Ted J. Vaughan

Strain amplification in bone mechanobiology: a computational investigation of the in vivo mechanics of osteocytes

The osteocyte is believed to act as the main sensor of mechanical stimulus in bone, controlling signalling for bone growth and resorption in response to changes in the mechanical demands placed on our bones throughout life. However, the precise mechanical stimuli that bone cells experience in vivo are not yet fully understood. The objective of this study is to use computational methods to predict the loading conditions experienced by osteocytes during normal physiological activities. Confocal imaging of the lacunar–canalicular network was used to develop three-dimensional finite element models of osteocytes, including their cell body, and the surrounding pericellular matrix (PCM) and extracellular matrix (ECM). We investigated the role of the PCM and ECM projections for amplifying mechanical stimulation to the cells. At loading levels, representing vigorous physiological activity (3000 µɛ), our results provide direct evidence that (i) confocal image-derived models predict 350–400% greater strain amplification experienced by osteocytes compared with an idealized cell, (ii) the PCM increases the cell volume stimulated more than 3500 µɛ by 4–10% and (iii) ECM projections amplify strain to the cell by approximately 50–420%. These are the first confocal image-derived computational models to predict osteocyte strain in vivo and provide an insight into the mechanobiology of the osteocyte.

A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone

Bone is an exceptional material that is lightweight for efficient movement but also exhibits excellent strength and stiffness imparted by a composite material of organic proteins and mineral crystals that are intricately organised on many scales. Experimental and computational studies have sought to understand the role of bone composition and organisation in regulating the biomechanical behaviour of bone. However, due to the complex hierarchical arrangement of the constituent materials, the reported experimental values for the elastic modulus of trabecular and cortical tissue have conflicted greatly. Furthermore, finite element studies of bone have largely made the simplifying assumption that material behaviour was homogeneous or that tissue variability only occurred at the microscale, based on grey values from micro-CT scans. Thus, it remains that the precise role of nanoscale tissue constituents and microscale tissue organisation is not fully understood and more importantly that these have never been incorporated together to predict bone fracture or implant outcome in a multiscale finite element framework. In this paper, a three-scale finite element homogenisation scheme is presented which enables the prediction of homogenised effective properties of tissue level bone from its fundamental nanoscale constituents of hydroxyapatite mineral crystals and organic collagen proteins. Two independent homogenisation steps are performed on representative volume elements which describe the local morphological arrangement of both the nanostructural and microstructural levels. This three-scale homogenisation scheme predicts differences in the tissue level properties of bone as a function of mineral volume fraction, mineral aspect ratio and lamellar orientation. These parameters were chosen to lie within normal tissue ranges derived from experimental studies, and it was found that the predicted stiffness properties at the lamellar level correlate well with experimental nanoindentation results from cortical and trabecular bone. Furthermore, these studies show variations in mineral volume fraction, mineral crystal size and lamellar orientation could be responsible for previous discrepancies in experimental reports of tissue moduli. We propose that this novel multiscale modelling approach can provide a more accurate description of bone tissue properties in continuum/organ level finite element models by incorporating information regarding tissue structure and composition from advanced imaging techniques. This approach could thereby provide a preclinical tool to predict bone mechanics following prosthetic implantation or bone fracture during disease.

The Effect of Substrate Stiffness, Thickness, and Cross-Linking Density on Osteogenic Cell Behavior

Osteogenic cells respond to mechanical changes in their environment by altering their spread area, morphology, and gene expression profile. In particular, the bulk modulus of the substrate, as well as its microstructure and thickness, can substantially alter the local stiffness experienced by the cell. Although bone tissue regeneration strategies involve culture of bone cells on various biomaterial scaffolds, which are often cross-linked to enhance their physical integrity, it is difficult to ascertain and compare the local stiffness experienced by cells cultured on different biomaterials. In this study, we seek to characterize the local stiffness at the cellular level for MC3T3-E1 cells plated on biomaterial substrates of varying modulus, thickness, and cross-linking concentration. Cells were cultured on flat and wedge-shaped gels made from polyacrylamide or cross-linked collagen. The cross-linking density of the collagen gels was varied to investigate the effect of fiber cross-linking in conjunction with substrate thickness. Cell spread area was used as a measure of osteogenic differentiation. Finite element simulations were used to examine the effects of fiber cross-linking and substrate thickness on the resistance of the gel to cellular forces, corresponding to the equivalent shear stiffness for the gel structure in the region directly surrounding the cell. The results of this study show that MC3T3 cells cultured on a soft fibrous substrate attain the same spread cell area as those cultured on a much higher modulus, but nonfibrous substrate. Finite element simulations predict that a dramatic increase in the equivalent shear stiffness of fibrous collagen gels occurs as cross-linking density is increased, with equivalent stiffness also increasing as gel thickness is decreased. These results provide an insight into the response of osteogenic cells to individual substrate parameters and have the potential to inform future bone tissue regeneration strategies that can optimize the equivalent stiffness experienced by a cell.

The In Situ Mechanics of Trabecular Bone Marrow: The Potential for Mechanobiological Response

Bone adapts to habitual loading through mechanobiological signaling. Osteocytes are the primary mechanical sensors in bone, upregulating osteogenic factors and downregulating osteoinhibitors, and recruiting osteoclasts to resorb bone in response to microdamage accumulation. However, most of the cell populations of the bone marrow niche,which are intimately involved with bone remodeling as the source of bone osteoblast and osteoclast progenitors, are also mechanosensitive. We hypothesized that the deformation of trabecular bone would impart mechanical stress within the entrapped bone marrow consistent with mechanostimulation of the constituent cells. Detailed fluid-structure interaction models of porcine femoral trabecular bone and bone marrow were created using tetrahedral finite element meshes. The marrow was allowed to flow freely within the bone pores, while the bone was compressed to 2000 or 3000 microstrain at the apparent level.Marrow properties were parametrically varied from a constant 400 mPas to a power law rule exceeding 85 Pas. Deformation generated almost no shear stress or pressure in the marrow for the low viscosity fluid, but exceeded 5 Pa when the higher viscosity models were used. The shear stress was higher when the strain rate increased and in higher volume fraction bone. The results demonstrate that cells within the trabecular bone marrow could be mechanically stimulated by bone deformation, depending on deformation rate, bone porosity, and bone marrow properties. Since the marrow contains many mechanosensitive cells, changes in the stimulatory levels may explain the alterations in bone marrow morphology with aging and disease, which may in turn affect the trabecular bone mechanobiology and adaptation.

Bone cell mechanosensation of fluid flow stimulation: a fluid–structure interaction model characterising the role integrin attachments and primary cilia

Load-induced fluid flow acts as an important biophysical signal for bone cell mechanotransduction in vivo, where the mechanical environment is thought to be monitored by integrin and primary cilia mechanoreceptors on the cell body. However, precisely how integrin- and primary cilia-based mechanosensors interact with the surrounding fluid flow stimulus and ultimately contribute to the biochemical response of bone cells within either the in vitro or in vivo environment remains poorly understood. In this study, we developed fluid–structure interaction models to characterise the deformation of integrin- and primary cilia-based mechanosensors in bone cells under fluid flow stimulation. Under in vitro fluid flow stimulation, these models predicted that integrin attachments on the cell–substrate interface were highly stimulated

Multiscale Modeling of Trabecular Bone Marrow: Understanding the Micromechanical Environment of Mesenchymal Stem Cells During Osteoporosis

(\varepsilon _\mathrm{eq}> 200{,}000\,\upmu \upvarepsilon )

The role of integrin αVβ3 in osteocyte mechanotransduction

(εeq>200,000με), while the presence of a primary cilium on the cell also resulted in significant strain amplifications, arising at the ciliary base. As such, these mechanosensors likely play a role in mediating bone mechanotransduction in vitro. Under in vivo fluid flow stimulation, integrin attachments along the canalicular wall were highly stimulated and likely play a role in mediating cellular responses in vivo. The role of the primary cilium as a flow sensor in vivo depended upon its configuration within the lacunar cavity. Specifically, our results showed that a short free-standing primary cilium could not effectively fulfil a flow sensing role in vivo. However, a primary cilium that discretely attaches the lacunar wall can be highly stimulated, due to hydrodynamic pressure in the lacunocanalicular system and, as such, could play a role in mediating bone mechanotransduction in vivo.

Cell morphology and focal adhesion location alters internal cell stress.

Bone continuously adapts its internal structure to accommodate the functional demands of its mechanical environment and strain-induced flow of interstitial fluid is believed to be the primary mediator of mechanical stimuli to bone cells in vivo. In vitro investigations have shown that bone cells produce important biochemical signals in response to fluid flow applied using parallel-plate flow chamber (PPFC) systems. However, the exact mechanical stimulus experienced by the cells within these systems remains unclear. To fully understand this behaviour represents a most challenging multi-physics problem involving the interaction between deformable cellular structures and adjacent fluid flows. In this study, we use a fluid–structure interaction computational approach to investigate the nature of the mechanical stimulus being applied to a single osteoblast cell under fluid flow within a PPFC system. The analysis decouples the contribution of pressure and shear stress on cellular deformation and for the first time highlights that cell strain under flow is dominated by the pressure in the PPFC system rather than the applied shear stress. Furthermore, it was found that strains imparted on the cell membrane were relatively low whereas significant strain amplification occurred at the cell–substrate interface. These results suggest that strain transfer through focal attachments at the base of the cell are the primary mediators of mechanical signals to the cell under flow in a PPFC system. Such information is vital in order to correctly interpret biological responses of bone cells under in vitro stimulation and elucidate the mechanisms associated with mechanotransduction in vivo.