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Updated: May 14, 2026
09:02
Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population
Published on: January 31, 2025
Theoretical study of bone's microstructural effects on Rayleigh wave propagation
Maria G Vavva1, Leonidas N Gergidis, Antonis Charalambopoulos
1Fotiadis are in the Unit of Medical Technologyand Intelligent Information Systems, Department of Material Science and Engineering, University of Ioannina, GR 45110, Ioannina, Greece. mvavva@cc.uoi.gr
Summary
Gradient elasticity theory accurately predicts Rayleigh wave dispersion in bone, overcoming limitations of classical elasticity. This advancement aids in the ultrasonic characterization of bone
Area of Science:
- Biomechanics
- Materials Science
- Solid Mechanics
Background:
- Classical elasticity fails to model bone's complex mechanical behavior and the observed dispersive nature of Rayleigh waves.
- Mindlin Form II gradient elasticity theory offers a more suitable framework for analyzing heterogeneous materials like bone.
- Previous work demonstrated Rayleigh wave dispersion using Boundary Element Method (BEM) simulations based on gradient elasticity.
Purpose of the Study:
- To analytically determine the dispersion of Rayleigh waves in an isotropic semi-infinite medium with bone-like properties using Mindlin Form II gradient elasticity.
- To investigate the influence of microstructural effects and internal constants on Rayleigh wave dispersion.
- To validate the analytical model by comparing results with computational simulations and classical elastic theory.
Main Methods:
- Analytical derivation of Rayleigh wave dispersion using Mindlin Form II gradient elasticity theory.
- Modeling an isotropic semi-infinite space with mechanical properties mimicking bone.
- Performing calculations for various combinations of internal constants (l(1), l(2), h(1), h(2)) derived from realistic models and osteon dimensions.
- Comparing analytical results with Boundary Element Method (BEM) computational results and classical elasticity.
Main Results:
- The analytical results derived from Mindlin Form II gradient elasticity theory showed perfect agreement with the computational results.
- The study successfully demonstrated the dispersive nature of Rayleigh waves, which is not captured by classical elasticity.
- The effectiveness of gradient elasticity in predicting wave dispersion in a bone-like material was confirmed.
Conclusions:
- Mindlin Form II gradient elasticity theory accurately predicts Rayleigh wave dispersion in bone.
- This analytical approach provides a powerful tool for understanding wave propagation in heterogeneous biological tissues.
- The findings represent a significant step towards the ultrasonic characterization of bone properties.
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