Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage.

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.

Length-scale dependency of biomimetic hard-soft composites.

Biomimetic composites are usually made by combining hard and soft phases using, for example, multi-material additive manufacturing (AM). Like other fabrication methods, AM techniques are limited by the resolution of the device, hence, setting a minimum length scale. The effects of this length scale on the performance of hard-soft composites are not well understood. Here, we studied how this length scale affects the fracture toughness behavior of single-edge notched specimens made using random, semi-random, and ordered arrangements of the hard and soft phases with five different ratios of hard to soft phases. Increase in the length scale (40 to 960 µm) was found to cause a four-fold drop in the fracture toughness. The effects of the length scale were also modulated by the arrangement and volumetric ratio of both phases. A decreased size of the crack tip plastic zone, a crack path going through the soft phase, and highly strained areas far from the crack tip were the main mechanisms explaining the drop of the fracture toughness with the length scale.

Radiation endurance in Al2O3 nanoceramics.

The lack of suitable materials solutions stands as a major challenge for the development of advanced nuclear systems. Most issues are related to the simultaneous action of high temperatures, corrosive environments and radiation damage. Oxide nanoceramics are a promising class of materials which may benefit from the radiation tolerance of nanomaterials and the chemical compatibility of ceramics with many highly corrosive environments. Here, using thin films as a model system, we provide new insights into the radiation tolerance of oxide nanoceramics exposed to increasing damage levels at 600 °C -namely 20, 40 and 150 displacements per atom. Specifically, we investigate the evolution of the structural features, the mechanical properties, and the response to impact loading of Al2O3 thin films. Initially, the thin films contain a homogeneous dispersion of nanocrystals in an amorphous matrix. Irradiation induces crystallization of the amorphous phase, followed by grain growth. Crystallization brings along an enhancement of hardness, while grain growth induces softening according to the Hall-Petch effect. During grain growth, the excess mechanical energy is dissipated by twinning. The main energy dissipation mechanisms available upon impact loading are lattice plasticity and localized amorphization. These mechanisms are available in the irradiated material, but not in the as-deposited films.

Poroelastic response of articular cartilage by nanoindentation creep tests at different characteristic lengths.

Nanoindentation is an experimental technique which is attracting increasing interests for the mechanical characterization of articular cartilage. In particular, time dependent mechanical responses due to fluid flow through the porous matrix can be quantitatively investigated by nanoindentation experiments at different penetration depths and/or by using different probe sizes. The aim of this paper is to provide a framework for the quantitative interpretation of the poroelastic response of articular cartilage subjected to creep nanoindentation tests. To this purpose, multiload creep tests using spherical indenters have been carried out on saturated samples of mature bovine articular cartilage achieving two main quantitative results. First, the dependence of indentation modulus in the drained state (at equilibrium) on the tip radius: a value of 500 kPa has been found using the large tip (400 µm radius) and of 1.7 MPa using the smaller one (25 µm). Secon, the permeability at microscopic scale was estimated at values ranging from 4.5×10(-16) m(4)/N s to 0.1×10(-16) m(4)/N s, from low to high equivalent deformation. Consistently with a poroelastic behavior, the size-dependent response of the indenter displacement disappears when characteristic size and permeability are accounted for. For comparison purposes, the same protocol was applied to intrinsically viscoelastic homogeneous samples of polydimethylsiloxane (PDMS): both indentation modulus and time response have been found size-independent.

Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage.

Articular cartilage is a soft hydrated tissue that facilitates proper load transfer in diarthroidal joints. The mechanical properties of articular cartilage derive from its structural and hierarchical organization that, at the micrometric length scale, encompasses three main components: a network of insoluble collagen fibrils, negatively charged macromolecules and a porous extracellular matrix. In this work, a constituent-based constitutive model for the simulation of nanoindentation tests on articular cartilage is presented: it accounts for the multi-constituent, non-linear, porous, and viscous aspects of articular cartilage mechanics. In order to reproduce the articular cartilage response under different loading conditions, the model considers a continuous distribution of collagen fibril orientation, swelling, and depth-dependent mechanical properties. The model's parameters are obtained by fitting published experimental data for the time-dependent response in a stress relaxation unconfined compression test on adult bovine articular cartilage. Then, model validation is obtained by simulating three independent experimental tests: (i) the time-dependent response in a stress relaxation confined compression test, (ii) the drained response of a flat punch indentation test and (iii) the depth-dependence of effective Poisson's ratio in a unconfined compression test. Finally, the validated constitutive model has been used to simulate multiload spherical nanoindentation creep tests. Upon accounting for strain-dependent tissue permeability and intrinsic viscoelastic properties of the collagen network, the model accurately fits the drained and undrained curves and time-dependent creep response. The results show that depth-dependent tissue properties and glycosaminoglycan-induced tissue swelling should be accounted for when simulating indentation experiments.

Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation.

PURPOSE: The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. METHODS: Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. RESULTS: The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). CONCLUSIONS: The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue.

A finite element model was developed for numerical simulations of nanoindentation tests on cortical bone. The model allows for anisotropic elastic and post-yield behavior of the tissue. The material model for the post-yield behavior was obtained through a suitable linear transformation of the stress tensor components to define the properties of the real anisotropic material in terms of a fictitious isotropic solid. A tension-compression yield stress mismatch and a direction-dependent yield stress are allowed for. The constitutive parameters are determined on the basis of literature experimental data. Indentation experiments along the axial (the longitudinal direction of long bones) and transverse directions have been simulated with the purpose to calculate the indentation moduli and the tissue hardness in both the indentation directions. The results have shown that the transverse to axial mismatch of indentation moduli was correctly simulated regardless of the constitutive parameters used to describe the post-yield behavior. The axial to transverse hardness mismatch observed in experimental studies (see, for example, Rho et al. [1999, "Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation," J. Biomed. Mater. Res., 45, pp. 48-54] for results on human tibial cortical bone) can be correctly simulated through an anisotropic yield constitutive model. Furthermore, previous experimental results have shown that cortical bone tissue subject to nanoindentation does not exhibit piling-up. The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.

Calibration issues for nanoindentation experiments: direct atomic force microscopy measurements and indirect methods.

This article discusses calibration issues for shallow depth nanoindentation experiments with Berkovich tips with respect to the accurate measurement of the diamond area function (DAF). For this purpose, two different calibration procedures are compared: (i) the direct measurement of the DAF through atomic force microscopy (AFM) imaging of the Berkovich tip at shallow depth and (ii) a novel indirect calibration method based on an iterative robust and converging scheme in which both reduced modulus and indentation hardness are simultaneously used. These results are obtained by indentation measurements on a standard specimen of fused silica, performed in the 0.5-200 mN load range with a Berkovich indenter. Direct tip shape measurements were carried out through different AFM methods. Comparisons with the standard indirect calibration procedure are also reported. For both the indirect calibration procedures a sensitivity and convergence study is presented.

Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects.

The aim of this work is to assess the fracture risk prediction of the cancellous bone in the body of a lumbar vertebra when the mechanical parameters of the bone, i.e. stiffness, porosity, and strength anisotropy, of elderly and osteoporotic subjects are considered. For this purpose, a non-linear three-dimensional continuum-based finite element model of the lumbar functional spinal unit L4-L5 was created and strength analyses of the spongy tissue of the vertebral body were carried out. A fabric-dependent strength criterion, which accounts for the micro-architecture of the cancellous bone, based on histomorphometric analyses was used. The strength analyses have shown that the cancellous bone of none of the subject types undergoes failure under loading applied during normal daily life like axial compression; however, bone failure occurs for the osteoporotic segment, subjected to a combination of the compression preloading and moments in the sagittal or in the frontal plane, which are conditions that may not be considered to occur 'daily'. In particular, critical stress conditions are met because of the high porosity values in the horizontal direction within the cancellous bone. The computational approach presented in the paper can potentially predict the material fracture risk of the cancellous bone in the vertebral body and it may be usefully employed to draw failure maps representing, for a given micro-architecture of the spongy tissue, the critical loading conditions (forces and moments) that may lead to such a risk. This approach could be further developed in order to assess the effectiveness of biomedical devices within an engineering approach to the clinical problem of the spinal diseases.

A mechanical comparison of high-flexion and conventional total knee arthroplasty.

The question addressed in this study was whether high-flexion total knee arthroplasty (TKA) designs improve the mechanical behaviour of TKAs in high flexion and whether they maintain the mechanical performance of conventional TKAs at normal flexion angles. A finite element study was performed in which the mechanical behaviour of the conventional Sigma RP and the new high-flexion Sigma RP-F were compared, during a dynamic simulation of a high-flexion squatting activity. Forces, stresses, and contact positions were calculated during different stages of the simulations. In general, higher stresses were found with larger flexion angles for both designs. Mechanical parameters were similar in normal flexion. In high flexion, lower stress and deformation values were found for the high-flexion Sigma RP-F, except for the contact stress at the post of the insert. This study confirms that a high-flexion design can improve mechanical behaviour at high-flexion without changing the performance in normal flexion. Hence, although a high-flexion TKA may show a similar or better performance in comparison with a conventional TKA, high-flexion activities still cause an increase in the implant stress levels. Therefore, the patient's demand for large flexion angles may reduce the longevity of TKA implants.

Modeling and mechanobiology of cerebral aneurysms.

The purpose of this work is to review the computational models of the adaptive behavior of the cerebral vascular wall aimed at simulating aneurysm formation and enlargement. Cerebral aneurysms are localized abnormal enlargements of the intracranial arterial vessels. The origin of this pathology is still unclear: however, aneurysm formation is thought to be the result of interplay between biomechanical properties of the vessel wall and their possible changes, such as adaptive response to mechanical stimuli. Recently, different computational approaches were suggested in the literature aiming to describe the mechanobiology of the cerebral vascular wall. Most of the computational adaptive models showed a common approach for the geometrically non-linear kinematic description of the phenomenon, whilst the constitutive laws defining the rates of growth variables may differ considerably according to the specific phenomenon considered. These studies allowed the reproduction of some peculiar aspects of aneurysm mechanobiology; however, continued interdisciplinary research is mandatory for a better understanding of the mechanisms involved in the evolution of cerebral aneurysms.

An axisymmetric computational model of skin expansion and growth.

Skin expansion is the principal technique used in plastic surgery to repair large cutaneous defects, typically after tumour removal, burn care, craniofacial surgery and post-mastectomy breast reconstruction. It allows a gain of new tissue by means of gradual expansion of a prosthesis, surgically implanted beneath the patient's skin. Nevertheless, wide clinical use is not supported by a deep quantitative knowledge of the phenomena occurring during the expansion. A finite element model of the skin expansion was developed to evaluate the stresses and the strains of the skin due to the expander inflation and validated by proper in vitro experiments; furthermore, a growth model based on the mechanical stimulus was implemented to estimate the skin area gain. The developed computational approach, composed of the skin expansion model interaction and the growth law, proved its validity to investigate skin expansion phenomena: its use suggests a new predictive tool to optimize clinical procedures and the expander devices' design.

A constituent-based model for the nonlinear viscoelastic behavior of ligaments.

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.

A discrete-time approach to the formulation of constitutive models for viscoelastic soft tissues.

This paper presents a novel approach to constitutive modeling of viscoelastic soft tissues. This formulation combines an anisotropic strain energy function, accounting for preferred material directions, to define the elastic stress-strain relationship, and a discrete time black-box dynamic model, borrowed from the theory of system identification, to describe the time-dependent behavior. This discrete time formulation is straightforwardly oriented to the development of a recursive time integration scheme that calculates the current stress state by using strain and stress values stored at a limited number of previous time instants. The viscoelastic model and the numerical procedure are assessed by implementing two numerical examples, the simulation of a uniaxial tensile test and the inflation of a thin tube. Both simulations are performed using parameter values based on previous experiments on preserved bovine pericardium. Parameters are then adjusted to investigate the sensitivity of the model. The hypotheses the model relies upon are discussed and the main limitations are stated.

Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons--a computational study from molecular to microstructural level.

Experimental studies on immature tendons have shown that the collagen fibril net is discontinuous. Manifold evidences, despite not being conclusive, indicate that mature tissue is discontinuous as well. According to composite theory, there is no requirement that the fibrils should extend from one end of the tissue to the other; indeed, an interfibrillar matrix with a low elastic modulus would be sufficient to guarantee the mechanical properties of the tendon. Possible mechanisms for the stress-transfer involve the interfibrillar proteoglycans and can be related to the matrix shear stress and to electrostatic non-covalent forces. Recent studies have shown that the glycosaminoglycans (GAGs) bound to decorin act like bridges between contiguous fibrils connecting adjacent fibril every 64-68 nm; this architecture would suggest their possible role in providing the mechanical integrity of the tendon structure. The present paper investigates the ability of decorin GAGs to transfer forces between adjacent fibrils. In order to test this hypothesis the stiffness of chondroitin-6-sulphate, a typical GAG associated to decorin, has been evaluated through the molecular mechanics approach. The obtained GAG stiffness is piecewise linear with an initial plateau at low strains (<800%) and a high stiffness region (3.1 x 10(-11)N/nm) afterwards. By introducing the calculated GAG stiffness in a multi-fibril model, miming the relative mature tendon architecture, the stress-strain behaviour of the collagen fibre was determined. The fibre incremental elastic modulus obtained ranges between 100 and 475 MPa for strains between 2% and 6%. The elastic modulus value depends directly on the fibril length, diameter and inversely on the interfibrillar distance. In particular, according to the obtained results, the length of the fibril is likely to play the major role in determining stiffness in mature tendons.

Effects of metal-inlay thickness in polyethylene cups with metal-on-metal bearings.

A way to prevent polyethylene wear in total hip replacements is to use metal-on-metal bearings. The cup design of these bearings may be a metal inlay in a polyethylene cup. However, these metal inlays are relatively thin and may deform on loading. The purpose of the current study was to determine whether these potential problems become actual for a realistic range of metal-inlay components having a thickness greater than 1 mm. For this purpose, the effects of thickness variation of a metal inlay in an ultrahigh molecular weight polyethylene cup were determined using three-dimensional finite element techniques. The results showed no indications for jamming of the bearing assuming a realistic inlay thickness (3-5 mm), even with a small clearance (25 microm). The metal inlay acted rigidly beyond a thickness of approximately 5 mm. Metal inlays thinner than 1.5 mm led to a considerable increase in contact area and a reduction in contact peak stress, which may be beneficial for the bearing performance. Currently, these thin liners have too many unknown characteristics and therefore the current authors recommend using rigid metal liners that have a thickness greater than 5 mm.

Quantitative evaluation of the prosthetic head damage induced by microscopic third-body particles in total hip replacement.

The increase of the femoral head roughness in artificial hip joints is strongly influenced by the presence of abrasive particulate entrapped between the articulating surfaces. The aim of the present study is to evaluate the dependence of such damage on the geometry of the particles entrapped in the joint, with reference to the UHMWPE/chrome-cobalt coupling. Five chrome-cobalt femoral heads and their coupled UHMWPE acetabular cups, retrieved at revision surgery after a short period of in situ functioning, have been investigated for the occurrence of third-body damage. This was found on all the prosthetic heads, where the peak-to-valley height of the scratches, as derived from profilometry evaluations, ranged from 0.3-1.3 microm. The observed damage has been divided into four classes, related to the particle motion while being embedded into the polymer. Two kinds of particle morphology have been studied, spherical and prismatic, with size ranging from 5-50 microm. In order to provide an estimation of the damage induced by such particles, a finite element model of the third-body interaction was set up. The peak-to-valley height of the impression due to the particle indentation on the chrome-cobalt surface is assumed as an index of the induced damage. The calculated values range from 0.1-0.5 microm for spherical particles of size ranging from 10-40 microm. In the case of prismatic particles, the peak-to-valley height can reach 1.3 microm and depends both on the size and width of the particle's free corner, indenting the chrome-cobalt. As an example, a sharp-edged particle of size 30 microm can induce on the chrome-cobalt an impression with peak-to-valley height of 0.75 microm, when embedded into the polyethylene with a free edge of 5 microm facing the metallic surface. Negligible damage is induced, if a free edge of 7.5 microm is indenting the counterface. Our findings offer new support to the hypothesis that microscopic third-body particles are capable of causing increased roughening of the femoral head and provide a quantitative evaluation of the phenomenon.

Sensitivity Analysis and Optimal Shape Design for Bone-Prosthesis Interfaces in a Femoral Head Surface Replacement.

A numerical optimization procedure has been applied for the shape optimal design of a femoral head surface replacement. The failure modes of the prosthesis that were considered in the formulation of the objective functions concerned the interface stress magnitude and the bone remodelling activity beneath the implant. In order to find a compromising solution between different requirements demanded by the two objective functions, a two step optimization procedure has been developed. Through step 1 the minimization of interface stress was achieved, through step 2 the minimization of bone remodelling was achieved with constraints on interface stresses. The results obtained provided an optimal design that generates limited bone remodelling activity with controlled interface stress distribution. The computational procedure was based on the application of the finite element method, linked to a mathematical programming package and a design sensitivity analysis package.