Homogenization theories and inverse problems

Robert P. Gilbert, Ana Vasilic, Sandra Ilic

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)


Various approaches are presented for modelling the acoustic response of cancellous bone to ultrasound interrogation. As the characteristic pore size in cancellous bone is much smaller than a typical bone sample, there is a clear scale separation (micro versus macro). Thus, our modelling methods are mainly based on homogenization techniques and numerical upscaling. First, we consider the so-called direct problems and present models for both periodically perforated domain and a domain with random distribution of pores, as well as nonlinear model with a shear-thinning viscoelastic material emulating the blood-marrow mixture. A numerical procedure is given for the upscaling of a diphasic mixture using different trabeculae thicknesses and various frequencies for the ultrasound excitation. Finally, the results of a quite accurate two-dimensional inversion for the Biot parameters are presented. Further details for these different problems are amply described in the literature cited in the bibliography.

Original languageEnglish
Title of host publicationBone Quantitative Ultrasound
PublisherSpringer Netherlands
Number of pages35
ISBN (Electronic)9789400700178
ISBN (Print)9789400700161
Publication statusPublished - 2011


  • Cancellous bone
  • Homogenization
  • Inverse problems

ASJC Scopus subject areas

  • General Medicine


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