Three-dimensional biomechanical modeling of cylindrical bone-like porous materials subject to acoustic waves

Abstract

This paper describes a three-dimensional (3D) analytical solution for the acoustic response of cancellous bone-like porous materials saturated with a viscous fluid. The effect of dynamic tortuosity, especially in clinically relevant ultrasound frequency ranges, is considered to investigate the effect of viscous interaction between the fluid and solid phases. The solution includes the effects of both fast and slow longitudinal waves as well as transverse waves propagating through the medium. The scattering operators and radial displacements are derived in terms of ultrasonic waveforms by applying the Helmholtz decomposition. The effect of different porosities, wall thickness ratios, and frequencies of incident waves on the radial displacement and scattering operators are investigated by considering various incident wave angles at forward and sideward directions. The results demonstrate that the incident wave angle has a significant effect on the radial displacement and scattering operators regardless of the porosity, wall thickness ratio, and viscosity of pore fluid. Furthermore, the distribution pattern of the radial displacement and scattering operators in relatively low frequency ranges is almost symmetric while asymmetric in relatively high frequency ranges. It is shown that the bone characterization using ultrasonic techniques is not only based on the mineral density, as used currently by electromagnetic wave-based tools, but also other biomechanical factors such as the porosity, viscosity of pore fluid, and wall thickness ratio of a cancellous bone structure. Also, the pattern of the reflected pressure can be an indicator of the state of a cancellous bone (healthy versus osteoporosis).