École Nationale Supérieure de
Techniques Avancées

Abstract

This report presents a modeling and numerical simulation study of wave propagation in the human cochlea, carried out at MAP5 (26/05/2025--23/08/2025). The basilar membrane is modeled as a linear elastic structure coupled with a quasi-incompressible fluid, within a two-dimensional fluid--structure interaction (FSI) framework. After a concise review of ear anatomy and tonotopic principles, two variational formulations are derived for the solid (first acoustic, then elastic) and one for the fluid, with analytically derived boundary conditions. We conduct three families of simulations. (1) A first acoustic model serves as a conceptual preconditioning step to identify parameters and verify boundary-condition choices. (2) A finite-element elastic model (FreeFEM), coupled to a fluid treated under a plane-wave assumption and using mesh deformation, reproduces displacement amplitudes on the order of a few nanometers, consistent with biological measurements. The location of vibration peaks along the basilar membrane agrees well with Greenwood's function at high frequencies, although our low-frequency results remain insufficiently precise. (3) An FSI model that solves the full Navier--Stokes equations confirms the validity of the plane-wave approximation at physiological viscosities and yields pressure and displacement fields that are nearly indistinguishable. The main limitations arise at low frequencies, where the 2D framework and the assumption of an isotropic solid prove inadequate. We therefore propose several avenues for future work: a 3D orthotropic extension of the basilar membrane, refined basal boundary conditions (stapes/oval window), and parameter calibration.\\