A CT-Based High-Order Finite Element Analysis of the Human Proximal Femur Compared to In-vitro Experiments

Four regions of the fresh-frozen bone model. The trabecular region was divided into three subregions, low trabecular, trochanter, and head, each with a different spatial field for the Young’s modulus. In the right we show the location at which the head was trimmed to mimic the applied load in the experiment.

The steps for generating the p-FE model: (a) outer surface border points; (b) approximated smooth surface; (c) solid body having a cortical/trabecular separating surface; and (d) meshed model with two different mesh regions

Apparent density on one of the “worse approximated” slices of the investigated bone: (a)ρapp computed from HU; (b)ρapp distribution after moving average; (c)ρappLMS represented by the LMS function

Relations between Young’s modulus and apparent density as reported in past publications for the trabecular (top) and cortical (bottom) bone

Femur under load and representing FE model. Load is applied at an angle of 20deg to the shaft axis.

Bone mounting jig (dimensions in mm): (1) slider - controls the bone’s inclination angle; (2) steel cylinder (3) 4× M6 bolts (4) base and rail (5) stopper. Load and displacements measurements (embalmed bone): Load cell, ball, and socket joint for load transmission and the LVDT.

Strain gauges locations: (A) neck superior, (B) neck inferior, (C) shaft medial, and (D) shaft lateral

Experiments on fresh–frozen bone at different inclination angles (from left to right): 0deg, 7deg, 15deg, 20deg

Fresh-frozen bone at 7deg inclination under 1500N load: (top) Different strain gauges versus load; (bottom) strain (neck superior) versus load at neck inferior

Fresh-frozen load vis. time response for 1500N load at 15deg inclination. Linear response is noticed after 200N preload.

Fresh-frozen femur shows insensitive behavior to different strain rates (at 7deg inclination): head’s displacement vis. load (top) and neck superior strain vis. load (bottom)

Inclination angle influence on strains at neck superior (top) and inferior (bottom)

Resultant force (Fz) versus degree of freedom (DOF) under head displacement of 1mm(0deg tilt): (top) influence of different FE meshes and (bottom) moving average box sizes

Resultant force [N] due to head displacement of 1mm for 0deg inclination angle: convergence of FEA resultant force according to several E(ρapp) relations

von Mises stress (MPa) for a 1500N load in the bone at 0deg inclination angle

FEA results using Cody relations compared to experimental observations: Femur head displacement at 1500N compression at several inclination angles (error bars indicate min. and max. measured values)