Valid μ finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions

Abstract

Osteoporosis-related vertebral fractures represent a major public health problem. Anatomy-specific CT-based finite element (FE) simulations could help in identifying which vertebrae have the highest risk of fracture and thus help to decide upon the need for vertebroplasty or other surgical intervention. Continuum level FE simulations require effective macroscopic material properties of the vertebra. Micro finite element (μFE) models can be used to circumvent the difficult experiments that are necessary to determine these effective properties. From a quantitative point of view, these μFE models depend critically on the chosen trabecular tissue properties. The question remains whether linear elastic μFE models of vertebral trabecular bone with and without specimen-specific tissue properties yield similar results as non-destructive macroscopic experiments under moist conditions. μFE models were set up from μCT scans with specimen-specific or average tissue moduli measured by nanoindentation under dry and wet testing conditions. Non-destructive macroscopic mechanical compression, tension and torsion tests were performed. Experimentally obtained and simulated apparent stiffnesses were compared. No significant difference was found when comparing μFE simulations with wet tissue properties and experiments for tension, compression and torsion ( p > 0.05 ) . Concordance correlation coefficients were high for tension and compression ( r c wet ≥ 0.96 , p < 0.05 ) but moderate for torsion ( r c wet = 0.81 , p < 0.05 ) . The agreement between simulation and experiment was confirmed by Bland–Altman plots which showed mean differences ≤ 10 MPa . Surprisingly, the agreement between simulation and experiment was not reduced by using an average tissue modulus. The results indicate that valid μFE models can be set up using average tissue properties obtained under wet indentation conditions.