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..., , # Bone Multi-Topology Optimization Dataset

## File: `bone_multitopopt.zip`

### Overview

This dataset contains computational code and results from bone multi-scale optimization simulations for bone materials to carry out bone remodeling in Python.\
The research investigates 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 hierarchical length scales of bone.

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### Repository Structure

```
bone_multitopopt/
├── src/ # Main source code
│ ├── __init__.py
│ ├── bone_assembly_util.py # Finite element assembly utilities
│ ├── bone_element_util.py # Element-level estimation operations
│ ├── bone_material_optim_util.py # Material-level optimization algorithms
│ ├── bone_micro_util.py # Continuum micromechanics-based homogenization ...,