A multiscale optimization framework for bone remodeling: Integrating material and structural adaptations across hierarchical scales

Bone exhibits a hierarchical organization across multiple length scales,
integrating functional properties through adaptive remodeling 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 behavior.
This enables computationally tractable optimization independent of the
number of hierarchical scales, addressing key limitations of conventional
remodeling 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 model 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.