Finite element analysis of interaction between actin cytoskeleton and intracellular fluid in prechondrocytes and chondrocytes subjected to compressive loading

Prechondrocytes exhibit a change in their actin cytoskeletal arrangement when subjected to loading. This study looks at the implications of the altered solid-fluid interactions due to this change. A 2-D Finite element model of a cell was developed. A solid-fluid interaction solution procedure was validated and used to determine fluid flow/pressure in a cell when subject to deformation. These values were then used to calculate fluid flow induced stresses on individual actin fibers. The results suggest that prechondrocytes alter their cytoskeletal structure to reduce stresses as a result of fluid flow due to deformation of the cell

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

On the effects of mechanical stress of biological membranes in modeling of swelling dynamics of biological systems

We highlight mechanical stretching and bending of membranes and the importance of membrane deformations in the analysis of swelling dynamics of biological systems, including cells and subcellular organelles. Membrane deformation upon swelling generates tensile stress and internal pressure, contributing to volume changes in biological systems. Therefore, in addition to physical (internal/external) and chemical factors, mechanical properties of the membranes should be considered in modeling analysis of cellular swelling. Here we describe an approach that considers mechanical properties of the membranes in the analysis of swelling dynamics of biological systems. This approach includes membrane bending and stretching deformations into the model, producing a more realistic description of swelling. We also discuss the effects of membrane stretching on swelling dynamics. We report that additional pressure generated by membrane bending is negligible, compared to pressures generated by membrane stretching, when both membrane surface area and volume are variable parameters. Note that bending deformations are reversible, while stretching deformation may be irreversible, leading to membrane disruption when they exceed a certain threshold level. Therefore, bending deformations need only be considered in reversible physiological swelling, whereas stretching deformations should also be considered in pathological irreversible swelling. Thus, the currently proposed approach may be used to develop a detailed biophysical model describing the transition from physiological to pathological swelling mode.National Aeronautics & Space Administration (NASA):80NSSC19M0049; PR Space Grant (NASA):NNX15AI11Hinfo:eu-repo/semantics/publishedVersio

Evaluation of Testing Methods for Suction-Volume Change of Natural Clay Soils

abstract: Design and mitigation of infrastructure on expansive soils requires an understanding of unsaturated soil mechanics and consideration of two stress variables (net normal stress and matric suction). Although numerous breakthroughs have allowed geotechnical engineers to study expansive soil response to varying suction-based stress scenarios (i.e. partial wetting), such studies are not practical on typical projects due to the difficulties and duration needed for equilibration associated with the necessary laboratory testing. The current practice encompasses saturated “conventional” soil mechanics testing, with the implementation of numerous empirical correlations and approximations to obtain an estimate of true field response. However, it has been observed that full wetting rarely occurs in the field, leading to an over-conservatism within a given design when partial wetting conditions are ignored. Many researchers have sought to improve ways of estimation of soil heave/shrinkage through intense studies of the suction-based response of reconstituted clay soils. However, the natural behavior of an undisturbed clay soil sample tends to differ significantly from a remolded sample of the same material. In this study, laboratory techniques for the determination of soil suction were evaluated, a methodology for determination of the in-situ matric suction of a soil specimen was explored, and the mechanical response to changes in matric suction of natural clay specimens were measured. Suction-controlled laboratory oedometer devices were used to impose partial wetting conditions, similar to those experienced in a natural setting. The undisturbed natural soils tested in the study were obtained from Denver, CO and San Antonio, TX. Key differences between the soil water characteristic curves of the undisturbed specimen test compared to the conventional reconstituted specimen test are highlighted. The Perko et al. (2000) and the PTI (2008) methods for estimating the relationship between volume and changes in matric suction (i.e. suction compression index) were evaluated by comparison to the directly measured values. Lastly, the directly measured partial wetting swell strain was compared to the fully saturated, one-dimensional, oedometer test (ASTM D4546) and the Surrogate Path Method (Singhal, 2010) to evaluate the estimation of partial wetting heave.Dissertation/ThesisMasters Thesis Engineering 201

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today

Mathematical and Experimental Approaches for Designing Less Toxic Cryopreservation Methods

Successful cryopreservation of all biological specimens would have an untold positive impact on medicine and scientific research. However, cryopreservation of the most complex biological specimens, such as tissues and organs, remains elusive. Vitrification, or ice-free cryopreservation, is promising for cryopreservation of complex specimens. The biggest challenge, though, is the toxicity imparted by the large concentration of cryoprotectant(s) (CPAs) required to suppress ice formation. There are several approaches to overcome toxicity that have been proposed in the field, but our group has proposed the use of mathematical modeling to minimize toxicity. The optimization strategy revolves around design of a vitrification protocol that minimizes the toxicity cost function. In a previous work, this approach was used to identify a vitrification protocol using glycerol as the CPA that was less toxic for endothelial cells when compared to conventional protocols used in the field. This previous work serves as a foundation for the current work presented here, which seeks to expand the utility of the toxicity cost function approach. In the first research chapter of this work, an automated liquid handling methodology is proposed to characterize CPA toxicity, and five of the most common CPAs and their binary and ternary combinations are characterized. This approach lays the foundation for future high-throughput screening of CPA toxicity, and the data set that was obtained will inform future models for predicting the toxicity of multi-CPA mixtures. To apply the toxicity cost function approach to tissues and organs, more complicated mass transfer models are required to predict the flow of CPAs and calculate the toxicity imparted. In the second research chapter of this work, a general mass transfer model is proposed for tissues. This model augments an acellular cartilage-based model in the literature by adding cells and accounting for their effects on mass transfer within tissues. We show that this modeling approach is applicable to the two very different tissues of cartilage and pancreatic islets. Moving to the organ regime and the third and final research chapter of this work, mass transfer within kidneys is investigated. Specifically, slaughterhouse porcine kidneys are perfused with various CPA solutions and the overall mass response is compared to that of a single cell. Also, an experimental method is proposed to measure the CPA concentration within the kidney as a function of space and time using computed tomography (CT). Another experimental method utilizing a lactate dehydrogenase (LDH) assay is also proposed that could measure damage imparted from CPA addition and removal. The third research chapter provides a basis for informing organ-based mass transfer models in the future. Overall, it is the hope that the chapters of this work provide a solid foundation for future research of furthering the toxicity cost function approach within all specimen regimes of cryopreservation

Mathematical modelling of the complex mechanics of biological gels

Biological tissues are comprised of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. A range of natural and synthetic gels are used in such experiments, with these gels primarily consisting of solvent and polymer. In this thesis, we develop mathematical models that incorporate cell-gel interactions together with osmotic pressure to better understand the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. We investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel’s composition) and the types of behaviour that can arise as a result. We begin by developing a multiphase model to study gel swelling and contraction. In this model, the volume fractions of polymer and solvent (which together form the gel) are tracked alongside cell density as the gel evolves. We consider the novel addition of cell traction forces in this framework alongside chemical potentials in the polymer and solvent. We then study this model in one-dimensional coordinates. We find that a number of qualitatively different behaviours are possible, depending on the composition of the gel and the strength of cell traction forces. We discover spatially varying steady states as well as an unusual case where the components of the gel oscillate between swelling and contraction. Since gels used in experiments are often formed as thin layers, we extend the model to study the gel as a two-dimensional thin sheet. We derive an extensional flow model by using the gel’s thinness to scale certain parameters; in this model, key variables are functions of axial position and time. This allows us to derive a new leading order, one dimensional model from the initial 2D system of equations. We consider the thin film model for uniform and non-uniform initial conditions separately. With uniform initial conditions, we find that the model reduces to a system driven by an ordinary differential equation in the gel’s height. For non-uniform initial conditions, spatially varying equilibrium solutions can be found. In this thesis, we develop and analyse new mathematical models for a cell-gel system incorporating cell-induced gel contraction alongside osmotic effects. We find new emergent behaviours, derive a new leading order model from the two-dimensional thin film problem, and compare the gel’s behaviours in 1D and 2D settings. We show that adding cells can provide a switch between gel swelling and contraction, and that the balance between chemical potentials and cell forces is pivotal in the system’s stability and equilibrium outcomes.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 202

Membrane behavior and diffusion in unsaturated sodium bentonite

2015 Spring.Includes bibliographical references.Sodium-bentonite (Na-bentonite) is a highly active clay commonly used as a barrier or a component of a barrier for chemical containment applications (e.g., landfills, waste impoundments, vertical cutoff walls) due to the ability of Na-bentonite to limit solute (contaminant) transport resulting from high swell and low hydraulic conductivity. However, Na-bentonite also may exhibit semipermeable membrane behavior or solute restriction, which can result in enhanced performance of the barrier by reducing liquid and contaminant flux. Experimental studies to date have focused on the correlation between membrane behavior and diffusion of solutes almost exclusively under fully saturated conditions (i.e., degree of water saturation, S, of 1.0). However, clay barriers can exist at various degrees of water saturation (S < 1.0), and, based on our current, conceptual understanding of the mechanisms causing membrane behavior in saturated clays, the influence of membrane behavior on solute transport is likely to be even more significant in clays under unsaturated conditions. Based on these considerations, an innovative testing apparatus was developed to allow for the simultaneous measurement of membrane behavior and diffusion in unsaturated Na-bentonite. The test specimens were prepared using a dialysis method that allowed for control of the cation species on the exchange complex of the bentonite, removal of excess soluble salts, and estimation of diffusion properties. Membrane efficiencies (ω) and effective diffusion coefficients (D*) of bentonite specimens with S ranging from 0.79 to 1.0 were measured by performing multistage tests using solutions of potassium chloride (KCl). The source concentrations (Cot) of the KCl solutions were 20 mM, 30 mM, and 50 mM, which resulted in average concentrations in the specimen at steady-state diffusion (Cave) of approximately 10 mM, 15 mM, and 25 mM. For all values of S, a decrease in S correlated with an increase in ω and a decrease in D*. For example, for Cot of 50 mM, ω increased from 0.31 to 0.41 and D* for chloride decreased from 4.1 x 10-10 m2/s to 3.1 x 10-10 m2/s as S decreased from 1.0 to 0.84. The results of this study advance our fundamental understanding of solute transport mechanisms in Na-bentonite and contribute to the base of knowledge that must be established prior to incorporating membrane behavior effects in the design of barriers for chemical containment facilities