Mechanical Behavior Of Cortical Bone Research Articles

Constitutive relationships for osteonal microcracking in human cortical bone using statistical mechanics

The post-elastic mechanical behavior of cortical bone, which is represented by extensive microcracking once the elastic regime is exceeded, has been characterized by a nonlinear constitutive relationship for osteonal microcracking. The relationship/model is based on the formalism of Statistical Mechanics, allowing the degree of irreversibility to be calculated using the increase in entropy associated with the progression of microcracking. Specific tensile and bending tests were conducted to compare theoretical predictions of constitutive relationships to empirical curves. In addition, the tests were utilized to determine the model’s parameters, whose values were used to explicitly calculate the entropy increase. A large sample was used: 51 cortical bone coupons (dog-bone-shaped specimens) were extracted from the 4th ribs of numerous individuals and subjected to uniaxial tensile testing. Additionally, fifteen complete 4th ribs were used for bending tests. Displacement and strain fields were measured for both types of tests using digital image correlation or video recordings of the tests. All experimental specimen data were successfully fitted to the model, and all constitutive parameter values were found to be correlated with anthropometric variables. Explicit entropy calculations indicate that microcracking is minimal for low strain and, initially, stress is nearly proportional to strain. After a certain point, significant microcracking occurs, and the relationship between stress and strain becomes invalid. Several significant associations between constitutive parameters and age have also been identified.

Mineralized Collagen Fibrils: An Essential Component in Determining the Mechanical Behavior of Cortical Bone

Bone comprises mechanically different materials in a specific hierarchical structure. Mineralized collagen fibrils (MCFs), represented by tropocollagen molecules and hydroxyapatite nanocrystals, are the fundamental unit of bone. The mechanical characterization of MCFs provides the unique adaptive mechanical competence to bone to withstand mechanical load. The structural and mechanical role of MCFs is critical in the deformation mechanisms of bone and the marvelous strength and toughness possessed by bone. However, the role of MCFs in the mechanical behavior of bone across multiple length scales is not fully understood. In the present study, we shed light upon the latest progress regarding bone deformation at multiple hierarchical levels and emphasize the role of MCFs during bone deformation. We propose the concept of hierarchical deformation of bone to describe the interconnected deformation process across multiple length scales of bone under mechanical loading. Furthermore, how the deterioration of bone caused by aging and diseases impairs the hierarchical deformation process of the cortical bone is discussed. The present work expects to provide insights on the characterization of MCFs in the mechanical properties of bone and lays the framework for the understanding of the multiscale deformation mechanics of bone.

Investigation of the mechanical response and deformation mechanism of cortical bone material under combined compression and bending loads

Objective service load is the load pattern of cortical bone in practical conditions. The objective service load conditions of cortical bone are complicated, usually including two or more load patterns. The mechanical behavior and deformation mechanism of cortical bone material under coupling load pattern and single load pattern are diametrically different. However, nowadays, researches on the mechanical response of cortical bone have been heavily focused on the single load pattern, which couldn’t reveal the potential deformation mechanism accurately. For the purpose of obtaining the objective mechanical properties under complicated loading patterns, the mechanical response and deformation mechanism of bone material under compression-bending coupling load were investigated by in-situ test. The research shows that bending strength increased under the compression-bending coupling load than the single bending load. By in-situ observation, the variations of surface strain distribution and cracks directions were the potential reasons for the increase of the bending strength. It was found that the cracks changed from transverse fracture to integrated patterns with transverse fracture and longitudinal fracture. Larger fracture range and tortuous crack propagation increased the fracture energy dissipation, which led to an enlarged bending strength under the compression-bending coupling load. Through theoretical analysis and numerical calculation, the impeded effect to the increasing of bending deflection was dominant before the final fracture with the adding of the compression load. The numerical calculation result was consistent with the result of the experiment. This present work would provide new references to further studies on the mechanical behavior of cortical bone under complicated loading patterns.

Computational study of the mechanical influence of lacunae and perilacunar zones in cortical bone microcracking

The mechanical behavior of cortical bone is influenced by microstructural components such as osteons, Haversian canals, and osteocyte lacunae that arise from biological remodeling processes. This study takes a computational approach to investigate the role of the perilacunar zones formed by the local remodeling processes of lacunar-dwelling osteocytes by utilizing phase-field finite element models based on histological imaging of human bone. The models simulated the microdamage accumulation that occurs in cortical bone under transverse compression in bone without lacunae, with lacunae, and with a perilacunar zone surrounding lacunae in order to investigate the role of these features. The results of the simulations found that while lacunae create stress concentration which initiate further damage, perilacunar regions can delay or prevent the emergence and growth of microcracks.

Research on Anisotropic Fracture Mechanical Behavior of Cortical Bone with Combined Method of Fractal and Gray Level Co-Occurrence Matrix

The irregular fracture surface of cortical bone, which is caused by complex multilevel micro-nanostructure, reflects the mechanical properties and fracture mechanisms. It is of great significance to characterize some characteristic parameters from the fracture surfaces of bone. In this research, anisotropic fracture mechanical properties of bovine femoral cortical bone along transverse, longitudinal and radial direction are firstly obtained by three-point bend experiment. Then the fracture routes and fracture surfaces are observed by scanning electron microscope. The observation shows that the formed fracture surfaces, which are caused by different crack routes, are extremely rough and have complex textures. Lastly, the combined method of fractal and gray level co-occurrence matrix are adopted to describe the morphology of fracture surface of cortical bone objectively and quantitatively. It is shown that the fracture surface of cortical bone has obvious fractal characteristics and four statistical texture feature parameters (contrast,angular second moment, correlation and entropy) of GLCM of fracture surfaces can describe a certain fracture texture character. The relationship between the characteristic parameters and macroscopic mechanical properties are established. The quantitative analysis and automatic class identification for the fracture surfaces of cortical bone can be achieved.

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.

Effect of modifications in mineralized collagen fibril and extra-fibrillar matrix material properties on submicroscale mechanical behavior of cortical bone.

A key length scale of interest in assessing the fracture resistance of bone is the submicroscale which is composed of mineralized collagen fibrils (MCF) and extra-fibrillar matrix (EFM). Although the processes through which the submicroscale constituents of bone contribute to the fracture resistance in bone have been identified, the extent of the modifications in submicroscale mechanical response due to the changes in individual properties of MCFs and EFM has not been determined. As a result, this study aims to quantify the influence of individual MCF and EFM material property modifications on the mechanical behavior (elastic modulus, ultimate strength, and resistance to failure) of bone at the submicroscale using a novel finite element modeling approach that incorporate 3D networks of MCFs with three different orientations as well as explicit representation of EFM. The models were evaluated under tensile loading in transverse (representing MCF separation) and longitudinal (representing MCF rupture) directions. The results showed that the apparent elastic modulus at the submicroscale under both loading directions for all orientations was only affected by the change in the elastic modulus of MCFs. MCF separation and rupture strengths were mainly dependent on the ultimate strength of EFM and MCFs, respectively, with minimal influence of other material properties. The extent of damage during MCF separation increased with increasing ultimate strength of EFM and decreased with increasing fracture energy of EFM with minimal contribution from elastic modulus of MCFs. For MCF rupture, there was an almost one-to-one linear relationship between the percent change in fracture energy of MCFs and the percent change in the apparent submicroscale fracture energy. The ultimate strength and elastic modulus of MCFs had moderate to limited influence on the MCF rupture fracture energy. The results of this study quantified the extent of changes that may be seen in the energy dissipation processes during MCF rupture and separation relative to the changes in the individual constituents of the tissue. This new knowledge significantly contributes to improving the understanding of how the material property alterations at the submicroscale that can occur due to diseases, age-related changes, and treatments affect the fracture processes at larger length scales.

Mechanical behavior of cortical bone after creep loading

Mechanical behavior of cortical bone after creep loading

Dealloying-based metal-polymer composites for biomedical applications

Here, we developed interpenetrating-phase metal-polymer composites mimicking mechanical behavior of cortical bone and occupying previously unclaimed region at the Ashby diagram in the area of intermediate strength and low stiffness. The composites consist of dealloying-based open porous TixHf100−x alloys (scaffolds) impregnated by polymer. The scaffolds significantly contribute to strength (215–266MPa) and stiffness (15.6–20.8GPa) of the composites while the polymer phase provides their high strain rate sensitivity (0.037–0.044). Tuning scaffolds' connectivity by preloading and/or their chemical composition allows fine optimization of composites' mechanical properties. The results suggest that the composites may provide a basis for promising future implant materials.

The Role of Water Compartments in the Material Properties of Cortical Bone.

Comprising ~20% of the volume, water is a key determinant of the mechanical behavior of cortical bone. It essentially exists in two general compartments: within pores and bound to the matrix. The amount of pore water-residing in the vascular-lacunar-canalicular space-primarily reflects intracortical porosity (i.e., open spaces within the matrix largely due to Haversian canals and resorption sites) and as such is inversely proportional to most mechanical properties of bone. Movement of water according to pressure gradients generated during dynamic loading likely confers hydraulic stiffening to the bone as well. Nonetheless, bound water is a primary contributor to the mechanical behavior of bone in that it is responsible for giving collagen the ability to confer ductility or plasticity to bone (i.e., allows deformation to continue once permanent damage begins to form in the matrix) and decreases with age along with fracture resistance. Thus, dehydration by air-drying or by solvents with less hydrogen bonding capacity causes bone to become brittle, but interestingly, it also increases stiffness and strength across the hierarchical levels of organization. Despite the importance of matrix hydration to fracture resistance, little is known about why bound water decreases with age in hydrated human bone. Using (1)H nuclear magnetic resonance (NMR), both bound and pore water concentrations in bone can be measured ex vivo because the proton relaxation times differ between the two water compartments, giving rise to two distinct signals. There are also emerging techniques to measure bound and pore water in vivo with magnetic resonance imaging (MRI). The NMR/MRI-derived bound water concentration is positively correlated with both the strength and toughness of hydrated bone and may become a useful clinical marker of fracture risk.

Relationship between microstructure and mechanical behavior of cortical bone

Relationship between microstructure and mechanical behavior of cortical bone

Variability and anisotropy of mechanical behavior of cortical bone in tension and compression

The mechanical properties of cortical bone vary not only from bone to bone; they demonstrate a spatial viability even within the same bone due to its changing microstructure. They also depend considerably on different loading modes and orientations. To understand the variability and anisotropic mechanical behavior of a cortical bone tissue, specimens cut from four anatomical quadrants of bovine femurs were investigated both in tension and compression tests. The obtained experimental results revealed a highly anisotropic mechanical behavior, depending also on the loading mode (tension and compression). A compressive longitudinal loading regime resulted in the best load-bearing capacity for cortical bone, while tensile transverse loading provided significantly poorer results. The distinctive stress–strain curves obtained for tension and compression demonstrated various damage mechanisms associated with different loading modes. The variability of mechanical properties for different cortices was evaluated with two-way ANOVA analyses. Statistical significances were found among different quadrants for the Young's modulus. The results of microstructure analysis of the entire transverse cross section of a cortical bone also confirmed variations of volume fractions of constituents at microscopic level between anatomic quadrants: microstructure of the anterior quadrant was dominated by plexiform bone, whereas secondary osteons were prominent in the posterior quadrant. The effective Young's modulus predicted using the modified Voigt-Reuss-Hill averaging scheme accurately reproduced our experimental results, corroborating additionally a strong effect of random and heterogeneous microstructure on variation of mechanical properties in cortical bone.

Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading

The hierarchical arrangement of collagen and mineral into bone tissue presumably maximizes fracture resistance with respect to the predominant strain mode in bone. Thus, the ability of cortical bone to dissipate energy may differ between compression and tension for the same anatomical site. To test this notion, we subjected bone specimens from the anterior quadrant of human cadaveric tibiae to a progressive loading scheme in either uniaxial tension or uniaxial compression. One tension (dog-bone shape) and one compression specimen (cylindrical shape) were collected each from tibiae of nine middle aged male donors. At each cycle of loading-dwell-unloading-dwell-reloading, we calculated maximum stress, permanent strain, modulus, stress relaxation, time constant, and three pathways of energy dissipation for both loading modes. In doing so, we found that bone dissipated greater energy through the mechanisms of permanent and viscoelastic deformation in compression than in tension. On the other hand, however, bone dissipated greater energy through the release of surface energy in tension than in compression. Moreover, differences in the plastic and viscoelastic properties after yielding were not reflected in the evolution of modulus loss (an indicator of damage accumulation), which was similar for both loading modes. A possible explanation is that differences in damage morphology between the two loading modes may favor the plastic and viscoelastic energy dissipation in compression, but facilitate the surface energy release in tension. Such detailed information about failure mechanisms of bone at the tissue-level would help explain the underlying causes of bone fractures.

Tensile behavior of cortical bone: Dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic–perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress–strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress–strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.

The influence of water removal on the strength and toughness of cortical bone

Although the effects of dehydration on the mechanical behavior of cortical bone are known, the underlying mechanisms for such effects are not clear. We hypothesize that the interactions of water with the collagen and mineral phases each have a unique influence on mechanical behavior. To study this, strength, toughness, and stiffness were measured with three-point bend specimens made from the mid-diaphysis of human cadaveric femurs and divided into six test groups: control (hydrated), drying in a vacuum oven at room temperature (21 °C) for 30 min and at 21, 50, 70, or 110 °C for 4 h. The experimental data indicated that water loss significantly increased with each increase in drying condition. Bone strength increased with a 5% loss of water by weight, which was caused by drying at 21 °C for 4 h. With water loss exceeding 9%, caused by higher drying temperatures (⩾70 °C), strength actually decreased. Drying at 21 °C (irrespective of time in vacuum) significantly decreased bone toughness through a loss of plasticity. However, drying at 70 °C and above caused toughness to decrease through decreases in strength and fracture strain. Stiffness linearly increased with an increase in water loss. From an energy perspective, the water–mineral interaction is removed at higher temperatures than the water–collagen interaction. Therefore, we speculate that loss of water in the collagen phase decreases the toughness of bone, whereas loss of water associated with the mineral phase decreases both bone strength and toughness.