J. Patrick McGarry

Numerical investigation of the active role of the actin cytoskeleton in the compression resistance of cells.

Numerous in-vitro studies have established that cells react to their physical environment and to applied mechanical loading. However, the mechanisms underlying such phenomena are poorly understood. Previous modelling of cell compression considered the cell as a passive homogenous material, requiring an artificial increase in the stiffness of spread cells to replicate experimentally measured forces. In this study, we implement a fully 3D active constitutive formulation that predicts the distribution, remodelling, and contractile behaviour of the cytoskeleton. Simulations reveal that polarised and axisymmetric spread cells contain stress fibres which form dominant bundles that are stretched during compression. These dominant fibres exert tension; causing an increase in computed compression forces compared to round cells. In contrast, fewer stress fibres are computed for round cells and a lower resistance to compression is predicted. The effect of different levels of cellular contractility associated with different cell phenotypes is also investigated. Highly contractile cells form more dominant circumferential stress fibres and hence provide greater resistance to compression. Computed predictions correlate strongly with published experimentally observed trends of compression resistance as a function of cellular contractility and offer an insight into the link between cell geometry, stress fibre distribution and contractility, and cell deformability. Importantly, it is possible to capture the behaviour of both round and spread cells using a given, unchanged set of material parameters for each cell type. Finally, it is demonstrated that stress distributions in the cell cytoplasm and nucleus computed using the active formulation differ significantly from those computed using passive material models.

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

The inelastic pressure dependent compressive behaviour of bovine trabecular bone is investigated through experimental and computational analysis. Two loading configurations are implemented, uniaxial and confined compression, providing two distinct loading paths in the von Mises-pressure stress plane. Experimental results reveal distinctive yielding followed by a constant nominal stress plateau for both uniaxial and confined compression. Computational simulation of the experimental tests using the Drucker-Prager and Mohr-Coulomb plasticity models fails to capture the confined compression behaviour of trabecular bone. The high pressure developed during confined compression does not result in plastic deformation using these formulations, and a near elastic response is computed. In contrast, the crushable foam plasticity models provide accurate simulation of the confined compression tests, with distinctive yield and plateau behaviour being predicted. The elliptical yield surfaces of the crushable foam formulations in the von Mises-pressure stress plane accurately characterise the plastic behaviour of trabecular bone. Results reveal that the hydrostatic yield stress is equal to the uniaxial yield stress for trabecular bone, demonstrating the importance of accurate characterisation and simulation of the pressure dependent plasticity. It is also demonstrated in this study that a commercially available trabecular bone analogue material, cellular rigid polyurethane foam, exhibits similar pressure dependent yield behaviour, despite having a lower stiffness and strength than trabecular bone. This study provides a novel insight into the pressure dependent yield behaviour of trabecular bone, demonstrating the inadequacy of uniaxial testing alone. For the first time, crushable foam plasticity formulations are implemented for trabecular bone. The enhanced understanding of the inelastic behaviour of trabecular bone established in this study will allow for more realistic simulation of orthopaedic device implantation and failure.

The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force–indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force–indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force–indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force–indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling–experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

Numerous experimental studies have established that cells can sense the stiffness of underlying substrates and have quantified the effect of substrate stiffness on stress fibre formation, focal adhesion area, cell traction, and cell shape. In order to capture such behaviour, the current study couples a mixed mode thermodynamic and mechanical framework that predicts focal adhesion formation and growth with a material model that predicts stress fibre formation, contractility, and dissociation in a fully 3D implementation. Simulations reveal that SF contractility plays a critical role in the substrate-dependent response of cells. Compliant substrates do not provide sufficient tension for stress fibre persistence, causing dissociation of stress fibres and lower focal adhesion formation. In contrast, cells on stiffer substrates are predicted to contain large amounts of dominant stress fibres. Different levels of cellular contractility representative of different cell phenotypes are found to alter the range of substrate stiffness that cause the most significant changes in stress fibre and focal adhesion formation. Furthermore, stress fibre and focal adhesion formation evolve as a cell spreads on a substrate and leading to the formation of bands of fibres leading from the cell periphery over the nucleus. Inhibiting the formation of FAs during cell spreading is found to limit stress fibre formation. The predictions of this mutually dependent material-interface framework are strongly supported by experimental observations of cells adhered to elastic substrates and offer insight into the inter-dependent biomechanical processes regulating stress fibre and focal adhesion formation.

Full and surface tibial cementation in total knee arthroplasty: A biomechanical investigation of stress distribution and remodeling in the tibia

BACKGROUND Aseptic tibial component loosening remains a major cause of total knee arthroplasty failure. The cementation technique used to achieve fixation may play a major role in loosening. Despite this, the optimum technique remains unanswered. This study aims to investigate stress and strain distributions in the proximal tibia for full cementation and surface cementation of the Genesis II tibial component. METHODS Principal cortical bone strains were measured experimentally in intact, surface cemented and fully cemented synthetic tibiae using strain gauges. Both axial and 15° flexion loading were considered. Finite element models were used to assess both cortical and cancellous bone stresses and strains. Using a bone remodeling algorithm potential sites of bone formation and resorption were identified post-implantation. FINDINGS Principal cortical bone strain results demonstrate strong correlations between the experimental and finite element analyses (R(2)≥0.81, RMSE(%)≤17.5%). Higher cortical strains are measured for surface cementation, as full cementation creates a stiffer proximal tibial structure. Simulations reveal that both cementation techniques result in lower cancellous stresses under the baseplate compared to the intact tibia, with greater reductions being computed for full cementation. The surface cementation model displays the closest cancellous stress distribution to the intact model. In addition, bone remodeling simulations predict more extensive bone resorption under the baseplate for full cementation (43%) than for surface cementation (29%). INTERPRETATION Full cementation results in greater stress reduction under the tibial baseplate than surface cementation, suggesting that surface cementation will result in less proximal bone resorption, thus reducing the possibility of aseptic loosening.

Computational investigation of in situ chondrocyte deformation and actin cytoskeleton remodelling under physiological loading.

Previous experimental studies have determined local strain fields for both healthy and degenerate cartilage tissue during mechanical loading. However, the biomechanical response of chondrocytes in situ, in particular the response of the actin cytoskeleton to physiological loading conditions, is poorly understood. In the current study a three-dimensional (3-D) representative volume element (RVE) for cartilage tissue is created, comprising a chondrocyte surrounded by a pericellular matrix and embedded in an extracellular matrix. A 3-D active modelling framework incorporating actin cytoskeleton remodelling and contractility is implemented to predict the biomechanical behaviour of chondrocytes. Physiological and abnormal strain fields, based on the experimental study of Wong and Sah (J. Orthop. Res. 2010; 28: 1554-1561), are applied to the RVE. Simulations demonstrate that the presence of a focal defect significantly affects cellular deformation, increases the stress experienced by the nucleus, and alters the distribution of the actin cytoskeleton. It is demonstrated that during dynamic loading cyclic tension reduction in the cytoplasm causes continuous dissociation of the actin cytoskeleton. In contrast, during static loading significant changes in cytoplasm tension are not predicted and hence the rate of dissociation of the actin cytoskeleton is reduced. It is demonstrated that chondrocyte behaviour is affected by the stiffness of the pericellular matrix, and also by the anisotropy of the extracellular matrix. The findings of the current study are of particular importance in understanding the biomechanics underlying experimental observations such as actin cytoskeleton dissociation during the dynamic loading of chondrocytes.

Cortical bone failure mechanisms during screw pullout

An experimental and computational study of screw pullout from cortical bone has been conducted. A novel modification of standard pullout tests providing real time image capture of damage mechanisms during screw pullout was developed. Pullout forces, measured using the novel test rig, have been validated against standard pullout tests. Pullout tests were conducted, considering osteon alignment, to investigate the effect of osteons aligned parallel to the axis of the orthopaedic screw (longitudinal pullout) as well as the effect of osteons aligned perpendicular to the axis of the screw (transverse pullout). Distinctive alternate failure mechanisms, for longitudinally and transversely orientated cortical bone during screw pullout, were uncovered. Vertical crack propagation, parallel to the axis of the screw, was observed for a longitudinal pullout. Horizontal crack propagation, perpendicular to the axis of the screw, was observed for a transverse pullout. Finite element simulation of screw pullout, incorporating material damage and crack propagation, was also performed. Simulations revealed that a homogenous material model for cortical bone predicts vertical crack propagation patterns for both longitudinal and transverse screw pullout. A bi-layered composite model representing cortical bone microstructure was developed. A unique set of material and damage properties was used for both transverse and longitudinal pullout simulations, with only layer orientations being changed. Simulations predicted: (i) higher pullout forces for transverse pullout; (ii) horizontal crack paths perpendicular to screw axis for transverse pullout, whereas vertical crack paths were computed for longitudinal pullout. Computed results agreed closely with experimental observations in terms of pullout force and crack propagation.

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.

On the role of the actin cytoskeleton and nucleus in the biomechanical response of spread cells

Micropipette aspiration (MA) has been used extensively in biomechanical investigations of un-adhered cells suspended in media. In the current study, a custom MA system is developed to aspirate substrate adhered spread cells. Additionally, the system facilitates immuno-fluorescent staining of aspirated cells to investigate stress fibre redistribution and nucleus deformation during MA. In response to an applied pressure, significantly lower aspiration length is observed for untreated contractile cells compared to cells in which actin polymerisation is chemically inhibited, demonstrating the important contribution of stress fibres in the biomechanical behaviour of spread cells. Additional experiments are performed in which untreated contractile cells are subjected to a range of applied pressures. Computational finite element simulations reveal that a viscoelastic material model for the cell cytoplasm is incapable of accurately predicting the observed aspiration length over the range of applied pressures. It is demonstrated that an active computational framework that incorporates stress fibre remodelling and contractility must be used in order to accurately simulate MA of untreated spread cells. Additionally, the stress fibre distribution observed in immuno-fluorescent experimental images of aspirated cells is accurately predicted using the active stress fibre modelling framework. Finally, a detailed experimental-computational investigation of the nucleus mechanical behaviour demonstrates that the nucleus is highly deformable in cyto, reaching strain levels in excess of 100% during MA. The characterisation of stress fibres and nucleus biomechanics in spread cells presented in the current study can potentially be used to guide tissue engineering strategies to control cell behaviour and gene expression.

Simulation of the mechanical response of cells on micropost substrates.

Experimental studies where cells are seeded on micropost arrays in order to quantify their contractile behavior are becoming increasingly common. Interpretation of the data generated by this experimental technique is difficult, due to the complexity of the processes underlying cellular contractility and mechanotransduction. In the current study, a coupled framework that considers strain rate dependent contractility and remodeling of the cytoskeleton is used in tandem with a thermodynamic model of tension dependent focal adhesion formation to investigate the biomechanical response of cells adhered to micropost arrays. Computational investigations of the following experimental studies are presented: cell behavior on different sized arrays with a range of post stiffness; stress fiber and focal adhesion formation in irregularly shaped cells; the response of cells to deformations applied locally to individual posts; and the response of cells to equibiaxial stretching of micropost arrays. The predicted stress fiber and focal adhesion distributions; in addition to the predicted post tractions are quantitatively and qualitatively supported by previously published experimental data. The computational models presented in this study thus provide a framework for the design and interpretation of experimental micropost studies.