Optimal design of triply-periodic minimal surface implants for bone repair Optimal design of triply-periodic minimal surface implants

• Published in: Structural and multidisciplinary optimization Vol. 68; no. 6
• Main Authors: Cohen, David, Norato, Julián A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 14.06.2025
• Subjects: Computational Mathematics and Numerical Analysis; Engineering; Engineering Design; Research Paper; Theoretical and Applied Mechanics; Design; Bone growth; TPMS; Hip implant; Optimization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-025-04032-9

This work proposes a gradient-based method to design bone implants using triply-periodic minimal surfaces (TPMS) of spatially varying thickness to maximize bone in-growth. Bone growth into the implant is estimated using a finite element based mechanobiological model considering the magnitude and frequency of in-vivo loads, as well as the density distribution of the surrounding bone. The wall thicknesses of the implant unit cells are determined via linear interpolation of the thicknesses over a user defined grid of control points, avoiding mesh dependency and providing control over the sensitivity computation costs. The TPMS structure is modeled as a homogenized material to reduce computational cost. Local properties of the implant are determined at run-time on an element-by-element basis using a pre-constructed surrogate model of the TPMS’s physical and geometric properties as a function of the local wall thickness and the density of in-grown bone. Design sensitivities of the bone growth within the implant are computed using the direct sensitivity method. The methodology is demonstrated on a cementless hip, optimizing the implant for bone growth subject to wall thickness constraints to ensure manufacturability and allow cell infiltration.