Salah Naili

Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale

Cortical bone is a multiscale composite material. Its elastic properties are anisotropic and heterogeneous across its cross-section, due to endosteal bone resorption which might affect bone strength. The aim of this paper was to describe a homogenization method leading to the estimation of the variation of the elastic coefficients across the bone cross-section and along the bone longitudinal axis. The method uses the spatial variations of bone porosity and of the degree of mineralization of the bone matrix (DMB) obtained from the analysis of 3-D synchrotron micro-computed tomography images. For all three scales considered (the foam (100 nm), the ultrastructure (5 microm) and the mesoscale (500 microm)), the elastic coefficients were determined using the Eshelbys inclusion problem. DMB values were used at the scale of the foam. Collagen was introduced at the scale of the ultrastructure and bone porosity was introduced at the mesoscale. The pores were considered as parallel cylinders oriented along the bone axis. Each elastic coefficient was computed for different regions of interest, allowing an estimation of its variations across the bone cross-section and along the bone longitudinal axis. The method was applied to a human femoral neck bone specimen, which is a site of osteoporotic fracture. The computed elastic coefficients for cortical bone were in good agreement with experimental results, but some discrepancies were obtained in the endosteal part (trabecular bone). These results highlight the importance of accounting for the heterogeneity of cortical bone properties across bone cross-section and along bone longitudinal axis.

Biomechanical determinants of the stability of dental implants: Influence of the bone–implant interface properties

Dental implants are now widely used for the replacement of missing teeth in fully or partially edentulous patients and for cranial reconstructions. However, risks of failure, which may have dramatic consequences, are still experienced and remain difficult to anticipate. The stability of biomaterials inserted in bone tissue depends on multiscale phenomena of biomechanical (bone-implant interlocking) and of biological (mechanotransduction) natures. The objective of this review is to provide an overview of the biomechanical behavior of the bone-dental implant interface as a function of its environment by considering in silico, ex vivo and in vivo studies including animal models as well as clinical studies. The biomechanical determinants of osseointegration phenomena are related to bone remodeling in the vicinity of the implants (adaptation of the bone structure to accommodate the presence of a biomaterial). Aspects related to the description of the interface and to its space-time multiscale nature will first be reviewed. Then, the various approaches used in the literature to measure implant stability and the bone-implant interface properties in vitro and in vivo will be described. Quantitative ultrasound methods are promising because they are cheap, non invasive and because of their lower spatial resolution around the implant compared to other biomechanical approaches.

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.

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.

Study of the Influence of Fibrous Pericellular Matrix in the Cortical Interstitial Fluid Movement With Hydroelectrochemical Effects

Fluid flow within cortical bone tissue is modeled through an upscaling approach of a local description of the fluid movement. At the pore scale, the coupled phenomena (Poiseuille effect, osmosis, and electro-osmosis) governing the interstitial fluid movement are considered. Thus, actions of electro-osmotic and osmotic motions, in addition to the classical Poiseuille flow, are studied at the canaliculus scale by deriving a coupled Darcy law. The addition of a Brinkman-like term in this macroscopic result helps us to take into account the influence of the pericellular matrix on the coupled transport phenomena. At the canaliculus scale, the general trends that can be drawn from this study are as follows: (i) The presence of the fibrous matrix tends to reduce the fluid flow considerably; (ii) the role of osmotic and electro-osmotic effects is no longer negligible for dense fibrous media.

What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective.

Cortical bone, constituting the outer shell of long bones, is continuously renewed by bone cells in response to daily stimuli. This process, known as bone remodelling, is essential for proper bone functioning in both physiological and pathological conditions. Classical bone remodelling models do not, or only implicitly do, take into account physico-chemical phenomena, focussing on the mechanosensitivity property of the tissue. The aim of this paper is to carry out an investigation of the multiphysical phenomena occuring in bone life. Using a recent multiscale model combining piezoelectricity and electrokinetics to poromechanics, the usual viewpoint of bone remodelling models is questioned and new research avenues are proposed.

A multiscale theoretical investigation of electric measurements in living bone : piezoelectricity and electrokinetics.

This paper presents a theoretical investigation of the multiphysical phenomena that govern cortical bone behaviour. Taking into account the piezoelectricity of the collagen–apatite matrix and the electrokinetics governing the interstitial fluid movement, we adopt a multiscale approach to derive a coupled poroelastic model of cortical tissue. Following how the phenomena propagate from the microscale to the tissue scale, we are able to determine the nature of macroscopically observed electric phenomena in bone.

Anatomical distribution of the degree of mineralization of bone tissue in human femoral neck: Impact on biomechanical properties

Osteoporotic hip fractures represent a major public health problem associated with high human and economic costs. The anatomical variation of the tissue mineral density (TMD) and of the elastic constants in femoral neck cortical bone specimens is an important determinant of bone fragility. The purpose of this study was to show that a Synchrotron radiation microcomputed tomography system coupled with a multiscale biomechanical model allows the determination of the 3-D anatomical dependence of TMD and of the elastic constants (i.e. the mechanical properties of an anisotropic material) in human femoral neck. Bone specimens from the inferior femoral neck were obtained from 18 patients undergoing standard hemiarthroplasty. The specimens were imaged using 3-D synchrotron micro-computed tomography with a voxel size of 10.13 μm, leading to the determination of the anatomical distributions of porosity and TMD. The elastic properties of bone tissue were computed using a multiscale model. The model uses the experimental data obtained at the scale of several micrometers to estimate the components of the elastic tensor of bone at the scale of the organ. Statistical analysis (ANOVA) revealed a significant effect of the radial position on porosity and TMD and a significant effect of axial position on TMD only. Porosity was found to increase in the radial direction moving from the periosteum inwards (p<10(-5)). At any given distance from the periosteum, porosity does not vary noticeably along the bone axis. TMD was found to be significantly higher (p<10(-5)) in the periosteal region than in other bone locations and decreases from the periosteal to the endosteal region with an average slope of 10.05 g.cm(-3).m(-1), the decrease being faster in the porous part of the samples (average slope equal of 30.04 g.cm(-3).m(-1)) than in dense cortical bone. TMD was found to decrease from the distal to the proximal part of the femur neck (average slope of 6.5 g.cm(-3).m(-1)). Considering TMD variations in the radial direction induces weak changes of bone properties compared to constant TMD. TMD variations in the axial direction are responsible for a significant variation of elastic constants. These results demonstrate that the anatomical variations of TMD affect the bone elastic properties, which could be explained by the complex stress field in bone affecting bone remodeling. TMD spatial variations should be taken into account to properly describe the spatial heterogeneity of elastic coefficients of bone tissue at the organ scale.

Multiphysical modelling of fluid transport through osteo-articular media

In this study, a multiphysical description of fluid transport through osteo-articular porous media is presented. Adapted from the model of Moyne and Murad, which is intended to describe clayey materials behaviour, this multiscale modelling allows for the derivation of the macroscopic response of the tissue from microscopical information. First the model is described. At the pore scale, electrohydrodynamics equations governing the electrolyte movement are coupled with local electrostatics (Gauss-Poisson equation), and ionic transport equations. Using a change of variables and an asymptotic expansion method, the macroscopic description is carried out. Results of this model are used to show the importance of couplings effects on the mechanotransduction of compact bone remodelling.

On the paradoxical determinations of the lacuno-canalicular permeability of bone

The lacuno-canalicular permeability has been shown to play a key role in the behavior of bone tissue. The aim of this study is, by giving an overview of the determinations of this parameter, to question the paradoxical values provided by theoretical predictions and recent experimental measurements. We propose therefore a Kozeny-like law obtained by a numerical method which relates the permeability to the textural parameters of cortical bone microstructure. Moreover, we suggest possible explanations for this paradox considering the empirical difficulties and possible multiphysical effects.