0031 - Non-linear Behavior of Trabecular Bone at Small Strains

Introduction: Study of the non-linear behavior of trabecular bone at habitual “small” strains (<0.4% strain [1]) is vital for further investigation of the cellular response to mechanical loading of bone tissue, in vivo energy dissipation mechanisms, implant interface mechanics, and biomechanical constitutive modeling. Perceptions of the initial non-linearity in the stressstrain curve have shifted as testing protocols have changed. Traditional platens methods produced curves with an initial concave toe that is recognized as an end-artifact [2]. Recent protocols designed to eliminate this artifact have reported an initial linear region [3,4], but upon closer investigation we have noticed that even at strains below 0.4%, trabecular bone exhibits a subtle but highly significant convex non-linearity [5]. Consequently, the value of the elastic modulus may depend on the strain range chosen for the linear fit, and if an offset method is used to define the yield point [3,6], so may values of yield stress and strain. This can confound comparisons of these properties between bone from different anatomic sites or of different densities and may obscure subtle effects of diseases such as osteoporosis. More importantly, the nonlinearity, should it be substantial, may motivate a fundamental paradigm shift in the characterization of the stress-strain curve for trabecular bone. The goal of this study was to characterize this initial non-linear behavior of trabecular bone from a variety of anatomic sites. Our specific objectives were to: 1) quantify the extent of the non-linearity in bone from a range of anatomic sites for both tension and compression; and 2) determine how changing the strain range used to define modulus affects the values of modulus and yield properties. From this, a more robust protocol is introduced for characterizing the non-linear elastic stress-strain behavior.