Simulation of ultrasonic waves reflection at the bone-implant interface using a hybrid computational method

Osseointegration, which encompasses the remodeling and anchoring mechanisms of bone tissue to an implant, can be assessed using quantitative ultrasound, by analyzing the reflection of ultrasonic waves at the bone-implant interface (BII). Although experimental studies have highlighted the sensitivity of this technique to the bone quantity at the BII, its limited resolution, along with the complexity of the retrieved ultrasonic signals, make local assessment of osseointegration difficult. Here we introduce a hybrid computational model to simulate a setup dedicated to the measurement of ultrasonic waves reflected at the BII. A three-dimensional FDTD method in the vicinity of the implant is coupled to a semi-analytical approach to compute the wave propagation between the probe and the bone-implant system. The modeling strategy incorporates key features of the experiment, such as the focusing of ultrasonic waves over a long water distance and their interactions with specimen-specific bone-implant systems, whose spatial tissue distribution is based on high-resolution images. Our results indicate that the proposed model reduces the numerical dispersion and computational cost typically associated with full FDTD approaches, thus allowing recovery of global and local ultrasonic indicators, reflecting the contributions of the tissue at the BII and underneath.