Probabilistic analysis of mechanical behaviour of mandibular trabecular bone using a calibrated stochastic homogenization model

Surgical success of drilling in oral implantology depends on the sense of force on the fingers or feeling of a dental clinician, which is related to the quality of trabecular bone in the jawbone expressed by apparent mechanical characteristics. As the mechanical properties of trabecular bone depend on the bone volume fraction, microstructure, and many other factors closely related to individual differences, a probabilistic numerical procedure to assess drilling force is proposed. Using a micro-CT-based jawbone model, a first-order perturbation-based stochastic homogenization method was employed to estimate the possible scattering of apparent mechanical properties of the trabecular bone region. The complicated drilling problem was simplified to sequential linear static FEAs, to which the predicted apparent Young’s modulus and shearing moduli in the drilling direction were applied. The FEAs demonstrated that the homogenized mechanical properties showed anisotropy, which might lead to differences in the drilling forces at different drilling angles. The numerically estimated drilling forces were shown by the expected value, 50 %-probability result, and 90%-probability result and revealed that one patient among two or ten patients would probably have poor bone quality. There was a remarkable difference in the drilling forces between the expected value and the 90%-probability result.