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

TL;DR

This paper introduces a gradient-based optimization method for designing triply-periodic minimal surface (TPMS) bone implants with spatially varying thickness, aiming to maximize bone in-growth while considering mechanical and biological factors.

Contribution

It presents a novel, mesh-independent design approach using a surrogate model for TPMS properties and a mechanobiological model for bone growth estimation.

Findings

Optimized hip implant design enhances bone in-growth.

Method reduces computational cost via homogenization and surrogate modeling.

Design constraints ensure manufacturability and biological functionality.

Abstract

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.