Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 5, pp 1269–1279 | Cite as

Sensitivity analysis of ultrasonic guided waves propagating in trilayered bone models: a numerical study

  • Tho N. H. T. Tran
  • Lawrence H. LeEmail author
  • Mauricio D. Sacchi
  • Vu-Hieu Nguyen
Original Paper


The fundamental ultrasonic guided modes are consistently observed in long bones ex vivo and in vivo. However, the responses of ultrasonic guided waves to the changes of cortical thickness, cortical elastic parameters, and thickness of the overlying soft tissues are not comprehensively understood. This paper systematically presents a sensitivity analysis of leaky Lamb modes to the geometry and material characteristics of layered bone model by means of semi-analytical finite element modeling. The stratified bone model is consisted of a transversely isotropic cortex with an overlying soft tissue and underlying marrow. The study is important as it offers guidance to the parameter inversion process about the optimal selection of guided modes and regions of sensitivity for better inversion results.


Ultrasonic guided waves Leaky Lamb waves Osteoporosis Cortical bone Sensitivity Phase velocity Dispersion Semi-analytical finite element method 



This work is supported by the Discovery Grant (L. Le) from the Natural Sciences and Engineering Research Council of Canada (NSERC). Tho N.H.T. Tran would like to thank Alberta Innovates-Technology Futures and the generous supporters of the Lois Hole Hospital through the Women and Children’s Health Research Institute (WCHRI) for their graduate studentship supports. Vu-Hieu Nguyen has been supported by the PEPS program (V.H. Nguyen, 15R03051A-METCARMAT) from the French National Center for Scientific Research (CNRS) and Université Paris-Est, France.

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Radiology and Diagnostic ImagingUniversity of AlbertaEdmontonCanada
  2. 2.Department of PhysicsUniversity of AlbertaEdmontonCanada
  3. 3.Laboratoire Modélisation et Simulation Multi Echelle UMR 8208 CNRSUniversité Paris EstCréteilFrance

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