Research Papers

Dynamic Properties of Human Stapedial Annular Ligament Measured With Frequency–Temperature Superposition

[+] Author and Article Information
Xiangming Zhang

School of Aerospace and
Mechanical Engineering and
OU Bioengineering Center,
University of Oklahoma,
Norman, OK 73019

Rong Z. Gan

Department of Biomedical Engineering,
School of Aerospace and
Mechanical Engineering and
Bioengineering Center,
University of Oklahoma,
865 Asp Avenue, Room 200,
Norman, OK 73019
e-mail: rgan@ou.edu

1Corresponding author.

Manuscript received December 10, 2013; final manuscript received April 20, 2014; accepted manuscript posted May 14, 2014; published online June 2, 2014. Assoc. Editor: Guy M. Genin.

J Biomech Eng 136(8), 081004 (Jun 02, 2014) (7 pages) Paper No: BIO-13-1571; doi: 10.1115/1.4027668 History: Received December 10, 2013; Revised April 20, 2014; Accepted May 14, 2014

Stapedial annular ligament (SAL) is located at the end of human ear ossicular chain and provides a sealed but mobile boundary between the stapes footplate and cochlear fluid. Mechanical properties of the SAL directly affect the acoustic-mechanical transmission of the middle ear and the changes of SAL mechanical properties in diseases (e.g., otosclerosis) may cause severe conductive hearing loss. However, the mechanical properties of SAL have only been reported once in the literature, which were obtained under quasi-static condition (Gan, R. Z., Yang, F., Zhang, X., and Nakmali, D., 2011, “Mechanical Properties of Stapedial Annular Ligament,” Med. Eng. Phys., 33, pp. 330–339). Recently, the dynamic properties of human SAL were measured in our lab using dynamic-mechanical analyzer (DMA). The test was conducted at the frequency range from 1 to 40 Hz at three different temperatures: 5 °C, 25 °C, and 37 °C. The frequency–temperature superposition (FTS) principle was applied to extend the testing frequency range to a much higher level. The generalized Maxwell model was employed to describe the constitutive relation of the SAL. The storage shear modulus G′ and the loss shear modulus G″ were obtained from seven specimens. The mean storage shear modulus was 31.7 kPa at 1 Hz and 61.9 kPa at 3760 Hz. The mean loss shear modulus was 1.1 kPa at 1 Hz and 6.5 kPa at 3760 Hz. The dynamic properties of human SAL obtained in this study provide a better description of the damping behavior of soft tissues than the classic Rayleigh type damping, which was widely used in the published ear models. The data reported in this study contribute to ear biomechanics and will improve the accuracy of finite element (FE) model of the human ear.

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Fig. 1

(a) The schematic of the experiment setup for dynamic test of the SAL specimen in DMA. (b) The enlarged image for the fixation of stapes head to the mounting fixture. The SAL was hiding behind the bony structures.

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Fig. 2

Images of the stapes footplate (a) and oval window (b) stapes, and (c) obtained after experiments on one temporal bone specimen for measuring the dimensions of SAL

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Fig. 3

The complex shear modulus–frequency curves obtained at 5  °C, 25 °C, and 37 °C from two SAL specimens: (a) sample SAL-1 and (b) sample SAL-6.

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Fig. 4

The master curves of the complex shear modulus at 37 °C obtained from two SAL sample: (a) sample SAL-1 and (b) sample SAL-6

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Fig. 5

The master curves of the storage modulus and loss modulus at 37 °C from seven SAL samples and the mean master curves of the storage modulus and loss modulus

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Fig. 6

The theoretical fitting of generalized Maxwell model to the experimental complex modulus for (a) sample SAL-1, (b) sample SAL-6, and (c) the mean experimental complex modulus

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Fig. 7

(a) Damping of the SAL calculated using Rayleigh type coefficient with β = 0.000075 and (b) damping of the SAL calculated from the viscoelastic model determined from the dynamic test in this study




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