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

Abstract

PublisherSpringer-Verlag AbstractInterbody 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 micro-computed 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.

An investigation of the inelastic behaviour of trabecular bone during the press-fit implantation of a tibial component in total knee arthroplasty

“…Highly localised pressures are computed near the bone-implant interface for the CFI plasticity formulation which leads to high levels of localised plastic yielding directly at the interface; hence, lower stresses and pressures are computed further into the trabecular material. Although the present study focuses on PU, a synthetic trabecular analogue material, the ability of a CFI plasticity formulation to capture the multiaxial pressure dependent plasticity of natural trabecular bone has previously been observed [14,16]. Highly localised peri-prosthetic plasticity has also been observed experimentally during vertebral fusion device subsidence [16].…”

“…With ever increasing computational power, microstructural based models of macroscale bone-implant applications that include complex non-linear material behaviour, contact conditions and finite deformation may be feasible in the near future. As demonstrated by , the explicit modelling of the trabecular bone microstructure will still require plastic yielding or damage at a material level in order to provide realistic macroscopic behaviour [16].…”

“…However, such microstructural models are generally limited to small specimens with limited material behaviour, contact conditions and deformation due to the high computational expense. Using both microstructural based models and continuum based models, a recent study by the authors demonstrated that the apparent level pressure-dependent yielding of trabecular bone occurs as a result of localised stress concentrations and yielding in the trabeculae at a microstructural level without the requirement that the localised yield is pressure dependent [16]. With ever increasing computational power, microstructural based models of macroscale bone-implant applications that include complex non-linear material behaviour, contact conditions and finite deformation may be feasible in the near future.…”

“…Although the present study focuses on PU, a synthetic trabecular analogue material, the ability of a CFI plasticity formulation to capture the multiaxial pressure dependent plasticity of natural trabecular bone has previously been observed [14,16]. Highly localised peri-prosthetic plasticity has also been observed experimentally during vertebral fusion device subsidence [16]. Correct prediction of this stress distribution at the bone implant-interface will have implications for device design and in particular for peri-prosthetic bone remodelling and initial implant stability of the tibial component, which have been investigated in previous biomechanical studies [7,[17][18][19][20][21].…”

Maximum principal strain as a criterion for prediction of orthodontic mini-implants failure in subject-specific finite element models

“…[9][10][11] Most studies that evaluated OMIs using FEA have assessed their results using equivalent stress. [2][3][4][5][6][7][8] Recent studies 26 showed that von Mises stress does not reliably predict the yielding behavior of bone and that the principal strain criterion correctly identified the risk of failure. 13,27 Consistent with these studies we found equivalent stress to be significantly correlated to stability only in zone 2, and it explained only a small amount of the variation in stability observed in the sample (R 2 5 0.1706).…”