Mathematical relationships between bone density and mechanical properties: a literature review

In many published studies, elastic properties of bone are correlated to the bone density, in order to derive an empirical elasticity-density relationship. The most common use of these relationships is the prediction of the bone local properties from medical imaging data in subject-specific numerical simulation studies. The proposed relationships are substantially different one from the other. It is unclear whether such differences in elasticity-density relationships can be entirely explained in terms of methodological discrepancies among studies.

All relevant literature was reviewed. Only elasticity-density relationships derived from similarly controlled experiments were included and properly normalized. The resulting relationships were grouped according to the most important methodological differences: type of end support during testing, specimen geometry, and anatomical sampling location.

Even after normalization with respect to strain rate and densitometric measurement unit, substantial inter-study differences do exist, and they can only be partially explained by the methodological differences between studies.

Some recommendations are made for the application of elasticity-density relationships to subject-specific finite element studies. The importance of defining a standardized mechanical testing methodology for bone specimens is stressed, and some guidelines that emerged from the literature are proposed. To identify density-elasticity relationships suitable for use in subject-specific FE studies, the development of a benchmark study is also proposed, where the elasticity-density relationship is taken as the variable under study, and a numerical model of known numerical accuracy predicts experimental strain measurements.