Mechanisms governing the inelastic deformation of cortical bone and application to trabecular bone

Effect of inelastic deformation on strain rate-dependent mechanical behaviour of human cortical bone

In this study, the role of inelastic deformation of bone on its strain rate-dependent mechanical behaviour was investigated. For this, human cortical bone samples were cyclically loaded to accumulate inelastic strain and subsequently, mechanical response was investigated under compressive loading at different strain rates. The strain rate behaviour of fatigued samples was compared with non-loaded control samples. Furthermore, cyclic loading-induced microdamage was quantified through histological analysis. The compression test results show that the strength of fatigue-loaded bone reduced significantly at low strain rates but not at high strain rates. The difference in microcrack density was not significant between fatigued and control groups. The results indicate that the mechanism of load transfer varies between low strain rate and high strain rate regimes. The inelastic deformation mechanisms are more prominent at low strain rates but not at high strain rates. This study shed light on the role of inelastic deformation on the rate-dependent behaviour of cortical bone.

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres

The hierarchical design of bio-based nanostructured materials such as bone enables them to combine unique structure-mechanical properties. As one of its main components, water plays an important role in bone's material multiscale mechanical interplay. However, its influence has not been quantified at the length-scale of a mineralised collagen fibre. Here, we couple in situ micropillar compression, and simultaneous synchrotron small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) with a statistical constitutive model. Since the synchrotron data contain statistical information on the nanostructure, we establish a direct connection between experiment and model to identify the rehydrated elasto-plastic micro- and nanomechanical fibre behaviour. Rehydration led to a decrease of 65%-75% in fibre yield stress and compressive strength, and 70% in stiffness with a 3x higher effect on stresses than strains. While in agreement with bone extracellular matrix, the decrease is 1.5-3x higher compared to micro-indentation and macro-compression. Hydration influences mineral more than fibril strain with the highest difference to the macroscale when comparing mineral and tissue levels. The effect of hydration seems to be strongly mediated by ultrastructural interfaces while results provide insights towards mechanical consequences of reported water-mediated structuring of bone apatite. The missing reinforcing capacity of surrounding tissue for an excised fibril array is more pronounced in wet than dry conditions, mainly related to fibril swelling. Differences leading to higher compressive strength between mineralised tissues seem not to depend on rehydration while the lack of kink bands supports the role of water as an elastic embedding influencing energy-absorption mechanisms. STATEMENT OF SIGNIFICANCE: Characterising structure-property-function relationships in hierarchical biological materials helps us to elucidate mechanisms that enable their unique properties. Experimental and computational methods can advance our understanding of their complex behaviour with the potential to inform bio-inspired material development. In this study, we close a gap for bone's fundamental mechanical building block at micro- and nanometre length scales. We establish a direct connection between experiments and simulations by coupling in situ synchrotron tests with a statistical model and quantify the behaviour of rehydrated single mineralised collagen fibres. Results suggest a high influence of hydration on structural interfaces, and the role of water as an elastic embedding by outlining important differences between wet and dry elasto-plastic properties of mineral nanocrystals, fibrils and fibres.

Experimental and numerical study on failure mechanisms of bone simulants subjected to projectile impact

Analyses of the human bones failure mechanisms under projectile impact conditions can be made through performing of a large number of ballistic trials. But the amount of data that can be collected during ballistic experiments is limited due to the high dynamics of the process and its destructive character. Numerical analyses may support experimental methodologies allowing to better understand the principles of the phenomenon. Therefore, the main aim of the study was to create and to verify a numerical model of commercially available synthetic bone material-Synbone®. The model could be used in the future as a supporting tool facilitating forensic studies or designing processes of personal protection systems (helmets, bulletproof vests, etc.). Although Synbone® is commonly used in the ballistic experiments, the literature lacks reliable numerical models of this material. In order to define a numerical model of Synbone®, mechanical experiments characterizing the response of the material to the applied loads in a wide range of strains and strain rates were carried out. Based on the mechanical tests results, an appropriate material model was selected for the Synbone® composite and the values of constants in its equations were determined. Material characterization experiments were subsequently reproduced with numerical simulations and a high correlation of the results was obtained. The final validation of the material model was based on the comparison of the ballistic impact experiments and simulation results. High similarity obtained (relative error lower than 10%) demonstrates that the numerical model of Synbone® material was properly defined.

Anatomical and Biomechanical Stability of Single/Double Screw-Cancellous Bone Fixations of Regan-Morry Type III Ulnar Coronoid Fractures in Adults: CT Measurement and Finite Element Analysis

OBJECTIVE

At present, it is still uncertain whether single screw has the same stability as double screws in the treatment of ulnar coronal process basal fracture (Regan-Morry type III). So, we aimed to compare the pull-out force and anti-rotation torque of anterior single/double screw-cancellous bone fixation (aSSBF, aDSBF) in this fracture, and further study the influencing factors on anatomical and biomechanical stability of smart screw internal fixations.

METHODS

A total of 63 adult volunteers with no history of elbow injury underwent elbow CT scanning with associated three-dimensional reconstruction that enabled the measurements of bone density and fixed length of the proximal ulna and coronoid. The models of coronal process basal fracture, aSSBF and aDSBF, were developed and validated. Using the finite element model test, the sensitivity analysis of pull-out force and rotational torque was carried out.

RESULTS

The pull-out force of aSSBF model was positively correlated with the density of the cancellous bone and linearly related to the fixed depth of the screw. The load pattern of pull-out force of aDSBF model was similar to that of aSSBF model. The ultimate torque of aDSBF model was higher than that of aSSBF model, but the load pattern of ultimate torque of both models was similar to each other when the fracture reset was satisfactory, and the screw nut attaches closely to coronoid process. Moreover, with enhancement of initial pre-tightening force, the increase of ultimate torque of both models was small.

CONCLUSIONS

In addition to three pull-out stability factors of smart screw fixations, fracture surface fitting degree and nut fitting degree are the other two important anatomical and biomechanical stability factors of smart screw fixations both for rotational stability. When all pull-out stability and rotational stability factors meet reasonable conditions simultaneously, single or double screw fixation methods are stable for the treatments of ulnar coronoid basal fractures.

Comparison of Cortical Bone Fracture Patterns Under Compression Loading Using Finite Element–Discrete Element Numerical Modeling Approach and Destructive Testing

Finite element analysis may not be the only method by which bone fracture initiation and propagation may be analyzed. This study compares fracture patterns generated from compression testing of bone to fracture patterns generated using a combination of both the finite element method (FEM) and discrete element method (DEM) as defined by the finite discrete element method (FDEM). Before testing, a three-dimensional bone model was developed using CT. Force and displacement data were collected during testing. The tested specimen was reimaged using CT. The solid model was discretized and material properties adjusted such that finite element-discrete element macro behavior matched the force-displacement data. A qualitative comparison of the fracture patterns demonstrates that FDEM can successfully be used to simulate and predict fracturing in bone, with this study representing the first time this has been done and reported.

Mechanical response and in-situ deformation mechanism of cortical bone materials under combined compression and torsion loads

Bone fracture is an extremely dangerous health risk to human. Actually, cortical bone is often subjected to the complicated loading patterns. The mechanical properties and deformation mechanism under the complicated loading pattern could provide a more precise understanding for the bone fracture. For this purpose, the mechanical response and multi-scale deformation mechanism of cortical bone material were investigated by in-situ experimental research using the compression-torsion coupling loads as an example. It was found that the torsion strength and shear modulus all decreased under the compression-torsion coupling loads than single torsion load. This indicated bone would suffer greater risk of fracture under the compression-torsion coupling loads. Based on in-situ observation, it was found that the rapid reduction of the anisotropy of bone material under the compression load was the potential influencing factor. Because of the redistribution of the principal strain and the variations of cracks propagation, the comprehensive fracture pattern containing both transverse and longitudinal fracture was shown under the coupling loads, and finally resulted in the reduction of the torsion properties. This research could provide new references for researches on mechanical properties of cortical bone material under complicated loading patterns.

Tibial Stem Extension versus Standard Configuration in Total Knee Arthroplasty: A Biomechanical Assessment According to Bone Properties

Background and Objectives: This study’s purpose was to examine the benefit of using a tibial extension in the primary operation of total knee arthroplasty (TKA). This is important because it is not a common practice to use the extension in a primary TKA, a standard configuration offering sufficient stability and good long-term survivorship. The following question arises: which situation requires the use of a standard configuration implant (without a stem) and which situation requires using the extension? Materials and Methods: The opportunity to use the tibial extension in the primary TKA was analyzed in correlation to the tibial bone structural properties. Using finite elements (FEs), the virtual model of the tibial bone was connected to that of the prosthetic implant, with and without a stem, and its behavior was analyzed during static and dynamic stresses, both in the situation in which the bone had normal physical properties, as well as in the case in which the bone had diminished physical properties. Results: The maximum stress and displacement values in the static compression regime show that adding a stem is only beneficial to structurally altered bone. Compression fatigue was reduced to almost half in the case of altered bone when adding a stem. Dynamic compression showed slightly better results with the tibial stem in both healthy and degraded bone. Conclusions: It was concluded that, if the bone is healthy and has good structural properties, it is not necessary to use the tibial extension in the primary operation; and if the bone has diminished physical properties, it is necessary to use the tibial extension at the primary operation, enhancing the stability, fixation, and implant lifespan.

Multifunctional polyethylene imine hybrids decorated by silica bioactive glass with enhanced mechanical properties, antibacterial, and osteogenesis for bone repair

Inorganic/organic hybrids and bioactive glasses demonstrate promising potential as bone substitute biomaterials. A sol-gel hybrid consisting of silica bioactive glass and biodegradable polymer can combine the high bioactivity of a glass with the toughness of a polymer. In this study, multifunctional hybrids with a combination of organic-inorganic hybrid structure class II consisting of polyethyleneimine (PEI) generation 4 (G4) and bioactive glass with enhanced mechanical properties, mineralization, antibacterial, and osteogenesis activities were synthesized by the sol-gel method. Glycidoxypropyl) trimethoxysilane (GPTMS) with different concentrations was used as a covalent bonding agent between PEI polymer and bioactive glass. The effect of GPTMS content was assessed in the presence and absence of calcium in the hybrid structures in terms of morphology, wettability, mechanical properties, antibacterial activity, cell viability, and in vitro osteogenic differentiation properties. By increasing the amount of GPTMS, the compressive strength increased from 1.95 MPa to 2.34 MPa, which was comparable to human trabecular bone. All the hybrids presented antibacterial activity against Staphylococcus aureus, forming an inhibition zone of 13-16 mm. An increase in cell viability of 82.22% in PSCaG90 was obtained after 1 day of MG-63 cell culture. Alkaline phosphatase expression and mineralization of MG-63 cells increased in the PSCaG90 hybrid in the absence of an osteogenic medium compared to PSG60 and PSG90. The PSCaG90 hybrid indicated considerable in vitro osteogenic capacity in the absence of a differentiation medium, expressing high levels of bone-specific proteins including collagen I (COL1A1), Runt-related transcription factor 2 (RUNX2), osteopontin (OPN), and osteocalcin (OCN), compared to calcium-free hybrids. Overall, our results suggest that the presence of calcium in the PSCaG90 leads to a significant increase in osteogenic differentiation of MG-63 cells even in the absence of differentiation medium, which suggests these hybrid structures with multifunctional properties as promising candidates for bone repair.

Development of a crushable foam model for human trabecular bone

Finite element (FE) simulations can be used to evaluate the mechanical behavior of human bone and allow for quantitative prediction of press-fit implant fixation. An adequate material model that captures post-yield behavior is essential for a realistic simulation. The crushable foam (CF) model is a constitutive model that has recently been proposed in this regard. Compression tests under uniaxial and confined loading conditions were performed on 59 human trabecular bone specimens. Three essential material parameters were obtained as a function of bone mineral density (BMD) to develop the isotropic CF model. The related constitutive rule was implemented in FE models and the results were compared to the experimental data. The CF model provided an accurate simulation of uniaxial compression tests and the post-yield behavior of the stress-strain was well-matched with the experimental results. The model was able to reproduce the confined response of the bone up to 15% of strain. This model allows for simulation of the mechanical behavior of the cellular structure of human bone and adequately predicts the post-yield response of trabecular bone, particularly under uniaxial loading conditions. The model can be further improved to simulate bone collapse due to local overload around orthopaedic implants.

An experimentally informed statistical elasto-plastic mineralised collagen fibre model at the micrometre and nanometre lengthscale

Bone is an intriguingly complex material. It combines high strength, toughness and lightweight via an elaborate hierarchical structure. This structure results from a biologically driven self-assembly and self-organisation, and leads to different deformation mechanisms along the length scales. Characterising multiscale bone mechanics is fundamental to better understand these mechanisms including changes due to bone-related diseases. It also guides us in the design of new bio-inspired materials. A key-gap in understanding bone's behaviour exists for its fundamental mechanical unit, the mineralised collagen fibre, a composite of organic collagen molecules and inorganic mineral nanocrystals. Here, we report an experimentally informed statistical elasto-plastic model to explain the fibre behaviour including the nanoscale interplay and load transfer with its main mechanical components. We utilise data from synchrotron nanoscale imaging, and combined micropillar compression and synchrotron X-ray scattering to develop the model. We see that a 10-15% micro- and nanomechanical heterogeneity in mechanical properties is essential to promote the ductile microscale behaviour preventing an abrupt overall failure even when individual fibrils have failed. We see that mineral particles take up 45% of strain compared to collagen molecules while interfibrillar shearing seems to enable the ductile post-yield behaviour. Our results suggest that a change in mineralisation and fibril-to-matrix interaction leads to different mechanical properties among mineralised tissues. Our model operates at crystalline-, molecular- and continuum-levels and sheds light on the micro- and nanoscale deformation of fibril-matrix reinforced composites.

Time-Resolved PIV Measurements and Turbulence Characteristics of Flow Inside an Open-Cell Metal Foam

Open-cell metal foams are porous medium for thermo-fluidic systems. However, their complex geometry makes it difficult to perform time-resolved (TR) measurements inside them. In this study, a TR particle image velocimetry (PIV) method is introduced for use inside open-cell metal foam structures. Stereolithography 3D printing methods and conventional post-processing methods cannot be applied to metal foam structures; therefore, PolyJet 3D printing and post-processing methods were employed to fabricate a transparent metal foam replica. The key to obtaining acceptable transparency in this method is the complete removal of the support material from the printing surfaces. The flow characteristics inside a 10-pore-per-inch (PPI) metal foam were analyzed in which porosity is 0.92 while laminar flow condition is applied to inlet. The flow inside the foam replica is randomly divided and combined by the interconnected pore network. Robust crosswise motion occurs inside foam with approximately 23% bulk speed. Strong influence on transverse motion by metal foam is evident. In addition, span-wise vorticity evolution is similar to the integral time length scale of the stream-wise center plane. The span-wise vorticity fluctuation through the foam arrangement is presented. It is believed that this turbulent characteristic is caused by the interaction of jets that have different flow directions inside the metal foam structure. The finite-time Lyapunov exponent method is employed to visualize the vortex ridges. Fluctuating attracting and repelling material lines are expected to enhance the heat and mass transfer. The results presented in this study could be useful for understanding the flow characteristics inside metal foams.

A comparative study of tapped and untapped pilot holes for bicortical orthopedic screws – 3D finite element analysis with an experimental test

The aim of this study was to compare the screw-to-bone fixation strength of two insertion techniques: self-tapping screw (STS) and non-self-tapping screw (NSTS). Finite element analysis (FEA) was used for the comparison by featuring three tests (insertion, pull-out and shear) in a human tibia bone model. A non-linear material behavior with ductile damage properties was chosen for the modeling. To validate the numerical models, experimental insertion and pull-out tests were carried out using a synthetic bone. The experimental and numerical results of pull-out tests correlated well. Thread forming was successfully simulated during the insertion process of STS and NSTS. It is demonstrated that the STS generates higher insertion torque, induces a higher amount of stress after the insertion process and relatively more strength under the pull-out and shear tests than the NSTS. However, the NSTS induces more stiffness under the two tests (pull-out and shear) and less damage to the screw-bone interface compared to the STS. It is concluded that the use of STS ensures tighter bony contact and enables higher pull-out strength; however, the use of NSTS improves the stiffness of the fixation and induces less damage to the cortical bone-screw fixation and thus minimum risk is obtained in terms of bone necrosis.

Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro- and nanoscale

The increasing incidence of osteoporotic bone fractures makes fracture risk prediction an important clinical challenge. Computational models can be utilised to facilitate such analyses. However, they critically depend on bone's underlying hierarchical material description. To understand bone's irreversible behaviour at the micro- and nanoscale, we developed an in situ testing protocol that allows us to directly relate the experimental data to the mechanical behaviour of individual mineralised collagen fibres and its main constitutive phases, the mineralised collagen fibrils and the mineral nanocrystals, by combining micropillar compression of single fibres with small angle X-ray scattering (SAXS) and X-ray diffraction (XRD). Failure modes were assessed by SEM. Strain ratios in the elastic region at fibre, fibril and mineral levels were found to be approximately 22:5:2 with strain ratios at the point of compressive strength of 0.23 ± 0.11 for fibril-to-fibre and 0.07 ± 0.01 for mineral-to-fibre levels. Mineral-to-fibre levels showed highest strain ratios around the apparent yield point, fibril-to-fibre around apparent strength. The mineralised collagen fibrils showed a delayed mechanical response, contrary to the mineral phase, which points towards preceding deformations of mineral nanocrystals in the extrafibrillar matrix. No damage was measured at the level of the mineralised collagen fibre which indicates an incomplete separation of the mineral and collagen, and an extrafibrillar interface failure. The formation of kink bands and the gradual recruitment of fibrils upon compressive loading presumably led to localised strains. Our results from a well-controlled fibrillar architecture provide valuable input for micromechanical models and computational non-linear bone strength analyses that may provide further insights for personalised diagnosis and treatment as well as bio-inspired implants for patients with bone diseases. STATEMENT OF SIGNIFICANCE: Musculoskeletal diseases such as osteoporosis, osteoarthritis or bone cancer significantly challenge health care systems and make fracture risk prediction and treatment optimisation important clinical goals. Computational methods such as finite element models have the potential to optimise analyses but highly depend on underlying material descriptions. We developed an in situ testing set-up to directly relate experimental data to the mechanical behaviour of bone's fundamental building block, the individual mineralised collagen fibre and its main constituents. Low multilevel strain ratios suggest high deformations in the extrafibrillar matrix and energy dissipation at the interfaces, the absence of damage indicates both an incomplete separation between mineral and collagen and an extrafibrillar interface failure. The formation of kink bands in the fibril-reinforced composite presumably led to localised strains. The deformation behaviour of a well-controlled fibrillar architecture provides valuable input for non-linear bone strength analyses.

A theory of biological composites undergoing plastic deformations

Natural biological composites such as bone, dentin, nacre and enamel exhibit anisotropic microstructures, giving rise to orientation-dependent mechanical properties. Although the mechanical properties of these materials have been studied extensively, there is limited progress on modeling the common features associated with the orientation-dependent plastic deformation of biological composites. In this study, we develop a continuum theory for elastic-viscoplastic deformations of anisotropic biological composites. The pressure-sensitive and plastically dilatant plastic flow is incorporated into the theory, and the plastic spin related to the kinematics of the underlying substructure during macroscopic plastic deformation is explicitly taken into account. A special set of constitutive equations are implemented in a finite element program. Furthermore, the material parameters have been calibrated and numerical simulations of elastic-plastic deformation in bone are performed. It is found that the theory can capture the major features of plastic deformation of biological composites. The numerical simulations are in good agreement with experiments, demonstrating that the model is capable of predicting the complex plastic deformation of bone.

Structural role of osteocalcin and osteopontin in energy dissipation in bone

Non-collagenous proteins are a vital component of bone matrix. Amongst them, osteocalcin (OC) and osteopontin (OPN) hold special significance due to their intimate interaction with the mineral and collagenous matrix in bone. Both proteins have been associated with microdamage and fracture, but their structural role in energy dissipation is unclear. This study used bone tissue from genetic deficient mice lacking OC and/or OPN and subjected them to a series of creep-fatigue-creep tests. To this end, whole tibiae were loaded in four-point bending to 70% stiffness loss which captured the three characteristic phases of fatigue associated with initiation, propagation, and coalescence of microdamage. Fatigue loading preceded and followed creep tests to determine creep and dampening parameters. Microdamage in the form of linear microcracks and diffuse damage were analyzed by histology. It was shown that OC and OPN were 'activated' following stiffness loss associated with fatigue damage where they facilitated creep and dampening parameters (i.e. increased energy dissipation). More specifically, post-fatigue creep rate and dampening were significantly greater in wild-types (WTs) than genetic deficient mice (p < 0.05). These results were supported by microdamage analysis which showed significant increase in creep-associated diffuse damage formation in WTs compared to genetic deficient groups (p < 0.05). Based on these findings, we propose that during local yield events, OC and OPN rely on ionic interactions of their charged side chains and on hydrogen bonding to dissipate energy in bone.

How a pilot hole size affects osteosynthesis at the screw-bone interface under immediate loading

An inappropriate pilot hole size (PHS) is one of several factors that affects the stiffness of the screw-bone fixation. The present study uses finite element models to investigate the effect of varying the PHS on the biomechanical environment of the screw-bone interface of the fractured bone, after the screw insertion and under the immediate body weight pressure (BWP). Four PHS from 71% up to 85% of the screw external diameter (SED) were considered for analysis. A non linear material behaviour of the bone with ductile damage properties was used in the study. To validate the numerical models, an experimental pull-out test was carried out using a synthetic bone. The results of the insertion process demonstrated that the relatively smaller holes (71% and 75.5% of SED) increased the insertion torque value within the recommended level, caused more bone radial extension deformation and maximized the contact area between the bone threads and the screw, in comparison to the PHS higher than 80% of SED. Under the immediate BWP after osteosynthesis, the stress level exceeds the elastic limit and becomes high enough to initiate the ductile damage of the bone. Also, enlarging PHS from 71% to 75.5% of SED increased the bone microdisplacement at the screw-bone interface from 75 up to 100 μm, and that reduced the stiffness of the fixation.

Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

Clinical hip fracture is accompanied by compression induced failure in the superior cortex of the femoral neck

Hip fractures pose a major health problem throughout the world due to their devastating impact. Current theories for why these injuries are so prevalent in the elderly point to an increased propensity to fall and decreases in bone mass with ageing. However, the fracture mechanisms, particularly the stress and strain conditions leading to bone failure at the hip remain unclear. Here, we directly examined the cortical bone from clinical intra-capsular hip fractures at a microscopic level, and found strong evidence of compression induced failure in the superior cortex. A total of 143 sections obtained from 24 femoral neck samples that were retrieved from 24 fracturing patients at surgery were examined using laser scanning confocal microscopy (LSCM) after fluorescein staining. The stained microcracks showed significantly higher density in the superior cortex than in the inferior cortex, indicating a greater magnitude of strain in the superior femoral neck during the failure-associated deformation and fracture process. The predominant stress state for each section was reconstructed based on the unique correlation between the microcrack pattern and the stress state. Specifically, we found clear evidence of longitudinal compression and buckling as the primary failure mechanisms in the superior cortex. These findings demonstrate the importance of microcrack analysis in studying clinical hip fractures, and point to the central role of the superior cortex failure as an important aspect of the failure initiation in clinical intra-capsular hip fractures.

Computational Modeling of Interfacial Behaviors in Nanocomposite Materials

Towards understanding the bulk material response in nanocomposites, an interfacial zone model was proposed to define a variety of material interface behaviors (e.g. brittle, ductile, rubber-like, elastic-perfectly plastic behavior etc.). It also has the capability to predict bulk material response though independently control of the interface properties (e.g. stiffness, strength, toughness). The mechanical response of granular nanocomposite (i.e. nacre) was investigated through modeling the "relatively soft" organic interface as an interfacial zone among "hard" mineral tablets and simulation results were compared with experimental measurements of stress-strain curves in tension and compression tests. Through modeling varies material interfaces, we found out that the bulk material response of granular nanocomposite was regulated by the interfacial behaviors. This interfacial zone model provides a possible numerical tool for qualitatively understanding of structure-property relationships through material interface design.

Nanoindentation analysis of the micromechanical anisotropy in mouse cortical bone

Studies investigating micromechanical properties in mouse cortical bone often solely focus on the mechanical behaviour along the long axis of the bone. Therefore, data on the anisotropy of mouse cortical bone is scarce. The aim of this study is the first-time evaluation of the anisotropy ratio between the longitudinal and transverse directions of reduced modulus and hardness in mouse femurs by using the nanoindentation technique. For this purpose, nine 22-week-old mice (C57BL/6) were sacrificed and all femurs extracted. A total of 648 indentations were performed with a Berkovich tip in the proximal (P), central (C) and distal (D) regions of the femoral shaft in the longitudinal and transverse directions. Higher values for reduced modulus are obtained for indentations in the longitudinal direction, with anisotropy ratios of 1.72 ± 0.40 (P), 1.75 ± 0.69 (C) and 1.34 ± 0.30 (D). Hardness is also higher in the longitudinal direction, with anisotropic ratios of 1.35 ± 0.27 (P), 1.35 ± 0.47 (C) and 1.17 ± 0.19 (D). We observed a significant anisotropy in the micromechanical properties of the mouse femur, but the correlation for reduced modulus and hardness between the two directions is low (r² < 0.3) and not significant. Therefore, we highly recommend performing independent indentation testing in both the longitudinal and transverse directions when knowledge of the tissue mechanical behaviour along multiple directions is required.

Nanoindentation analysis of the micromechanical anisotropy in mouse cortical bone

Studies investigating micromechanical properties in mouse cortical bone often solely focus on the mechanical behaviour along the long axis of the bone. Therefore, data on the anisotropy of mouse cortical bone is scarce. The aim of this study is the first-time evaluation of the anisotropy ratio between the longitudinal and transverse directions of reduced modulus and hardness in mouse femurs by using the nanoindentation technique. For this purpose, nine 22-week-old mice (C57BL/6) were sacrificed and all femurs extracted. A total of 648 indentations were performed with a Berkovich tip in the proximal (P), central (C) and distal (D) regions of the femoral shaft in the longitudinal and transverse directions. Higher values for reduced modulus are obtained for indentations in the longitudinal direction, with anisotropy ratios of 1.72 ± 0.40 (P), 1.75 ± 0.69 (C) and 1.34 ± 0.30 (D). Hardness is also higher in the longitudinal direction, with anisotropic ratios of 1.35 ± 0.27 (P), 1.35 ± 0.47 (C) and 1.17 ± 0.19 (D). We observed a significant anisotropy in the micromechanical properties of the mouse femur, but the correlation for reduced modulus and hardness between the two directions is low (r² < 0.3) and not significant. Therefore, we highly recommend performing independent indentation testing in both the longitudinal and transverse directions when knowledge of the tissue mechanical behaviour along multiple directions is required.

An improved interfacial bonding model for material interface modeling

An improved interfacial bonding model was proposed from potential function point of view to investigate interfacial interactions in polycrystalline materials. It characterizes both attractive and repulsive interfacial interactions and can be applied to model different material interfaces. The path dependence of work-of-separation study indicates that the transformation of separation work is smooth in normal and tangential direction and the proposed model guarantees the consistency of the cohesive constitutive model. The improved interfacial bonding model was verified through a simple compression test in a standard hexagonal structure. The error between analytical solutions and numerical results from the proposed model is reasonable in linear elastic region. Ultimately, we investigated the mechanical behavior of extrafibrillar matrix in bone and the simulation results agreed well with experimental observations of bone fracture.

Assessment of compressive failure process of cortical bone materials using damage-based model

The main failure factors of cortical bone are aging or osteoporosis, accident and high energy trauma or physiological activities. However, the mechanism of damage evolution coupled with yield criterion is considered as one of the unclear subjects in failure analysis of cortical bone materials. Therefore, this study attempts to assess the structural response and progressive failure process of cortical bone using a brittle damaged plasticity model. For this reason, several compressive tests are performed on cortical bone specimens made of bovine femur, in order to obtain the structural response and mechanical properties of the material. Complementary finite element (FE) model of the sample and test is prepared to simulate the elastic-to-damage behavior of the cortical bone using the brittle damaged plasticity model. The FE model is validated in a comparative method using the predicted and measured structural response as load-compressive displacement through simulation and experiment. FE results indicated that the compressive damage initiated and propagated at central region where maximum equivalent plastic strain is computed, which coincided with the degradation of structural compressive stiffness followed by a vast amount of strain energy dissipation. The parameter of compressive damage rate, which is a function dependent on damage parameter and the plastic strain is examined for different rates. Results show that considering a similar rate to the initial slope of the damage parameter in the experiment would give a better sense for prediction of compressive failure.

Contribution of extrafibrillar matrix to the mechanical behavior of bone using a novel cohesive finite element model

The mechanical behavior of bone is determined at all hierarchical levels, including lamellae (the basic building block of bone) that are comprised of mineralized collagen fibrils and extrafibrillar matrix. The mechanical behavior of mineralized collagen fibrils has been investigated intensively using both experimental and computational approaches. Yet, the contribution of the extrafibrillar matrix to bone mechanical properties is poorly documented. In this study, we intended to address this issue using a novel cohesive finite element (FE) model, in conjunction with the experimental observations reported in the literature. In the FE model, the extrafibrillar matrix was considered as a nanocomposite of hydroxyapatite (HA) crystals bounded through a thin organic interface modeled as a cohesive interfacial zone. The parameters required by the cohesive FE model were defined based on the experimental data reported in the literature. This hybrid nanocomposite model was tested in two loading modes (i.e. tension and compression) and under two hydration conditions (i.e. wet and dry). The simulation results indicated that (1) the failure modes of the extrafibrillar matrix predicted using the cohesive FE model were closely coincided with those experimentally observed in tension and compression tests; (2) the pre-yield deformation (i.e. internal strain) of HA crystals with respect to the applied strain was consistent with that obtained from the synchrotron X-ray scattering measurements irrespective of the loading modes and hydration status; and (3) the mechanical behavior of the extrafibrillar matrix was dictated by the properties of the organic interface between the HA crystals. Taken together, we postulate that the extrafibrillar matrix plays a major role in the pre-yield deformation and the failure mode of bone, thus, giving rise to important insights in the ultrastructural origins of bone fragility.

Ductile silica/methacrylate hybrids for bone regeneration

Hybrids consisting of co-networks of high cross-linking density polymethacrylate and silica (class II hybrid) were synthesised as a potential new generation of scaffold materials.

Fabrication method, structure, mechanical, and biological properties of decellularized extracellular matrix for replacement of wide bone tissue defects

The present paper was focused on the development of a new method of decellularized extracellular matrix (DECM) fabrication via a chemical treatment of a native bone tissue. Particular attention was paid to the influence of chemical treatment on the mechanical properties of native bones, sterility, and biological performance in vivo using the syngeneic heterotopic and orthotopic implantation models. The obtained data indicated that after a chemical decellularization treatment in 4% aqueous sodium chlorite, no noticeable signs of the erosion of compact cortical bone surface or destruction of trabeculae of spongy bone in spinal channel were observed. The histological studies showed that the chemical treatment resulted in the decellularization of both bone and cartilage tissues. The DECM samples demonstrated no signs of chemical and biological degradation in vivo. Thorough structural characterization revealed that after decellularization, the mineral frame retained its integrity with the organic phase; however clotting and destruction of organic molecules and fibers were observed. FTIR studies revealed several structural changes associated with the destruction of organic molecules, although all organic components typical of intact bone were preserved. The decellularization-induced structural changes in the collagen constituent resulted changed the deformation under compression mechanism: from the major fracture by crack propagation throughout the sample to the predominantly brittle fracture. Although the mechanical properties of radius bones subjected to decellularization were observed to degrade, the mechanical properties of ulna bones in compression and humerus bones in bending remained unchanged. The compressive strength of both the intact and decellularized ulna bones was 125-130 MPa and the flexural strength of humerus bones was 156 and 145 MPa for the intact and decellularized samples, respectively. These results open new avenues for the use of DECM samples as the replacement of wide bone tissue defects.

The sensitivity of nonlinear computational models of trabecular bone to tissue level constitutive model

Microarchitectural finite element models have become a key tool in the analysis of trabecular bone. Robust, accurate, and validated constitutive models would enhance confidence in predictive applications of these models and in their usefulness as accurate assays of tissue properties. Human trabecular bone specimens from the femoral neck (n = 3), greater trochanter (n = 6), and lumbar vertebra (n = 1) of eight different donors were scanned by μ-CT and converted to voxel-based finite element models. Unconfined uniaxial compression and shear loading were simulated for each of three different constitutive models: a principal strain-based model, Drucker-Lode, and Drucker-Prager. The latter was applied with both infinitesimal and finite kinematics. Apparent yield strains exhibited minimal dependence on the constitutive model, differing by at most 16.1%, with the kinematic formulation being influential in compression loading. At the tissue level, the quantities and locations of yielded tissue were insensitive to the constitutive model, with the exception of the Drucker-Lode model, suggesting that correlation of microdamage with computational models does not improve the ability to discriminate between constitutive laws. Taken together, it is unlikely that a tissue constitutive model can be fully validated from apparent-level experiments alone, as the calculations are too insensitive to identify differences in the outcomes. Rather, any asymmetric criterion with a valid yield surface will likely be suitable for most trabecular bone models.

Shear deformation and fracture of human cortical bone

Bone can be viewed as a nano-fibrous composite with complex hierarchical structures. Its deformation and fracture behaviors depend on both the local structure and the type of stress applied. In contrast to the extensive studies on bone fracture under compression and tension, there is a lack of knowledge on the fracture process under shear, a stress state often exists in hip fracture. This study investigated the mechanical behavior of human cortical bone under shear, with the focus on the relation between the fracture pattern and the microstructure. Iosipescu shear tests were performed on notched rectangular bar specimens made from human cortical bone. They were prepared at different angles (i.e. 0°, 30°, 60° and 90°) with respect to the long axis of the femoral shaft. The results showed that human cortical bone behaved as an anisotropic material under shear with the highest shear strength (~50MPa) obtained when shearing perpendicular to the Haversian systems or secondary osteons. Digital image correlation (DIC) analysis found that shear strain concentration bands had a close association with long bone axis with an average deviation of 11.8° to 18.5°. The fracture pattern was also greatly affected by the structure with the crack path generally following the direction of the long axes of osteons. More importantly, we observed unique peripheral arc-shaped microcracks within osteons, using laser scanning confocal microscopy (LSCM). They were generally long cracks that developed within a lamella without crossing the boundaries. This microcracking pattern clearly differed from that created under either compressive or tensile stress: these arc-shaped microcracks tended to be located away from the Haversian canals in early-stage damaged osteons, with ~70% developing in the outer third osteonal wall. Further study by second harmonic generation (SHG) and two-photon excitation fluorescence (TPEF) microscopy revealed a strong influence of the organization of collagen fibrils on shear microcracking. This study concluded that shear-induced microcracking of human cortical bone follows a unique pattern that is governed by the lamellar structure of the osteons.

Study of indentation of a sample equine bone using finite element simulation and single cycle reference point indentation

In an attempt to study the mechanical behavior of bone under indentation, methods of analyses and experimental validations have been developed, with a selected test material. The test material chosen is from an equine cortical bone. Stress-strain relationships are first obtained from conventional mechanical property tests. A finite element simulation procedure is developed for indentation analyses. The simulation results are experimentally validated by determining (1) the maximum depth of indentation with a single cycle type of reference point indentation, and (2) the profile and depth of the unloaded, permanent indentation with atomic force microscopy. The advantage of incorporating in the simulation a yield criterion calibrated by tested mechanical properties, with different values in tension and compression, is demonstrated. In addition, the benefit of including damage through a reduction in Young's modulus is shown in predicting the permanent indentation after unloading and recovery. The expected differences in response between two indenter tips with different sharpness are predicted and experimentally observed. Results show predicted indentation depths agree with experimental data. Thus, finite element simulation methods with experimental validation, and with damage approximation by a reduction of Young's modulus, may provide a good approach for analysis of indentation of cortical bone. These methods reveal that multiple factors affect measured indentation depth and that the shape of the permanent indentation contains useful information about bone material properties. Only further work can determine if these methods or extensions to these methods can give useful insights into bone pathology, for example the bone fragility of thoroughbred racehorses.

In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Ageing societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the hierarchical organization of bone. Here, we investigate the mechanical response under monotonic and cyclic compression of both single osteonal lamellae and macroscopic samples containing numerous osteons. Micropillar compression tests in a scanning electron microscope, microindentation and macroscopic compression tests were performed on dry ovine bone to identify the elastic modulus, yield stress, plastic deformation, damage accumulation and failure mechanisms. We found that isolated lamellae exhibit a plastic behaviour, with higher yield stress and ductility but no damage. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behaviour of bone at the microscale to a quasi-brittle response driven by the growth of cracks along interfaces or in the vicinity of pores at the macroscale.

Effect of bone material properties on effective region in screw-bone model: an experimental and finite element study

Background

There have been numerous studies conducted to investigate the pullout force of pedicle screws in bone with different material properties. However, fewer studies have investigated the region of effect (RoE), stress distribution and contour pattern of the cancellous bone surrounding the pedicle screw.

Methods

Screw pullout experiments were performed from two different foams and the corresponding reaction force was documented for the validation of a computational pedicle screw-foam model based on finite element (FE) methods. After validation, pullout simulations were performed on screw-bone models, with different bone material properties to model three different age groups (<50, 50–75 and >75 years old). At maximum pullout force, the stress distribution and average magnitude of Von Mises stress were documented in the cancellous bone along the distance beyond the outer perimeter pedicle screw. The radius and volume of the RoE were predicted based on the stress distribution.

Results

The screw pullout strengths and the load–displacement curves were comparable between the numerical simulation and experimental tests. The stress distribution of the simulated screw-bone vertebral unit showed that the radius and volume of the RoE varied with the bone material properties. The radii were 4.73 mm, 5.06 mm and 5.4 mm for bone properties of ages >75, 75 > ages >50 and ages <50 years old, respectively, and the corresponding volumes of the RoE were 6.67 mm³, 7.35 mm³ and 8.07 mm³, respectively.

Conclusions

This study demonstrated that there existed a circular effective region surrounding the pedicle screw for stabilization and that this region was sensitive to the bone material characteristics of cancellous bone. The proper amount of injection cement for augmentation could be estimated based on the RoE in the treatment of osteoporosis patients to avoid leakage in spine surgery.

A computational study on the effect of fracture intrusion distance in three- and four-part trochanteric fractures treated with Gamma nail and sliding hip screw

Using finite element analysis, the behaviors of the Gamma nail and the sliding hip screw (SHS) were compared in an osteoporotic bone model for the fixation of three- and four-part trochanteric fractures (31-A2 in the AO classification, types IV and V in Evans' classification). The size of the medial fragment was varied based on clinical data, and the case of a fractured greater trochanter was also considered. Our results showed that for Evans' type V stabilized with a Gamma nail and for Evans' types IV and V with the SHS, cancellous bone around the lag screw is susceptible to yielding, thus indicating a risk of cut-out. The volume of bone susceptible to yielding increases with an increase in size of the medial fragment. Conversely, Evans' type IV with a Gamma nail was not predicted to cut out. Our findings suggest that future clinical trials investigating fixation of unstable proximal fractures should include the size of the medial fragment and the integrity of the greater trochanter as covariables and be powered to evaluate whether intramedullary devices are superior to SHSs for Evans' type IV fractures and inferior/equivalent for type V.

Potential of in vivo MRI-based nonlinear finite-element analysis for the assessment of trabecular bone post-yield properties

PURPOSE

Bone strength is the key factor impacting fracture risk. Assessment of bone strength from high-resolution (HR) images have largely relied on linear micro-finite element analysis (μFEA) even though failure always occurs beyond the yield point, which is outside the linear regime. Nonlinear μFEA may therefore be more informative in predicting failure behavior. However, existing nonlinear models applied to trabecular bone (TB) have largely been confined to micro-computed tomography (μCT) and, more recently, HR peripheral quantitative computed tomography (HR-pQCT) images, and typically have ignored evaluation of the post-yield behavior. The primary purpose of this work was threefold: (1) to provide an improved algorithm and program to assess TB yield as well as post-yield properties; (2) to explore the potential benefits of nonlinear μFEA beyond its linear counterpart; and (3) to assess the feasibility and practicality of performing nonlinear analysis on desktop computers on the basis of micro-magnetic resonance (μMR) images obtained in vivo in patients.

METHODS

A method for nonlinear μFE modeling of TB yield as well as post-yield behavior has been designed where material nonlinearity is captured by adjusting the tissue modulus iteratively according to the tissue-level effective strain obtained from linear analysis using a computationally optimized algorithm. The software allows for images at in vivo μMRI resolution as input with retention of grayscale information. Associations between axial stiffness estimated from linear analysis and yield as well as post-yield parameters from nonlinear analysis were investigated from in vivo μMR images of the distal tibia (N = 20; ages: 58-84) and radius (N = 20; ages: 50-75).

RESULTS

All simulations were completed in 1 h or less for 61 strain levels using a desktop computer (dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM). Although yield stress and ultimate stress correlated strongly (R(2) > 0.95, p < 0.001) with axial stiffness, toughness correlated moderately at the distal tibia (R(2) = 0.81, p < 0.001) and only weakly at the distal radius (R(2) = 0.34, p = 0.007). Further, toughness was found to vary by up to 16% for bone of very similar axial stiffness (<2%).

CONCLUSIONS

The work demonstrates the practicality of nonlinear μFE simulations at in vivo μMRI resolution, as well as its potential for providing additional information beyond that obtainable from linear analysis. The data suggest that a direct assessment of toughness may provide information not captured by stiffness.

Nanomechanics insights into the performance of healthy and osteoporotic bones

In situ nanoscopic observations of healthy and osteoporotic bone nanopillars under compression were performed. The structural-mechanical property relationship at the atomic scale suggests that cortical bone performance is correlated to the feature, arrangement, movement, distortion, and fracture of hydroxyapatite nanocrystals. Healthy bone comprising tightly bound mineral nanocrystals shows high structural stability with nanoscopic lattice distortions and dislocation activities. On the other hand, osteoporotic bone exhibits brittleness owing to the movements of dispersed minerals in and intergranular fracture along a weak organic matrix.