On the uncertainty propagation in multiscale modeling of cortical bone elasticity

Uncertainty in experimental data is a major concern in biomechanical modeling – even more in a multiscale framework, where details of material microstructure are often hardly accessible. Since input data are uncertain, deterministic modeling is limited and new approaches are required. Probability theory can be used to account for uncertain model parameters and propagate this uncertainty through the scales (Soize 2008). We have recently proposed a stochastic multiscale model of cortical bone based on continuum micromechanics and the maximum entropy (MaxEnt) principle (Sansalone et al. 2014). This model was used to predict bone elasticity at the organ scale while accounting for the uncertainties in bone elasticity. In this contribution, we extend this approach to account for the uncertainties in the composition of a human bone sample. It is shown that, unlike a deterministic model which only provides nominal results, the stochastic model can provide statistics (mean, confidence intervals ...) of the elastic coefficients of the cortical tissue which allow assessing the reliability of these results.