Phase velocity measurement of flexural waves in human tibia

Abstract

A method is proposed to measure the phase velocities of the first mode of flexural waves in the human tibia. Keeping in mind the dispersive nature of flexural waves in beam-like bodies, a two point measurement method was developed which enables the calculation of the phase difference of the propagating wave between two observation points for a selected frequency range. The method for dispersion analysis was tested with synthetic and observed signals for a cylinder. This was done by comparison of observed radial acceleration on the surface of a PVC-cylinder with computed synthetic signals consisting only of first mode flexural waves. An in vivo study was performed with 43 subjects. The phase velocity measurements in human tibia show a good correlation with the bone mineral content estimated by means of the Cameron-Sorenson technique (Cameron and Sorenson, 1963). The bone mineral loss is reflected by decreasing phase velocities. This indicates that phase velocity measurements of flexural waves can be used for an estimation of bone mineral content in vivo.