Reflection of an ultrasonic wave on a bone-interface implant: a numerical study of the multiscale roughness

Abstract : Quantitative ultrasound is used to characterize and stimulate osseointegration processes at the bone-implant interface (BII). However, the interaction between an ultrasonic wave and the implant remains poorly understood. This study aims at investigating the sensitivity of the ultrasonic response to the microscopic and macroscopic properties of the BII and to osseointegration processes. The reflection coefficient R of the BII was modeled for different frequencies using a two-dimensional finite element model. The implant surface roughness was modeled by a sinusoidal function with varying amplitude h and spatial frequency L. A soft tissue layer of thickness W was considered between bone tissue and the implant in order to model non-mineralized fibrous tissue. For microscopic roughness, R is shown to increase from around 0.55 until 0.9 when kW increases from 0 to 1 and to be constant for kW > 1, where k is the wavenumber in the implant. These results allow us to show that R depends on the properties of bone tissue located at a distance comprised between 1 and 25 μm from the implant surface. For macroscopic roughness, R is highly dependent on h and this dependence may be explained by phase cancellation and multiple scattering effects for high roughness parameters.