Identification of material parameters based on Mohr-Coulomb failure criterion for bisphosphonate treated canine vertebral cancellous bone

Abstract

Nanoindentation has been widely used to study bone tissue mechanical properties. The common method and equations for analyzing nanoindentation, developed by Oliver and Pharr, are based on the assumption that the material is linearly elastic. In the present study, we adjusted the constraint of linearly elastic behavior and use nonlinear finite element analysis to determine the change in cancellous bone material properties caused by bisphosphonate treatment, based on an isotropic form of the Mohr–Coulomb failure model. Thirty-three canine lumbar vertebrae were used in this study. The dogs were treated daily for 1 year with oral doses of alendronate, risedronate, or saline vehicle at doses consistent, on a mg/kg basis, to those used clinically for the treatment of post-menopausal osteoporosis. Two sets of elastic modulus and hardness values were calculated for each specimen using the Continuous Stiffness Measurement (CSM) method (ECSM and HCSM) from the loading segment and the Oliver–Pharr method (EO–P and HO–P) from the unloading segment, respectively. Young's modulus (EFE), cohesion (c), and friction angle (ϕ) were identified using a finite element model for each nanoindentation. The bone material properties were compared among groups and between methods for property identification. Bisphosphonate treatment had a significant effect on several of the material parameters. In particular, Oliver–Pharr hardness was larger for both the risedronate- and alendronate-treated groups compared to vehicle and the Mohr–Coulomb cohesion was larger for the risedronate-treated compared to vehicle. This result suggests that bisphosphonate treatment increases the hardness and shear strength of bone tissue. Shear strength was linearly predicted by modulus and hardness measured by the Oliver–Pharr method (r2 = 0.99). These results show that bisphosphonate-induced changes in Mohr–Coulomb material properties, including tissue shear cohesive strength, can be accurately calculated from Oliver–Pharr measurements of Young's modulus and hardness.