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.

Photo-induced SI-ATRP for the synthesis of photoclickable intercalated clay nanofillers

Design of functional and hairy nanoclay intercalated assemblies using tandem photoinduced surface initiated ATRP-1,3 dipolar cycloaddition/thiol-yne click reactions.

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.

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.

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 Eshelby's 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.

Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption

Speed of sound measurements are widely used clinically to assess bone strength. Trabecular bone is an attenuating composite material in which negative values of velocity dispersion have been measured, this behavior remaining poorly explained physically. The aim of this work is to describe the ultrasonic propagation in trabecular bone modeled by infinite cylinders immersed in a saturating matrix, and to derive the physical determinants of velocity dispersion. A homogenization model accounting for the coupling of multiple scattering and absorption phenomena allows the computation of phase velocity and of dispersion while varying bone properties. The present model is adapted from the generalized self-consistent method developed in the work of Yang and Mal [(1994). "Multiple-scattering of elastic waves in a fiber-reinforced composite," J. Mech. Phys. Solids 42, 1945-1968]. It predicts negative values of velocity dispersion, in agreement with experimental results obtained in phantoms mimicking trabecular bone. In trabecular bone, mostly negative and also positive values of velocity dispersion are predicted by the model, which span within the range of values measured experimentally. Scattering effects are responsible for the negative values of dispersion, whereas the frequency dependence of the absorption coefficient in bone marrow and/or in the trabeculae results in an increase in dispersion, which may then become positive.

[Cardiac perforation and tamponade during TIPS placement]

A patient developed an acute severe haemodynamic compromise immediately after a transjugular intrahepatic portosystemic shunt (TIPS) procedure for intractable ascites. Rapid clinical and echographic evaluation disclosed pericardial blood and cardiac tamponade, probably due to right heart perforation from guidewire and catheter manipulation. Needle drainage of pericardial fluid restored the haemodynamic status. A right ventricular perforation was then successfully treated (sternotomy and closure of right ventricle perforation) and the patient survived. Cardiac tamponade should be considered in the differential diagnosis of patients who develop hypotension and haemodynamic impairment during or immediately after TIPS placement.

Developing steady laminar flow through uniform straight tubes with varying wall cross curvature

Numerical calculations are used to determine not only the wall shear stress but also the entry length in a laminar steady flow of an incompressible Newtonian fluid. The fluid is conveyed through rigid straight tubes with axially uniform cross sections, which mimic collapsed vessels. For each tube configuration, the "Navier-Stokes" equations are solved using the finite element method. The numerical tests are performed with the same value of the volume flow-rate whatever the tube configuration for three "Reynolds numbers". The wall shear stress is computed and determined along the axis of the tube, then the entry length is estimated by introducing two indexes by using: (i) the axial fluid velocity, and (ii) the wall shear stress. The results are analysed in order to exhibit the mechanical environment of cultured endothelial cells in the flow chamber for which the test conditions will be well-defined. For example, in a tube configuration where the opposite walls are in contact for which the inner perimeter and the area of the cross section are respectively given by 45 mm and 37.02 mm(2), the computed entry lengths with the criteria defined by (i) and (ii) are equals to about 118 and 126 mm, respectively for R(e0) = 500.

Ion induced deformation of soft tissue

In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Lai et al. (1990, Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myers et al. (1984, ASME J. biomech. Engng, 106, 151-158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to account for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility of approximate analytic solutions in certain cases.

Collapse of thin-walled elliptical tubes for high values of major-to-minor axis ratio

The topic of this study concerns principally representative models of some elliptical thin-walled anatomic vessels and polymeric tubes under uniform negative transmural pressure p (internal pressure minus external pressure). The ellipse's ellipticity k(o), defined as the major-to-minor axis ratio, varies from 1 up to 10. As p decreases from zero, at first the cross-section becomes somewhat oval, then the opposite sides touch in one point at the first-contact pressure pc. If p is lowered beneath pc, the curvature of the cross-section at the point of contact decreases until it becomes zero at the osculation pressure or the first line-contact pressure pl. For p < pl, the contact occurs along a straight-line segment, the length of which increases as p decreases. The pressures pc and pl are determined numerically for various values of the wall thickness of the tubes. The nature of contact is especially described. The solution of the related nonlinear, two-boundary-values problem is compared with previous experimental results which give the luminal cross-sectional area (from two tubes), and the area of the mid-cross-section (from a third tube).