An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Fabric-mechanical property relationships of trabecular bone allografts are altered by supercritical CO2 treatment and gamma sterilization

Tissue grafts are implanted in orthopedic surgery every day. In order to minimize infection risk, bone allografts are often delipidated with supercritical CO2 and sterilized prior to implantation. This treatment may, however, impair the mechanical behavior of the bone graft tissue. The goal of this study was to determine clinically relevant mechanical properties of treated/sterilized human trabecular bone grafts, e.g. the apparent modulus, strength, and the ability to absorb energy during compaction. They were compared with results of identical experiments performed previously on untreated/fresh frozen human trabecular bone from the same anatomical site (Charlebois, 2008). We tested the hypothesis that the morphology–mechanical property relationships of treated cancellous allografts are similar to those of fresh untreated bone. The morphology of the allografts was determined by μCT. Subsequently, cylindrical samples were tested in unconfined and confined compression. To account for various morphologies, the experimental data was fitted to phenomenological mechanical models for elasticity, strength, and dissipated energy density based on bone volume fraction (BV/TV) and the fabric tensor determined by MIL. The treatment/sterilization process does not appear to influence bone graft stiffness. However, strength and energy dissipation of the bone grafts were found to be significantly reduced by 36% to 47% and 66% to 81%, respectively, for a broad range of volume fraction (0.14 < BV/TV < 0.39) and degree of anisotropy (1.24 < DA < 2.18). Since the latter properties are strongly dominated by BV/TV, the clinical consequences of this reduction can be compensated by using grafts with lower porosity. The data of this study suggests that an increase of 5–10% in BV/TV is sufficient to compensate for the reduced post-yield mechanical properties of treated/sterilized bone in monotonic compression. In applications where graft stiffness needs to be matched and strength is not a concern, treated allograft with the same BV/TV as an appropriate fresh bone graft may be used.

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R2 = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.

Continuum damage interactions between tension and compression in osteonal bone

Skeletal diseases such as osteoporosis impose a severe socio-economic burden to ageing societies. Decreasing mechanical competence causes a rise in bone fracture incidence and mortality especially after the age of 65 y. The mechanisms of how bone damage is accumulated under different loading modes and its impact on bone strength are unclear. We hypothesise that damage accumulated in one loading mode increases the fracture risk in another. This study aimed at identifying continuum damage interactions between tensile and compressive loading modes. We propose and identify the material constants of a novel piecewise 1D constitutive model capable of describing the mechanical response of bone in combined tensile and compressive loading histories. We performed several sets of loading–reloading experiments to compute stiffness, plastic strains, and stress-strain curves. For tensile overloading, a stiffness reduction (damage) of 60% at 0.65% accumulated plastic strain was detectable as stiffness reduction of 20% under compression. For compressive overloading, 60% damage at 0.75% plastic strain was detectable as a stiffness reduction of 50% in tension. Plastic strain at ultimate stress was the same in tension and compression. Compression showed softening and tension exponential hardening in the post-yield regime. The hardening behaviour in compression is unaffected by a previous overload in tension but the hardening behaviour in tension is affected by a previous overload in compression as tensile reloading strength is significantly reduced. This paper demonstrates how damage accumulated under one loading mode affects the mechanical behaviour in another loading mode. To explain this and to illustrate a possible implementation we proposed a theoretical model. Including such loading mode dependent damage and plasticity behaviour in finite element models will help to improve fracture risk analysis of whole bones and bone implant structures.

New aspects of airway mechanics in pre-term infants

High-frequency respiratory impedance data measured noninvasively by the high-speed interrupter technique (HIT), particularly the first antiresonance frequency (f(ar,1)), is related to airway wall mechanics. The aim of this study was to evaluate the feasibility and repeatability of HIT in unsedated pre-term infants, and to compare values of f(ar,1) from 18 pre-term (post-conceptional age 32-37 weeks, weight 1,730-2,910 g) and 18 full-term infants (42-47 weeks, 3,920-5,340 g). Among the pre-term infants, there was good short-term repeatability of f(ar,1) within a single sleep epoch (mean (sd) coefficient of variance: 8 (1.7)%), but 95% limits of agreement for repeated measures of f(ar,1) after 3-8 h were relatively wide (-41 Hz; 37 Hz). f(ar,1) was significantly lower in pre-term infants (199 versus 257 Hz), indicating that wave propagation characteristics in pre-term airways are different from those of full-term infants. The present authors suggest that this is consistent with developmental differences in airway wall structure and compliance, including the influence of the surrounding tissue. Since flow limitation is determined by wave propagation velocity and airway cross-sectional area, it was hypothesised that the physical ability of the airways to carry large flows is fundamentally different in pre-term than in full-term infants.

Estimation of heart weight by post-mortem cardiac magnetic resonance imaging

Introduction The aim of this study was to determine which single measurement on post-mortem cardiac MR reflects actual heart weight as measured at autopsy, assess the intra- and inter-observer reliability of MR measurements, derive a formula to predict heart weight from MR measurements and test the accuracy of the formula to prospectively predict heart weight. Materials and methods 53 human cadavers underwent post-mortem cardiac MR and forensic autopsy. In Phase 1, left ventricular area and wall thickness were measured on short axis and four chamber view images of 29 cases. All measurements were correlated to heart weight at autopsy using linear regression analysis. In Phase 2, single left ventricular area measurements on four chamber view images (LVA_4C) from 24 cases were used to predict heart weight at autopsy based on equations derived during Phase 1. Intra-class correlation coefficient (ICC) was used to determine inter- and intra-reader agreement. Results Heart weight strongly correlates with LVA_4C (r=0.78 M; p<0.001). Intra-reader and inter-reader reliability was excellent for LVA_4C (ICC=0.81–0.91; p<0.001 and ICC=0.90; p<0.001 respectively). A simplified formula for heart weight ([g]≈LVA_4C [mm2]×0.11) was derived based on linear regression analysis. Conclusions This study shows that single circumferential area measurements of the left ventricle in the four chamber view on post-mortem cardiac MR reflect actual heart weight as measured at autopsy. These measurements yield an excellent intra- and inter-reader reliability and can be used to predict heart weight prior to autopsy or to give a reasonable estimate of heart weight in cases where autopsy is not performed.