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

Abstract

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= ap(b) were used to apply material properties to models of eight ulnae. All equations passed through a point (1.85, Ec), where p = 1.85 g/cm3 represents the average density of cortical bone. For custom equations (1) to (3), Ec 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 Ec 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 Ec = 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 Ec. Overall, a customized density-modulus relationship for the ulna was generated, which provided improved results over using previously reported density-modulus equations.

Experimental validation of finite element predicted bone strain in the human metatarsal

“…Density-elasticity relationships have also been developed using optimization techniques for the human femur (8,194,195), tibia (8,196), humerus (8), radius (8), and ulna (197).…”

“…Such equations have shown that a single equation can be used for both the trabecular and cortical bone (194,195,197). However, the optimized density-elasticity equations still illustrate site-and cohort-specificity (194).…”

Bone stresses before and after insertion of two commercially available distal ulnar implants using finite element analysis

“…15,17 A custom density-modulus relationship (E ¼ 8346r 1.5 ) was used to apply the tissue properties; this relationship showed lower root mean squared errors to experimental results than previously published relationships when applied to an ulnar model. 17 The Wright implant stem is manufactured of titanium, while the Wright head, SBI stem, and SBI head are made of cobalt chrome (CoCr). The elastic modulus values of titanium, CoCr, and bone cement were set to 110, 214, and 1.95 GPa, respectively.…”

“…21 The proximal end of the ulna was assumed to be fully fixed. The same coordinate system defined for native models in previous studies 15,17 were used to define the loading direction in the implant models.…”

“…The same regions were defined in the previous native bone models 15,17 to allow comparison of the same regions before and after implant insertion. von Mises stresses of all nodes that fell within each of the eight regions were averaged, and then normalized to those found at the same location in the native models.…”