A theoretical analysis in the time-domain of wave reflection on a bone plate

This paper presents an original method for simulating ultrasonic wave reflection on a fluid-loaded plate. Geometrical and material parameters used are relevant to the “axial transmission technique” (ATT) setup. Devices based on the ATT are used for the assessment of cortical bone strength (estimate of a fracture risk). In this work, the cortical bone layer is represented as a plate of infinite extent surrounded by fluid (soft tissues). A line source and a receiver are placed in the fluid. Transient waves generated upon reflection at the plate–fluid interfaces are addressed. Analytic Greenʹs functions are derived with the generalized ray/Cagniard-de Hoop method. The acoustic response is obtained upon convolution of Greenʹs functions with a given source pulse. The method associates each wave amplitude in the time-domain (lateral waves, reflected body waves, etc.) to a specific term of the final solution. The method is ideally suited to a detailed analysis of the ultrasonic signal for various geometrical and mechanical parameters. The results presented highlight the potential of the method for the understanding of wave phenomena involved in the ATT and similar setups. They also bring new elements that reinforce our theoretical knowledge of the ATT.