Mechanical functional zoning of the proximal femoral trabecular bone revealed by two-dimensional topology optimization without a predefined structure.

Abstract

This study investigated the mechanics-driven structural optimization of proximal femoral trabecular bone using two-dimensional topology optimization without a predefined trabecular pattern. A high-resolution two-dimensional finite element model (696, 271 nodes, 691, 230 elements) was developed from CT data. Solid Isotropic Material with Penalization (SIMP) topology optimization was performed under combined physiological loading: single-leg stance, abduction, and adduction (weighted ratio 6:2:2). The objective was minimization of total strain energy, and a trabecular feature size constraint of 70-200 μm was imposed. After 67 iterations (2 h 14 min), the model spontaneously converged to a trabecular distribution closely resembling native proximal femoral anatomy, accurately reproducing the five principal trabecular groups and Ward's triangle. Principal stress-based visualization revealed distinct tensile and compressive functional zones adapted to regional mechanical demands. Measured intersection angles between tensile and compressive trabeculae were 71.0° in the femoral neck and 91.1° in the lesser trochanter, consistent with human anatomical data. These findings demonstrate that topology optimization effectively simulates trabecular adaptation, providing planar numerical observations consistent with Wolff's law. This optimization-visualization approach offers a foundation for understanding structure-mechanics relationships and guiding biomimetic implant design.