Hierarchical multiscale model for biomechanics analysis of microfilament networks

The mechanisms of force generation and transference via microfilament networks are crucial to the understandings of mechanobiology of cellular processes in living cells. However, there exists an enormous challenge for all-atom physics simulation of real size microfilament networks due to scale limitation of molecular simulation techniques. Following biophysical investigations of constitutive relations between adjacent globular actin monomers on filamentous actin, a hierarchical multiscale model was developed to investigate the biomechanical properties of microfilament networks. This model was validated by previous experimental studies of axial tension and transverse vibration of single F-actin. The biomechanics of microfilament networks can be investigated at the scale of real eukaryotic cell size (10 μm). This multiscale approach provides a powerful modeling tool which can contribute to the understandings of actin-related cellular processes in living cells.

Cyclic mechanical strain guides capillary-like morphology in vitro

Introduction Stretching of tissue stimulates angiogenesis but increased motion at a fracture site hinders revascularisation. In vitro studies have indicated that mechanical stimuli promote angiogenic responses in endothelial cells, but can either inhibit or enhance responses when applied directly to angiogenesis assays. We anticipated that cyclic tension applied during endothelial network assembly would increase vascular structure formation up to a certain threshold. Methods Fibroblast/HUVEC co-cultures were subjected to cyclic equibiaxial strain (1 Hz; 6 h/day; 7 days) using the FlexerCell FX-4000T system and limiting rings for simultaneous application of multiple strain magnitudes (0–13%). Cells were labelled using anti-PECAM-1, and image analysis provided measures of endothelial network length and numbers of junctions. Results Cyclic stretching had no significant effect on the total length of endothelial networks (P > 0.2) but resulted in a strain-dependent decrease in branching and localised alignments of endothelial structures, which were in turn aligned with the supporting fibroblastic construct. Conclusion The organisation of endothelial networks under cyclic strain is dominated by structural adaptation to the supporting construct. It may be that, in fracture healing, the formation and integrity of the granulation tissue and callus is ultimately critical in revascularisation and its failure under severe strain conditions.

Mechanical tension as a driver of connective tissue growth in vitro

We propose the progressive mechanical expansion of cell-derived tissue analogues as a novel, growth-based approach to in vitro tissue engineering. The prevailing approach to producing tissue in vitro is to culture cells in an exogenous “scaffold” that provides a basic structure and mechanical support. This necessarily pre-defines the final size of the implantable material, and specific signals must be provided to stimulate appropriate cell growth, differentiation and matrix formation. In contrast, surgical skin expansion, driven by increments of stretch, produces increasing quantities of tissue without trauma or inflammation. This suggests that connective tissue cells have the innate ability to produce growth in response to elevated tension. We posit that this capacity is maintained in vitro, and that order-of-magnitude growth may be similarly attained in self-assembling cultures of cells and their own extracellular matrix. The hypothesis that growth of connective tissue analogues can be induced by mechanical expansion in vitro may be divided into three components: (1) tension stimulates cell proliferation and extracellular matrix synthesis; (2) the corresponding volume increase will relax the tension imparted by a fixed displacement; (3) the repeated application of static stretch will produce sustained growth and a tissue structure adapted to the tensile loading. Connective tissues exist in a state of residual tension, which is actively maintained by resident cells such as fibroblasts. Studies in vitro and in vivo have demonstrated that cellular survival, reproduction, and matrix synthesis and degradation are regulated by the mechanical environment. Order-of-magnitude increases in both bone and skin volume have been achieved clinically through staged expansion protocols, demonstrating that tension-driven growth can be sustained over prolonged periods. Furthermore, cell-derived tissue analogues have demonstrated mechanically advantageous structural adaptation in response to applied loading. Together, these data suggest that a program of incremental stretch constitutes an appealing way to replicate tissue growth in cell culture, by harnessing the constituent cells’ innate mechanical responsiveness. In addition to offering a platform to study the growth and structural adaptation of connective tissues, tension-driven growth presents a novel approach to in vitro tissue engineering. Because the supporting structure is secreted and organised by the cells themselves, growth is not restricted by a “scaffold” of fixed size. This also minimises potential adverse reactions to exogenous materials upon implantation. Most importantly, we posit that the growth induced by progressive stretch will allow substantial volumes of connective tissue to be produced from relatively small initial cell numbers.

Design, characterisation and in vivo testing of a new, adjustable stiffness, external fixator for the rat femur

Very little is known about the infl uence of the mechanical environment on the healing of large segmental defects. This partly reflects the lack of standardised, well characterised technologies to enable such studies. Here we report the design, construction and characterisation of a novel external fixator for use in conjunction with rat femoral defects. This device not only imposes a predetermined axial stiffness on the lesion, but also enables the stiffness to be changed during the healing process. The main frame of the fi xator consists of polyethylethylketone with titanium alloy mounting pins. The stiffness of the fi xator is determined by interchangeable connection elements of different thicknesses. Fixators were shown to stabilise 5 mm femoral defects in rats in vivo for at least 8 weeks during unrestricted cage activity. No distortion or infections, including pin infections, were noted. The healing process was simulated in vitro by inserting into a 5 mm femoral defect, materials whose Young’s moduli approximated those of the different tissues present in regenerating bone. These studies confirmed that, although the external fixator is the major determinant of axial stiffness during the early phase of healing, the regenerate within the lesion subsequently dominates this property. There is much clinical interest in altering the mechanics of the defect to enhance bone healing. Our data suggest that, if alteration of the mechanical environment is to be used to modulate the healing of large segmental defects, this needs to be performed before the tissue properties become dominant.

Cross-scale biophysics modelling of F-actin cytoskeleton in cell

This thesis is a comparative study of the modelling of mechanical behaviours of F-actin cytoskeleton which is an important structural component in living cells. A new granular model was developed for F-actin cytoskeleton based on the concept of multiscale modelling. This framework overcomes difficulties encountered in physical modelling of cytoskeleton in conventional continuum mechanics modelling, and the computational challenges in all-atom molecular dynamics simulation. The thermostat algorithm was further modified to better predict the thermodynamic properties of F-actin cytoskeleton in modelling. This multiscale modelling framework was applied in explaining the physical mechanisms of cytoskeleton responses to external mechanical loads.

Understanding the relationship between interfragmentary movement and callus growth in fracture healing: A novel computational approach

Introduction & Aims Optimising fracture treatments requires a sound understanding of relationships between stability, callus development and healing outcomes. This has been the goal of computational modelling, but discrepancies remain between simulations and experimental results. We compared healing patterns vs fixation stiffness between a novel computational callus growth model and corresponding experimental data. Hypothesis We hypothesised that callus growth is stimulated by diffusible signals, whose production is in turn regulated by mechanical conditions at the fracture site. We proposed that introducing this scheme into computational models would better replicate the observed tissue patterns and the inverse relationship between callus size and fixation stiffness. Method Finite element models of bone healing under stiff and flexible fixation were constructed, based on the parameters of a parallel rat femoral osteotomy study. An iterative procedure was implemented, to simulate the development of callus and its mechanical regulation. Tissue changes were regulated according to published mechano-biological criteria. Predictions of healing patterns were compared between standard models, with a pre-defined domain for callus development, and a novel approach, in which periosteal callus growth is driven by a diffusible signal. Production of this signal was driven by local mechanical conditions. Finally, each model’s predictions were compared to the corresponding histological data. Results Models in which healing progressed within a prescribed callus domain predicted that greater interfragmentary movements would displace early periosteal bone formation further from the fracture. This results from artificially large distortional strains predicted near the fracture edge. While experiments showed increased hard callus size under flexible fixation, this was not reflected in the standard models. Allowing the callus to grow from a thin soft tissue layer, in response to a mechanically stimulated diffusible signal, results in a callus shape and tissue distribution closer to those observed histologically. Importantly, the callus volume increased with increasing interfragmentary movement. Conclusions A novel method to incorporate callus growth into computational models of fracture healing allowed us to successfully capture the relationship between callus size and fixation stability observed in our rat experiments. This approach expands our toolkit for understanding the influence of different fixation strategies on healing outcomes.

Adjustable stiffness, external fixator for the rat femur osteotomy and segmental bone defect models

The mechanical environment around the healing of broken bone is very important as it determines the way the fracture will heal. Over the past decade there has been great clinical interest in improving bone healing by altering the mechanical environment through the fixation stability around the lesion. One constraint of preclinical animal research in this area is the lack of experimental control over the local mechanical environment within a large segmental defect as well as osteotomies as they heal. In this paper we report on the design and use of an external fixator to study the healing of large segmental bone defects or osteotomies. This device not only allows for controlled axial stiffness on the bone lesion as it heals, but it also enables the change of stiffness during the healing process in vivo. The conducted experiments have shown that the fixators were able to maintain a 5 mm femoral defect gap in rats in vivo during unrestricted cage activity for at least 8 weeks. Likewise, we observed no distortion or infections, including pin infections during the entire healing period. These results demonstrate that our newly developed external fixator was able to achieve reproducible and standardized stabilization, and the alteration of the mechanical environment of in vivo rat large bone defects and various size osteotomies. This confirms that the external fixation device is well suited for preclinical research investigations using a rat model in the field of bone regeneration and repair.

Development of a novel experimental model to investigate the influence of mechanics on bone healing

This dissertation proposed a novel experimental model combining a defect configuration with an active instrumented fixation device to investigate the influence of mechanics on bone healing. The proposed defect configuration aimed to minimise physiological loading within an experimental fracture gap and the instrumented fixator was used for the application of controlled displacements and in vivo stiffness monitoring of the healing process. This thesis has provided a novel approach to advance current knowledge and understanding of mechanobiology, which has been limited in previous experimental models.

Regional variations in the nonlinearity and anisotropy of bovine aortic elastin

Arterial walls have a regular and lamellar organization of elastin present as concentric fenestrated networks in the media. In contrast, elastin networks are longitudinally oriented in layers adjacent to the media. In a previous model exploring the biomechanics of arterial elastin, we had proposed a microstructurally motivated strain energy function modeled using orthotropic material symmetry. Using mechanical experiments, we showed that the neo-Hookean term had a dominant contribution to the overall form of the strain energy function. In contrast, invariants corresponding to the two fiber families had smaller contributions. To extend these investigations, we use biaxial force-controlled experiments to quantify regional variations in the anisotropy and nonlinearity of elastin isolated from bovine aortic tissues proximal and distal to the heart. Results from this study show that tissue nonlinearity significantly increases distal to the heart as compared to proximally located regions (). Distally located samples also have a trend for increased anisotropy (), with the circumferential direction stiffer than the longitudinal, as compared to an isotropic and relatively linear response for proximally located elastin samples. These results are consistent with the underlying tissue histology from proximally located samples that had higher optical density (), fiber thickness (), and trend for lower tortuosity () in elastin fibers as compared to the thinner and highly undulating elastin fibers isolated from distally located samples. Our studies suggest that it is important to consider elastin fiber orientations in investigations that use microstructure-based models to describe the contributions of elastin and collagen to arterial mechanics.

Dynamics of cell–matrix mechanical interactions in three dimensions

The forces cells apply to their surroundings control biological processes such as growth, adhesion, development, and migration. In the past 20 years, a number of experimental techniques have been developed to measure such cell tractions. These approaches have primarily measured the tractions applied by cells to synthetic two-dimensional substrates, which do not mimic in vivo conditions for most cell types. Many cell types live in a fibrous three-dimensional (3D) matrix environment. While studying cell behavior in such 3D matrices will provide valuable insights for the mechanobiology and tissue engineering communities, no experimental approaches have yet measured cell tractions in a fibrous 3D matrix.

This thesis describes the development and application of an experimental technique for quantifying cellular forces in a natural 3D matrix. Cells and their surrounding matrix are imaged in three dimensions with high speed confocal microscopy. The cell-induced matrix displacements are computed from the 3D image volumes using digital volume correlation. The strain tensor in the 3D matrix is computed by differentiating the displacements, and the stress tensor is computed by applying a constitutive law. Finally, tractions applied by the cells to the matrix are computed directly from the stress tensor.

The 3D traction measurement approach is used to investigate how cells mechanically interact with the matrix in biologically relevant processes such as division and invasion. During division, a single mother cell undergoes a drastic morphological change to split into two daughter cells. In a 3D matrix, dividing cells apply tensile force to the matrix through thin, persistent extensions that in turn direct the orientation and location of the daughter cells. Cell invasion into a 3D matrix is the first step required for cell migration in three dimensions. During invasion, cells initially apply minimal tractions to the matrix as they extend thin protrusions into the matrix fiber network. The invading cells anchor themselves to the matrix using these protrusions, and subsequently pull on the matrix to propel themselves forward.

Lastly, this thesis describes a constitutive model for the 3D fibrous matrix that uses a finite element (FE) approach. The FE model simulates the fibrous microstructure of the matrix and matches the cell-induced matrix displacements observed experimentally using digital volume correlation. The model is applied to predict how cells mechanically sense one another in a 3D matrix. It is found that cell-induced matrix displacements localize along linear paths. These linear paths propagate over a long range through the fibrous matrix, and provide a mechanism for cell-cell signaling and mechanosensing. The FE model developed here has the potential to reveal the effects of matrix density, inhomogeneity, and anisotropy in signaling cell behavior through mechanotransduction.

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. © 2013 Springer-Verlag Berlin Heidelberg.

Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents

The design of medical devices could be very much improved if robust tools were available for computational simulation of tissue response to the presence of the implant. Such tools require algorithms to simulate the response of tissues to mechanical and chemical stimuli. Available methodologies include those based on the principle of mechanical homeostasis, those which use continuum models to simulate biological constituents, and the cell-centred approach, which models cells as autonomous agents. In the latter approach, cell behaviour is governed by rules based on the state of the local environment around the cell; and informed by experiment. Tissue growth and differentiation requires simulating many of these cells together. In this paper, the methodology and applications of cell-centred techniques-with particular application to mechanobiology-are reviewed, and a cell-centred model of tissue formation in the lumen of an artery in response to the deployment of a stent is presented. The method is capable of capturing some of the most important aspects of restenosis, including nonlinear lesion growth with time. The approach taken in this paper provides a framework for simulating restenosis; the next step will be to couple it with more patient-specific geometries and quantitative parameter data.