Assessing the effective elastic properties of the tendon-to-bone insertion: a multiscale modeling approach.

The interphase joining tendon to bone plays the crucial role of integrating soft to hard tissues, by effectively transferring stresses across two tissues displaying a mismatch in mechanical properties of nearly two orders of magnitude. The outstanding mechanical properties of this interphase are attributed to its complex hierarchical structure, especially by means of competing gradients in mineral content and collagen fibers organization at different length scales. The goal of this study is to develop a multiscale model to describe how the tendon-to-bone insertion derives its overall mechanical behavior. To this end, the effective anisotropic stiffness tensor of the interphase is predicted by modeling its elastic response at different scales, spanning from the nanostructural to the mesostructural levels, using continuum micromechanics methods. The results obtained at a lower scale serve as inputs for the modeling at a higher scale. The obtained predictions are in good agreement with stochastic finite element simulations and experimental trends reported in literature. Such model has implication for the design of bioinspired bi-materials that display the functionally graded properties of the tendon-to-bone insertion.

Cell Colonization Ability of a Commercialized Large Porous Alveolar Scaffold.

The use of filling biomaterials or tissue-engineered large bone implant-coupling biocompatible materials and human bone marrow mesenchymal stromal cells seems to be a promising approach to treat critical-sized bone defects. However, the cellular seeding onto and into large porous scaffolds still remains challenging since this process highly depends on the porous microstructure. Indeed, the cells may mainly colonize the periphery of the scaffold, leaving its volume almost free of cells. In this study, we carry out an in vitro study to analyze the ability of a commercialized scaffold to be in vivo colonized by cells. We investigate the influence of various physical parameters on the seeding efficiency of a perfusion seeding protocol using large manufactured bone substitutes. The present study shows that the velocity of the perfusion fluid and the initial cell density seem to impact the seeding results and to have a negative effect on the cellular viability, whereas the duration of the fluid perfusion and the nature of the flow (steady versus pulsed) did not show any influence on either the fraction of seeded cells or the cellular viability rate. However, the cellular repartition after seeding remains highly heterogeneous.

Water in hydroxyapatite nanopores: Possible implications for interstitial bone fluid flow.

The role of bone water in the activity of this organ is essential in structuring apatite crystals, providing pathways for nutrients and waste involved in the metabolism of bone cells and participating in bone remodelling mechanotransduction. It is commonly accepted that bone presents three levels of porosity, namely the vasculature, the lacuno-canalicular system and the voids of the collagen-apatite matrix. Due to the observation of bound state of water at the latter level, the interstitial nanoscopic flow that may exist within these pores is classically neglected. The aim of this paper is to investigate the possibility to obtain a fluid flow at the nanoscale. That is why a molecular dynamics based analysis of a water-hydroxyapatite system is proposed to analyze the effect of water confinement on transport properties. The main result here is that free water can be observed inside hydroxyapatite pores of a few nanometers. This result would have strong implications in the multiscale treatment of the poromechanical behaviour of bone tissue. In particular, the mechanical properties of the bone matrix may be highly controlled by nanoscopic water diffusion and the classical idea that osteocytic activity is only regulated by bone fluid flow within the lacuno-canalicular system may be discussed again.

Textural versus electrostatic exclusion-enrichment effects in the effective chemical transport within the cortical bone: a numerical investigation.

Interstitial fluid within bone tissue is known to govern the remodelling signals' expression. Bone fluid flow is generated by skeleton deformation during the daily activities. Due to the presence of charged surfaces in the bone porous matrix, the electrochemical phenomena occurring in the vicinity of mechanosensitive bone cells, the osteocytes, are key elements in the cellular communication. In this study, a multiscale model of interstitial fluid transport within bone tissues is proposed. Based on an asymptotic homogenization method, our modelling takes into account the physicochemical properties of bone tissue. Thanks to this multiphysical approach, the transport of nutrients and waste between the blood vessels and the bone cells can be quantified to better understand the mechanotransduction of bone remodelling. In particular, it is shown that the electrochemical tortuosity may have stronger implications in the mass transport within the bone than the purely morphological one.

Do calcium fluxes within cortical bone affect osteocyte mechanosensitivity?

Bone reacts to local mechanical environment by adapting its structure. Bone is also a key source of calcium for the body homeostasis. Osteocytes, cells located within the bone tissue, are thought to play a major role in sensing mechanical signals and regulating bone remodeling. Interestingly, osteocytes were also shown to directly participate in the calcium homeostasis by regulating dissolution and deposition of calcium in the perilacuno-pericanalicular space. However, it is not known if osteocyte's roles in mechanoregulation and calcium homeostasis have any significant crosstalk. Previously, a multi-scale mathematical model of the interstitial fluid flow through the canaliculus was developed, which took into account physicochemical phenomena including hydraulic effects, formation of electrical double layer, osmosis and electro-osmosis. We extended this model to include the directional movement of calcium from and into the bone tissue, and assessed the shear stress at the osteocyte membrane. We have found that in the bulk of the canalicular space the fluid flow due to chemical gradient generated by deposition or dissolution of calcium is negligible compared to the fluid flow due to hydraulic pressure. However, at the osteocyte proximity, the presence of calcium gradient generated sufficient fluid flow to induce significant changes in the shear stress on the osteocyte membrane. Calcium deposition and dissolution on the canalicular wall resulted in increased or decreased shear stress on the osteocyte membrane respectively. Thus, our data demonstrate that strong calcium fluxes due to whole body calcium homeostasis may affect mechanical forces experienced by osteocytes.

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.

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.

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone.

We compare theoretical predictions of the effective elastic moduli of cortical bone at both the meso- and macroscales. We consider the efficacy of three alternative approaches: the method of asymptotic homogenization, the Mori-Tanaka scheme and the Hashin-Rosen bounds. The methods concur for specific engineering moduli such as the axial Young's modulus but can vary for others. In a past study, the effect of porosity alone on mesoscopic properties of cortical bone was considered, taking the matrix to be isotropic. Here, we consider the additional influence of the transverse isotropy of the matrix. We make the point that micromechanical approaches can be used in two alternative ways to predict either the macroscopic (size of cortical bone sample) or mesoscopic (in between micro- and macroscales) effective moduli, depending upon the choice of representative volume element size. It is widely accepted that the mesoscale behaviour is an important aspect of the mechanical behaviour of bone but models incorporating its effect have started to appear only relatively recently. Before this only macroscopic behaviour was addressed. Comparisons are drawn with experimental data and simulations from the literature for macroscale predictions with particularly good agreement in the case of dry bone. Finally, we show how predictions of the effective mesoscopic elastic moduli can be made which retain dependence on the well-known porosity gradient across the thickness of cortical bone.

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.