Toward bone quality assessment: Interference of fast and slow wave modes with positive dispersion can account for the apparent negative dispersion

Abstract

The goal of this work was to show that apparently negative dispersion in bone can arise from interference between fast wave and slow wave longitudinal modes, each of positive dispersion. Simulations were carried out using two approaches, one based on the Biot-Johnson model and the second independent of that model. The resulting propagating fast wave and slow wave modes accumulated phase and suffered loss with distance traveled. Results of both types of simulation served as the input into a phase and magnitude spectroscopy algorithm (previously validated with experimental data) in order to determine the phase velocity as a function of frequency. Results based on both methods of simulation were mutually consistent. Depending upon the relative magnitudes and time relationships between the fast and slow wave modes, the apparent phase velocities as functions of frequency demonstrated either negative or positive dispersions. These results appear to account for measurements from many laboratories that report that the phase velocity of ultrasonic waves propagating in cancellous bone decreases with increasing frequency (negative dispersion) in about 90% of specimens but increases with frequency in about 10%. [Work supported in part by Grant NIH R37HL40302.]