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.

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.

Tensile and compressive behaviour of the bovine periodontal ligament.

The mechanical response of the bovine periodontal ligament (PDL) subjected to uniaxial tension and compression is reported. Several sections normal to the longitudinal axis of bovine incisors and molars were extracted from different depths. Specimens with dimensions 10 x 5 x 2 mm including dentine, PDL and alveolar bone were obtained from these sections. Scanning electron microscopy suggested a strong similarity between the bovine PDL and the human PDL microstructure described in the literature. The prepared specimens were tested in a custom made uniaxial testing machine. They were clamped on their bone and dentine extremities and immersed in a saline solution at 37 degrees C. Stress-strain curves indicated that the PDL is characterized by a non-linear and time-dependent mechanical behaviour with the typical features of collagenous soft tissues. The curves exhibited hysteresis and preconditioning effects. The mechanical parameters evaluated in tension were maximum tangent modulus, strength, maximizer strain and strain energy density. For the molars, all these parameters increased with depth except for the apical region. For the incisors, all parameters increased with depth except ultimate strain which decreased. It was assumed that collagen fibre density and orientation were responsible for these findings.

Experimental and computational approach for the evaluation of the biomechanical effects of dental bridge misfit.

Dental bridges supported by osseointegrated implants are commonly used to treat the partially or completely edentulous jaw. The bridges are manufactured in metal alloy using a sequence of technological steps which well match the requirement to get custom overstructures but does not guarantee geometrical and dimensional tolerances. Dentists often experience that a perfect fit of the bridge with the abutments is almost impossible to achieve. When a misfitting bridge is forced on the abutments, deformations may occur inducing a permanent preload at the fixture-bone interface and the greater the misfit the greater is the preload and the risk of implant failure. This work gives an evaluation of the biomechanical effects induced by a misfitting bridge when forced on two supporting dental implants. The strains induced in the bridge have been measured using two purposely designed and fabricated experimental devices allowing different types of misfit. FEM 3D models of the bridge and of the bridge anchored to the bone by implants have been developed. The former has been validated by simulating the same loading conditions as in the experimental tests and comparing the bridge strains. Both models have been used for the evaluation of the stress induced in the bridge and at the fixture-bone interface by bridge length errors. The results show that the method may help to estimate the stress distribution in the bridge and bone as a consequence of different dental bridge misfits.

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.

Lumbar dura mater biomechanics: experimental characterization and scanning electron microscopy observations.

UNLABELLED: There is no consensus about the anatomical structure of human dura mater. In particular, the orientation of collagen fibers, which are responsible for biomechanical behavior, is still controversial. The aim of this work was to evaluate the mechanical properties and the microstructure of the lumbar dura mater. We performed experimental mechanical characterization in longitudinal and circumferential directions and a scanning electron microscopy observation of the tissue. Specimens of human dura mater were removed from the dorsal-lumbar region (T12-L4/L5) of six subjects at autopsy; specimens of bovine dorsal-lumbar dura mater were obtained from two animals at slaughter. Human and bovine tissues both exhibited stronger tensile strength and stiffness in the longitudinal than in the circumferential direction. Scanning electron microscopy observations of dura mater showed that the collagen fibers are mainly oriented in a longitudinal direction, which accounts for its stronger tensile strength in this direction. We conclude that dura mater has a different mechanical response in the two directions investigated because the fiber orientation is predominantly longitudinal. IMPLICATIONS: In this experimental work, we studied the structural and functional relationship of human lumbar dura mater. We performed mechanical tests and microscopic observations on dura mater samples. The results show that the dura mater is mainly composed of longitudinally oriented collagen fibers, which account for higher tissue resistance in this direction.

Nonfatal methazolamide-induced aplastic anemia.

An 83-year-old man developed nonfatal aplastic anemia after taking methazolamide for three months. We made a diagnosis of methazolamide-induced aplastic anemia, discontinued all medication, gave the patient platelet and red blood cell transfusions, and treated him with oxymetholone. Approximately four months after initiation of treatment, the patient felt well, and he is currently receiving packed red blood cell transfusions every three weeks.