Characterisation of the dynamic compressive mechanical properties of cancellous bone from the human cervical spine

Abstract

A study was undertaken to characterise the mechanical properties of cancellous bone from the human cervical spine. Samples from eight male cadavers (aged 40–79 yr) were subjected to quasi-static and dynamic compression. Results from quasi-static compression tests show that the strength of cancellous bone can be described in terms of density using a power law relationship. It is also observed that the quasi-static mechanical response prior to attainment of the ultimate compressive strength may be approximated by linear elasticity, whereby Young's modulus is expressed as a power function of density. Dynamic tests were performed using an SHPB and the results show that the mechanical properties of fresh bone are rate dependent. The dynamic compressive strength of bone can be characterised by adding a dynamic enhancement factor governed by strain rate, to the static strength which depends on bone density. With the assumption that deformation prior to attainment of the dynamic strength is recoverable, a constitutive relationship comprising two terms can also be established; the first component defines quasi-static linear elasticity, which is a function of bone density, and the second corresponds to nonlinear viscoelasticity, which is independent of bone density. Furthermore, if it is assumed that the mechanical properties of bone are isotropic, the proposed one-dimensional nonlinear viscoelastic description can be expanded to a three-dimensional constitutive relationship in tensor form. Although it is recognised that cancellous bone is not isotropic, the proposed isotropic model is expected to constitute a useful initial approximation for numerical modelling of cervical spine response to rapid loads and trauma.