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.

Influence of loading condition and anatomical location on human cortical bone linear micro-cracks.

Human cortical bone fracture toughness depends on the anatomical locations under quasi-static loading. Recent results also showed that under fall-like loading, cortical bone fracture toughness is similar at different anatomical locations in the same donor. While cortical bone toughening mechanisms are known to be dependent on the tissue architecture under quasi-static loading, the fracture mechanisms during a fall are less studied. In the current study, the structural parameters of eight paired femoral diaphyses, femoral necks and radial diaphyses were mechanically tested under quasi-static and fall-like loading conditions (female donors, 70 ±â€¯14 y.o., [50-91 y.o.]). Synchrotron radiation micro-CT imaging was used to quantify the amount of micro-cracks formed during loading. The volume fraction of these micro-cracks was significantly higher within the specimens loaded under a quasi-static condition than under a loading representative of a fall. Under fall-like loading, there was no difference in crack volume fraction between the different paired anatomical locations. This result shows that the micro-cracking toughening mechanism depends both on the anatomical location and on the loading condition.

3D micro structural analysis of human cortical bone in paired femoral diaphysis, femoral neck and radial diaphysis.

Human bone is known to adapt to its mechanical environment in a living body. Both its architecture and microstructure may differ between weight-bearing and non-weight-bearing bones. The aim of the current study was to analyze in three dimensions, the morphology of the multi-scale porosities on human cortical bone at different locations. Eight paired femoral diaphyses, femoral necks, and radial diaphyses were imaged using Synchrotron Radiation µCT with a 0.7 µm isotropic voxel size. The spatial resolution facilitates the investigation of the multiscale porosities of cortical bone, from the osteonal canals system down to the osteocyte lacunar system. Our results showed significant differences in the microstructural properties, regarding both osteonal canals and osteocytes lacunae, between the different anatomical locations. The radius presents significantly lower osteonal canal volume fraction and smaller osteonal canals than the femoral diaphysis or neck. Osteocytes lacunae observed in the radius are significantly different in shape than in the femur, and lacunar density is higher in the femoral neck. These results show that the radius, a non-weight-bearing bone, is significantly different in terms of its microstructure from a weight-bearing bone such as the femur. This implies that the cortical bone properties evaluated on the femoral diaphysis, the main location studied within the literature, cannot be generalized to other anatomical locations.

Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone.

Resonant ultrasound spectroscopy (RUS) is the state-of-the-art method used to investigate the elastic properties of anisotropic solids. Recently, RUS was applied to measure human cortical bone, an anisotropic material with low Q-factor (20), which is challenging due to the difficulty in retrieving resonant frequencies. Determining the precision of the estimated stiffness constants is not straightforward because RUS is an indirect method involving minimizing the distance between measured and calculated resonant frequencies using a model. This work was motivated by the need to quantify the errors on stiffness constants due to different error sources in RUS, including uncertainties on the resonant frequencies and specimen dimensions and imperfect rectangular parallelepiped (RP) specimen geometry. The errors were first investigated using Monte Carlo simulations with typical uncertainty values of experimentally measured resonant frequencies and dimensions assuming a perfect RP geometry. Second, the exact specimen geometry of a set of bone specimens were recorded by synchrotron radiation micro-computed tomography. Then, a "virtual" RUS experiment is proposed to quantify the errors induced by imperfect geometry. Results show that for a bone specimen of ∼1° perpendicularity and parallelism errors, an accuracy of a few percent ( <6.2%) for all the stiffness constants and engineering moduli is achievable.

Bone canalicular network segmentation in 3D nano-CT images through geodesic voting and image tessellation.

Recent studies emphasized the role of the bone lacuno-canalicular network (LCN) in the understanding of bone diseases such as osteoporosis. However, suitable methods to investigate this structure are lacking. The aim of this paper is to introduce a methodology to segment the LCN from three-dimensional (3D) synchrotron radiation nano-CT images. Segmentation of such structures is challenging due to several factors such as limited contrast and signal-to-noise ratio, partial volume effects and huge number of data that needs to be processed, which restrains user interaction. We use an approach based on minimum-cost paths and geodesic voting, for which we propose a fully automatic initialization scheme based on a tessellation of the image domain. The centroids of pre-segmented lacunæ are used as Voronoi-tessellation seeds and as start-points of a fast-marching front propagation, whereas the end-points are distributed in the vicinity of each Voronoi-region boundary. This initialization scheme was devised to cope with complex biological structures involving cells interconnected by multiple thread-like, branching processes, while the seminal geodesic-voting method only copes with tree-like structures. Our method has been assessed quantitatively on phantom data and qualitatively on real datasets, demonstrating its feasibility. To the best of our knowledge, presented 3D renderings of lacunæ interconnected by their canaliculi were achieved for the first time.

3D osteocyte lacunar morphometric properties and distributions in human femoral cortical bone using synchrotron radiation micro-CT images.

Osteocytes, the most numerous bone cells, are thought to be actively involved in the bone modeling and remodeling processes. The morphology of osteocyte is hypothesized to adapt according to the physiological mechanical loading. Three-dimensional micro-CT has recently been used to study osteocyte lacunae. In this work, we proposed a computationally efficient and validated automated image analysis method to quantify the 3D shape descriptors of osteocyte lacunae and their distribution in human femurs. Thirteen samples were imaged using Synchrotron Radiation (SR) micro-CT at ID19 of the ESRF with 1.4µm isotropic voxel resolution. With a field of view of about 2.9×2.9×1.4mm(3), the 3D images include several tens of thousands of osteocyte lacunae. We designed an automated quantification method to segment and extract 3D cell descriptors from osteocyte lacunae. An image moment-based approach was used to calculate the volume, length, width, height and anisotropy of each osteocyte lacuna. We employed a fast algorithm to further efficiently calculate the surface area, the Euler number and the structure model index (SMI) of each lacuna. We also introduced the 3D lacunar density map to directly visualize the lacunar density variation over a large field of view. We reported the lacunar morphometric properties and distributions as well as cortical bone histomorphometric indices on the 13 bone samples. The mean volume and surface were found to be 409.5±149.7µm(3) and 336.2±94.5µm(2). The average dimensions were of 18.9±4.9µm in length, 9.2±2.1µm in width and 4.8±1.1µm in depth. We found lacunar number density and six osteocyte lacunar descriptors, three axis lengths, two anisotropy ratios and SMI, that are significantly correlated to bone porosity at a same local region. The proposed method allowed an automatic and efficient direct 3D analysis of a large population of bone cells and is expected to provide reliable biological information for better understanding the bone quality and diseases at cellular level.

3D microstructural architecture of muscle attachments in extant and fossil vertebrates revealed by synchrotron microtomography.

BACKGROUND: Firm attachments binding muscles to skeleton are crucial mechanical components of the vertebrate body. These attachments (entheses) are complex three-dimensional structures, containing distinctive arrangements of cells and fibre systems embedded in the bone, which can be modified during ontogeny. Until recently it has only been possible to obtain 2D surface and thin section images of entheses, leaving their 3D histology largely unstudied except by extrapolation from 2D data. Entheses are frequently preserved in fossil bones, but sectioning is inappropriate for rare or unique fossil material. METHODOLOGY/PRINCIPAL FINDINGS: Here we present the first non-destructive 3D investigation, by propagation phase contrast synchrotron microtomography (PPC-SRµCT), of enthesis histology in extant and fossil vertebrates. We are able to identify entheses in the humerus of the salamander Desmognathus from the organization of bone-cell lacunae and extrinsic fibres. Statistical analysis of the lacunae differentiates types of attachments, and the orientation of the fibres, reflect the approximate alignment of the muscle. Similar histological structures, including ontogenetically related pattern changes, are perfectly preserved in two 380 million year old fossil vertebrates, the placoderm Compagopiscis croucheri and the sarcopterygian fish Eusthenopteron foordi. CONCLUSIONS/SIGNIFICANCE: We are able to determine the position of entheses in fossil vertebrates, the approximate orientation of the attached muscles, and aspects of their ontogenetic histories, from PPC-SRµCT data. Sub-micron microtomography thus provides a powerful tool for studying the structure, development, evolution and palaeobiology of muscle attachments.