Computing porosity of cancellous bone using ultrasonic waves II: the muscle, cortical, cancellous bone system

Robert Gilbert (1) , Ying Liu (1) , Jean-Philippe Groby (2) , Erick Ogam (2) , Armand Wirgin (2) , Yongzhi S. Xu (3)

1 Department of Mathematical Sciences
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
3 Department of Mathematics

Based on a model and an algorithm proposed previously by Buchanan, Gilbert, Wirgin and Xu [J. L. Buchanan, R. P. Gilbert, A. Wirgin and Y. Xu: Transient reflection and transmission of ultrasonic waves in cancellous bones, Appl. Math. Comp. 142 (2003), 561–573, R. P. Gilbert, Y. Xu and Shangyou Zhang, Computing Porosity of Cancellous Bone Using Ultrasonic Waves] we numerically computed the dependence of the porosity of cancellous bone encased in cortical bone and muscle on the measured ultrasonic wave. The computation shows the bone porosity can be recovered very accurately. The numerical data show that the ultrasonic wave of higher frequency would produce a more accurate bone porosity.

Mots clés: Cancellous bone; Poroelastic medium; Biot's model

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Robert Gilbert, Ying Liu, Jean-Philippe Groby, Erick Ogam, Armand Wirgin, et al.. Computing porosity of cancellous bone using ultrasonic waves II: the muscle, cortical, cancellous bone system. Mathematical and Computer Modelling, 2009, 50 (3-4), pp.421-429. ⟨10.1016/j.mcm.2008.06.021⟩. ⟨hal-00387218⟩