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

Benedikt Helgason, Egon Perilli, Enrico Schileo, Fulvia Taddei, Sigurdur Brynjólfsson, Marco Viceconti

Research output: Contribution to journalArticle


Background: 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. Methods: 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. Findings: 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. Interpretation: 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.

Original languageEnglish
Pages (from-to)135-146
Number of pages12
JournalClinical Biomechanics
Issue number2
Publication statusPublished - Feb 2008


  • Bone
  • Constitutive law
  • Density
  • Elastic modulus
  • Mechanical properties
  • Subject-specific finite element models

ASJC Scopus subject areas

  • Orthopedics and Sports Medicine

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