Quentin Grimal

X-ray phase nanotomography resolves the 3D human bone ultrastructure.

Bone strength and failure are increasingly thought to be due to ultrastructural properties, such as the morphology of the lacuno-canalicular network, the collagen fiber orientation and the mineralization on the nanoscale. However, these properties have not been studied in 3D so far. Here we report the investigation of the human bone ultrastructure with X-ray phase nanotomography, which now provides the required sensitivity, spatial resolution and field of view. The 3D organization of the lacuno-canalicular network is studied in detail over several cells in osteonal and interstitial tissue. Nanoscale density variations are revealed and show that the cement line separating these tissues is hypermineralized. Finally, we show that the collagen fibers are organized as a twisted plywood structure in 3D.

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.

Investigation of the three-dimensional orientation of mineralized collagen fibrils in human lamellar bone using synchrotron X-ray phase nano-tomography.

We investigate the three-dimensional (3-D) organization of mineralized collagen fibrils in human cortical bone based on synchrotron X-ray phase nano-tomography images. In lamellar bone the collagen fibrils are assumed to have a plywood-like arrangement, but due to experimental limitations the 3-D fibril structure has only been deduced from section surfaces so far and the findings have been controversial. Breakthroughs in synchrotron tomographic imaging have given access to direct 3-D information on the bone structure at the nanoscale level. Using an autocorrelation-based orientation measure we confirm that the fibrils are unidirectional in quasi-planes of sub-lamellae and find two specific dominant patterns, oscillating and twisted plywoods coexisting in a single osteon. Both patterns exhibit smooth orientation changes between adjacent quasi-planes. Moreover, we find that the periodic changes in collagen fibril orientation are independent of fluctuations in local mass density. These data improve our understanding of the lamellar arrangement in bone and allow more detailed investigations of structure-function relationships at this scale, providing templates for bio-inspired materials. The presented methodology can be applied to non-destructive 3-D characterization of the sub-micron scale structure of other natural and artificial mineralized biomaterials.

Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission

The aim of this work is to evaluate the effect of a spatial gradient of material properties (mass density and stiffness coefficients) of cortical bone on its ultrasonic response obtained with an axial transmission device. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic linear source located in one fluid layer, delivering broadband ultrasonic pulses. The model couples the acoustic propagation in both fluid media with the elastodynamic response of the solid layer. A constant spatial gradient of material properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bone widths. For a thin bone (0.6 mm) compared to wavelength (around 4 mm at 1 MHz), the results are in good agreement with a S(0) Lamb wave assuming a homogeneous material with spatially averaged material properties. For a thick bone (4 mm), the results are in agreement with the propagation of a lateral wave and allow the derivation of an equivalent contributing depth in the case of a transverse isotropic inhomogeneous solid layer.

Assessment of cortical bone elasticity and strength: Mechanical testing and ultrasound provide complementary data

Cortical bone is a compact tissue with anisotropic macroscopic mechanical properties determined by a microstructure and the quality of a mineralised collagen matrix. Anisotropic elastic properties and strength are usually measured on different groups of sample which can hardly be pooled; as a consequence little is known on the relationships between strength and elasticity in the different anatomical directions. A method is presented to measure on a same cortical bone sample: (1) Youngs modulus and strength (sigma(max)) in the longitudinal direction; (2) stiffness (C(11)) in the transverse direction. Longitudinal and transverse direction are taken along and perpendicular to the diaphysis axis, respectively. Ultrasonic techniques yield Youngs modulus (E(a)) and C(11); three-point bending tests yield Youngs modulus (E) and sigma(max). The relationships between strength, elasticity and density and their anatomical distributions were investigated for 36 human femur samples. (i) A marginal negative correlation was obtained for E(a) and C(11) (R=-0.21; p=0.08); (ii) sigma(max) was significantly correlated to E and E(a) (R approximately 0.5; p<0.005) but not to C(11) (p>0.2); (iii) density was not correlated with E and moderately with strength (R=0.38; p<0.3). Small density variability (+/-30 kg m(-3)) may partly explain the results. The techniques presented are suited to a systematic characterization of bone samples.

Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission

Cortical bone and the surrounding soft tissues are attenuating and heterogeneous media, which might affect the signals measured with axial transmission devices. This work aims at evaluating the effect of the heterogeneous acoustic absorption in bone and in soft tissues on the bone ultrasonic response. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic viscoelastic solid layer, sandwiched between two viscous fluid layers. The model couples viscous acoustic propagation in both fluid media with the anisotropic viscoelastic response of the solid. A constant spatial gradient of material properties is considered for two values of bone thicknesses (0.6 and 4 mm). In the studied configuration, absorption in the surrounding fluid tissues does not affect the results, whereas bone viscoelastic properties have a significant effect on the first arriving signal (FAS) velocity. For a thin bone, the FAS velocity is governed by the spatially averaged bone properties. For a thick bone, the FAS velocity may be predicted using a one-dimensional model.

Spatial distribution of tissue level properties in a human femoral cortical bone.

The mechanical properties of cortical bone are determined by a combination bone tissue composition, and structure at several hierarchical length scales. In this study the spatial distribution of tissue level properties within a human femoral shaft has been investigated. Cylindrically shaped samples (diameter: 4.4mm, N=56) were prepared from cortical regions along the entire length (20-85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants). The samples were analyzed using scanning acoustic microscopy (SAM) at 50MHz and synchrotron radiation micro computed tomography (SRμCT). For all samples the average cortical porosity (Ct.Po), tissue elastic coefficients (c(ij)) and the average tissue degree of mineralization (DMB) were determined. The smallest coefficient of variation was observed for DMB (1.8%), followed by BV/TV (5.4%), c(ij) (8.2-45.5%), and Ct.Po (47.5%). Different variations with respect to the anatomical position were found for DMB, Ct.Po and c(ij). These data address the anatomical variations in anisotropic elastic properties and link them to tissue mineralization and porosity, which are important input parameters for numerical multi-scale bone models.

A two-parameter model of the effective elastic tensor for cortical bone.

Multiscale models of cortical bone elasticity require a large number of parameters to describe the organization and composition of the tissue. We hypothesize that the macro-scale anisotropic elastic properties of different bones can be modeled retaining only two variable parameters, and setting the others to universal values identical for all bones. Cortical bone is regarded as a two-phase composite material: a dense mineralized matrix (ultrastructure) and a soft phase (pores). The ultrastructure is assumed to be a homogeneous and transversely isotropic tissue whose elastic properties in different directions are mutually dependent and can be scaled with a single parameter driving the overall rigidity. This parameter is taken to be the volume fraction of mineral f(ha). The pore network is modeled as an ensemble of water-filled cylinders and described only by the porosity p. The effective macroscopic elasticity tensor C(ij)(f(ha),p) is calculated with a multiscale micromechanics approach starting from existing models. The modeled stiffness coefficients compare favorably to four literature datasets which were chosen because they provide the full stiffness tensors of groups of human samples. Since the physical counterparts of f(ha) and p were unknown for the datasets, their values which allow the best fit of experimental tensors by the modeled ones were determined by optimization. Optimum values of f(ha) and p are found to be unique and realistic. These results suggest that a two-parameter model may be sufficient to model the elasticity of different samples of human femora and tibiae. Such a model would in particular be useful in large-scale parametric studies of bone mechanical response.

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

Recently, the mesoscale of cortical bone has been given particular attention in association with novel experimental techniques such as nanoindentation, micro-computed X-ray tomography and quantitative scanning acoustic microscopy (SAM). A need has emerged for reliable mathematical models to interpret the related microscopic and mesoscopic data in terms of effective elastic properties. In this work, a new model of cortical bone elasticity is developed and used to assess the influence of mesoscale porosity on the induced anisotropy of the material. Only the largest pores (Haversian canals and resorption cavities), characteristic of the mesoscale, are considered. The input parameters of the model are derived from typical mesoscale experimental data (e.g. SAM data). We use the method of asymptotic homogenization to determine the local effective elastic properties by modelling the propagation of low-frequency elastic waves through an idealized material that models the local mesostructure. We use a novel solution of the cell problem developed by Parnell & Abrahams. This solution is stable for the physiological range of variation of mesoscopic porosity and elasticity found in bone. Results are computed efficiently (in seconds) and the solutions can be implemented easily by other workers. Parametric studies are performed in order to assess the influence of mesoscopic porosity, the assumptions regarding the material inside the mesoscale pores (drained or undrained bone) and the shape of pores. Results are shown to be in good qualitative agreement with existing schemes and we describe the potential of the scheme for future use in modelling more complex microstructures for cortical bone. In particular, the scheme is shown to be a useful tool with which to predict the qualitative changes in anisotropy due to variations in the structure at the mesoscale.

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.