An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence
Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.
KeywordsTrabecular bone Pressure-dependent yielding Hydrostatic compression Confined compression microCT finite element analysis Vertebral subsidence Crushable foam
Unable to display preview. Download preview PDF.
- Chevalier Y, Charlebois M, Pahr D, Varga P, Heini P, Schneider E, Zysset P (2008) A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads. Comput Method Biomech 11(5): 477–487. doi: 10.1080/10255840802078022 CrossRefGoogle Scholar
- Drucker DC, Prager W (1951) Soil mechanics and plastic analysis or limit design. Division of Applied Mathematics, Brown University, Brown University. Division of Applied, Mathematics United States. Office of Naval, ResearchGoogle Scholar
- Harrison NM, McDonnell P, Mullins L, Wilson N, O’Mahoney D, McHugh PE (2012) Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach. Biomech Model Mechanobiol 1–17. doi: 10.1007/s10237-012-0394-7
- Oxland TR, Grant JP, Dvorak MF, Fisher CG (2003) Effects of endplate removal on the structural properties of the lower lumbar vertebral bodies. Spine 28(8): 771–777Google Scholar
- Prendergast PJ, McHugh PE (2004) Topics in bio-mechanical engineering. In: Proceeding of the 1st symposium on biomechanical engineering, Ireland. Trinity Centre for Bio-Engineering, pp 58–93Google Scholar
- Reilly DT, Burstein AH (1974) The mechanical properties of cortical bone. J Bone Jt Surg Am 56(5): 1001–1022Google Scholar
- Zysset PK, Curnier A (1996) A 3D damage model for trabecular bone based on fabric tensors. J Biomech 29(12): 1549–1558Google Scholar