Mechanobiology of Bone Development and Computational Simulations

Bone is important because it provides the skeleton structural integrity and enables movement and locomotion. Its development and morphology follow its function. It adapts to changes of mechanical loading and has the ability to repair itself after damage or fracture. The processes of bone development, bone adaptation, and bone regeneration in fracture healing are regulated, in part, by mechanical stimuli that result when the bone is loaded.

Validation of β-actin used as endogenous control for gene expression analysis in mechanobiology studies : amendments

We write in response to the letter by Liu et al. [1] commenting on our article, ‘‘Mesenchymal Stem Cells Regulate Angiogenesis According to Their Mechanical Environment’’ [2]. The study by Liu et al. demonstrates that the commonly used endogeneous reference gene (ERG), b-actin, is upregulated by mechanical loading, indicating a potential bias in the determined target gene expression when normalizing to b-actin, such as in our report on unchanged vascular endothelial growth factor (VEGF) and hypoxia-inducible factors (HIF)-1a mRNA levels in mechanically loaded mesenchymal stem cells (MSCs).

Effects of strain artefacts arising from a pre-defined callus domain in models of bone healing mechanobiology

Iterative computational models have been used to investigate the regulation of bone fracture healing by local mechanical conditions. Although their predictions replicate some mechanical responses and histological features, they do not typically reproduce the predominantly radial hard callus growth pattern observed in larger mammals. We hypothesised that this discrepancy results from an artefact of the models’ initial geometry. Using axisymmetric finite element models, we demonstrated that pre-defining a field of soft tissue in which callus may develop introduces high deviatoric strains in the periosteal region adjacent to the fracture. These bone-inhibiting strains are not present when the initial soft tissue is confined to a thin periosteal layer. As observed in previous healing models, tissue differentiation algorithms regulated by deviatoric strain predicted hard callus forming remotely and growing towards the fracture. While dilatational strain regulation allowed early bone formation closer to the fracture, hard callus still formed initially over a broad area, rather than expanding over time. Modelling callus growth from a thin periosteal layer successfully predicted the initiation of hard callus growth close to the fracture site. However, these models were still susceptible to elevated deviatoric strains in the soft tissues at the edge of the hard callus. Our study highlights the importance of the initial soft tissue geometry used for finite element models of fracture healing. If this cannot be defined accurately, alternative mechanisms for the prediction of early callus development should be investigated.

Mechanical conditions in the initial phase of bone healing

Background: Bone healing is sensitive to the initial mechanical conditions with tissue differentiation being determined within days of trauma. Whilst axial compression is regarded as stimulatory, the role of interfragmentary shear is controversial. The purpose of this study was to determine how the initial mechanical conditions produced by interfragmentary shear and torsion differ from those produced by axial compressive movements. ----- ----- Methods: The finite element method was used to estimate the strain, pressure and fluid flow in the early callus tissue produced by the different modes of interfragmentary movement found in vivo. Additionally, tissue formation was predicted according to three principally different mechanobiological theories. ----- ----- Findings: Large interfragmentary shear movements produced comparable strains and less fluid flow and pressure than moderate axial interfragmentary movements. Additionally, combined axial and shear movements did not result in overall increases in the strains and the strain magnitudes were similar to those produced by axial movements alone. Only when axial movements where applied did the non-distortional component of the pressure–deformation theory influence the initial tissue predictions. ----- ----- Interpretation: This study found that the mechanical stimuli generated by interfragmentary shear and torsion differed from those produced by axial interfragmentary movements. The initial tissue formation as predicted by the mechanobiological theories was dominated by the deformation stimulus.

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing : a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Continuous passive motion applied to whole joints stimulates chondrocyte blosynthesis of PRG4

Continuous passive motion (CPM) is currently a part of patient rehabilitation regimens after a variety of orthopedic surgical procedures. While CPM can enhance the joint healing process, the direct effects of CPM on cartilage metabolism remain unknown. Recent in vivo and in vitro observations suggest that mechanical stimuli can regulate articular cartilage metabolism of proteoglycan 4 (PRG4), a putative lubricating and chondroprotective molecule found in synovial fluid and at the articular cartilage surface. ----- ----- Objectives: (1) Determine the topographical variation in intrinsic cartilage PRG4 secretion. (2) Apply a CPM device to whole joints in bioreactors and assess effects of CPM on PRG4 biosynthesis.----- ----- Methods: A bioreactor was developed to apply CPM to bovine stifle joints in vitro. Effects of 24 h of CPM on PRG4 biosynthesis were determined.----- ----- Results: PRG4 secretion rate varied markedly over the joint surface. Rehabilitative joint motion applied in the form of CPM regulated PRG4 biosynthesis, in a manner dependent on the duty cycle of cartilage sliding against opposing tissues. Specifically, in certain regions of the femoral condyle that were continuously or intermittently sliding against meniscus and tibial cartilage during CPM, chondrocyte PRG4 synthesis was higher with CPM than without.----- ----- Conclusions: Rehabilitative joint motion, applied in the form of CPM, stimulates chondrocyte PRG4 metabolism. The stimulation of PRG4 synthesis is one mechanism by which CPM may benefit cartilage and joint health in post-operative rehabilitation. (C) 2006 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

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.