Anisotropic viscoelastic properties of cortical bone

From bone to nacre - development of biomimetic materials for bone implants: a review

The field of bone repair and regeneration has undergone significant advancements, yet challenges persist in achieving optimal bone implants or scaffolds, particularly load-bearing bone implants. This review explores the current landscape of bone implants, emphasizing the complexity of bone anatomy and the emerging paradigm of biomimicry inspired by natural structures. Nature, as a master architect, offers insights into the design of biomaterials that can closely emulate the mechanical properties and hierarchical organization of bone. By drawing parallels with nacre, the mollusk shells renowned for their exceptional strength and toughness, researchers have endeavored to develop bone implants with enhanced biocompatibility and mechanical robustness. This paper surveys the literature on various nacre-inspired composites, particularly ceramic/polymer composites like calcium phosphate (CaP), which exhibit promising similarities to native bone tissue. By harnessing the principles of hierarchical organization and organic-inorganic interfaces observed in natural structures, researchers aim to overcome existing limitations in bone implant technology, paving the way for more durable, biocompatible, and functionally integrated solutions in orthopedic and dental applications.

Influence of test paradigm on loading dynamics during proximal femur fracture tests simulating sideways falls

Fall-related hip fractures are a serious public health issue in older adults. As most mechanistic hip fracture risk prediction models incorporate tissue tolerance, test methods that can accurately characterize the fracture force of the femur (and factors that influence it) are imperative. While bone possesses viscoelastic properties, experimental characterization of rate-dependencies has been inconsistent in the whole-femur literature. The goal of this study was to investigate the influence of experimental paradigm on loading rate and fracture force (both means and variability) during mechanical tests simulating lateral fall loadings on the proximal femur. Six pairs of matched femurs were split randomly between two test paradigms: a 'lower rate' materials testing system (MTS) with a constant displacement rate of 60 mm/s, and a hip impact test system (HIT) comprised of a custom-built vertical drop tower utilizing an impact velocity of 4 m/s. The loading rate was 88-fold higher for the HIT (mean (SD) = 2465.49 (807.38) kN/s) compared to the MTS (27.78 (10.03) kN/s) paradigm. However, no difference in fracture force was observed between test paradigms (mean (SD) = 4096.4 (1272.6) N for HIT, and 3641.3 (1285.8) N for MTS). Within-paradigm variability was not significantly different across paradigms for either loading rate or fracture force (coefficients of variation ranging from 0.311 to 0.361). Within each test paradigm, significant positive relationships were observed between loading rate and fracture force (HIT adjusted R2 = 0.833, p = 0.007; MTS adjusted R2 = 0.983, p < 0.0001). Overall, this study provides evidence that energy-based impact simulators can be a valid method to measure femoral bone strength in the context of fall-related hip fractures. This study motivates future research to characterize potential non-linear relationships between loading rate and fracture threshold at both macro and microscales.

Cortical and trabecular mechanical properties in the femoral neck vary differently with changes in bone mineral density

Graphical Abstract.

Rheological behavior of Pluronic/Pluronic diacrylate hydrogels used for bacteria encapsulation in engineered living materials

Pluronic (Plu) hydrogels mixed with variable fractions of Pluronic diacrylate (PluDA) have become popular matrices to encapsulate bacteria and control their growth in engineered living materials. Here we study the rheological response of 30 wt% Plu/PluDA hydrogels with PluDA fraction between 0 and 1. We quantify the range of viscoelastic properties that can be covered in this system by varying in the PluDA fraction. We present stress relaxation and creep-recovery experiments and describe the variation of the critical yield strain/stress, relaxation and recovery parameters of Plu/PluDA hydrogels as function of the covalent crosslinking degree using the Burgers and Weilbull models. The analyzed hydrogels present two stress relaxations with different timescales which can be tuned with the covalent crosslinking degree. We expect this study to help users of Plu/PluDA hydrogels to estimate the mechanical properties of their systems, and to correlate them with the behaviour of bacteria in future Plu/PluDA devices of similar composition.

Biomimetic Nacre-like Hydroxyapatite/Polymer Composites for Bone Implants

One of the most ambitious goals for bone implants is to improve bioactivity, incapability, and mechanical properties; to reduce the need for further surgery; and increase efficiency. Hydroxyapatite (HA), the main inorganic component of bones and teeth, has high biocompatibility but is weak and brittle material. Cortical bone is composed of 70% calcium phosphate (CaP) and 30% collagen and forms a complex hierarchical structure with anisotropic and lamellar microstructure (osteons) which makes bone a light, strong, tough, and durable material that can support large loads. However, imitation of concentric lamellar structure of osteons is difficult to achieve in fabrication. Nacre from mollusk shells with layered structures has now become the archetype of the natural "model" for bio-inspired materials. Incorporating a nacre-like layered structure into bone implants can enhance their mechanical strength, toughness, and durability, reducing the risk of implant catastrophic failure or fracture. The layered structure of nacre-like HA/polymer composites possess high strength, toughness, and tunable stiffness which matches that of bone. The nacre-like HA/polymer composites should also possess excellent biocompatibility and bioactivity which facilitate the bonding of the implant with the surrounding bone, leading to improved implant stability and long-term success. To achieve this, a bi-directional freeze-casting technique was used to produce elongated lamellar HA were further densified and infiltrated with polymer to produce nacre-like HA/polymer composites with high strength and fracture toughness. Mechanical characterization shows that increasing the ceramic fractions in the composite increases the density of the mineral bridges, resulting in higher flexural and compressive strength. The nacre-like HA/(methyl methacrylate (MMA) + 5 wt.% acrylic acid (AA)) composites with a ceramic fraction of 80 vol.% showed a flexural strength of 158 ± 7.02 MPa and a Young's modulus of 24 ± 4.34 GPa, compared with 130 ± 5.82 MPa and 19.75 ± 2.38 GPa, in the composite of HA/PMMA, due to the higher strength of the polymer and the interface of the composite. The fracture toughness in the composition of 5 wt.% PAA to PMMA improves from 3.023 ± 0.98 MPa·m1/2 to 5.27 ± 1.033 MPa·m1/2 by increasing the ceramic fraction from 70 vol.% to 80 vol.%, respectively.

Construction of Engineered Muscle Tissue Consisting of Myotube Bundles in a Collagen Gel Matrix

Tissue engineering methods that aim to mimic the hierarchical structure of skeletal muscle tissue have been widely developed due to utilities in various fields of biology, including regenerative medicine, food technology, and soft robotics. Most methods have aimed to reproduce the microscopical morphology of skeletal muscles, such as the orientation of myotubes and the sarcomere structure, and there is still a need to develop a method to reproduce the macroscopical morphology. Therefore, in this study, we aim to establish a method to reproduce the macroscopic morphology of skeletal muscle by constructing an engineered muscle tissue (EMT) by culturing embryonic chicken myoblast-like cells that are unidirectionally aligned in collagen hydrogels with micro-channels (i.e., MCCG). Whole mount fluorescent imaging of the EMT showed that the myotubes were unidirectionally aligned and that they were bundled in the collagen gel matrix. The myotubes contracted in response to periodic electrostimulations with a frequency range of 0.5-2.0 Hz, but not at 5.0 Hz. Compression tests of the EMT showed that the EMT had anisotropic elasticity. In addition, by measuring the relaxation moduli of the EMTs, an anisotropy of relaxation strengths was observed. The observed anisotropies could be attributed to differences in maturation and connectivity of myotubes in the directions perpendicular and parallel to the long axis of the micro-channels of the MCCG.

The multiscale meso-mechanics model of viscoelastic cortical bone

Cortical bone is a complex hierarchical structure consisting of biological fiber composites with transversely isotropic constituents, whose microstructures deserve extensive study to understand the mechanism of living organisms and explore development of biomimetic materials. Based on this, we establish a three-level hierarchical structure from microscale to macroscale and propose a multiscale micromechanics model of cortical bone, which considers Haversian canal, osteonal lamellae, cement line and interstitial lamellae. In order to study the microstructural effect on the elastic behavior of hierarchical structures, the Mori-Tanaka model and locally exact homogenization theory are introduced for the homogenization of heterogeneous materials of microstructure at each level. Within sub-microscale, Haversian canal and Osteonal lamella are treated as fiber and matrix, whose homogenization is surrounded with cement line matrix in microstructure (or what we called "osteon") for the second homogenization; finally, osteon and interstitial lamella establish the meso-structure for the third homogenization, predicting the effective moduli of cortical bone. The correctness of the model in this paper is verified against the data in literature with good agreement. Finally, the dynamic viscoelastic response of cortical bones is investigated from a multiscale perspective, where the measured data are substituted into the present models to study the hydration and aging effect on bones' stiffness and viscoelasticity. It is demonstrated that the hydration is much more influential in affecting the storage and loss moduli of cortical bone than the aging effect. We also present a few numerical investigations on microstructural material and geometric parameters on the overall mechanical properties of cortical bone.

The impact of fall-related loading rate on the formation of micro-damage in human cortical bone fracture

The quest for better predictive tools as well as new preventative and therapeutic measures for bone fragility and fracture has highlighted the need for greater mechanistic understanding of the bone fracture process. Cortical bone, the major load bearing part of the bone, employs different toughening mechanisms to either inhibit or slow down crack growth which leads to fracture. Among these toughening mechanisms, is the formation of a micro-damage process zone (MDPZ) around the region of the propagating crack. Investigations into the MDPZ to date have primarily been based on quasi-static or cyclic loading rate experiments which do not necessarily replicate physiological fracture rates. Consequently, the impact of fall-related loading rates on the formation of the micro-damage process zone was investigated comparing these to quasi-static loading rate equivalents. The size of MDPZ was found to be 42% smaller in the high-rate group compared to the quasi-static rate group. The smaller MDPZ size was associated with a brittle, unstable fracture behaviour and an overall smaller fracture resistance measure (J_max). This result points to the possibility of a strain rate hardening mechanism at the heart of micro-damage formation, which is hampered under high loading rates, resulting in lower overall fracture resistance.

A simplified homogenization model applied to viscoelastic behavior of cortical bone at ultrasonic frequencies

Cortical bone is a complex multiscale medium and its study is of importance for clinical fracture prevention. In particular, cortical attenuation is known to be linked with shock energy absorption and ability to resist fracture. However, the links between cortical bone absorption and its multiscale structure are still not well understood. This work is about the use of homogenized tensors in order to characterize the viscoelastic behavior of cortical bone at ultrasonic frequencies, i.e., about 0.1 to 10 MHz. Such tensors are derived from the cell problem via two-scale homogenization theory for linear elastic and Kelvin-Voigt viscoelastic descriptions. The elliptic formulations obtained from the cell problems are implemented within the range of medically-observed porosities. Microstructure is assessed considering cubic cells with cylindrical inclusion and transverse isotropic assumption. A simplified model, adding one temporal parameter τ per phase, allows a good agreement with experimental data. The corresponding attenuation is proportional to the square of the frequency, in agreement with Kramer-Kronig relations. This development is proposed in the context of robust clinical inverse problem approaches using a restricted number of parameter. Two main properties for the material filling the pores are adjusted and discussed: absorption and shear contribution. Best agreement with experimental data is observed for material inside the pores being solid and highly attenuating.

Graphene and its Derivatives for Bone Tissue Engineering: In Vitro and In Vivo Evaluation of Graphene-Based Scaffolds, Membranes and Coatings

Bone regeneration or replacement has been proved to be one of the most effective methods available for the treatment of bone defects caused by different musculoskeletal disorders. However, the great contradiction between the large demand for clinical therapies and the insufficiency and deficiency of natural bone grafts has led to an urgent need for the development of synthetic bone graft substitutes. Bone tissue engineering has shown great potential in the construction of desired bone grafts, despite the many challenges that remain to be faced before safe and reliable clinical applications can be achieved. Graphene, with outstanding physical, chemical and biological properties, is considered a highly promising material for ideal bone regeneration and has attracted broad attention. In this review, we provide an introduction to the properties of graphene and its derivatives. In addition, based on the analysis of bone regeneration processes, interesting findings of graphene-based materials in bone regenerative medicine are analyzed, with special emphasis on their applications as scaffolds, membranes, and coatings in bone tissue engineering. Finally, the advantages, challenges, and future prospects of their application in bone regenerative medicine are discussed.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Influence of non-enzymatic glycation on the mechanical properties of cortical bone

Poor bone quality induced by non-enzymatic glycation (NEG) of bone tissue in patients with type 2 diabetes mellitus (T2DM) is regarded as the major factor of bone fragility and affecting bone mechanical properties. A comprehensive and systemic mechanical investigation for evaluating the effect of NEG on bone was still lacking. In order to provide additional information for the bone quality of T2DM, the effects of NEG on mechanical properties of cortical bone were investigated in terms of elastoplasticity, fracture toughness and viscoelasticity. All samples of cortical bone, including the samples of strength test (n = 20), fracture toughness test (n = 40, quasi-static and fall-like conditions with displacement rates of 10^-3 mm/s and 10 mm/s, respectively) and stress relaxation test (n = 20), were harvested from bovine tibiae. The samples of each test were equally divided into incubated-control group and ribose-incubated group. All mechanical tests were performed after incubating all samples for 15 days. Post-yield strain (p = 0.014), post-yield energy (p < 0.0001) and damage fraction (p = 0.040) of ribose-incubated group were significantly lower than those of incubated-control group, but secant modulus (p = 0.029) of ribose-incubated group was significantly higher than that of incubated-control group. In quasi-static condition, the plastic contribution J_pl of fracture toughness (p = 0.043) of ribose-incubated group was significantly lower than that of incubated-control group. In fall-like condition, there were no differences in J_pl, elastic contribution J_el and J-integral in both two groups. The quasi-static J_el (p < 0.0001, p < 0.0001) of incubated-control and ribose-incubated groups and J-integral (p = 0.007) of incubated-control group were all significantly higher than those of fall-like condition. In stress relaxation test, initial modulus E₀ (p = 0.040) and equilibrium modulus (p = 0.029) of ribose-incubated group were significantly higher than those of incubated-control group. Reductions of relaxation modulus, which were the differences between two adjacent time points within 700 s-3000 s for ribose-incubated group, were significantly lower than those of incubated-control group. NEG could decrease the post-yield properties and quasi-static facture toughness of cortical bone, especially the plastic contribution of quasi-static fracture toughness. It could also decrease the viscoelasticity of cortical bone. The present study confirmed the negative effects of NEG on the mechanical properties of cortical bone in terms of elastoplasticity, fracture toughness and viscoelasticity, but NEG had no significant effect on the fracture toughness of cortical bone at fall-like loading. These results provided more evidence for increased fragility of cortical bone in patients with T2DM.

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.

Tissue-in-a-Tube: three-dimensional in vitro tissue constructs with integrated multimodal environmental stimulation

Three-dimensional (3D) in vitro tissue models are superior to two-dimensional (2D) cell cultures in replicating natural physiological/pathological conditions by recreating the cellular and cell-matrix interactions more faithfully. Nevertheless, current 3D models lack either the rich multicellular environment or fail to provide appropriate biophysical stimuli both of which are required to properly recapitulate the dynamic in vivo microenvironment of tissues and organs. Here, we describe the rapid construction of multicellular, tubular tissue constructs termed Tissue-in-a-Tube using self-assembly process in tubular molds with the ability to incorporate a variety of biophysical stimuli such as electrical field, mechanical deformation, and shear force of the fluid flow. Unlike other approaches, this method is simple, requires only oxygen permeable silicone tubing that molds the tissue construct and thin stainless-steel pins inserted in it to anchor the construct and could be used to provide electrical and mechanical stimuli, simultaneously. The annular region between the tissue construct and the tubing is used for perfusion. Highly stable, macroscale, and robust constructs anchored to the pins form as a result of self-assembly of the extracellular matrix (ECM) and cells in the bioink that is filled into the tubing. We demonstrate patterning of grafts containing cell types in the constructs in axial and radial modes with clear interface and continuity between the layers. Different environmental factors affecting cell behavior such as compactness of the structure and size of the constructs can be controlled through parameters such as initial cell density, ECM content, tubing size, as well as the distance between anchor pins. Using connectors, network of tubing can be assembled to create complex macrostructured tissues (centimeters length) such as fibers that are bifurcated or columns with different axial thicknesses which can then be used as building blocks for biomimetic constructs or tissue regeneration. The method is versatile and compatible with various cell types including endothelial, epithelial, skeletal muscle cells, osteoblast cells, and neuronal cells. As an example, long mature skeletal muscle and neuronal fibers as well as bone constructs were fabricated with cellular alignment dictated by the applied electrical field. The versatility, speed, and low cost of this method is suited for widespread application in tissue engineering and regenerative medicine.

Ratcheting-fatigue behavior of trabecular bone under cyclic tensile-compressive loading

This study aims to investigate the ratcheting-fatigue behaviors of trabecular bone under cyclic tension-compression, which are produced due to the accumulations of residual strain in trabecular bone. Simultaneously, the effects of different loading conditions on ratcheting behaviors of trabecular bone were probed. It is found that the gap between ratcheting strains under three stress amplitudes will gradually widen. As the stress amplitude increases, the ratcheting strain also increases. Mean stress has a significant effect on the ratcheting strain. When the mean stress is 0 MPa and 0.155 MPa, the ratcheting strain increases with the number of cycles. However, when the mean stress is -0.155 MPa, the ratcheting strain decreases as the cycle goes on. The existence of double stress peak holding time causes the creep deformation of trabecular bone, which leads to the increase of ratcheting strain. It is also noted that the ratcheting strain is greatly increased with prolongation of stress peak holding time. The digital image correlation (DIC) technique was applied to analyze the fatigue failure of trabecular bone under cyclic tension-compression. It is found that the increase of stress amplitude accelerates the damage of sample and further reduces its fatigue life. Cracks are observed in trabecular bone sample, and it is noted that the crack propagation is rapid during cyclic loading.

Biomechanical Behavior of Bioactive Material in Dental Implant: A Three-Dimensional Finite Element Analysis

Dental implants are widely accepted for the rehabilitation of missing teeth due to their aesthetic compliance, functional ability, and great survival rate. The various components in implant design like thread design, thread angle, pitch, and material used for manufacturing play a critical role in its success. Understanding these influencing factors and implementing them properly in implant design can reduce cases of potential implant failure. Recently, finite element analysis (FEA) is being widely used in the field of health sciences to solve problems in designing medical devices. It provides valid and accurate assessment in the clinical and in vitro analysis. Hence, this study was conducted to evaluate the impact of thread design of the implant and 3 different bioactive materials, titanium alloy, graphene, and reduced graphene oxide (rGO) on stress, strain, and deformation in the implant system using FEA. In this study, the FEA model of the bones and the tissues are modeled as homogeneous, isotropic, and linearly elastic material with a titanium implant system with an assumption of it 100% osseointegrated into the bone. The titanium was functionalized with graphene and graphene oxide. A modeling software tool Catia® and Ansys Workbench® is used to perform the analysis and evaluate the von Mises stress distribution, strain, and deformation at the implant and implant-cortical bone interface. The results showed that the titanium implant with a surface coating of graphene oxide exhibited better mechanical behavior than graphene, with mean von Mises stress of 39.64 MPa in pitch 1, 23.65 MPa in pitch 2, and 37.23 MPa in pitch 3. It also revealed that functionalizing the titanium implant will help in reducing the stress at the implant system. Overall, the study emphasizes the use of FEA analysis methods in solving various biomechanical issues about medical and dental devices, which can further open up for invivo study and their practical uses.

Length scale parameter of single trabecula in cancellous bone

In this paper, the material length scale parameter of the modified couple stress theory for trabecular bones is studied. For this reason, experimental data for the buckling of single wet and dry trabeculae from the subchondral region of the human medial tibial plateau are used from the literature. A material length scale parameter is extracted using the modified couple stress theory-based buckling relation and the experimental results. This parameter can capture the size-dependent behavior of trabeculae and can be beneficial for micro-mechanical investigation of trabecular bones. In addition, this paper proposes a size-dependent length scale parameter for trabeculae to estimate the buckling behaviors of dry and wet trabeculae, more accurately. Therefore, this paper confirms that the softening (weakening) effects of the modified couple stress theory and size-dependent behavior of the material length scale parameter can be considered for some special cases, and additionally, a correct value for the length scale parameter of the trabecula is revealed.

Studies on the Stress-Strain Relationship Bovine Cortical Bone Based on Ramberg–Osgood Equation

Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

Strain state dependent anisotropic viscoelasticity of tendon-to-bone insertion

Tendon-to-bone insertion tissues may be considered as functionally-graded connective tissues, providing a gradual transition from soft tendon to hard bone tissue, and functioning to alleviate stress concentrations at the junction of these tissues. The tendon-to-bone insertion tissues demonstrate pronounced viscoelastic behavior, like many other biological tissues, and are designed by the nature to alleviate stress at physiological load rates and strains states. In this paper we present experimental data showing that under biaxial tension tendon-to-bone insertion demonstrates rate-dependent behavior and that stress-strain curves for the in-plane components of stress and strain become less steep when strain rate is increased, contrary to a typical viscoelastic behavior, where the opposite trend is observed. Such behavior may indicate the existence of a protective viscoelastic mechanism reducing stress and strain during a sudden increase in mechanical loading, known to exist in some biological tissues. The main purpose of the paper is to show that such viscoelastic stress reduction indeed possible and is thermodynamically consistent. We, therefore, propose an anisotropic viscoelasticity model for finite strain. We identify the range of parameters for this model which yield negative viscoelastic contribution into in-plane stress under biaxial state of strain and simultaneously satisfy requirements of thermodynamics. We also find optimal parameters maximizing the observed protective viscoelastic effect for this particular state of strain. This model will be useful for testing and describing viscoelastic materials and for developing interfaces for dissimilar materials, considering rate effect and multiaxial loadings.

A mathematical model for fitting and predicting relaxation modulus and simulating viscoelastic responses

We propose a mathematical model for relaxation modulus and its numerical solution. The model formula is extended from sigmoidal function considering nonlinear strain hardening. Its physical meaning can be interpreted by a macroscale elastic network-viscous medium model with only five model parameters in a simpler format than the molecular-chain-based polymer models to represent general solid materials. We also developed a finite-element (FE) framework and robust numerical algorithm to implement this model for simulating responses under both static and dynamic loadings. We validated the model through both experimental data and numerical simulations on a variety of materials including asphalt concrete, polymer, spider silk, hydrogel, agar and bone. By satisfying the second law of thermodynamics in the form of Calusius-Duhem inequality, the model is able to simulate creep and sinusoidal deformation as well as energy dissipation. Compared to the Prony series, the widely used model with a large number of model parameters, the proposed model has improved accuracy in fitting experimental data and prediction stability outside of the experimental range with competitive numerical stability and computation speed. We also present simulation results of nonlinear stress-strain relationships of spider silk and hydrogels, and dynamic responses of a multilayer structure.

The relationship of whole human vertebral body creep to geometric, microstructural, and material properties

Creep, the time dependent deformation of a structure under load, is an important viscoelastic property of bone and may play a role in the development of permanent deformity of the vertebrae in vivo leading to clinically observable spinal fractures. To date, creep properties and their relationship to geometric, microstructural, and material properties have not been described in isolated human vertebral bodies. In this study, a range of image-based measures of vertebral bone geometry, bone mass, microarchitecture and mineralization were examined in multiple regression models in an effort to understand their contribution to creep behavior. Several variables, such as measures of mineralization heterogeneity, average bone density, and connectivity density persistently appeared as significant effects in multiple regression models (adjusted r²: 0.17-0.56). Although further work is needed to identify additional tissue properties to fully describe the portion of variability not explained by these models, these data are expected to help understand mechanisms underlying creep and improve prediction of vertebral deformities that eventually progress to a clinically observable fracture.

A homogenization approach for the effective drained viscoelastic properties of 2D porous media and an application for cortical bone

Closed-form solutions for the effective rheological properties of a 2D viscoelastic drained porous medium made of a Generalized Maxwell viscoelastic matrix and pore inclusions are developed and applied for cortical bone. The in-plane (transverse) effective viscoelastic bulk and shear moduli of the Generalized Maxwell rheology of the homogenized medium are expressed as functions of the porosity and the viscoelastic properties of the solid phase. When deriving these functions, the classical inverse Laplace-Carson transformation technique is avoided, due to its complexity, by considering the short and long term approximations. The approximated results are validated against exact solutions obtained from the inverse Laplace-Carson transform for a simple configuration when the later is available. An application for cortical bone with assumption of circular pore in the transverse plane shows that the proposed approximation fit very well with experimental data.

Sideways fall-induced impact force and its effect on hip fracture risk: a review

Osteoporotic hip fracture, mostly induced in falls among the elderly, is a major health burden over the world. The impact force applied to the hip is an important factor in determining the risk of hip fracture. However, biomechanical researches have yielded conflicting conclusions about whether the fall-induced impact force can be accurately predicted by the available models. It also has been debated whether or not the effect of impact force has been considered appropriately in hip fracture risk assessment tools. This study aimed to provide a state-of-the-art review of the available methods for predicting the impact force, investigate their strengths/limitations, and suggest further improvements in modeling of human body falling.

METHODS

We divided the effective parameters on impact force to two categories: (1) the parameters that can be determined subject-specifically and (2) the parameters that may significantly vary from fall to fall for an individual and cannot be considered subject-specifically.

RESULTS

The parameters in the first category can be investigated in human body fall experiments. Video capture of real-life falls was reported as a valuable method to investigate the parameters in the second category that significantly affect the impact force and cannot be determined in human body fall experiments.

CONCLUSIONS

The analysis of the gathered data revealed that there is a need to develop modified biomechanical models for more accurate prediction of the impact force and appropriately adopt them in hip fracture risk assessment tools in order to achieve a better precision in identifying high-risk patients. Graphical abstract Impact force to the hip induced in sideways falls is affected by many parameters and may remarkably vary from subject to subject.

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.

Graphene oxide as a scaffold for bone regeneration

Graphene oxide (GO), the oxidized form of graphene, holds great potential as a component of biomedical devices, deriving utility from its ability to support a broad range of chemical functionalities and its exceptional mechanical, electronic, and thermal properties. GO composites can be tuned chemically to be biomimetic, and mechanically to be stiff yet strong. These unique properties make GO-based materials promising candidates as a scaffold for bone regeneration. However, questions still exist as to the compatibility and long-term toxicity of nanocarbon materials. Unlike other nanocarbons, GO is meta-stable, water dispersible, and autodegrades in water on the timescale of months to humic acid-like materials, the degradation products of all organic matter. Thus, GO offers better prospects for biological compatibility over other nanocarbons. Recently, many publications have demonstrated enhanced osteogenic performance of GO-containing composites. Ongoing work toward surface modification or coating strategies could be useful to minimize the inflammatory response and improve compatibility of GO as a component of medical devices. Furthermore, biomimetic modifications could offer mechanical and chemical environments that encourage osteogenesis. So long as care is given to assure their safety, GO-based materials may be poised to become the next generation scaffold for bone regeneration. WIREs Nanomed Nanobiotechnol 2017, 9:e1437. doi: 10.1002/wnan.1437 For further resources related to this article, please visit the WIREs website.

Dynamic nanomechanical behaviour of healthy and OI human cortical bone

Viscoelasticity of bone has been of interest for many years because this time-dependent mechanical property relates to the fracture risk of bone under dynamic loading. Several factors have been claimed to contribute to this property including the nature of different constituents of bone and their interactions, as well as moisture content. In the present study, intact normal human cortical bone was demineralised, and molecular structures were identified using infrared spectroscopy. Osteogenesis imperfecta (OI) human cortical bone was also selected for comparison because OI bone has severe defects in collagen molecules, while its mineral phase is almost identical to that of normal bone. The dynamic nanomechanical behaviours of the intact, demineralised and OI human cortical bone specimens were examined using dynamic nanoindentation. Loss tangent, tan δ, was considered as a measure of the degree of the viscoelastic response. Variable dynamic load tests show that the viscoelastic responses of all bone specimens increase with frequency. With demineralisation, bone specimens show greater viscoelastic response than intact specimens. OI bone shows similar viscoelastic response as normal bone. Results suggest that the viscoelasticity of bone is mostly attributable to the mineral phase. The present study adds to the understanding of the viscoelastic response of bone material. In addition, the dynamic mechanical properties of OI bone are firstly reported here.

3D Viscoelastic traction force microscopy

Native cell-material interactions occur on materials differing in their structural composition, chemistry, and physical compliance. While the last two decades have shown the importance of traction forces during cell-material interactions, they have been almost exclusively presented on purely elastic in vitro materials. Yet, most bodily tissue materials exhibit some level of viscoelasticity, which could play an important role in how cells sense and transduce tractions. To expand the realm of cell traction measurements and to encompass all materials from elastic to viscoelastic, this paper presents a general, and comprehensive approach for quantifying 3D cell tractions in viscoelastic materials. This methodology includes the experimental characterization of the time-dependent material properties for any viscoelastic material with the subsequent mathematical implementation of the determined material model into a 3D traction force microscopy (3D TFM) framework. Utilizing this new 3D viscoelastic TFM (3D VTFM) approach, we quantify the influence of viscosity on the overall material traction calculations and quantify the error associated with omitting time-dependent material effects, as is the case for all other TFM formulations. We anticipate that the 3D VTFM technique will open up new avenues of cell-material investigations on even more physiologically relevant time-dependent materials including collagen and fibrin gels.

Timescales of self-healing in human bone tissue and polymeric ionic liquids

Strain (stress-free) relaxation in mechanically prestrained bone has a time constant of 75 s. It occurs by a reorganization of the proteoglycan-glycoprotein matrix between collagen fibers, which requires ionic interactions. Dissolving and relinking the ionic bonds is thus an important tool of nature to enable plastic deformation and to develop self-healing tissues. A way to transfer this approach to technical materials is the attachment of ionic end groups to polymeric chains. In these classes of materials, the so-called polymeric ionic liquids, structural recovery of thermally disorganized material is observed. A time constant between minutes and a week could be achieved, also by ionic rearrangement. The same mechanism, rearrangement of ionic bonds, can lead to vastly different relaxation times when the ionic interaction is varied by exchange of the cationic end groups or the anions.

Validation of an optical system to measure acetabular shell deformation in cadavers

Deformation of the acetabular shell at the time of surgery can result in poor performance and early failure of the hip replacement. The study aim was to validate an ATOS III Triple Scan optical measurement system against a co-ordinate measuring machine using in vitro testing and to check repeatability under cadaver laboratory conditions. Two sizes of custom-made acetabular shells were deformed using a uniaxial/two-point loading frame and measured at different loads. Roundness measurements were performed using both the ATOS III Triple Scan optical system and a co-ordinate measuring machine and then compared. The repeatability was also tested by measuring shells pre- and post-insertion in a cadaver laboratory multiple times. The in vitro comparison with the co-ordinate measuring machine demonstrated a maximum difference of 5 µm at the rim and 9 µm at the measurement closest to the pole of the shell. Maximum repeatability was below 1 µm for the co-ordinate measuring machine and 3 µm for the ATOS III Triple Scan optical system. Repeatability was comparable between the pre-insertion (below 2 µm) and post-insertion (below 3 µm) measurements in the cadaver laboratory. This study supports the view that the ATOS III Triple Scan optical system fulfils the necessary requirements to accurately measure shell deformation in cadavers.

Influence of thread pitch, helix angle, and compactness on micromotion of immediately loaded implants in three types of bone quality: a three-dimensional finite element analysis

This study investigated the influence of thread pitch, helix angle, and compactness on micromotion in immediately loaded implants in bone of varying density (D2, D3, and D4). Five models of the three-dimensional finite element (0.8 mm pitch, 1.6 mm pitch, 2.4 mm pitch, double-threaded, and triple-threaded implants) in three types of bone were created using Pro/E, Hypermesh, and ABAQUS software. The study had three groups: Group 1, different pitches (Pitch Group); Group 2, same compactness but different helix angles (Angle Group); and Group 3, same helix angle but different compactness (Compact Group). Implant micromotion was assessed as the comprehensive relative displacement. We found that vertical relative displacement was affected by thread pitch, helix angle, and compactness. Under vertical loading, displacement was positively correlated with thread pitch and helix angle but negatively with compactness. Under horizontal loading in D2, the influence of pitch, helix angle, and compactness on implant stability was limited; however, in D3 and D4, the influence of pitch, helix angle, and compactness on implant stability is increased. The additional evidence was provided that trabecular bone density has less effect on implant micromotion than cortical bone thickness. Bone type amplifies the influence of thread pattern on displacement.

Creep of trabecular bone from the human proximal tibia

Creep is the deformation that occurs under a prolonged, sustained load and can lead to permanent damage in bone. Creep in bone is a complex phenomenon and varies with type of loading and local mechanical properties. Human trabecular bone samples from proximal tibia were harvested from a 71-year old female cadaver with osteoporosis. The samples were initially subjected to one cycle load up to 1% strain to determine the creep load. Samples were then loaded in compression under a constant stress for 2h and immediately unloaded. All tests were conducted with the specimens soaked in phosphate buffered saline with proteinase inhibitors at 37 °C. Steady state creep rate and final creep strain were estimated from mechanical testing and compared with published data. The steady state creep rate correlated well with values obtained from bovine tibial and human vertebral trabecular bone, and was higher for lower density samples. Tissue architecture was analyzed by micro-computed tomography (μCT) both before and after creep testing to assess creep deformation and damage accumulated. Quantitative morphometric analysis indicated that creep induced changes in trabecular separation and the structural model index. A main mode of deformation was bending of trabeculae.

Power-law hereditariness of hierarchical fractal bones

In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law.

Initial anisotropy in demineralized bovine cortical bone in compressive cyclic loading-unloading

The mechanical properties of demineralized bovine cortical femur bone were investigated by cyclic loading-unloading compression in three anatomical directions (longitudinal, radial, transverse) within the physiological strain range. The loading responses in the radial and transverse directions were nearly linear up to 2% strain, while the response in longitudinal direction was strongly non-linear in that range. The unloading responses were non-linear for each anatomical direction, giving rise to overall loading-unloading hysteresis and cyclic dissipation of energy. The mechanical properties were observed to be anisotropic: the radial direction was found to be the most energy dissipative, while the longitudinal direction appeared to be the stiffest bone direction. The cyclic loading mostly affects the bone stiffness in the radial and transverse directions, while the longitudinal direction was found to be the least affected. These anisotropic properties can be attributed to the differences in collagen fibers alignment and different microstructural architecture in three different anatomical bone directions.

Biomechanical considerations on tooth-implant supported fixed partial dentures

This article discusses the connection of teeth to implants, in order to restore partial edentulism. The main problem arising from this connection is tooth intrusion, which can occur in up to 7.3% of the cases. The justification of this complication is being attempted through the perspective of biomechanics of the involved anatomical structures, that is, the periodontal ligament and the bone, as well as that of the teeth- and implant-supported fixed partial dentures.

Orientation dependence of progressive post-yield behavior of human cortical bone in compression

Identifying the underlying mechanisms of energy dissipation during post-yield deformation of bone is critical in understanding bone fragility fractures. However, the orientation-dependence of post-yield properties of bone is still poorly understood. Thus, the objective of this study was to determine the effect of loading direction on the evolution of post-yield behavior of bone using a progressive loading protocol. To do so, cylindrical compressive bone samples were prepared each in the longitudinal, circumferential and radial directions, from the mid-shaft of cadaveric femurs procured from eight middle-aged male donors (51.5 ± 3.3 years old). These specimens were tested in compression in a progressive loading scheme. The results exhibited that the elastic modulus, yield stress, and energy dissipation were significantly greater in the longitudinal direction than in the transverse (circumferential and radial) directions. However, no significant differences were observed in the yield strain as well as in the successive plastic strain with respect to the increasing applied strain among the three orientations. These results suggest that the initiation and progression of plastic strain are independent of loading orientations, thus implying that the underlying mechanism of plastic behavior of bone in compression is similar in all the orientations.

Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach

Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as 'interfibrillar mineral' and 'extrafibrillar mineral', respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils ('mineral-encrusted fibrils'), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230-252) - we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material 'bone'. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling.

RELATIONS OF ANISOTROPIC ELASTIC MODULI TO DENSITY AND CT NUMBER IN BOVINE CORTICAL BONE

It would be useful to be able to determine the mechanical properties of bone using a noninvasive technique such as computed tomography (CT). However, in contrast to cancellous bone tissue, quantifying the elastic modulus of cortical bone from bone density and CT number has not been investigated extensively. This study measured the elastic moduli of cortical bone from eight bovine femora in the longitudinal, circumferential, and radial directions using mechanical compressive testing. Before testing, the CT number and wet apparent bone density were obtained. The experimentally determined coefficient of determination between CT number and bone density was around 0.6. Bone density was a good predictor of the elastic modulus of cortical bone in the longitudinal direction (r2 > 0.79), but it could not be used to predict the elastic moduli in the circumferential (r2 < 0.4) and radial (r2 < 0.22) directions. The coefficient of determination between CT number and the elastic modulus in the longitudinal direction was higher than 0.41. However, the correlations between CT number and elastic moduli were weak in the circumferential (r2 < 0.21) and radial (r2 < 0.19) directions. Moreover, the elastic modulus was much higher in the longitudinal direction than the circumferential and radial directions, and hence cortical bone can be considered a transversely isotropic property.

New laboratory tools in the assessment of bone quality

Bone quality is a complex set of intricated and interdependent factors that influence bone strength. A number of methods have emerged to measure bone quality, taking into account the organic or the mineral phase of the bone matrix, in the laboratory. Bone quality is a complex set of different factors that are interdependent. The bone matrix organization can be described at five different levels of anatomical organization: nature (organic and mineral), texture (woven or lamellar), structure (osteons in the cortices and arch-like packets in trabecular bone), microarchitecture, and macroarchitecture. Any change in one of these levels can alter bone quality. An altered bone remodeling can affect bone quality by influencing one or more of these factors. We have reviewed here the main methods that can be used in the laboratory to explore bone quality on bone samples. Bone remodeling can be evaluated by histomorphometry; microarchitecture is explored in 2D on histological sections and in 3D by microCT or synchrotron. Microradiography and scanning electron microscopy in the backscattered electron mode can measure the mineral distribution; Raman and Fourier-transformed infra-red spectroscopy and imaging can simultaneously explore the organic and mineral phase of the matrix on multispectral images; scanning acoustic microscopy and nanoindentation provide biomechanical information on individual trabeculae. Finally, some histological methods (polarization, surface staining, fluorescence, osteocyte staining) may also be of interest in the understanding of quality as a component of bone fragility. A growing number of laboratory techniques are now available. Some of them have been described many years ago and can find a new youth; others having benefited from improvements in physical and computer techniques are now available.

Anisotropy in the compressive mechanical properties of bovine cortical bone and the mineral and protein constituents

The mechanical properties of fully demineralized, fully deproteinized and untreated cortical bovine femur bone were investigated by compression testing in three anatomical directions (longitudinal, radial and transverse). The weighted sum of the stress-strain curves of the treated bones was far lower than that of the untreated bone, indicating a strong molecular and/or mechanical interaction between the collagen matrix and the mineral phase. Demineralization and deproteinization of the bone demonstrated that contiguous, stand-alone structures result, showing that bone can be considered an interpenetrating composite material. Structural features of the samples from all groups were studied by optical and scanning electron microscopy. Anisotropic mechanical properties were observed: the radial direction was found to be the strongest for untreated bone, while the longitudinal one was found to be the strongest for deproteinized and demineralized bones. A possible explanation for this phenomenon is the difference in bone microstructure in the radial and longitudinal directions.

The effect of holding time on nanoindentation measurements of creep in bone

Viscoelasticity may affect both the elastic and fracture characteristics of bone. Nanoindentation can be used to measure the creep behavior of bone by fitting the depth vs. time data at constant load to rheological models. However, the creep data may be influenced by latent effects arising during the loading phase of indentation. As such, the loading protocol, particularly the holding time, may affect the measured creep time constants. To characterize the effect of holding time on the measures, four cortical bone samples were prepared from four bovine femora and subjected to nanoindentation to measure the creep behavior. The creep time constants were found by fitting the indentation depth vs. time curve to three different rheological models: the standard linear solid, Burgers model, and a two-dashpot Kelvin model. All three models provided good fits to the data, which were relatively insensitive to the initial parameter estimates. The calculated creep time constants increased monotonically with increasing holding time for all three models. However, the relative differences between measurements within a single osteon, within a single sample, and between samples were maintained for creep holding times over 16s. Hence, while the creep time constants measured by nanoindentation with hold times up to 30s may not provide accurate property measurements, comparisons between samples are valid if all are assessed at the same holding time. Considering the long-term viscosity of bone tissue, Burgers model provided the best performance in terms of stability and goodness of fit, and is recommended for future studies.