Wave propagation across the tendon-to-bone interphase modeled as an equivalent interface with specific surface properties

The integration between soft and hard materials often occurs through functionally graded interphases, which are typically designed as multilayers whose material properties gradually vary in space, in order to reduce mechanical stresses. In the musculoskeletal system in particular, the attachment between tendon and bone occurs through a specific functionally graded interphase called enthesis, which serves the challenging task of connecting these two highly dissimilar tissues over a very small region by means of finely tuned gradients in structure, composition and biomechanical properties at different length scales. Current computational models that aim at mimicking the biomechanical behavior of the tendon-to-bone complex at the organ scale generally fail in incorporating the impact of the microstructure across the interphase because of computational burden. In this study, we propose a modeling strategy that allows replacing the finite heterogeneous functionally graded interphase by an equivalent model with specific interface conditions. This can be achieved by enriching the equivalent interface model with proper forms of surface kinetic and potential energy densities, in order to retain the mechanics from the microstructure for a certain range of validity. The performance of this model is evaluated in the context of quantitative ultrasound, by comparing the calculated power reflection coefficient to that obtained using different baselines. The results show that our enriched model provides an accurate approximation of the reference interphase model over a broad frequency range, thus opening new perspectives for developing more sophisticated dynamic models targeting characterization or reattachment procedures at the organ scale. Number