A Concurrent Material-Structure Optimization Framework for Bone Remodelling Across Hierarchical Scales

  • Modak, Avinandan (Indian Institute of Technology Roorkee, India)
  • Sau, Arijit (Institute of Technology Roorkee, India)
  • Chowdhury, Rajib (Institute of Technology Roorkee, India)
  • Gangwar, Tarun (Institute of Technology Roorkee, India)

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Bone exhibits a hierarchical organization across multiple length scales, where adaptive remodelling mechanisms regulate the interaction between material microstructure and macroscale structure organization. In this work, we introduce a concurrent optimization framework that simultaneously optimizes macroscopic bone density and underlying microstructure attributes, including collagen and hydroxyapatite distributions and lacunar orientation, within a unified multiscale formulation capable of resolving the full hierarchical organization of bone. The problem is formulated as a compliance minimization problem with intrinsically coupled material and structure optimization sub-problems. We employ continuum micromechanics-based homogenization strategy to represent hierarchical material behavior efficiently, enabling scalable computations that remain independent of the number of resolved length scales—overcoming a central limitation of conventional bone remodelling models. The proposed framework is demonstrated on a human proximal femur subjected to physiologically realistic musculoskeletal loading conditions, where the resulting optimized configurations show self-organizing density and microstructure patterns consistent with Wolff’s law. The approach provides a physics-consistent basis for inferring plausible microstructure distributions of bone constituents and identifying deviations associated with compromised bone quality. Our framework establishes a foundation for future developments in personalized assessment, targeted intervention strategies, and regenerative medicine applications.