploring novel computational approaches. This framework supports plugins, which simplify the process of adding new features even more since plugins can be developed independently from the main source code. Using this new framework, this work extended FEBio in two important areas of interest in biomechanics. First, as tetrahedral elements continue to be the preferred modeling primitive for representing complex geometries, several tetrahedral formulations were investigated in terms of their robustness and accuracy for solving problems in computational biomechanics. The focus was on the performance of quadratic tetrahedral formulations in large deformation contact analyses, as this is an important area of application in biomechanics. Second, the application of prestrain to computational models has been recognized as an important component in simulations of biological tissues in order to accurately predict the mechanical response. As this remains challenging to do in existing software packages, a general computational framework for applying prestrain was incorporated in the FEBio software. The work demonstrated via several examples how plugins greatly simplify the development of novel features. In addition, it showed that the quadratic tetrahedral formulations studied in this work are viable alternatives for contact analyses. Finally, it demonstrated the newly developed prestrain plugin and showed how it can be used in various applications of prestrain

Continuum Models of Collective Migration in Living Tissues

This dissertation investigates the physical mechanics of collective cell migration in monolayers of epithelial cells. Coordinated cell motion underlies a number of biological processes, including wound healing, morphogenesis and cancer metastasis, and is controlled by the interplay of single cell motility, cell-cell adhesions, cell-substrate interaction, and cell contractility modulated by the acto-myosin cytoskeleton. Here we examine the competing roles of these mechanisms via a continuum model of a tissue as an active elastic medium, where mechanical deformations are coupled to and feed back onto chemical signaling. We begin in Chapter 1 with a brief review of cell migration at both the single-cell and many-cell levels, and of the experimental tools used to probe the mechanical properties of cells and tissues. In Chapter 2 we formulate our minimal continuum model of a tissue as an overdamped active elastic medium on a frictional substrate. The model couples mechanical deformations in the tissue to myosin-based contractile activity and to cell polarization. Two new ingredients of our model are: (i) a feedback between the on-off dynamics of myosin motors and the active contractile stresses they induce in the tissue, and (ii) the coupling of cell directed motion or polarization to tissue strain. In the following two chapters we employ this model to describe collective cell dynamics in expanding (Chapter 3) and confined (Chapter 4) tissues and compare with experiments. In expanding monolayers, as realized for instance in wound healing assays where an initially confined tissue is allowed to expand freely on a substrate, our model reproduces the propagating waves of mechanical stress observed in experiments and believed to play a key role in controlling the transmission of information across the tissue and mediating coordinated cell motion. Combining analytical and numerical work we construct a phase diagram that identifies various dynamical regimes in terms of single-cell properties, such as contractility and stiffness. In Chapter 4, we use our model to describe collective dynamics of cells confined to a circular geometry. In this case the propagating waves are replaced by standing sloshing waves guided by both contractility and polarization. The work on confined tissues was carried out in collaboration with the experimental group of Jeff Fredberg at the Harvard School of Public Health. By combining theory and experiment we can provide a quantitative understanding of how contractility and polarization regulate the mechanics of the tissue by renormalizing the tissue elastic moduli and controlling the frequency of oscillatory modes

Rapid dynamics of cell-shape recovery in response to local deformations

It is vital that cells respond rapidly to mechanical cues within their microenvironment through changes in cell shape and volume, which rely upon the mechanical properties of cells’ highly interconnected cytoskeletal networks and intracellular fluid redistributions. While previous research has largely investigated deformation mechanics, we now focus on the immediate cell-shape recovery response following mechanical perturbation by inducing large, local, and reproducible cellular deformations using AFM. By continuous imaging within the plane of deformation, we characterize the membrane and cortical response of HeLa cells to unloading, and model the recovery via overdamped viscoelastic dynamics. Importantly, the majority (90%) of HeLa cells recover their cell shape in o1 s. Despite actin remodelling on this time scale, we show that cell-shape recovery time is not affected by load duration, nor magnitude for untreated cells. To further explore this rapid recovery response, we expose cells to cytoskeletal destabilizers and osmotic shock conditions, which uncovers the interplay between actin and osmotic pressure. We show that the rapid dynamics of recovery depend crucially on intracellular pressure, and provide strong evidence that cortical actin is the key regulator in the cell-shape recovery processes, in both cancerous and non-cancerous epithelial cell

Rapid dynamics of cell-shape recovery in response to local deformations

It is vital that cells respond rapidly to mechanical cues within their microenvironment through changes in cell shape and volume, which rely upon the mechanical properties of cells’ highly interconnected cytoskeletal networks and intracellular fluid redistributions. While previous research has largely investigated deformation mechanics, we now focus on the immediate cell-shape recovery response following mechanical perturbation by inducing large, local, and reproducible cellular deformations using AFM. By continuous imaging within the plane of deformation, we characterize the membrane and cortical response of HeLa cells to unloading, and model the recovery via overdamped viscoelastic dynamics. Importantly, the majority (90%) of HeLa cells recover their cell shape in o1 s. Despite actin remodelling on this time scale, we show that cell-shape recovery time is not affected by load duration, nor magnitude for untreated cells. To further explore this rapid recovery response, we expose cells to cytoskeletal destabilizers and osmotic shock conditions, which uncovers the interplay between actin and osmotic pressure. We show that the rapid dynamics of recovery depend crucially on intracellular pressure, and provide strong evidence that cortical actin is the key regulator in the cell-shape recovery processes, in both cancerous and non-cancerous epithelial cell