Steady streaming in a two-dimensional box model of a passive cochlea

Abstract

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencies.

Identifying Mechanisms Behind the Tullio Phenomenon: a Computational Study Based on First Principles

“…They arise also from the fluid-structure coupling at the elastic walls of the membranous labyrinth. Such nonlinearities also appear in the cochlea (Edom et al 2014;Lighthill 1992). Investigating these nonlinear sources, we identify two mechanisms which have a significant effect on the formation of steady streaming within the phenomenologically relevant parameter range.…”

“…(5b). Another source of nonlinearity results inherently from the interaction between a flexible membrane (membranous duct) and a viscous fluid (endolymph) as it has been shown by Bradley (2012) and Edom et al (2014). Cupula and Eye Response.…”

“…In the context of the inner ear, streaming phenomena (in the cochlea) have already been identified by von Békésy (1960). Further theoretical and computational studies on streaming in the cochlea (Hallauer 1974;Lighthill 1992;Gerstenberger and Wolter 2013;Edom et al 2014) showed that the well-known traveling waves on the basilar membrane induce a large nonoscillating vortical flow on either side of the basilar membrane which is known as Békésy eddy (see Lesser and Berkley 1972, Figure 4).…”

“…(5b), i.e., setting (u e · ∇) u e = 0. In consequence, only the FSI-induced nonlinearities are able to provoke the resulting mean endolymph flow (see Bradley 2012, or Edom et al 2014, section 4.2.1). In a numerical experiment, we eliminated the advection term to demonstrate the effect of the absence of Reynolds stresses on the steady streaming.…”

Illustrations of Lighthill’s 1992 equations for the two-dimensional fluid motion and associated viscous dissipation within the cochlea

“…While Lighthill's 1981 publication on the energy flux in the cochlea 1 is probably his best known paper in our field, his paper about acoustic streaming in the cochlea 2 remained largely ignored, although its Appendix A contains a most detailed analytical descriptions of the two-dimensional particle trajectories and viscous energy dissipation in the cochlear fluid, which have been recently confirmed numerically by finite element simulation 3 . Although Lighthill asserts that his descriptions are even accurate enough to quantify the cochlear fluid motion at short wavelengths, with fluid motion supposedly being locally two-dimensional, his equations for the two-dimensional case do certainly describe qualitative phenomena, which apply also to the real three-dimensional cochlea.…”