Homogenizing the time-harmonic acoustics of bone: The monophasic case

Ming Fang, Robert P. Gilbert, Alexander Panchenko, Ana Vasilic

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


For the interrogation of cancellous bone using ultrasound, we undertake a derivation of the time-harmonic, acoustic equations, idealizing the bone as a periodic arrangement of a Kelvin-Voigt viscoelastic porous matrix containing a viscous fluid. Since we are interested in acoustics, rather than filtration, we assume that the fluid is slightly compressible. Moreover, we study the monophasic case. A priori estimates are obtained for the time-harmonic equations. By letting the characteristic size of the inhomogeneities tend to zero and passing to the limit in the sense of the two-scale convergence, the effective equations for the monophasic vibrations are obtained, for which we prove existence and uniqueness.

Original languageEnglish
Pages (from-to)331-340
Number of pages10
JournalMathematical and Computer Modelling
Issue number3-4
Publication statusPublished - Aug 2007
Externally publishedYes


  • Time-harmonic waves
  • Two scale convergence
  • Viscoelasticity of Kelvin-Voigt

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications


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