In vivo, cortical bone is currently investigated using ultrasonic velocity measurement in the megahertz frequency range. It is virtually impossible to analytically model the extremely complex field resulting from the interaction of an incident wave with cortical bone, taking into account 3-D geometry, boundary conditions, anisotropic and heterogeneous bone properties. Recently developed simulation methods based on finite difference offer a fertile alternative to inextricable analytic formulations. Wave propagation simulation is applied here to the problem of axial transmission along the radius. 3-D computations showed that different types of head wave propagate along the anisotropic cortex depending on the thickness-to-wavelength ratio. Simulated variations of SOS as a function of thickness are in good agreement with in vivo [Njeh (1999)] and in vivo [Prevrhal (2001)] observations. Cortical porosity leads to a velocity decrease of approximately 50 m<th>s-1 (respectively 25 m<th>s-1) per % of porosity increase in the axial (respectively, radial) direction. When the cortical thickness is larger than one compressional wavelength, the signal velocity reflects bone properties over a depth of about half a wavelength. Numerical simulation brings an insightful view into the influence of several bone properties on signal velocity, and can also be of great value in testing inverse calculation procedures.
Acoustical Society of America Journal
- Pub Date:
- October 2003