Optimising parameters of bone-adaptation model using experimental data

Trabecular bone is a living material that adapts its spatial organisation and mechanical properties when subjected to loading. There were efforts to describe adaptation in trabecular bone with mathematical models regulating resorption and formation activities as a function of mechanical stimuli. In this paper, an approach to optimise parameters of a bone-adaptation model is proposed and investigated, and the simulation results of trabecular-bone adaptation are quantitatively compared with high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of a distal tibia in a participant following six months of physiological loading. For this purpose, finite-element models were developed from baseline scans of the participant's trabecular bone and used as an initial domain to run simulations regulated by the bone-adaptation model implemented in a Fortran subroutine. The simulated results were element-by-element compared with the corresponding models from follow-up HR-pQCT scans. Mechanostat parameters of the bone-adaptation model were optimised to improve correspondence between the simulated and follow-up HR-pQCT-based models.

The developed approach captured the main trends in changes of bone volume fraction, trabecular thickness and separation and achieved 84 – 93 % of the element-by-element correspondence with the experimental models when utilising the optimised values of bone-adaptation parameters. These optimised values were different across the bone's cross-section. In the boundary conditions representing physiological loading, they predicted higher bone resorption rate in the inner regions of distal tibia than in the outer regions, intensified bone resorption in the anterior-inner, medial-inner and medial-outer regions, higher bone formation rate in the outer regions of distal tibia than in the inner regions, and intensified bone formation in the lateral-outer region.