Postfailure compressive behavior of tibial trabecular bone in three anatomic directions

Abstract

To obtain information describing the postfailure behavior of human proximal tibial trabecular bone, cube specimens of bone were mechanically tested in compression beyond the point of failure. Tests were performed in the three anatomic directions, plots of stress versus strain were obtained, and measures to describe the stress-strain relations before, during, and after failure were defined. These measures included elastic modulus, strength, postfailure slope, strain during maximum stress, and first postfailure minimum stress. For each anatomic direction, analyses were performed to correlate these parameters with ash density. Each of these measures was significantly correlated with ash density at the p < 0.05 level for all test directions, except for postfailure slope, which was correlated in the mediolateral and superior-inferior directions, and strain during maximum stress, which was correlated only in the superior-inferior direction. The data from this study enable trilinear stress-strain relations to be estimated for proximal tibial trabecular bone of various densities, and can serve as a first step toward modeling the behavior of trabecular bone before, during, and after failure.

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

“…To characterise the mechanical properties of trabecular bone previous studies have primarily relied on uniaxial compression testing of representative samples of trabecular bone (Goldstein 1987;Røhl et al 1991;Kopperdahl and Keaveny 1998;Morgan and Keaveny 2001;Keaveny et al 1993;Keyak et al 1996). Few studies have performed confined compression testing Linde and Hvid 1989;Charlebois et al 2010a) or multiaxial compression testing (Fenech and Keaveny 1999;Keaveny et al 1999;Rincon-Kohli and Zysset 2009) although trabecular bone is naturally constrained in vivo by the surrounding 6 cortex.…”

Incorporating in vivo fall assessments in the simulation of femoral fractures with finite element models

“…Other limitations were related to the mechanical behavior of elements, as we did not include asymmetric yielding (for example the Drucker Pragner criterion [19,29]), strain rate dependent behavior [33], or anisotropic behavior [34]. Furthermore, simulation of a realistic fall impact load should involve applying a dynamic impact load instead of a quasi-static load.…”

Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling

“…Let p e denote the cubical volume element derived from an image voxel p . The ash density $${\rho _{{\rm{ash}}}}( p )$$ at the voxel p and the elastic modulus $$E( {{p_{\rm{e}}}} )$$, maximum stress $${S_{{\rm{max}}}}( {{p_{\rm{e}}}} )$$, and saturation stress $${\sigma _{{\rm{min}}}}( {{p_{\rm{e}}}} )$$ at the element p e are defined as follows: 40 $$\begin{equation}{\rho _{{\rm{ash}}}} \left( p \right) = 0.0633 + 0.887{\rho _{{\rm{CHA}}}}\left( p \right),\ \end{equation}$$ $$\begin{equation} E\left( {{p_{\rm{e}}}} \right) = 21700{\left( {{\rho _{{\rm{ash}}}}\left( p \right)} \right)^{2.07}},\ \end{equation}$$ $$\begin{equation} {S_{{\rm{max}}}} \left( {{p_{\rm{e}}}} \right) = 137{\left( {{\rho _{{\rm{ash}}}}\left( p \right)} \right)^{1.88}},\ \end{equation}$$ …”