Bayesian parameter estimation of ligament properties based on tibio-femoral kinematics during squatting

Abstract

The objective of this study is to estimate the, probably correlated, ligament material properties and attachment sites in a highly non-linear, musculoskeletal knee model based on kinematic data of a knee rig experiment for seven specific specimens. Bayesian parameter estimation is used to account for uncertainty in the limited experimental data by optimization of a high dimensional input parameter space (50 parameters) consistent with all probable solutions. The set of solutions accounts for physiologically relevant ligament strain (ϵ<6%). The transitional Markov Chain Monte Carlo algorithm was used. Alterations to the algorithm were introduced in order to avoid premature convergence. To perform the parameter estimation with feasible computational cost, a surrogate model of the knee model was trained. Results show that there is a large intra- and inter-specimen variability in ligament properties, and that multiple sets of ligament properties fit the experimentally measured tibio-femoral kinematics. Although all parameters were allowed to vary significantly, large interdependence is only found between the reference strain and attachment sites. The large variation between specimens and interdependence between reference strain and attachment sites within one specimen, show the inability to identify a small range of ligament properties representative for the patient population. To limit ligament properties uncertainty in clinical applications, research will need to invest in establishing patient-specific uncertainty ranges and/or accurate in vivo measuring methods of the attachment sites and reference strain and/or alternative (combinations of) movements that would allow identifying a unique solution.