Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

Effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structures: a finite element investigation

BACKGROUND

Running with the appropriate intensity may produce a positive influence on the mechanical properties of cortical bone structure. However, few studies have discussed the effects of different running intensities on the mechanical properties at different levels, especially at the micro-level, because the micromechanical parameters are difficult to measure experimentally.

METHODS

An approach that combines finite element analysis and experimental data was proposed to predict a micromechanical parameter in the rat femoral cortical bone structure, namely, the micro-level failure strain. Based on the previous three-point bending experimental information, fracture simulations were performed on the femur finite element models to predict their failure process under the same bending load, and the micro-level failure strains in tension and compression of these models were back-calculated by fitting the experimental load-displacement curves. Then, the effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structure were investigated.

RESULTS

The micro-level failure strains of the cortical bone structures expressed statistical variations under different running intensities, which indicated that different mechanical stimuli of running had significant influences on the micromechanical properties. The greatest failure strain occurred in the cortical bone structure under low-intensity running, and the lowest failure strain occurred in the structure under high-intensity running.

CONCLUSIONS

Moderate and low-intensity running were effective in enhancing the micromechanical properties, whereas high-intensity running led to the weakening of the micromechanical properties of cortical bone. Based on these, the changing trends in the micromechanical properties were exhibited, and the effects of different running intensities on the fracture performance of rat cortical bone structures could be discussed in combination with the known mechanical parameters at the macro- and nano-levels, which provided the theoretical basis for reducing fracture incidence through running exercise.

2D titanium carbide(MXene) nanosheets and 1D hydroxyapatite nanowires into free standing nanocomposite membrane: in vitro and in vivo evaluations for bone regeneration

Bone loss or insufficiency remains a great challenge for implant integrated and subsequently functional loading, where developing biomaterials to augment bone quantity and regenerate alveolar bone defects at implant site is vitally necessary. Recently, MXene, as a large new family of 2D materials, exhibits a great prospect in biomedical applications owing to its ultrathin structure and morphology with a range of extraordinary properties such as chemical, electronic, optical and biological properties etc. Besides, hydroxyapatite is a favorable biomaterial with outstanding bioactivity and osteogenic capacity. In this study, we prepared free standing UHAPNWs/MXene nanocomposite membranes via introducing ultralong hydroxyapatite nanowires (UHAPNWs) with different weight ratios into MXene to explore their potential in bone regeneration. SEM, XPS, FTIR, XRD, tensile strength, Young's modulus and water contact angles were used to characterize the morphology, chemical composition, surface properties, mechanical properties and hydrophilicity of the materials. Subsequently, in vitro studies like cell adhesion, proliferation and osteogenic differentiation of MC3T3-E1 were evaluated. The incorporation of UHAPNWs improved mechanical properties and hydrophilicity with an enhancement in cell adhesion, proliferation, and osteogenic differentiation. More importantly, 10 wt% UHAPNWs/MXene exhibited the optimal mechanical properties while biological improvement was more pronounced along with the addition of UHAPNWs when the weight fraction of UHAPNWs was from 0 to 30 wt%. Furthermore, in vivo experiments the UHAPNWs/MXene nanocomposite membranes effectively enhanced bone tissue formation quantitatively and qualitatively in a rat calvarial bone defect. Therefore, an appropriate amount of UHAPNWs into MXene plays a positive and evident role in enhancing mechanical properties, biocompatibility and osteoinductivity, leading a novel inorganic composite material for regeneration of bone tissue.

Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

The strong dependence between cortical bone elasticity at the millimetre-scale (mesoscale) and cortical porosity has been evidenced by previous studies. However, bone is an anisotropic composite material made by mineral, proteins and water assembled in a hierarchical structure. Whether the variations of structural and compositional properties of bone affect the different elastic coefficients at the mesoscale is not clear. Aiming to understand the relationships between bone elastic properties and compositions and microstructure, we applied state-of-the-art experimental modalities to assess these aspects of bone characteristics. All elastic coefficients (stiffness tensor of the transverse isotropic bone material), structure of the vascular pore network, collagen and mineral properties were measured in 52 specimens from the femoral diaphysis of 26 elderly donors. Statistical analyses and micromechanical modeling showed that vascular pore volume fraction and the degree of mineralization of bone are the most important determinants of cortical bone anisotropic mesoscopic elasticity. Though significant correlations were observed between collagen properties and elasticity, their effects in bone mesoscopic elasticity were minor in our data. This work also provides a unique set of data exhibiting a range of variations of compositional and microstructural cortical bone properties in the elderly and gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone. STATEMENT OF SIGNIFICANCE: This study reports the relationships between microstructure, composition and the mesoscale anisotropic elastic properties of human femoral cortical bone in elderly. For the first time, we provide data covering the complete anisotropic elastic tensor, the microstructure of cortical vascular porosity, mineral and collagen characteristics obtained from the same or adjacent samples in each donor. The results revealed that cortical vascular porosity and degree of mineralization of bone are the most important determinants of bone anisotropic stiffness at the mesoscale. The presented data gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone.

Bone Mechanical Properties in Healthy and Diseased States

The mechanical properties of bone are fundamental to the ability of our skeletons to support movement and to provide protection to our vital organs. As such, deterioration in mechanical behavior with aging and/or diseases such as osteoporosis and diabetes can have profound consequences for individuals' quality of life. This article reviews current knowledge of the basic mechanical behavior of bone at length scales ranging from hundreds of nanometers to tens of centimeters. We present the basic tenets of bone mechanics and connect them to some of the arcs of research that have brought the field to recent advances. We also discuss cortical bone, trabecular bone, and whole bones, as well as multiple aspects of material behavior, including elasticity, yield, fracture, fatigue, and damage. We describe the roles of bone quantity (e.g., density, porosity) and bone quality (e.g., cross-linking, protein composition), along with several avenues of future research.

Raman spectroscopic investigation on the molecular structure of apatite and collagen in osteoporotic cortical bone

This study employed highly spectrally resolved Raman spectroscopy to examine the molecular composition of cortical bone tissue obtained from murine females in their healthy and ovariectomy- (OVX-) induced osteoporotic states. The aim of the study was to identify structural differences at the molecular scale both in apatite mineral and collagen fibrils between the two groups of samples. Raman spectroscopy was used to determine the chemical composition of cortical bone in regions including characteristic bands of both bone mineral and bone matrix. The results demonstrated that the mineral apatite of bone did not undergo significant amorphization in its diseased state, with the Raman microprobe also failing in recognizing a direct role of carbonate content in the embrittlement of OVX-diseased bone. On the other hand, complex off-stoichiometry variations could be detected in the columnar Ca-structure of the bony hydroxyapatite according to morphological variations of the Raman band belonging to the symmetric phosphate stretching (A₁) band at ~959cm^-1. A fundamental role was also recognized for collagen quality on the process of bone embrittlement. The so-called matrix maturity ratio, as systematically measured on Raman spectra in the Amide I region, increased with statistical significance in OVX-treated samples as compared to control samples. An 8% increase could be associated to a 115% increase in elastic stress intensification in the mineral phase of OVX-diseased tissue as compared to the control one, thus proving a degradation in the (elastic) energy-dissipative capacity of a diseased bone matrix.

Connection between elastic and electrical properties of cortical bone

The paper focuses on the connection between elastic and electrical properties of cortical bone. Both these properties are governed by microstructure that consists of several pore systems filled with mechanically soft and electrically conductive tissue. Microstructural changes induced by aging, various diseases, microgravity conditions etc. lead to variation in both properties. The paper address the problem of evaluation of the changes in mechanical performance (decrease in Young׳s moduli) via monitoring electrical conductivity. The theoretical results are verified experimentally.

Hydroxyapatite reinforced collagen scaffolds with improved architecture and mechanical properties

Hydroxyapatite (HA) reinforced collagen scaffolds have shown promise for synthetic bone graft substitutes and tissue engineering scaffolds. Freeze-dried HA-collagen scaffolds are readily fabricated and have exhibited osteogenicity in vivo, but are limited by an inherent scaffold architecture that results in a relatively small pore size and weak mechanical properties. In order to overcome these limitations, HA-collagen scaffolds were prepared by compression molding HA reinforcements and paraffin microspheres within a suspension of concentrated collagen fibrils (∼ 180 mg/mL), cross-linking the collagen matrix, and leaching the paraffin porogen. HA-collagen scaffolds exhibited an architecture with high porosity (85-90%), interconnected pores ∼ 300-400 μm in size, and struts ∼ 3-100 μm in thickness containing 0-80 vol% HA whisker or powder reinforcements. HA reinforcement enabled a compressive modulus of up to ∼ 1 MPa, which was an order of magnitude greater than unreinforced collagen scaffolds. The compressive modulus was also at least one order of magnitude greater than comparable freeze-dried HA-collagen scaffolds and two orders of magnitude greater than absorbable collagen sponges used clinically. Moreover, scaffolds reinforced with up to 60 vol% HA exhibited fully recoverable elastic deformation upon loading to 50% compressive strain for at least 100,000 cycles. Thus, the scaffold mechanical properties were well-suited for surgical handling, fixation, and bearing osteogenic loads during bone regeneration. The scaffold architecture, permeability, and composition were shown to be conducive to the infiltration and differentiation of adipose-derive stromal cells in vitro. Acellular scaffolds were demonstrated to induce angiogenesis and osteogenesis after subcutaneous ectopic implantation by recruiting endogenous cell populations, suggesting that the scaffolds were osteoinductive.

To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?

An evidence gap exists in fully understanding and reliably modeling the variations in elastic anisotropy that are observed at the millimeter scale in human cortical bone. The porosity (pore volume fraction) is known to account for a large part, but not all, of the elasticity variations. This effect may be modeled by a two-phase micromechanical model consisting of a homogeneous matrix pervaded by cylindrical pores. Although this model has been widely used, it lacks experimental validation. The aim of the present work is to revisit experimental data (elastic coefficients, porosity) previously obtained from 21 cortical bone specimens from the femoral mid-diaphysis of 10 donors and test the validity of the model by proposing a detailed discussion of its hypotheses. This includes investigating to what extent the experimental uncertainties, pore network modeling, and matrix elastic properties influence the model's predictions. The results support the validity of the two-phase model of cortical bone which assumes that the essential source of variations of elastic properties at the millimeter-scale is the volume fraction of vascular porosity. We propose that the bulk of the remaining discrepancies between predicted stiffness coefficients and experimental data (RMSE between 6% and 9%) is in part due to experimental errors and part due to small variations of the extravascular matrix properties. More significantly, although most of the models that have been proposed for cortical bone were based on several homogenization steps and a large number of variable parameters, we show that a model with a single parameter, namely the volume fraction of vascular porosity, is a suitable representation for cortical bone. The results could provide a guide to build specimen-specific cortical bone models. This will be of interest to analyze the structure-function relationship in bone and to design bone-mimicking materials.

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

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

New methods to study the composition and structure of the extracellular matrix in natural and bioengineered tissues

The extracellular matrix (ECM) comprises a gel of numerous biopolymers that occurs in a multitude of biological tissues. The ECM provides the basic support and mechanical strength of skeletal tissue and is responsible for shape retention. At the same time, the ECM is responsible for the viscoelastic properties and the elasticity of soft tissues. As expected, there are several important diseases that affect and degenerate the ECM with severe consequences for its properties. Bioengineering is a promising approach to support the regenerative capacity of the body. Unfortunately, the biomechanical properties of bioengineered ECM often only poorly meet the standards of their native counterparts. Many bioengineered tissues are characterized by an increased glycosaminoglycan (GAG) but decreased collagen content. This leads to an enhanced water content that strongly alters the viscoelastic and thus the biomechanical properties. Therefore, compositional analysis is important to estimate the tissue quality. We will show that nuclear magnetic resonance (NMR) spectroscopy and soft-ionization mass spectrometry (MS) represent useful techniques for ECM research both in natural and bioengineered tissues. Both methods are strongly complimentary: while MS techniques such as matrix-assisted laser desorption and ionization (MALDI) are excellent and very sensitive analytical tools to determine the collagen and the GAG contents of tissues, NMR spectroscopy provides insight into the molecular architecture of the ECM, its dynamics and other important parameters such as the water content of the tissue as well as the diffusion of molecules within the ECM.

Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method

The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data.

In situ mechanical behavior of mineral crystals in human cortical bone under compressive load using synchrotron X-ray scattering techniques

It is of great interest to delineate the effect of orientation distribution of mineral crystals on the bulk mechanical behavior of bone. Using a unique synergistic approach combining a progressive loading scheme and synchrotron X-ray scattering techniques, human cortical bone specimens were tested in compression to examine the in situ mechanical behavior of mineral crystals aligned in different orientations. The orientation distribution was quantitatively estimated by measuring the X-ray diffraction intensity from the (002) plane in mineral crystals. In addition, the average longitudinal (c-axis), transverse (a-axis), and shear strains of the subset of mineral crystals aligned in each orientation were determined by measuring the lattice deformation normal to three distinct crystallographic planes (i.e. 002, 310, and 213) in the crystals. The experimental results indicated that the in situ strain and stress of mineral crystals varied with orientations. The normal strain and stress in the longitudinally aligned mineral crystals were markedly greater than those in the transversely oriented crystals, whereas the shear stress reached a maximum for the crystals aligned in ±30° with respect to the loading direction. The maximum principal strain and stress were observed in the mineral crystals oriented along the loading axis, with a similar trend observed in the maximum shear strain and stress. By examining the in situ behavior, the contribution of mineral crystals to load bearing and the bulk behavior of bone are discussed.

Viscoelastic properties of human cortical bone tissue depend on gender and elastic modulus

Bone exhibits rate-dependent failure behavior, suggesting that viscoelasticity is a factor in the damage and fracture of bone. Microdamage initiates at scales below the macroscopic porosity in bone, and, as such, is affected by the intrinsic viscoelasticity of the bone tissue. The viscoelasticity of the bone tissue can be measured by nanoindentation and recording the creep behavior at constant load. The viscoelastic properties have been used to assess differences in tissue behavior with respect to fracture healing, aging, and mouse strains. In this study, we compared the viscoelastic behavior of human cortical bone between genders by using nanoindentation at a fixed load of 10 mN to measure the creep time constant. Bones from females had a significantly greater time constant, indicating slower creep and relaxation, than bones from males. The creep time constants decreased with increasing tissue modulus. The mineralization, collagen content, and collagen cross-link density, which were bulk measurements, were analyzed to determine if the differences in viscoelastic behavior were explained by compositional differences in the bone. However, none of the parameters differed between genders, nor were they correlated to the viscoelastic time constant. As such, the difference must depend on other matrix proteins that we did not assess or differences in the microstructural organization. This is one of the only intrinsic bone material properties that has been found to differ between males and females, and it may be important for assessing differences in fracture risk, since crack propagation is generally sensitive to viscoelastic properties.

Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women

At the mesoscale (i.e. over a few millimeters), cortical bone can be described as two-phase composite material consisting of pores and a dense mineralized matrix. The cortical porosity is known to influence the mesoscopic elasticity. Our objective was to determine whether the variations of porosity are sufficient to predict the variations of bone mesoscopic anisotropic elasticity or if change in bone matrix elasticity is an important factor to consider. We measured 21 cortical bone specimens prepared from the mid-diaphysis of 10 women donors (aged from 66 to 98 years). A 50-MHz scanning acoustic microscope (SAM) was used to evaluate the bone matrix elasticity (reflected in impedance values) and porosity. Porosity evaluation with SAM was validated against Synchrotron Radiation μCT measurements. A standard contact ultrasonic method was applied to determine the mesoscopic elastic coefficients. Only matrix impedance in the direction of the bone axis correlated to mesoscale elasticity (adjusted R(2)=[0.16-0.25], p<0.05). The mesoscopic elasticity was found to be highly correlated to the cortical porosity (adj-R(2)=[0.72-0.84], p<10(-5)). Multivariate analysis including both matrix impedance and porosity did not provide a better statistical model of mesoscopic elasticity variations. Our results indicate that, for the elderly population, the elastic properties of the mineralized matrix do not undergo large variations among different samples, as reflected in the low coefficients of variation of matrix impedance (less than 6%). This work suggests that change in the intracortical porosity accounts for most of the variations of mesoscopic elasticity, at least when the analyzed porosity range is large (3-27% in this study). The trend in the variation of mesoscale elasticity with porosity is consistent with the predictions of a micromechanical model consisting of an anisotropic matrix pervaded by cylindrical pores.

Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p < 0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p < 0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C(11)) from the mid-diaphysis toward the epiphyses (p < 0.05), since differences in the circumferential (C(22)) and longitudinal (C(33)) elastic constants were not statistically significant (p > 0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p < 0.0001, R(2) > 0.46), as expected, but was only weakly correlated with C(33)/C(11) (p < 0.05, R(2) = 0.04) and not significantly correlated with C(33)/C(22) and C(11)/C(22).

Improved accuracy of cortical bone mineralization measured by polychromatic microcomputed tomography using a novel high mineral density composite calibration phantom

PURPOSE

Microcomputed tomography (micro-CT) is increasingly used as a nondestructive alternative to ashing for measuring bone mineral content. Phantoms are utilized to calibrate the measured x-ray attenuation to discrete levels of mineral density, typically including levels up to 1000 mg HA/cm3, which encompasses levels of bone mineral density (BMD) observed in trabecular bone. However, levels of BMD observed in cortical bone and levels of tissue mineral density (TMD) in both cortical and trabecular bone typically exceed 1000 mg HA/cm3, requiring extrapolation of the calibration regression, which may result in error. Therefore, the objectives of this study were to investigate (1) the relationship between x-ray attenuation and an expanded range of hydroxyapatite (HA) density in a less attenuating polymer matrix and (2) the effects of the calibration on the accuracy of subsequent measurements of mineralization in human cortical bone specimens.

METHODS

A novel HA-polymer composite phantom was prepared comprising a less attenuating polymer phase (polyethylene) and an expanded range of HA density (0-1860 mg HA/cm3) inclusive of characteristic levels of BMD in cortical bone or TMD in cortical and trabecular bone. The BMD and TMD of cortical bone specimens measured using the new HA-polymer calibration phantom were compared to measurements using a conventional HA-polymer phantom comprising 0-800 mg HA/cm3 and the corresponding ash density measurements on the same specimens.

RESULTS

The HA-polymer composite phantom exhibited a nonlinear relationship between x-ray attenuation and HA density, rather than the linear relationship typically employed a priori, and obviated the need for extrapolation, when calibrating the measured x-ray attenuation to high levels of mineral density. The BMD and TMD of cortical bone specimens measured using the conventional phantom was significantly lower than the measured ash density by 19% (p < 0.001, ANCOVA) and 33% (p < 0.05, Tukey's HSD), on average, respectively. The BMD and TMD of cortical bone specimens measured using the HA-polymer phantom with an expanded range of HA density was significantly lower than the measured ash density by 8% (p < 0.001, ANCOVA) and 10% (p < 0.05, Tukey's HSD), on average, respectively.

CONCLUSIONS

The new HA-polymer calibration phantom with a less attenuating polymer and an expanded range of HA density resulted in a more accurate measurement of micro-CT equivalent BMD and TMD in human cortical bone specimens compared to a conventional phantom, as verified by ash density measurements on the same specimens.

Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur

Experimental investigations for anatomic variation in the magnitude and anisotropy of elastic constants in human femoral cortical bone tissue have typically focused on a limited number of convenient sites near the mid-diaphysis. However, the proximal and distal ends of the diaphysis are more clinically relevant to common orthopaedic procedures and interesting mechanobiology. Therefore, the objective of this study was to measure anatomic variation in the elastic anisotropy and inhomogeneity of human cortical bone tissue along the entire length (15%-85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants) of the femoral diaphysis, using ultrasonic wave propagation in the three orthogonal specimen axes. The elastic symmetry of tissue in the distal and extreme proximal portions of the diaphysis (15%-45% and 75%-85% of the total femur length, respectively) was, at most, orthotropic. In contrast, the elastic symmetry of tissue near the mid- and proximal mid-diaphysis (50%-70% of the total femur length) was reasonably approximated as transversely isotropic. The magnitudes of elastic constants generally reached maxima near the mid- and proximal mid-diaphysis in the lateral and medial quadrants, and decreased toward the epiphyses, as well as the posterior and anterior quadrants. The elastic anisotropy ratio in the longitudinal and radial anatomic axes showed the opposite trends. These variations were significantly correlated with the apparent tissue density, as expected. In summary, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology.