Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Muslov S. A., Sukhochev P. Y. Comparison of hyperelastic and formally defined deformation models of the stapedius tendon of the middle ear. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 2, pp. 251-264. DOI: 10.18500/1816-9791-2026-26-2-251-264, EDN: PRWOZZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Russian
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Article
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531/534+577.354
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PRWOZZ

Comparison of hyperelastic and formally defined deformation models of the stapedius tendon of the middle ear

Autors: 
Muslov Sergey A., Russian University of Medicine
Sukhochev Pavel Yu., Lomonosov Moscow State University
Abstract: 

This article examines some unresolved issues concerning the mechanical properties of the middle ear organs — its tendons, in particular the stapedius tendon. The mechanical properties of biological tissues are a central topic in biomechanics and bioengineering. Mechanical characteristics are important parameters in computer modeling of organs and tissues during their functioning or under external influences. Mechanical properties of the stapedius tendon of the human middle ear are examined within the framework of the most commonly used hyperelastic models in the literature, as well as formally defined deformation models that allow for the description of the experimental curve with minimal error. The calculations were performed in the Mathcad 15.0 computer algebra system using specially developed functionality. The agreement between mechanical test data and model data was assessed using descriptive statistics. The results showed that the polynomial, Veronda-Westmann, and exponential models were the most accurate in terms of fitting the experimental data. The Hill – Drucker criterion $E > 0$ and the condition $\partial E / \partial \lambda > 0$ are satisfied by the Ogden, Yeoh, Veronda – Westmann, Fung, and Gent models, as well as one formally defined model (the exponential model). It is not recommended to use the 2-parameter Mooney – Rivlin model in the undeformed state and under small deformations due to the loss of mechanical stability of the model in this range $\lambda$. The results obtained in the work can be used for practical purposes in the creation of a physical model and finite element modeling of the middle ear, as well as in reconstructive surgery in the selection of artificial replacement materials for prosthetics and plastic surgery (stapedoplasty).

Acknowledgments: 
The authors are grateful to Nasr Gairovich Shueb, an otorhinolaryngologist, for his advice on the anatomy of the middle ear organs.
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Received: 
26.09.2023
Accepted: 
02.03.2026
Published: 
01.06.2026