Determination of the representative static loads for cyclically repeated dynamic loads: a case study of bone...

Bone has the self-optimizing capability to adjust its structure in order to efficiently support external loads. Bone remodeling simulations have been developed to reflect the above characteristics in a more effective way. In most studies, however, only a set of static loads have been empirically determined although both static and dynamic loads affect bone remodeling phenomenon. The goal of this study is to determine the representative static loads (RSLs) to efficiently consider the statically equivalent effect of cyclically repeated dynamic loads on bone remodeling simulation.

Based on the concept of two-scale approach, the RSLs for the gait cycles are determined from five subjects. First, the gait profiles at the hip joint are selected from the public database and then are preprocessed. The finite element model of the proximal femur is constructed from the clinical CT scan data to determine the strain energy distribution during the gait cycles. An optimization problem is formulated to determine the candidate static loads that minimize the errors of the spatial strain energy distribution for five gait profiles. Then, all candidate static loads from five gait profiles are partitioned into multiple clusters. The RSLs and the corresponding coefficients can be determined at the center of the densest cluster. For verification, topology optimization is separately conducted with the whole gait cycle (reference), empirically determined loads (conventional), and the RSLs (proposed). The strain energy density-based bone remodeling simulation is also conducted for another comparison.

For the gait loads, the use of the RSLs enables a 99% reduction of the function calls with negligible errors in the bone spatial distribution (6.75% for two representative static loads and 6.24% for three representative static loads) and apparent stiffness (4.84% for two representative static loads and 4.47% for three representative static loads), compared with the use of a whole gait cycle as reference.

This study shows the feasibility of the RSLs and provides a theoretical foundation for investigating the relationship between static and dynamic loads in the aspect of bone remodeling simulation.