The effect of the density–modulus relationship selected to apply material properties in a finite element model of long bone

Material property assignment is a critical step in developing subject-specific finite element models of bone. Inhomogeneous material properties are often applied using an equation relating density and elastic modulus, with the density information coming from CT scans of the bone. Very few previous studies have investigated which density–elastic modulus relationships from the literature are most suitable for application in long bone. No such studies have been completed for the ulna. The purpose of this study was to investigate six such density–modulus relationships and compare the results to experimental strains from eight cadaveric ulnae. Subject-specific finite element models were developed for each bone using micro-CT scans. Six density–modulus equations were trialed in each bone, resulting in a total of 48 models. Data from a previously completed experimental study in which each bone was instrumented with twelve strain gauges were used for comparison. Although the relationship that best matched experimental strains was somewhat specimen and location dependent, there were two relations which consistently matched the experimental strains most closely. One of these under-estimated and one over-estimated the experimental strain values, by averages of 15% and 31%, respectively. The results of this study suggest that the ideal relationship for the ulna may lie somewhere in between these two relations.