Development of a customized density-modulus relationship for use in subject-specific finite element models of the ulna

Assigning an appropriate density-modulus relationship is an important factor when applying inhomogeneous material properties to finite element models of bone. The purpose of this study was to develop a customized density-modulus equation for the distal ulna, using beam theory combined with experimental results. Five custom equations of the form E = a(rho)(b) were used to apply material properties to models of eight ulnae. All equations passed through a point (1.85, E-c), where rho = 1.85 g/cm(3) represents the average density of cortical bone. For custom equations (1) to (3), E-c was predicted using beam theory, and the value of b was varied within the range reported in the literature. Custom equations (4) and (5) used other values of E-c from the literature, while keeping b constant. Results obtained from the custom equations were compared with those from other equations in the literature, and with experimental results. The beam theory analysis predicted E-c = 21 +/- 1.6 GPa, and the three custom equations using this value tended to have the lowest errors. The power of the equations did not affect the results as much as the value used for E-c. Overall, a customized density-modulus relationship for the ulna was generated, which provided improved results over using previously reported density-modulus equations.