Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Abstract

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towards the prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Accuracy of finite element analyses of CT scans in predictions of vertebral failure patterns under axial compression and anterior flexion

“…Large errors in FE predictions were found for both sets of material properties, which differed in elastic anisotropy and yield criterion but not post-yield constitutive behavior. Recent studies have shown good qualitative correspondence between patterns of frank vertebral collapse observed at very large applied displacements vs. patterns predicted by FE analyses using a damage-plastic constitutive model (Clouthier et al, 2015; Hosseini et al, 2014). In contrast, further refinements to the modeling of elastic anisotropy have only a minor effect on FE predictions of vertebral deformation (Unnikrishnan et al, 2013).…”

Trabecular Bone Loss at a Distant Skeletal Site Following Noninvasive Knee Injury in Mice

“…This finding may be particularly important for future fracture risk, as damage within vertebral bodies has been shown to initiate within the trabecular bone compartment [34,35]. For example, Eswaran et al showed that during compressive loading of human vertebral bodies, high-risk tissue was first observed in the trabecular bone region, and the largest proportion of high-risk bone tissue was in the trabecular bone [34].…”

An over‐nonlocal implicit gradient‐enhanced damage‐plastic model for trabecular bone under large compressive strains

“…The nonlocal damage variable ensures preventing the localization of the inelastic process into an arbitrarily small volume. The Helmholtz Equation (33) is solved together with the balance of linear momentum Equation (35) to take into account the effect of damage induced by the plastic strain at the neighboring integration points. This results in reduced mesh dependency of the classical local model beyond the peak.…”

“…is the non-standard internal force vector, related to the discrete form of Helmholtz equation (33). Satisfaction of the governing equations in the weak sense is tested for the state at the end of the step.…”