Journal Article

On the strain–stress state of the reconstructed middle ear after inserting a malleus–incus prosthesis

Gennady Mikhasev, Sergey Ermochenko and Matthias Bornitz

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 27, issue 4, pages 289-312
Published in print December 2010 | ISSN: 1477-8599
Published online November 2009 | e-ISSN: 1477-8602 | DOI:
On the strain–stress state of the reconstructed middle ear after inserting a malleus–incus prosthesis

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  • Applied Mathematics
  • Biomathematics and Statistics


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The reconstructed middle ear (RME) consists of a thin annular plate made from cartilage, the intact stapes and a T-like prosthesis replacing the malleus–incus chain and interposed between the stapes and the reconstructed eardrum. Inserting the prosthesis leads inevitably to an initial pretension in the reconstructed ear. A high pretension can lead to a stiffening of the ligaments and a significant shift of the eigenfrequency spectrum of the middle-ear system. Only a weak pretension is required for satisfactory sound transmission. This paper presents a static model of the RME permitting one to estimate the initial strain–stress state of the sound-conducting system after insertion of a prosthesis. Several positions of the prosthesis with respect to the eardrum are considered. The anisotropic stiffness of the stapes annular ligament is represented by a fully occupied stiffness matrix. The equilibrium of the modelled system is described by four vector equations. In the case of small eccentricity of attachment of the prosthesis plate to the eardrum, the perturbation method and the Fourier series are used for solving the plate equation. Otherwise, the finite-difference method is applied. The influence of the geometrical dimensions of the inclined prosthesis and its position on the stresses in the prosthesis–stapes coupling as well as on the pretension of the annular ligament are analysed. Analysis of the calculations performed allows one to conclude that in order to avoid high pretensions and exclude possible luxation of the stapes, the prosthesis should be positioned as close to the centre of the reconstructed eardrum as possible.

Keywords: reconstructed middle ear; eardrum; prosthesis; strain–stress state

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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