Orientation and size-dependent mechanical modulation within individual secondary osteons in cortical bone tissue.

Anisotropy is one of the most peculiar aspects of cortical bone mechanics; however, its anisotropic mechanical behaviour should be treated only with strict relationship to the length scale of investigation. In this study, we focus on quantifying the orientation and size dependence of the spatial mechanical modulation in individual secondary osteons of bovine cortical bone using nanoindentation. Tests were performed on the same osteonal structure in the axial (along the long bone axis) and transverse (normal to the long bone axis) directions along arrays going radially out from the Haversian canal at four different maximum depths on three secondary osteons. Results clearly show a periodic pattern of stiffness with spatial distance across the osteon. The effect of length scale on lamellar bone anisotropy and the critical length at which homogenization of the mechanical properties occurs were determined. Further, a laminate-composite-based analytical model was applied to the stiffness trends obtained at the highest spatial resolution to evaluate the elastic constants for a sub-layer of mineralized collagen fibrils within an osteonal lamella on the basis of the spatial arrangement of the fibrils. The hierarchical arrangement of lamellar bone is found to be a major determinant for modulation of mechanical properties and anisotropic mechanical behaviour of the tissue.

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response.

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ∼3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ∼6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.

A finite element model of the L4-L5 spinal motion segment: biomechanical compatibility of an interspinous device.

The biomechanical compatibility of an interspinous device, used for the "dynamic stabilization" of a diseased spinal motion segment, was investigated. The behaviour of an implant made of titanium based alloy (Ti6Al4V) and that of an implant made of a super-elastic alloy (Ni-Ti) have been compared. The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitable constitutive laws have been adopted for the annulus fibrosus and for the metal alloys. The model was aimed at simulating the healthy, the nucleotomized and the treated L4-L5 lumbar segment, subjected to compressive force and flexion-extension as well as lateral flexion moments. The computational model has shown that both the implants were able to achieve their main design purpose, which is to diminish the forces acting on the apophyseal joints. Nevertheless, the Ni-Ti implant has shown a more physiological flexural stiffness with respect to the Ti6Al4V implant, which exhibited an excessive stiffness and permanent strains (plastic strains), even under physiological loads. The computational models presented in this paper seems to be a promising tool able to predict the effectiveness of a biomedical device and to select the materials to be used for the implant manufacturing, within an engineering approach to the clinical problem of the spinal diseases.

An in vitro methodology for evaluating the mechanical properties of aortic vascular prostheses.

The main problem in the replacement of pathological segments of the aorta with vascular prostheses consists of matching the fluid admittance of the host artery and the graft. This mismatch results from the different compliance between natural and prosthetic vessels and from the plastic dilatation of the prosthesis diameter that occurs after implantation. An experimental procedure was set up for evaluating the mechanical properties of aortic vascular prostheses. An MTS 858 MiniBionix testing machine was equipped with a purposely designed testing apparatus, which allows loading a ring-shaped prosthesis specimen with forces that can be related easily to the transmural pressure acting on the prostheses in vivo. The reference pressure waveforms are simulated from a lumped parameter model of the cardiovascular system. Preliminary tests on 3 different (woven, warp knitted, and carbon-coated warp knitted fabric) aortic prostheses point out a good reproducibility of the results. The fabric strongly affects the circumferential elasticity and the dimensional stability of the graft. Simulation of hypertension promotes larger diameter dilatation and reduction in compliance. Agreement between in vitro and clinical diameter measurements has been assessed for 8 prosthesis samples and found to be adequate. This method is thus a potentially useful means for preclinical evaluation of compliance of vascular prostheses for the purpose of matching to native vessels.

A discrete-time nonlinear Wiener model for the relaxation of soft biological tissues.

The present paper is devoted to introducing discrete-time models for the relaxation function of soft biological tissues. Discrete-time models are suitable for the analysis of sampled data and for digital simulations of continuous systems. Candidate models are searched for within both linear ARX structures and nonlinear Wiener models, consisting of an ARX element followed in cascade by a polynomial function. Both these discrete-time models correspond to sampling continuous-time exponential function series, thus preserving physical interpretation for the proposed relaxation model. The estimation data set consists of normalized stress relaxation curves drawn from experiments performed on samples of bovine pericardium. The normalized relaxation curves are found to be almost insensitive to both the magnitude of strain and the loading direction, and so a single model for the whole relaxation curves is assumed. In order to identify the parameters of the Wiener model an iterative algorithm is purposely designed. Over the ARX one, the nonlinear Wiener model exhibits higher capability of representing the experimental relaxation curves over the whole observation period. The stability of the solution for the iterative algorithm is assessed, and hence physical interpretation as material properties can be attached to the parameters of the nonlinear model. Suitable features of the Wiener model for computational application are also briefly presented.