Validity of the Liouville--Green (or WKB) method for cochlear mechanics.

Abstract:

:This article presents a comparison of Liouville-Green (LG) calculations and exact solutions of 2- and 3-dimensional cochlea models. The agreement is in general quite good. For certain choices of the model parameters, however, the 2- and 3-dimensional LG solutions show appreciable errors in the region just beyond the location of maximum amplitude of the basilar membrane response. The origin of these errors appears to be the non-uniqueness of the (complex) LG wave number k(x) in 2- and 3-dimensional models: the 'eikonal equation' from which k(x) has to be solved has multiple roots. To study this problem somewhat deeper, the properties of the locus of k=k(x) formed when x is varied, are investigated. Erratic behaviour of the LG solution is found to occur when this root locus approaches one of the saddle points of a complex function of k- called Q(k)- which plays the major role in the eikonal equation. Apart from this specific problem, the LG approximation is very well suited to unravel the mechanisms governing wave propagation and attenuation in the cochlea. The analysis shows clearly why and how the response of the basilar membrane builds up to a maximum and which factors cause a turnover and a rapid decrease to occur, in both the long-wave and the short-wave cases. A special discussion is dedicated to the relation between the LG approximation and the absence of wave reflection in cochlea models of the type studied.

journal_name

Hear Res

journal_title

Hearing research

authors

de Boer E,Viergever MA

doi

10.1016/0378-5955(82)90071-5

subject

Has Abstract

pub_date

1982-10-01 00:00:00

pages

131-55

issue

2

eissn

0378-5955

issn

1878-5891

pii

0378-5955(82)90071-5

journal_volume

8

pub_type

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