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

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 [1–4]. During the stapes footplate piston-like vibration, in which the footplate moves inward and outward the cochlear fluid [5,6], the SAL mainly sustains high-frequency shear deformation. Mechanical properties of the SAL directly affect the acoustic-mechanical transmission function of the middle ear [7] and the abnormal changes of SAL induced by ear diseases may cause severe conductive hearing loss. For example, in otosclerosis, the abnormal ossification of the SAL reduces the movement of the stapes and causes the conductive hearing loss [8,9]. Moreover, since the transmission of sound energy from the middle ear to cochlear fluid is largely dependent on SAL mechanical behavior, the properties of SAL have affected the outcomes of stapedotomy or stapesplasty surgical approaches with different prostheses or SAL grafts [10–12]. Therefore, understanding the mechanical properties of the SAL is one of important research subjects in middle ear biomechanics. Despite the importance, mechanical properties of the SAL have only been reported once in the literature by Gan et al. [13]. They measured the shear modulus of human SAL through the quasi-static pulling test and the results showed that the SAL had typical nonlinear mechanical behaviors and the shear modulus varied from 3.6 to 220 kPa when the shear stress increased from 2 to 140 kPa. However, the ear tissues work under the auditory frequency range from 20 to 20,000 Hz. The lack of dynamic properties of SAL over the auditory frequency range affects fully understanding of sound transmission from the middle ear to cochlea and the development of an accurate FE model of the ear. In most FE models of the human ear, mechanical properties of the SAL were assumed through the cross-calibration process and a constant elastic modulus varying from 0.065 to 5.5 MPa was used for the FE models [14–16]. There is an urgent need to measure SAL dynamic properties in the auditory frequency range. DMA is widely used to measure dynamic properties of materials in the frequency domain. However, the current commercial DMA has limited higher frequency access and cannot reach the human auditory frequency range. Recently, a study on measuring the dynamic properties of human tympanic membrane based on the FTS principle has been reported by our group [17]. The basic theory of FTS considers the dynamic behavior of some materials as a function of two principle variables: frequency and temperature. The effect of temperature changing on dynamic properties of the material is equivalent to that of frequency changing [18,19]. The FTS as an empirical method has been validated by our previous study on tympanic membrane and can be applied to measure the dynamic properties of ear tissues in auditory frequencies. In this paper, following the method developed in our previous paper [17], the dynamic properties of human SAL were measured using the DMA. The test was conducted at frequencies from 1 to 40 Hz at three different temperatures: 5 °C, 25 °C, and 37 °C. The FTS principle was applied to extend the testing frequency to a much higher level (at least 3760 Hz). 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 SAL specimens. The data reported in this study contribute to the biomechanics of the middle ear.