Micromechanical modelling of cortical bone

Effect of geometrical structure variations on strength and damage onset of cortical bone using multi-scale cohesive zone based finite element method

Three-dimensional multi-scale finite element models were designed to examine the effects of geometrical structure variations on the damage onset in cortical bone at multiple structural scales. A cohesive zone finite element approach, together with anisotropic damage initiation criteria, is used to predict the onset of damage. The finite element models are developed to account for the onset of microdamage from the microscopic length scales consisting of collagen fibres, to the macroscopic level consisting of osteons and the Haversian canals. Numerical results indicated that the yield strain at the initiation of microcracks is independent of variations in the local mineral volume fraction at each structural scale. Further, the yield strain and strength properties of cortical bone are dependent on its structural anisotropy and hierarchical structure. A positive correlation is observed between bone strength and mineral content at each length scale.

Damage analysis of human cortical bone under compressive and tensile loadings

Developing advanced fracture tools can increase the understanding of crack growth trajectories in human cortical bone. The present study investigates fracture micromechanics of human cortical bone under compressive and tensile loadings utilizing a phase field method. We construct two-dimensional finite element models from cortical microstructure of a human tibia cross section. We apply compression on the cortical bone models to create compressive microcracks. Then, we simulate the fracture of these models under tension to discover influential parameters on microcracks formation and post-yielding behavior. The results show that cement lines are susceptible sites to damage nucleation under compression rather than tension. The findings of this study also indicate a higher accumulation of initial damage (induced by compression) can lead to a lower microscopic stiffness as well as a less resistant material to damage initiation under tension. The simulations further indicate that the post-yielding properties (e.g., toughness) can be dependent on different variables such as morphological information of the osteons, the initial accumulation of microcracks, and the total length of cement lines.

Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling

Multi-scale finite element analysis is performed to ascertain the effect of geometrical changes at multiple structural scales on the mechanical properties of cortical bone. Finite element models are developed, with reference to experimental data from existing literature, to account for bone's viscoelastic behaviour and anisotropic structure from the most fundamental level of bone consisting of mineralised collagen fibrils, up to the macroscopic level consisting of osteons and the Haversian canals. A statistical approach is incorporated to perform sensitivity analyses on the effects of different geometrical parameters on the effective material properties of cortical bone at each length scale. Numerical results indicate that there is an exponential correlation between the mineral volume fraction and the effective stiffness constants at each length scale. This contributes to the exponential behaviour of the instantaneous moduli describing cortical bone's two-phase stress relaxation process: a fast and slow response relaxation behaviour. Results indicate that the fast response relaxation time is independent of bone's structural anisotropy, whilst being dependent on variations in the global mineral volume fraction between length scales. However, the slow response relaxation time is independent of the changes in mineral volume fraction. It is also observed that the slow response relaxation time varies with bone's anisotropic structure, and therefore, contributes to the anisotropic properties of bone.

A three-dimensional geometric quantification of human cortical canals using an innovative method with micro-computed tomographic data

The complex architecture of bone has been investigated for several decades. Some pioneer works proved an existing link between microstructure and external mechanical loading applied on bone. Due to sinuous network of canals and limitations of experimental acquisition technique, there has been little quantitative analysis of three-dimensional description of cortical network. The aim of this study is to provide an algorithmic process, using Python 3.5, in order to identify 3D geometrical characteristics of voids considered as canals. This script is based on micro-computed tomographic slices of two bone samples harvested from the humerus and femur of male cadaveric subject. Slice images are obtained from 2.94 μm isotropic resolution. This study provides a generic method of image processing which considers beam hardening artefact so as to avoid heuristic choice of global threshold value. The novelty of this work is the quantification of numerous three-dimensional canals features, such as orientation or canal length, but also connectivity features, such as opening angle, and the accurate definition of canals as voids which ranges from connectivity to possibly another intersection. The script was applied to one humeral and one femoral samples in order to analyse the difference in architecture between bearing and non-bearing cortical bones. This preliminary study reveals that the femoral specimen is more porous than the humeral one whereas the canal network is denser and more connected.

Cortical and trabecular morphology is altered in the limb bones of mice artificially selected for faster skeletal growth

Bone strength is influenced by mineral density and macro- and microstructure. Research into factors that contribute to bone morphology and strength has focused on genetic, environmental and morphological factors (e.g., body mass index), but little is known regarding the impact of rates of skeletal elongation on adult skeletal morphology and strength. Using micro-CT, we examined the impact of rates of skeletal elongation on bone cortical and trabecular morphology, and on rates of estrogen-dependent bone loss in the tibia in CD-1 mice, and in mice with accelerated skeletal growth (Longshanks). Groups of adult mice (n = 7/group) were subjected to ovariectomy or sham surgeries, scanned for 6 weeks, and indices of bone morphology were collected. Results show that Longshanks mice had significantly less trabecular bone at skeletal maturity, characterized by fewer, thinner trabeculae, and furthermore lost trabecular bone more slowly in response to ovariectomy. Artificial selection for rapid skeletal growth relative to somatic growth thus had a significant impact on trabecular bone morphology in Longshanks. Our data do not unequivocally demonstrate a causal relationship between rapid bone growth and reduced trabecular bone quality, but suggest that rapid linear bone growth may influence the risk of cancellous bone fragility.

Phospho1 deficiency transiently modifies bone architecture yet produces consistent modification in osteocyte differentiation and vascular porosity with ageing

PHOSPHO1 is one of principal proteins involved in initiating bone matrix mineralisation. Recent studies have found that Phospho1 KO mice (Phospho1-R74X) display multiple skeletal abnormalities with spontaneous fractures, bowed long bones, osteomalacia and scoliosis. These analyses have however been limited to young mice and it remains unclear whether the role of PHOSPHO1 is conserved in the mature murine skeleton where bone turnover is limited. In this study, we have used ex-vivo computerised tomography to examine the effect of Phospho1 deletion on tibial bone architecture in mice at a range of ages (5, 7, 16 and 34 weeks of age) to establish whether its role is conserved during skeletal growth and maturation. Matrix mineralisation has also been reported to influence terminal osteoblast differentiation into osteocytes and we have also explored whether hypomineralised bones in Phospho1 KO mice exhibit modified osteocyte lacunar and vascular porosity. Our data reveal that Phospho1 deficiency generates age-related defects in trabecular architecture and compromised cortical microarchitecture with greater porosity accompanied by marked alterations in osteocyte shape, significant increases in osteocytic lacuna and vessel number. Our in vitro studies examining the behaviour of osteoblast derived from Phospho1 KO and wild-type mice reveal reduced levels of matrix mineralisation and modified osteocytogenic programming in cells deficient in PHOSPHO1. Together our data suggest that deficiency in PHOSPHO1 exerts modifications in bone architecture that are transient and depend upon age, yet produces consistent modification in lacunar and vascular porosity. It is possible that the inhibitory role of PHOSPHO1 on osteocyte differentiation leads to these age-related changes in bone architecture. It is also intriguing to note that this apparent acceleration in osteocyte differentiation evident in the hypomineralised bones of Phospho1 KO mice suggests an uncoupling of the interplay between osteocytogenesis and biomineralisation. Further studies are required to dissect the molecular processes underlying the regulatory influences exerted by PHOSPHO1 on the skeleton with ageing.

Micromechanical modeling of elastic properties of cortical bone accounting for anisotropy of dense tissue

The paper analyzes the connection between microstructure of the osteonal cortical bone and its overall elastic properties. The existing models either neglect anisotropy of the dense tissue or simplify cortical bone microstructure (accounting for Haversian canals only). These simplifications (related mostly to insufficient mathematical apparatus) complicate quantitative analysis of the effect of microstructural changes - produced by age, microgravity, or some diseases - on the overall mechanical performance of cortical bone. The present analysis fills this gap; it accounts for anisotropy of the dense tissue and uses realistic model of the porous microstructure. The approach is based on recent results of Sevostianov et al. (2005) and Saadat et al. (2012) on inhomogeneities in a transversely-isotropic material. Bone's microstructure is modeled according to books of Martin and Burr (1989), Currey (2002), and Fung (1993) and includes four main families of pores. The calculated elastic constants for porous cortical bone are in agreement with available experimental data. The influence of each of the pore types on the overall moduli is examined.

3D osteocyte lacunar morphometric properties and distributions in human femoral cortical bone using synchrotron radiation micro-CT images

Osteocytes, the most numerous bone cells, are thought to be actively involved in the bone modeling and remodeling processes. The morphology of osteocyte is hypothesized to adapt according to the physiological mechanical loading. Three-dimensional micro-CT has recently been used to study osteocyte lacunae. In this work, we proposed a computationally efficient and validated automated image analysis method to quantify the 3D shape descriptors of osteocyte lacunae and their distribution in human femurs. Thirteen samples were imaged using Synchrotron Radiation (SR) micro-CT at ID19 of the ESRF with 1.4μm isotropic voxel resolution. With a field of view of about 2.9×2.9×1.4mm(3), the 3D images include several tens of thousands of osteocyte lacunae. We designed an automated quantification method to segment and extract 3D cell descriptors from osteocyte lacunae. An image moment-based approach was used to calculate the volume, length, width, height and anisotropy of each osteocyte lacuna. We employed a fast algorithm to further efficiently calculate the surface area, the Euler number and the structure model index (SMI) of each lacuna. We also introduced the 3D lacunar density map to directly visualize the lacunar density variation over a large field of view. We reported the lacunar morphometric properties and distributions as well as cortical bone histomorphometric indices on the 13 bone samples. The mean volume and surface were found to be 409.5±149.7μm(3) and 336.2±94.5μm(2). The average dimensions were of 18.9±4.9μm in length, 9.2±2.1μm in width and 4.8±1.1μm in depth. We found lacunar number density and six osteocyte lacunar descriptors, three axis lengths, two anisotropy ratios and SMI, that are significantly correlated to bone porosity at a same local region. The proposed method allowed an automatic and efficient direct 3D analysis of a large population of bone cells and is expected to provide reliable biological information for better understanding the bone quality and diseases at cellular level.

Alterations of mass density and 3D osteocyte lacunar properties in bisphosphonate-related osteonecrotic human jaw bone, a synchrotron µCT study

Osteonecrosis of the jaw, in association with bisphosphonates (BRONJ) used for treating osteoporosis or cancer, is a severe and most often irreversible side effect whose underlying pathophysiological mechanisms remain largely unknown. Osteocytes are involved in bone remodeling and mineralization where they orchestrate the delicate equilibrium between osteoclast and osteoblast activity and through the active process called osteocytic osteolysis. Here, we hypothesized that (i) changes of the mineralized tissue matrix play a substantial role in the pathogenesis of BRONJ, and (ii) the osteocyte lacunar morphology is altered in BRONJ. Synchrotron µCT with phase contrast is an appropriate tool for assessing both the 3D morphology of the osteocyte lacunae and the bone matrix mass density. Here, we used this technique to investigate the mass density distribution and 3D osteocyte lacunar properties at the sub-micrometer scale in human bone samples from the jaw, femur and tibia. First, we compared healthy human jaw bone to human tibia and femur in order to assess the specific differences and address potential explanations of why the jaw bone is exclusively targeted by the necrosis as a side effect of BP treatment. Second, we investigated the differences between BRONJ and control jaw bone samples to detect potential differences which could aid an improved understanding of the course of BRONJ. We found that the apparent mass density of jaw bone was significantly smaller compared to that of tibia, consistent with a higher bone turnover in the jaw bone. The variance of the lacunar volume distribution was significantly different depending on the anatomical site. The comparison between BRONJ and control jaw specimens revealed no significant increase in mineralization after BP. We found a significant decrease in osteocyte-lacunar density in the BRONJ group compared to the control jaw. Interestingly, the osteocyte-lacunar volume distribution was not altered after BP treatment.

Are all osteocytes equal? Multiscale modelling of cortical bone to characterise the mechanical stimulation of osteocytes

Bone continuously adapts its internal structure to accommodate the functional demands of its mechanical environment. This process is orchestrated by a network of mechanosensitive osteocytes that respond to external mechanical signals and recruit osteoblasts and osteoclasts to alter bone mass to meet loading demands. Because of the irregular hierarchical microarchitecture of bone tissue, the precise mechanical stimuli experienced by osteocytes located in different regions of the tissue is not well-understood. The objective of this study is to characterise the local stimulus experienced by osteocytes distributed throughout the tissue structure. Our models predict that an inhomogeneous microstructural strain field contributes to osteocytes receiving vastly different stimuli at the cellular level, depending on their location within the microstructure. In particular, osteocytes located directly adjacent to micropores experienced strain amplifications in their processes of up to nine times the applied global strain. Furthermore, it was found that the principal orientation of lamellar regions was found to contribute significantly to the magnitude of the stimulus being received at the cellular level. These findings indicate that osteocytes are not equal in terms of the mechanical stimulus being received, and we propose that only a subset of osteocytes may be sufficiently stimulated to function as mechanoreceptors.

Cement lines and interlamellar areas in compact bone as strain amplifiers - contributors to elasticity, fracture toughness and mechanotransduction

Bone is multi-scale hierarchical composite material making the prediction of fragility, as well as pinning it to a certain cause, complicated. For proper mechanical simulation and reflection of bone properties in models, microscopic structural features of bone tissue need to be included. This study sets out to gain a mechanistic insight into the role of various microstructural features of bone tissue in particular cement lines and interlamellar areas. Further the hypothesis that compliant interlamellar areas and cement lines within osteonal bone act as strain amplifiers was explored. To this end, a series of experimentally-based micromechanical finite element models of bovine osteonal bone were developed. Different levels of detail for the bone microstructure were considered and combined with the results of physical three-point bending tests and an analytical composite model of a single osteon. The objective was to examine local and global effects of interface structures. The geometrical and microstructural characteristics of the bone samples were derived from microscopy imaging. Parametric finite element studies were conducted to determine optimal values of the elastic modulus of interstitial bone and interlamellar areas. The average isotropic elastic modulus of interfaces suggested in this study is 88.5MPa. Based on the modelling results, it is shown that interfaces are areas of accumulated strain in bone and are likely to act as potential paths for crack propagation. The strain amplification capability of interface structures in the order of 10 predicted by the models suggests a new explanation for the levels of strain required in bone homoeostasis for maintenance and adaptation.

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.

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 effects of immobilization on vascular canal orientation in rat cortical bone

It is well established that bone is capable of adapting to changes in loading; however, little is known regarding how loading specifically affects the internal 3D microarchitecture of cortical bone. The aim of this study was to experimentally test the hypothesis that loading is a determinant of the 3D orientation of primary vascular canals in the rat tibial diaphysis. Left tibiae from 10 rats (30 weeks old) that had been immobilized (sciatic neurectomy) for 27 weeks, right SHAM-operated tibiae from these same rats (internal control) and right tibiae from 10 normal age-matched rats (external control) were scanned by micro-CT. Mean canal orientation (for the whole bone segment and by region), percent porosity, canal diameter and canal separation were quantitatively assessed in 3D. Canal orientation in the immobilized tibiae was significantly (P < 0.001) more radial (by 9.9°) compared to the external controls but did not differ from the internal controls (P = 0.310). Comparing the external and internal controls, orientation was significantly (P < 0.05) more radial in the internal control group (by 6.8°). No differences were found for percent porosity and canal separation. Canal diameter was significantly greater in the immobilized vs. internal (P < 0.001) and external control (P < 0.001) tibiae. The differences in orientation relative to the external controls indicated that the organization of cortical bone in the rat is affected by loading. Although the predicted difference in canal orientation was not detected between immobilized and internal control groups, the distributions of individual canal orientations, from which the mean values were derived, revealed distinctive patterns for all three groups. The internal controls exhibited an intermediate position between the immobilized and external controls, suggesting that paralysis on the contralateral side resulted in altered loading relative to the normal state represented by the external control. This was also evident in a regional analysis by quadrant. The loaded bones had the same cross-sectional shape; however, their internal structure differed. These results provide novel insights into the impact of loading on the 3D organization of primary cortical bone and have implications for understanding the relation between cortical bone adaptation, disease and mechanical properties.

Interaction of microstructure and microcrack growth in cortical bone: a finite element study

Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behaviour in cortical bone. This study aims to develop a computational mechanics approach to evaluate microscale fracture mechanisms in bone. In this study, finite element models based on actual human cortical bone images that allow for arbitrary crack growth were utilised to determine the crack propagation behaviour. The simulations varied the cement line and osteon strength and fracture toughness in different bone microstructures to assess the crack propagation trajectory, stress-strain relationship and nonlinear strain energy density. The findings of this study provide additional insight into the individual influence of microstructural features and their properties on crack growth behaviour in bone using a computational approach.

Morphology based cohesive zone modeling of the cement-bone interface from postmortem retrievals

In cemented total hip arthroplasty, the cement-bone interface can be considerably degenerated after less than one year in vivo service; this makes the interface much weaker relative to the direct post-operative situation. It is, however, still unknown how these degenerated interfaces behave under mixed-mode loading and how this is related to the interface morphology. In this study, we used a finite element (FE) approach to analyze the mixed-mode response of the cement-bone interface taken from postmortem retrievals. We investigated whether it was feasible to generate a fully elastic and a failure cohesive model based on only morphological input parameters. Computed tomography-based FE-models of postmortem cement-bone interfaces were generated and the interface morphology was determined. The models were loaded until failure in multiple directions by allowing cracking of the bone and cement components and including periodic boundary conditions. The resulting stiffness was related to the interface morphology. A closed form mixed-mode cohesive model that included failure was determined and related to the interface morphology. The responses of the FE-simulations compare satisfactorily with experimental observations, albeit the magnitude of the strength and stiffness are somewhat overestimated. Surprisingly, the FE-simulations predict no failure under shear loading and a considerable normal compression is generated which prevents dilation of the interface. The obtained mixed-mode stiffness response could subsequently be related to the interface morphology and subsequently be formulated into an elastic cohesive zone model. Finally, the acquired data could be used as an input for a cohesive model that also includes interface failure.

Mixed-mode loading of the cement-bone interface: a finite element study

While including the cement-bone interface of complete cemented hip reconstructions is crucial to correctly capture their response, its modelling is often overly simplified. In this study, the mechanical mixed-mode response of the cement-bone interface is investigated, taking into account the effects of the well-defined microstructure that characterises the interface. Computed tomography-based plain strain finite element analyses models of the cement-bone interface are built and loaded in multiple directions. Periodic boundaries are considered and the failure of the cement and bone fractions by cracking of the bulk components are included. The results compare favourably with experimental observations. Surprisingly, the analyses reveal that under shear loading no failure occurs and considerable normal compression is generated to prevent interface dilation. Reaction forces, crack patterns and stress fields provide more insight into the mixed-mode failure process. Moreover, the cement-bone interface analyses provide details which can serve as a basis for the development of a cohesive law.

A Finite Element Prediction of Strain on Cells in a Highly Porous Collagen-Glycosaminoglycan Scaffold

Tissue engineering often involves seeding cells into porous scaffolds and subjecting the scaffold to mechanical stimulation. Current experimental techniques have provided a plethora of data regarding cell responses within scaffolds, but the quantitative understanding of the load transfer process within a cell-seeded scaffold is still relatively unknown. The objective of this work was to develop a finite element representation of the transient and heterogeneous nature of a cell-seeded collagen-GAG-scaffold. By undertaking experimental investigation, characteristics such as scaffold architecture and shrinkage, cellular attachment patterns, and cellular dimensions were used to create a finite element model of a cell-seeded porous scaffold. The results demonstrate that a very wide range of microscopic strains act at the cellular level when a sample value of macroscopic (apparent) strain is applied to the collagen-GAG-scaffold. An external uniaxial strain of 10% generated a cellular strain as high as 49%, although the majority experienced less than ∼5% strain. The finding that the strain on some cells could be higher than the macroscopic strain was unexpected and proves contrary to previous in vitro investigations. These findings indicate a complex system of biophysical stimuli created within the scaffolds and the difficulty of inducing the desired cellular responses from artificial environments. Future in vitro studies could also corroborate the results from this computational prediction to further explore mechanoregulatory mechanisms in tissue engineering.