Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Finite-difference computation: a numerical tool for ultrasonic bone characterization

P. Laugiera,* E. Bossyb, F. Jensona, M. Talmanta, Frédéric Padillaa
aUniversité Pierre et Marie Curie, Laboratoire d'Imagerie Paramétrique UMR CNRS 7623, 75006 Paris, France bESPCI, Laboratoire d'Optique UPR CN RS 5, 75005 Paris, France

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Our objective here is to show the usefulness of computational methods in the field of ultrasonic bone strength characterization. Recently developed methods based on finite differences offer a fertile alternative to inextricable analytic formulations. Such numerical simulations of wave propagation have been applied to the problem of cortical axial transmission along the radius and transverse transmission through cortical bone (phalanx) or through cancellous bone (calcaneus). In each case, modelling has been found to be of great value in giving insight into the interaction mechanisms and properties of propagating waves (nature, pathway). Numerical simulation has already brought answers to the following issues: influence of complex 3-D geometry on ultrasound measurements, role played by structural anisotropy, sensitivity of axial transmission to porosity and cortical thickness. In the future, it will also provide insight into the role played by mechanical anisotropy, structural and mechanical heterogeneity, trabecular microstructure and physical loss mechanisms.

Keywords:  Bone; Finite differences; Osteoporosis; Propagation; Ultrasound

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