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In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy

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Published on: July 2, 2021

Forward and inverse optimality problems of bone adaptation at the homogenised RVE level.

Philippe K Zysset¹

¹ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland. philippe.zysset@unibe.ch.

Biomechanics and Modeling in Mechanobiology

|January 13, 2026

Summary

This study introduces new analytical solutions for bone adaptation, considering both density and fabric. These findings could improve personalized bone strength assessments and load estimations in clinical diagnostics.

Keywords:

Anisotropic elasticity Bone adaptation Bone density Fabric Inverse problem Structural optimisation

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Last Updated: Jan 15, 2026

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Published on: June 24, 2025

Area of Science:

Biomechanics
Computational Biology
Materials Science

Background:

Bone adapts to mechanical loading via a mechanostat.
Current models use density but lack microarchitecture detail for personalized strength.
Existing theories don't fully predict bone fabric using local optimization.

Purpose of the Study:

Formulate analytical solutions for optimal bone adaptation at the RVE level.
Incorporate bone density and fabric relationships.
Provide forward and inverse solutions for bone adaptation and loading.

Main Methods:

Developed analytical solutions for optimal bone adaptation.
Utilized density- and fabric-mechanical property relationships.
Applied three distinct mechanostat criteria.

Main Results:

Provided forward solutions for density and fabric based on local stress.
Derived inverse solutions for local stress from given density and fabric.
Specialized 3D solutions to 2D and 1D for clarity.

Conclusions:

The developed solutions enable forward simulation of personalized bone adaptation.
Future work will integrate these solutions into clinical diagnostic tools.
This approach enhances the estimation of bone loading and personalized strength.