Reflection of an ultrasonic wave on the bone-implant interface: A numerical study of the effect 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.

Reflection of an ultrasonic wave on the bone−implant interface: Effect of the roughness parameters

“…Figure 4a shows that for implants with laser-modified surfaces, ro reaches a local maximum for a value of W comprised between 30 and 60 μm depending on the surface roughness. This result may be explained by constructive interferences of the echoes of the soft tissue -bone interface and of the implant -soft tissue interface, as already described in (Heriveaux et al, 2018). When the value of W is sufficiently high so that these interferences disappear, ro finally decreases to reach a final value of around 0.88.…”

“…The governing equations have been described in details in (Heriveaux et al, 2018) and the reader is referred to this publication for further details. Briefly, the classical equations of elastodynamic wave propagation in isotropic solids were considered.…”

“…(Heriveaux et al, 2018) is the only study investigating the impact of microscopic implant roughness on the ultrasonic response of the BII but a sinusoidal profile was then considered. The variation of r as a function of W obtained in (Heriveaux et al, 2018) in the case of a microscopic roughness is in qualitative agreement with the results of the present paper (see Fig. 4a), which justifies the comparison between both models developed in sections II.E and III.C.…”

“…Since osseointegration was only modeled through variations of the biomechanical properties of periprosthetic bone tissue, the influence of the BIC ratio could not be considered either. More recently, a 2-D FEM has been developed to investigate the sensitivity of the ultrasonic response to multiscale surface roughness properties of the BII and to osseointegration processes (Heriveaux et al, 2018). The implant roughness was modeled by a simple sinusoidal profile and the thickness of a soft tissue layer comprised between the bone and the implant was progressively reduced to simulate osseointegration phenomena.…”

Resonant frequency analysis of dental implants

“…Another method consists of using quantitative ultrasound (QUS) (De Almeida et al 2007) to investigate the properties of the bone-implant interface. The principle of the measurement relies on the dependence of ultrasonic propagation within the implant on the boundary conditions prescribed by the biomechanical properties of the boneimplant interface (Mathieu et al 2011b) (Vayron et al 2013) (Vayron et al 2018b) (Vayron et al 2014a) (Vayron et al 2014b) (Vayron et al 2018a) (Mathieu et al 2011a) (Vayron et al 2015(Vayron et al , 2016Hériveaux et al 2018).…”