Interfacial mechanical behaviour of protein–mineral nanocomposites: A molecular dynamics investigation

Biological composite materials, such as bone, tooth and nacre, are comprised of a mixture of nano-sized hard components (e.g. mineral platelets) and soft components (e.g. protein molecules). Their mechanical behaviour greatly depends on the protein–mineral interfaces. This paper investigates the effects of mineral surface nanostructures on the interfacial interaction and mechanical behaviour of protein–mineral nanocomposites. Interfacial shear between osteopontin (OPN) and hydroxyapatite (HA) mineral layers with surface nanostructures is investigated using the atomistic molecular dynamics (MD) simulations. The results indicate that the OPN residues can be attached to HA surfaces but the surface nanostructures greatly affect the interfacial interaction and mechanical behaviour. The HA layers with a higher number of nano-sized grooves (defects) increase the surface roughness but reduce the pulling force and energy dissipation.     

The Molecular Mechanism Underlying Mechanical Anisotropy of the Protein GB1

Mechanical responses of elastic proteins are crucial for their biological function and nanotechnological use. Loading direction has been identified as one key determinant for the mechanical responses of proteins. However, it is not clear how a change in pulling direction changes the mechanical unfolding mechanism of the protein. Here, we combine protein engineering, single-molecule force spectroscopy, and steered molecular dynamics simulations to systematically investigate the mechanical response of a small globular protein GB1. Force versus extension profiles from both experiments and simulations reveal marked mechanical anisotropy of GB1. Using native contact analysis, we relate the mechanically robust shearing geometry with concurrent rupture of native contacts. This clearly contrasts the sequential rupture observed in simulations for the mechanically labile peeling geometry. Moreover, we identify multiple distinct mechanical unfolding pathways in two loading directions. Implications of such diverse unfolding mechanisms are discussed. Our results may also provide some insights for designing elastomeric proteins with tailored mechanical properties.     

An Anisotropic Internal-External Bone Adaptation Model Based on a Combination of CAO and Continuum Damage Mechanics Technologies

Abstract

In this work, a complete internal-external bone-remodelling scheme is presented and implemented into a finite element code. This model uses a combination of an anisotropic internal remodelling model based on a new Continuum "Damage-Repair" theory and an external adaptation approach that follows the idea, early introduced by Mattheck et ah, to simulate the growth behaviour of biological systems, known as CAO method. This combined scheme qualitatively resembles most of the main features of the bone adaptive behaviour, like the bone mass distribution (heterogeneity and porosity), the directional internal structure (anisotropy), the alignment of the microstructure with the constitutive principal directions and these with those of the stress tensor when permanently loaded by a unique stress state (WolfFs law). It is also thermodynamically consistent, fulfilling a principle of minimum mechanical dissipation. Finally, the comparison between the predicted results and the ones obtained by different experimental tests allows us to conclude that this model is able of reproducing qualitatively the global behaviour of bone tissue when subjected to external mechanical loads.     

The influence of cement mantle thickness and stem geometry on fatigue damage in two different cemented hip femoral prostheses

Experimental models can be used for pre-clinical testing of cemented and other type of hip replacements. Total hip replacement (THR) failure scenarios include, among others, cement damage accumulation and the assessment of accurate stress and strain magnitudes at the cement mantle interfaces (stem-cement and cement-bone) can be used to predict mechanical failure. The aseptic loosening scenario in cemented hip replacements is currently not fully understood, and methods of evaluating medical devices must be developed to improve clinical performance. Different results and conclusions concerning the cement micro-cracking mechanism have been reported.The aim of this study was to verify the in vitro behavior of two cemented femoral stems with respect to fatigue crack formation. Fatigue crack damage was assessed at the medial, lateral, anterior and posterior sides of the Lubinus SPII and Charnley stems. All stems were loaded and tested in stair climbing fatigue loading during one million cycles at 2 Hz. After the experiments each implanted synthetic femur was sectioned and analyzed. We observed more damage (cracks per area) for the Lubinus SPII stem, mainly on the proximal part of the cement mantle. The micro-cracking formation initiated in the stem–cement interface and grew towards the direction of cortical bone of the femur.Overall, the cement–bone interface seems to be crucial for the success of the hip replacement. The Charnley stem provoked more damage on the cement–bone interface. A failure index (maximum length of crack/maximum thickness of cement) considered was higher for the cement–stem interface of the Lubinus SPII stem. For a cement mantle thickness higher than 5 mm, cracking initiated at the cement–bone interface and depended on the opening canal process (reaming procedure and instrumentation). The analysis also showed that fatigue-induced damage on the cement mantle, increasing proximally, and depended on the axial position of the stem. The cement thickness is an important factor for the success of THR and this study evidenced that cement thickness higher than 2 mm apparently does not affect the mechanical behavior of the cement mantel and induce more crack formation on the cement–bone interface.     

Effect of sequence variation on the mechanical response of amyloid fibrils probed by steered molecular dynamics simulation

The mechanical failure of mature amyloid fibers produces fragments that act as seeds for the growth of new fibrils. Fragmentation may also be correlated with cytotoxicity. We have used steered atomistic molecular dynamics simulations to study the mechanical failure of fibrils formed by the amyloidogenic fragment of human amylin hIAPP20-29 subjected to force applied in a variety of directions. By introducing systematic variations to this peptide sequence in silico, we have also investigated the role of the amino-acid sequence in determining the mechanical stability of amyloid fibrils. Our calculations show that the force required to induce mechanical failure depends on the direction of the applied stress and upon the degree of structural order present in the β-sheet assemblies, which in turn depends on the peptide sequence. The results have implications for the importance of sequence-dependent mechanical properties on seeding the growth of new fibrils and the role of breakage events in cytotoxicity.     

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed mucosa–submucosa layer under large deformation

Mechanical characterisation of the layer-specific, viscoelastic properties of the human oesophagus is crucial in furthering the development of devices emerging in the field, such as robotic endoscopic biopsy devices, as well as in enhancing the realism, and therefore effectiveness, of surgical simulations. In this study, the viscoelastic and stress-softening behaviour of the passive human oesophagus was investigated through ex vivo cyclic mechanical tests. Due to restrictions placed on the laboratory as a result of COVID-19, only oesophagi from cadavers fixed in formalin were allowed for testing. Three oesophagi in total were separated into their two main layers and the mucosa–submucosa layer was investigated. A series of uniaxial tensile tests were conducted in the form of increasing stretch level cyclic tests at two different strain rates: 1% s\(^{-1}\) and 10% s\(^{-1}\). Rectangular samples in both the longitudinal and circumferential directions were tested to observe any anisotropy. Histological analysis was also performed through a variety of staining methods. Overall, the longitudinal direction was found to be much stiffer than the circumferential direction. Stress-softening was observed in both directions, as well as permanent set and hysteresis. Strain rate-dependent behaviour was also apparent in the two directions, with an increase in strain rate resulting in an increase in stiffness. This strain rate dependency was more pronounced in the longitudinal direction than the circumferential direction. Finally, the results were discussed in regard to the histological content of the layer, and the behaviour was modelled and validated using a visco-hyperelastic matrix-fibre model.

     

Mechanical properties of cancellous bone in the human mandibular condyle are anisotropic

The objective of the present study was (1) to test the hypothesis that the elastic and failure properties of the cancellous bone of the mandibular condyle depend on the loading direction, and (2) to relate these properties to bone density parameters. Uniaxial compression tests were performed on cylindrical specimens (n=47) obtained from the condyles of 24 embalmed cadavers. Two loading directions were examined, i.e., a direction coinciding with the predominant orientation of the plate-like trabeculae (axial loading) and a direction perpendicular to the plate-like trabeculae (transverse loading). Archimedes' principle was applied to determine bone density parameters. The cancellous bone was in axial loading 3.4 times stiffer and 2.8 times stronger upon failure than in transverse loading. High coefficients of correlation were found among the various mechanical properties and between them and the apparent density and volume fraction. The anisotropic mechanical properties can possibly be considered as a mechanical adaptation to the loading of the condyle in vivo.     

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

A study of the interface strength between protein and mineral in biological materials

Bone, tooth, mineralized tendon and sea shells are nanocomposites of protein and mineral with superior mechanical properties. As the mineral is so small at nanoscale, the volume fraction of the protein-mineral interface in the bulk materials can be enormously large; therefore, the mechanics of the interface should be critically important for the integrity of these biomaterials. Currently, people do not have a good understanding of the interface between protein and mineral, a hybrid interface between organic and inorganic constituents in biological materials. In this paper, a tension-shear chain (TSC) model is introduced into the Dugdale model for estimating the fracture energy of biomaterials. The strength of the hybrid interface is then studied with a "soft-hard" bi-layer fracture model, by which we find for the first time that the interface strength depends on both the size and geometry of the mineral crystal, and has been highly optimized through the miniaturization of mineral at nanoscale. This study may provide important insights into the mechanics of bone and tooth at small scale for tissue engineering in biomedical applications.     

Autophagy Is Possibly Involved in Osteoblast Responses to Mechanical Loadings

Both mechanical loading and autophagy play important roles in regulating bone growth and remodeling, but the relationship between the two remains unclear. In this study, we examined bone structure with micro-CT imaging and measured bone mechanical properties with three-point bending experiments using bones from wild-type (WT) mice and conditional knockout (cKO) mice with Atg7 deletion in their osteoblasts. We found that the knockout mice had significantly less bone volume, bone thickness, bone ultimate breaking force, and bone stiffness compared to wild-type mice. Additionally, bone marrow cells from knockout mice had reduced differentiation and mineralization capacities in terms of alkaline phosphatase and calcium secretion, as well as Runx2 and osteopontin expression. Knockout mice also had significantly less relative bone formation rate due to mechanical loading. Furthermore, we found that the osteoblasts from wild-type mice had stronger responses to mechanical stimulation compared to autophagy-deficient osteoblasts from knockout mice. When inhibiting autophagy with 3 MA in wild-type osteoblasts, we found similar results as we did in autophagy-deficient osteoblasts. We also found that mechanical loading-induced ATP release is able to regulate ERK1/2, Runx2, alkaline phosphatase, and osteopontin activities. These results suggest that the ATP pathway may play an important role in the possible involvement of autophagy in osteoblast mechanobiology.     

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.     

Mechanical strength of the cement-bone interface is greater in shear than in tension.

The objective of this study was to determine the relative mechanical properties of the cement-bone interface due to tensile or shear loading. Mechanical tests were performed on cement-bone specimens in tensile (n = 51) or shear (n = 55) test jigs under the displacement control at 1 mm/min until complete failure. Before testing, the quantity of bone interdigitated with the cement was determined and served as a covariate in the study. The apparent strength of the cement-bone interface was significantly higher (p < 0.0001) for the interface when loaded in shear (2.25 MPa) when compared to tensile loading (1.35 MPa). Significantly higher energies to failure (p < 0.0001) and displacement before failure (p < 0.01) were also determined for the shear specimens. The post-yield softening response was not different for the two test directions. The data obtained herein suggests that cement-bone interfaces with equal amounts of tensile and shear stress would be more likely to fail under tensile loading.     

Biomolecular phases in transverse palatal distraction: A review

Transverse palatal distraction is a biological process of regenerating new bone and enveloping soft tissues in the maxillary palate region. This technique is similar to Osteo-distraction (OD) procedure for bone lengthening in which gradual and controlled traction forces are applied on the osteotomy gaps to produce new bone in between the surgically separated bone segments. This review describes the different phases after osteotomy and the biological process involved during the new bone and soft tissue formation. The mechanical environment formed in the distraction area is due to the traction forces by the distractor appliance. This environment stimulates differentiation of pluripotent cells, neovascularization, osteogenesis and remodeling of newly formed bone. The role of different pro-inflammatory cytokines, interleukins, bone morphogenic proteins, transforming growth factors, fibroblast growth factors-2) and extracellular matrix proteins (osteonectin, osteopontin) during the distraction phases has been described in detail. Also, an important note on the nutritional aspect during Osteo-distraction will benefit the clinicians to guide their patients after osteotomy throughout the distraction process.     

Directional dependence of hydroxyapatite-collagen interactions on mechanics of collagen

Bone is a biological nanocomposite composed primarily of collagen and hydroxyapatite. The collagen molecules self-assemble to from a structure known as a fibril that comprises of about 85–95% of the total bone protein. In a fibril, the molecular level interactions at the interface between molecular collagen and hydroxyapatite nanocrystals have a significant role on its mechanical response. In this study, we have used molecular dynamics and steered molecular dynamics to study directional dependence of deformation response of collagen with respect to the hydroxyapatite surface. We have also studied mechanical response of collagen in the proximity of (0 0 0 1) and (1 0 1¯0) surfaces of hydroxyapatite. Our simulations indicate that the mechanics of collagen pulled in different directions with respect to hydroxyapatite is significantly different. Similar results were obtained for collagen pulled in the proximity of different crystallographic surfaces of hydroxyapatite.     

On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation

The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613–621 (2008), which is capable of reproducing the behaviour of a population of cells cultured on an elastic substrate in response to a variety of stimuli. In particular, we examine the conditions under which stable spatial patterns can emerge with this model, focusing on the influence of mechanical stimuli and the interplay of non-local phenomena. To this end, we have performed a linear stability analysis and numerical simulations based on a mixed finite element formulation, which have allowed us to study the dynamical behaviour of the system in terms of the qualitative shape of the dispersion relation. We show that the consideration of mechanotaxis, namely changes in migration speeds and directions in response to mechanical stimuli alters the conditions for pattern formation in a singular manner. Furthermore without non-local effects, responses to mechanical stimuli are observed to result in dispersion relations with positive growth rates at arbitrarily large wavenumbers, in turn yielding heterogeneity at the cellular level in model predictions. This highlights the sensitivity and necessity of non-local effects in mechanically influenced biological pattern formation models and the ultimate failure of the continuum approximation in their absence.     

Influence of defect locations and nitrogen doping configurations on the mechanical properties of armchair graphene nanoribbons

The effect of defect locations on the mechanical properties of armchair graphene nanoribbons (AGNRs) and the various configurations of nitrogen (N) doping on the mechanical properties of AGNRs were examined using molecular dynamics (MD) simulations. The variation of the Young’s modulus (YM) and the ultimate tensile strength (UTS) of pyridinic-N, graphitic-N, and pyrrolic-N by increasing the concentration of N doping was investigated. The results of MD simulations show that the defect location has a significant effect on the UTS and failure strain (FS) of AGNRs in both vertical and horizontal directions. In the horizontal direction, variations of the UTS and FS are lower than in the vertical direction. On the other hand, the variations of the YM is almost similar in vertical and horizontal directions. The results of this work indicate that the UTS and FS of AGNRs are more sensitive than the YM of AGNRs for different defect directions. Pyridinic-N improves the mechanical properties of the defective AGNR and performs better YM and UTS values than the graphitic-N. Substitution N atoms, which are located at the defective sites and/or at the edges of AGNRs, are mechanically more favorable. Pyrrolic-N configuration has the lowest mechanical properties among the other configurations. Furthermore, pyrrolic-N with Stone-Wales-1 (SW-1) type of defect has higher mechanical properties than pyrrolic-N with Stone-Wales-2 (SW-2) type of defect.     

植入了骨修复材料的小型猪腰椎椎体不脱钙病理组织切片制备方法

摘要 目的：建立植入了骨修复材料小型猪腰椎椎体骨组织标本的不脱钙病理组织切片制备方法。方法：将含骨修复材料的腰椎椎体骨组织标本进行分割暴露组织切面,梯度浓度乙醇脱水后经Technovit 7200 VLC光聚树脂浸润,经黄蓝光共同辐照进行光聚合包埋,借助硬组织病理切磨系统制备含骨修复材料不脱钙病理组织切片。结果：结果显示通过上述方法制备的病理组织切片,经苏木精-伊红（HE）染色及甲苯胺蓝染色后光学显微镜下观察能较好地显示骨的各种组织细胞结构,可清晰的观察到骨小梁的走向及连接情况。结论：研究建立了含骨修复材料骨组织标本病理组织切片制备方法,实现了含骨修复材料不脱钙骨组织病理切片的制备,经病理染色后实现了带植入物的组织学观察,为生物材料及医疗器械动物试验研究提供了新的病理检测手段及组织学评价途径。     

Bone ingrowth on the surface of endosseous implants. Part 1: Mathematical model

Osseointegration, understood as an intimate apposition and interdigitation of bone to a biomaterial, is usually regarded as a major condition for the long-term clinical success of bone implants. Clearly, the anchorage of an implant to bone tissue critically relies on the formation of new bone between the implant and the surface of the old peri-implant bone and depends on factors such as the surface microtopography, chemical composition and geometry of the implant, the properties of the surrounding bone and the mechanical loading process. The main contribution of this work is the proposal of a new mathematical framework based on a set of reaction-diffusion equations that try to model the main biological interactions occurring at the surface of implants and is able to reproduce most of the above mentioned biological features of the osseointegration phenomenon. This is a two-part paper. In this first part, a brief biological overview is initially given, followed by the presentation and discussion of the model. In addition, two-dimensional finite element simulations of the bone-ingrowth process around a dental implant with two different surface properties are included to assess the validity of the model. Numerical solutions show the ability of the model to reproduce features such as contact/distance osteogenesis depending upon the specific surface microtopography. In Part 2 [Moreo, P., García-Aznar, J.M., Doblaré, M., 2008. Bone ingrowth on the surface of endosseous implants. Part 2: influence of mechanical stimulation, type of bone and geometry. J. Theor. Biol., submitted for publication], two simplified versions of the whole model are proposed. An analytical study of the stability of fixed points as well as the existence of travelling wave-type solutions has been done with both simplified models, providing a significant insight into the behaviour of the model and giving clues to interpret the effectiveness of recently proposed clinical therapies. Furthermore, we also show that, although the mechanical state of the tissue is not directly taken into account in the model equations, it is possible to analyse in detail the effect that mechanical stimulation would have on the predictions of the model. Finally, numerical simulations are also included in the second part of the paper, with the aim of looking into the influence of implant geometry on the osseointegration process.     

A bone remodelling model including the directional activity of BMUs

Bone is able to adapt itself to the mechanical and biological environment by changing its porosity and/or orientation of its internal microstructure in a process known as bone remodelling. As a consequence, a change of bone mechanical properties is produced leading to an optimum structure, able to bear the external loads with the minimum weight. This adaptation is carried out by a temporal association of cells known as BMUs (basic multicellular units) that resorb old bone and sometimes produce new organic extracellular matrix (osteoid) that is later mineralized. This involves changes in porosity, damage level (density of microcracks accumulated by cyclic loads) and mineral content. All of these features were taken into account in a previous model, but the whole process and therefore the resulting bone constitutive behaviour was considered isotropic. The model proposed herein, recognizing that bone is actually anisotropic, tries to explain how BMUs modify the anisotropy by changing their progressing direction. We check the potential of the model to predict the alignment of the bone microstructure with the external loads in different situations. Then, the model is also applied to obtain the anisotropy and mechanical properties of the human proximal femur under physiological loads with initial conditions corresponding to a heterogeneous, but otherwise isotropic bone.