A multiscale optimization framework for bone remodelling: integrating material and structural adaptations across hierarchical scales.

Abstract

Bone exhibits a hierarchical organization across multiple length scales, integrating functional properties through adaptive remodelling mechanisms. In this article, we present a concurrent material-structure optimization framework that identifies optimal macroscale bone density and microstructural configurations, including collagen and hydroxyapatite distribution and lacunae orientation, across the length scales in bone's hierarchical organization. Our framework formulates a compliance minimization problem with coupled material and structure optimization sub-problems and leverages a continuum micromechanics-based homogenization approach to efficiently capture bone's hierarchical material behaviour. This enables computationally tractable optimization independent of the number of hierarchical scales, addressing key limitations of conventional remodelling approaches. We apply the framework to a human proximal femur under realistic musculoskeletal loading conditions and demonstrate its ability to capture self-optimizing mechanisms consistent with physiological adaptation. While not intended as a clinical diagnostic tool at this stage, the framework provides a physics-based rationale for estimating microstructural distributions of bone constituents and highlights deviations that may inform future assessments of bone quality. These findings offer a foundation for targeted therapeutic strategies, personalized diagnostics and regenerative medicine applications.