Optimization of the density–elasticity relationship for rabbit hindlimb bones

Abstract

The rabbit is a popular experimental model in orthopaedic biomechanics due to the presence of natural Haversian remodeling, allowing for better translational relevance to the mechanobiology of human bone over traditional rodent models. Although rabbits are often used with computational modeling approaches such as the finite element (FE) method, a validated and widely agreed upon density–elasticity relationship, which is required to make subject-specific predictions, does not exist. Therefore, the purpose of this study was to determine and validate an accurate density–elasticity relationship for rabbit hindlimb bones using mathematical optimization. Fourteen tibiae and thirteen femora were harvested from New Zealand White Rabbits, imaged with computed tomography (CT), and cyclically loaded in uniaxial compression while strain gauge rosette data were recorded. The CT images were processed into subject-specific FE models which were used in a Nelder–Mead optimization routine to determine a density–elasticity relationship that minimized the error between experimentally measured and FE-predicted principal strains. Optimizations were performed for the tibiae and femora independently, and for both bones combined. A subset of 4 tibiae and 4 femora that were excluded from the optimization were then used to validate the derived relationships. All equations that were determined by the initial optimization exhibited a $Y=X$ type of relationship with strong correlations (Tibiae: $R^2=0.96$; Femora: $R^2=0.85$; Combined: $R^2=0.90$) and good agreement. The validation groups yielded similar results with strong correlations (Tibiae: $R^2=0.94$; Femora: $R^2=0.87$; Combined: $R^2=0.91$). These findings suggest that any of the derived density–elasticity relationships are suitable for computational modeling of the rabbit hindlimb and that a single relationship could be used for the whole rabbit hindlimb in studies where greater computational efficiency is necessary.