The influence of mesoscale porosity on cortical bone anisotropy. Investigations via asymptotic homogenization

A lumped model for long bone behavior based on poroelastic deformation and Darcy flow

The present paper provides a simplified model for compact bone behavior by accounting for bone fluid flow coupled to the elasticity of the porous structure. The lumped model considers the bone material as a layered poroelastic structure and predicts normal pressure versus displacement, i.e, a stress-strain curve. There is a parametric dependency on porosity and permeability but, in addition, on pressure history. Specifically, the pressure impulse (the integral of pressure versus time) plays a key role. This factor is alluded to in several past studies, but not highlighted in a simplified fashion. Based on a global flow balance, bone displacement depends on the fluid flow in a channel according to the classical Darcy model of 1856, and on the rate of change of fluid within the porous solid according to the 1941 classical model of Biot. The present results agree with those of Perrin et al. which, in turn, agree with results of a detailed numerical simulation.

Investigating the post-yield behavior of mineralized bone fibril arrays using a 3D non-linear finite element unit-cell model

In this study, we propose a 3D non-linear finite element (FE) unit-cell model to investigate the post-yield behavior of mineralized collagen fibril arrays (FAY). We then compare the predictions of the model with recent micro-tensile and micropillar compression tests in both axial and transverse directions. The unit cell consists of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM), and the FE mesh is equipped with cohesive interactions and a custom plasticity model. The simulation results confirm that MCF plays a dominant role in load bearing prior to yielding under axial tensile loading. Damage was initiated via debonding in shear and progressive sliding at the MCF/EFM interface, and resulted in MCF pull-out until brittle failure. In transverse tensile loading, EFM carried most of the load in pre-yield deformation, and then mixed normal/shear debonding between MCF and EFM began to form, which eventually produced brittle delamination of the two phases. The loading/unloading FE analysis in compression along both axial and transverse directions demonstrated perfect plasticity without any reduction in elastic modulus, i.e., damage due to the interfaces as seen in micropillar compression. Beyond the brittle and ductile nature of the stress-strain curves, in tensile and compressive loading, the simulated post-yield behavior and failure mechanism are in good quantitative agreement with the experimental observations. Our rather simple but efficient unit-cell FE model can reproduce qualitatively and quantitatively the mechanical behavior of bone ECM under tensile and compressive loading along the two main orientations. The model's integration into higher length scales may be useful in describing the macroscopic post-yield and failure behavior of trabecular and cortical bone in greater detail.

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.

Laser-excited elastic guided waves reveal the complex mechanics of nanoporous silicon

Nanoporosity in silicon leads to completely new functionalities of this mainstream semiconductor. A difficult to assess mechanics has however significantly limited its application in fields ranging from nanofluidics and biosensorics to drug delivery, energy storage and photonics. Here, we present a study on laser-excited elastic guided waves detected contactless and non-destructively in dry and liquid-infused single-crystalline porous silicon. These experiments reveal that the self-organised formation of 100 billions of parallel nanopores per square centimetre cross section results in a nearly isotropic elasticity perpendicular to the pore axes and an 80% effective stiffness reduction, altogether leading to significant deviations from the cubic anisotropy observed in bulk silicon. Our thorough assessment of the wafer-scale mechanics of nanoporous silicon provides the base for predictive applications in robust on-chip devices and evidences that recent breakthroughs in laser ultrasonics open up entirely new frontiers for in-situ, non-destructive mechanical characterisation of dry and liquid-functionalised porous materials.

Assessing mechanics of nanoporous silicon is challenging, but important for new applications. Here, the authors use non-destructive laser-excited elastic guided waves detected contactless, to study dry and liquid-infused single-crystalline porous silicon, revealing its complex mechanics and significant deviations from bulk silicon.

Maximum effect of the heterogeneity of tissue mineralization on the effective cortical bone elastic properties

The mineralization level is heterogeneous in cortical bone extracellular matrix as a consequence of remodeling. Models of the effective elastic properties at the millimeter scale have been developed based on idealizations of the vascular pore network and matrix properties. Some popular models do not take into account the heterogeneity of the matrix. However, the errors on the predicted elasticity when the difference in elastic properties between osteonal and interstitial tissues is not modeled have not been quantified. This work provides an estimation of the maximum error. We compare the effective elasticity of a representative volume element (RVE) assuming (1) different elastic properties in osteonal and interstitial tissues vs. (2) average matrix properties. In order to account for the variability of bone microstructure, we use a collection of high resolution images of the pore network to build RVEs. In each RVE we assumed a constant osteonal wall thickness and we artificially varied this thickness between 35 and 140 [Formula: see text]m to create RVEs with different amounts of osteonal tissue. The homogenization problem was solved with a fast Fourier transform (FFT)-based numerical scheme. We found that the error depends on pore volume fraction and varies on average from 1 to [Formula: see text] depending on the assumed diameter of the osteons. The results suggest that matrix heterogeneity may be disregarded in cortical bone models in most practical cases.

What is the influence of two strain rates on the relationship between human cortical bone toughness and micro-structure?

Cortical bone fracture mechanisms are well studied under quasi-static loading. The influence of strain rate on crack propagation mechanisms needs to be better understood, however. We have previously shown that several aspects of the bone micro-structure are involved in crack propagation, such as the complete porosity network, including the Haversian system and the lacunar network, as well as biochemical aspects, such as the maturity of collagen cross-links. The aim of this study is to investigate the influence of strain rate on the toughness of human cortical bone with respect to its microstructure and organic non-collagenous composition. Two strain rates will be considered: quasi-static loading (10−4 s−1), a standard condition, and a higher loading rate (10−1 s−1), representative of a fall. Cortical bone samples were extracted from eight female donors (age 50–91 years). Three-point bending tests were performed until failure. Synchrotron radiation micro-computed tomography imaging was performed to assess bone microstructure including the Haversian system and the lacunar system. Collagen enzymatic cross-link maturation was measured using a high performance liquid chromatography column. Results showed that that under quasi-static loading, the elastic contribution of the fracture process is correlated to both the collagen cross-links maturation and the microstructure, while the plastic contribution is correlated only to the porosity network. Under fall-like loading, bone organization appears to be less linked to crack propagation.

Estimation of the elastic modulus of child cortical bone specimens via microindentation

Purpose: Non-pathological child cortical bone (NPCCB) studies can provide clinicians with vital information and insights. However, assessing the anisotropic elastic properties of NPCCB remains a challenge for the biomechanical engineering community. For the first time, this paper provides elastic moduli values for NPCCB specimens in two perpendicular directions (longitudinal and transverse) and for two different structural components of bone tissue (osteon and interstitial lamellae). Materials and Methods: Microindentation is one of the reference methods used to measure bone stiffness. Here, 8 adult femurs (mean age 82 ± 8.9 years), 3 child femurs (mean age 13.3 ± 2.1 years), and 16 child fibulae (mean age 10.2 ± 3.9 years) were used to assess the elastic moduli of adult and child bones by microindentation. Results: For adult specimens, the mean moduli measured in this study are 18.1 (2.6) GPa for osteons, 21.3 (2.3) GPa for interstitial lamellae, and 13.8 (1.7) GPa in the transverse direction. For child femur specimens, the mean modulus is 14.1 (0.8) GPa for osteons, lower than that for interstitial lamellae: 15.5 (1.5) GPa. The mean modulus is 11.8 (0.7) GPa in the transverse direction. Child fibula specimens show a higher elastic modulus for interstitial lamellae 15.8 (1.5) than for osteons 13.5 (1.6), with 10.2 (1) GPa in the transverse direction. Conclusion: For the first time, NPCCB elastic modulus values are provided in longitudinal and transverse directions at the microscale level.

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.

Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity

With ageing and various diseases, the vascular pore volume fraction (porosity) in cortical bone increases, and the morphology of the pore network is altered. Cortical bone elasticity is known to decrease with increasing porosity, but the effect of the microstructure is largely unknown, while it has been thoroughly studied for trabecular bone. Also, popular micromechanical models have disregarded several micro-architectural features, idealizing pores as cylinders aligned with the axis of the diaphysis. The aim of this paper is to quantify the relative effects on cortical bone anisotropic elasticity of porosity and other descriptors of the pore network micro-architecture associated with pore number, size and shape. The five stiffness constants of bone assumed to be a transversely isotropic material were measured with resonant ultrasound spectroscopy in 55 specimens from the femoral diaphysis of 29 donors. The pore network, imaged with synchrotron radiation X-ray micro-computed tomography, was used to derive the pore descriptors and to build a homogenization model using the fast Fourier transform (FFT) method. The model was calibrated using experimental elasticity. A detailed analysis of the computed effective elasticity revealed in particular that porosity explains most of the variations of the five stiffness constants and that the effects of other micro-architectural features are small compared to usual experimental errors. We also have evidence that modelling the pore network as an ensemble of cylinders yields biased elasticity values compared to predictions based on the real micro-architecture. The FFT homogenization method is shown to be particularly efficient to model cortical bone.

Monte Carlo type Simulations of Mineralized Collagen Fibril based on Two Scale Asymptotic Homogenization

A multi-scale model for mineralized collagen fibril is proposed by taking into account the uncertainties associated with the geometrical properties of mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli at two hierarchical length scales, namely: microfibril and mineralized collagen fibril. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes. A total 100 realizations for mineralized collagen fibril model with random distribution have been generated using an in-house MATLAB® code and Monte-Carlo type simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (= 10%) and large (= 10%) strain regimes. The stress transformation mechanism has also been explored in microfibril which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for microfibril under small and large strain have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as input for upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the mineralized collagen fibril in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics simulations in the literature with a significant reduction in the computational cost.

Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Bone cortical thickness and porosity assessment using ultrasound guided waves: An ex vivo validation study

Several studies showed the ability of the cortex of long bones such as the radius and tibia to guide mechanical waves. Such experimental evidence has given rise to the emergence of a category of quantitative ultrasound techniques, referred to as the axial transmission, specifically developed to measure the propagation of ultrasound guided waves in the cortical shell along the axis of long bones. An ultrasound axial transmission technique, with an automated approach to quantify cortical thickness and porosity is described. The guided modes propagating in the cortex are recorded with a 1-MHz custom made linear transducer array. Measurement of the dispersion curves is achieved using a two-dimensional spatio-temporal Fourier transform combined with singular value decomposition. Automatic parameters identification is obtained through the solution of an inverse problem in which the dispersion curves are predicted with a two-dimensional transverse isotropic free plate model. Thirty-one radii and fifteen tibiae harvested from human cadavers underwent axial transmission measurements. Estimates of cortical thickness and porosity were obtained on 40 samples out of 46. The reproducibility, given by the root mean square error of the standard deviation of estimates, was 0.11 mm for thickness and 1.9% for porosity. To assess accuracy, site-matched micro-computed tomography images of the bone specimens imaged at 9 μm voxel size served as the gold standard. Agreement between micro-computed tomography and axial transmission for quantification of thickness and porosity at the radius and tibia ranged from R²=0.63 for porosity (root mean square error RMSE=1.8%) to 0.89 for thickness (RMSE=0.3 mm). Despite an overall good agreement for porosity, the method performs less well for porosities lower than 10%. The heterogeneity and general complexity of cortical bone structure, which are not fully accounted for by our model, are suspected to weaken the model approximation. This study presents the first validation study for assessing cortical thickness and porosity using the axial transmission technique. The automatic signal processing minimizes operator-dependent errors for parameters determination. Recovering the waveguide characteristics, that is to say cortical thickness and porosity, could provide reliable information about skeletal status and future fracture risk.

Histology-based homogenization analysis of soft tissue: application to prostate cancer

It is well known that the changes in tissue microstructure associated with certain pathophysiological conditions can influence its mechanical properties. Quantitatively relating the tissue microstructure to the macroscopic mechanical properties could lead to significant improvements in clinical diagnosis, especially when the mechanical properties of the tissue are used as diagnostic indices such as in digital rectal examination and elastography. In this study, a novel method of imposing periodic boundary conditions in non-periodic finite-element meshes is presented. This method is used to develop quantitative relationships between tissue microstructure and its apparent mechanical properties for benign and malignant tissue at various length scales. Finally, the inter-patient variation in the tissue properties is also investigated. Results show significant changes in the statistical distribution of the mechanical properties at different length scales. More importantly the loss of the normal differentiation of glandular structure of cancerous tissue has been demonstrated to lead to changes in mechanical properties and anisotropy. The proposed methodology is not limited to a particular tissue or material and the example used could help better understand how changes in the tissue microstructure caused by pathological conditions influence the mechanical properties, ultimately leading to more sensitive and accurate diagnostic technologies.

Characterization of a new ultrasound device designed for measuring cortical porosity at the human tibia: A phantom study

Quantitative ultrasound (QUS) measurements of trabecular bone are a useful tool for the assessment of osteoporotic fracture risk. However, cortical bone properties (e.g. porosity) have an impact on bone strength as well and thus current research is focused on QUS assessment of cortical bone properties. Simulation studies of ultrasound propagation through cortical bone indicate that anisotropy, calculated from the ratio of the velocities in axial and tangential directions, is correlated with porosity. However, this relationship is affected by error sources, specifically bone surface curvature and variability of probe positioning. With the aim of in vivo estimation of cortical porosity a new ultrasound device was developed, which sequentially measures velocities in 3 different directions (axial=0° and ±37.5°) using the axial transmission method. Measurements on planar porosity phantoms (0-25%) were performed to confirm the results of the afore mentioned simulation studies. Additionally, measurements on cylindrical phantoms without pores (min. radius=34mm for strongest curvature) were performed to estimate the influence of surface curvature on velocity measurements (the tibia bone surface is fairly flat but may show surface curvature in some patients). The velocities in the axial and ±37.5° directions were used to calculate an anisotropy index. The velocities measured on the porosity phantoms showed a decrease by -6.3±0.2m/s and -10.1±0.2m/s per percent increase in porosity in axial and ±37.5° directions, respectively. Surface curvature had an effect on the velocities measured in ±37.5° directions which could be minimized by a correction algorithm resulting in an error of 5m/s. The anisotropy index could be used to estimate porosity with an accuracy error of 1.5%. These results indicate that an estimation of porosity using velocity measurements in different directions might be feasible, even in bones with curved surface. These results obtained on phantom material indicate that the approach tested may be suited for porosity measurements on human tibia bone.

Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C(Micro) of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C(Meso) were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c33 measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1-21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R(2) ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

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.

Ultrasound to assess bone quality

Bone quality is determined by a variety of compositional, micro- and ultrastructural properties of the mineralized tissue matrix. In contrast to X-ray-based methods, the interaction of acoustic waves with bone tissue carries information about elastic and structural properties of the tissue. Quantitative ultrasound (QUS) methods represent powerful alternatives to ionizing x-ray based assessment of fracture risk. New in vivo applicable methods permit measurements of fracture-relevant properties, [eg, cortical thickness and stiffness at fragile anatomic regions (eg, the distal radius and the proximal femur)]. Experimentally, resonance ultrasound spectroscopy and acoustic microscopy can be used to assess the mesoscale stiffness tensor and elastic maps of the tissue matrix at microscale resolution, respectively. QUS methods, thus, currently represent the most promising approach for noninvasive assessment of components of fragility beyond bone mass and bone microstructure providing prospects for improved assessment of fracture risk.

Modeling of femoral neck cortical bone for the numerical simulation of ultrasound propagation

Quantitative ultrasound assessment of the cortical compartment of the femur neck (FN) is investigated with the goal of achieving enhanced fracture risk prediction. Measurements at the FN are influenced by bone size, shape and material properties. The work described here was aimed at determining which FN material properties have a significant impact on ultrasound propagation around 0.5 MHz and assessing the relevancy of different models. A methodology for the modeling of ultrasound propagation in the FN, with a focus on the modeling of bone elastic properties based on scanning acoustic microscopy data, is introduced. It is found that the first-arriving ultrasound signal measured in through-transmission at the FN is not influenced by trabecular bone properties or by the heterogeneities of the cortical bone mineralized matrix. In contrast, the signal is sensitive to variations in cortical porosity, which can, to a certain extent, be accounted for by effective properties calculated with the Mori-Tanaka method.

The preliminary evaluation of a 1 MHz ultrasound probe for measuring the elastic anisotropy of human cortical bone

Our objective is to evaluate an ultrasound probe for measurements of velocity and anisotropy in human cortical bone (tibia). The anisotropy of cortical bone is a known and mechanically relevant property in the context of osteoporotic fracture risk. Current in vivo quantitative ultrasound devices measuring the velocity of ultrasound in long bones can only be applied in the axial direction. For anisotropy measurements a second direction for velocity measurements preferably perpendicular to the axial direction is necessary. We developed a new ultrasound probe which permits axial transmission measurements with a simultaneous second perpendicular direction (tangential). Anisotropy measurements were performed on isotropic and anisotropic phantoms and two excised human female tibiae (age 63 and 82). Anisotropy ratios (AI; ratio of squared ultrasound velocities in the two directions) were for the isotropic phantom 1.06 ± 0.01 and for the anisotropic phantom 1.14 ± 0.03 (mean ± standard deviation). AI was 1.83 ± 0.29 in the tibia from the older donor and 1.37 ± 0.18 in the tibia from the younger donor. The AIs were in the expected range and differed significantly (p<0.05, t-test) between the tibiae. Measured sound velocities were reproducible (mean standard deviation of short time precision of both channels for phantom measurements 31 m/s) and in agreement with reported velocities of the phantom material. Our results document the feasibility of anisotropy measurements at long bones using a single probe. Further improvements in the design of the probe and tests in vivo are warranted. If this approach can be evaluated in vivo an additional tool for assessing the bone status is available for clinical use.

Mapping human long bone compartmentalisation during ontogeny: a new methodological approach

Throughout ontogeny, human bones undergo differentiation in terms of shape, size and tissue type; this is a complex scenario in which the variations in the tissue compartmentalisation of the cortical bone are still poorly understood. Currently, compartmentalisation is studied using methodologies that oversimplify the bone tissue complexity. Here, we present a new methodological approach that integrates a histological description and a mineral content analysis to study the compartmentalisation of the whole mineralised and non-mineralised tissues (i.e., spatial distribution in long bone sections). This new methodology, based on Geographical Information System (GIS) software, allows us to draw areas of interest (i.e., tracing vectorial shapes which are quantifiable) in raw images that are extracted from microscope and compared them spatially in a semi-automatic and quantitative fashion. As an example of our methodology, we have studied the tibiae from individuals with different age at death (infant, juvenile and adult). The tibia's cortical bone presents a well-formed fibrolamellar bone, in which remodelling is clearly evidenced from early ontogeny, and we discuss the existence of "lines of arrested growth". Concurrent with the histological variation, Raman and FT-IR spectroscopy analyses corroborate that the mineral content in the cortical bone changes differentially. The anterior portion of the tibia remains highly pierced and is less crystalline than the rest of the cortex during growth, which is evidence of more active and continuous remodelling. Finally, while porosity and other "non-mineralised cavities" are largely modified, the mineralised portion and the marrow cavity size persist proportionally during ontogeny.

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.

Spatial-temporal mapping of bone structural and elastic properties in a sheep model following osteotomy

The course of bone healing in animal models is conventionally monitored by morphologic approaches, which do not allow the determination of the material properties of the tissues involved. Mechanical characterization techniques are either dedicated to the macroscopic evaluation of the entire organ or to the microscopic evaluation of the tissue matrix. The latter provides insight to regionally specific alterations at the tissue level in the course of healing. In this study, quantitative scanning acoustic microscopy was used at 50 MHz to investigate microstructural and elastic alterations of mineralized callus and cortical tissue after transverse osteotomy in sheep tibiae. Analyses were performed after 2, 3, 6 and 9 weeks of consolidation with stabilization by either a rigid or a semi-rigid external fixator. Increased stiffness and decreased porosity were observed in the callus tissue over the course of the healing process, which was dependent on the fixator type. In the adjacent cortical tissue, stiffness decreased during the first 3 weeks. Cortical porosity increased over time but the time-dependence was different between the two fixator types. The changes of stiffness of cortical and callus tissues were measured with respect to the distance to the periosteal cortex-callus boundary. Stiffness of cortex and callus tissue smoothly decreased as a function of the distance from the inner cortical region. The data obtained in this study can help to understand the processes involved in tissue maturation during endogenous bone healing.