Subject-specific Femoral Finite Element Modeling

A FE model was created for each femur based on the subject-specific hexahedral mesh and the loading conditions obtained from the MSK simulations. All models were fixed at the femoral epicondyles and HCF and muscle forces were applied as nodal forces for the nine load instances.
For each load instance the HCF was distributed to the closest 100 surface nodes (approximately 2.25 cm²) in the direction of the HCF orientation. For each muscle a node was identified which was the closest node to the muscle attachment obtained from the OpenSim simulations (van Arkel et al., 2013 (link)). Due to discrepancies in the geometry, e.g., bending of the shaft, between OpenSim’s femur and the participants’ femur derived from MRI an algorithm was used to ensure that the defined muscle attachment was on the same side (anterior/posterior or medial/lateral) of the femur. Nodal forces were applied to this node in x/y/z directions according to the muscle directions obtained from the additional muscle analysis (van Arkel et al., 2013 (link)) in order that the resulting force was equal to the muscle force estimated by the static optimization algorithm.
The FE model was duplicated and two different sets of linear elastic materials with Young’s modulus and Poisson ratio described in Table 1 were assigned to the different parts of the femur. The chosen values for material properties were based on literature and previously used values in mechanobiological growth studies (Linde et al., 1985 (link); Rho et al., 1993 (link); Carriero et al., 2011 (link); Yadav et al., 2016 (link); Kainz et al., 2020 (link)). A transition zone of three layers (out of the ten layers within the growth plate) between trabecular bone and the growth plate was modeled with linearly decreasing Young’s modulus from the trabecular bone to the growth plate to represent the mineralizing bone tissue (Kainz et al., 2020 (link)). FEBio 3 (Maas et al., 2012 (link)) was used for FE simulations and to calculate principal stresses.