Modeling the eardrum as a string with distributed force

Abstract

In this paper, an analytical model of the tympanic membrane is introduced where the two-dimensional tympanic membrane is reduced to a one-dimensional string. It is intended to bridge the gap between lumped-element models and finite-element models. In contrast to known lumped-element models, the model takes the distributed effect of the sound field on the tympanic membrane into account. Compared to finite-element models, it retains the advantage of a low number of parameters. The model is adjusted to forward and reverse transfer functions of the guinea-pig middle ear. Although the fitting to experimental data is not perfect, important conclusions can be drawn. For instance, the model shows that the delay of surface waves on the tympanic membrane can be different from the signal transmission delay of the tympanic membrane. In a similar vein, the standing wave ratio on the tympanic membrane and within the ear canal can considerably differ. Further, the model shows that even in a low-loss tympanic membrane the effective area, which commonly is associated with the transformer ratio in a lumped-element and some hybrid circuit models, not only is frequency-dependent, but also different for forward and reverse transduction.

Wave motion on the surface of the human tympanic membrane: Holographic measurement and modeling analysis

“…This model formalized the concept of impedance matching at multiple places within the ossicular system: Between air in the ear canal and the TM, between the TM and the ossicular chain, and between the ossicular chain and the inner ear. These ideas are further developed in the TM transmission-line models of Allen (2007, 2010), and the string model of Goll and Dalhoff (2011).…”

“…For example, Goll and Dalhoff (2011) suggest that the ME delay they see in their model depends on the location of the reference stimulus along their string. We are investigating the possibility that the ear canal delays can alter the wave motions we see by using a glass-backed artificial ear canal that mimics the angulation of the TM ring and the canal terminus but allows observation of most of the TM surface.…”

“…Therefore, the traveling waves we observe on the TM surface are fundamentally different from those predicted by Puria and Allen (1998). (e) In a variation of the transmission line model, Goll and Dalhoff (2011) assume the TM is a collection of strings that are bound at the TM ring, and the umbo at the center of the TM. They also assume that the force acting on the surface of the string varies linearly with distance along the string.…”

In-plane and out-of-plane motions of the human tympanic membrane

“…The combination of 3D motion measurements and shape allow us to not only describe the motions normal to the surface, but now we also quantify motions that are tangential to the local TM surface, the socalled in-plane motions. Quantification of these motions allows us to test the applicability of the Kirchhoff-Love thin shell approximation and also investigate suggestions that inplane motions are involved in the transformation of acoustic energy into the mechanical energy associated with the motion of the malleus and ossicles (Goll and Dalhoff, 2011;Jackson et al, 2012;Decraemer et al, 2014). A description of our methods and some preliminary results have been published previously (Khaleghi et al, 2015).…”

“…While there are multiple model descriptions of TM structure and function, progressing from simple piston models (Shaw and Stinson, 1983), through curved-membrane catenary-dependent models (Goll and Dalhoff, 2011), to complex three-dimensional (3D) finite element models (e.g., Funnell et al, 1987;Williams and Lesser, 1990;Blayney et al, 1997;Gan et al, 2002;Koike et al, 2002;Fay et al, 2005), there is no complete description of how the surface of the TM moves in response to sound to test these models. The most complete descriptions of sound-induced TM motion come from recent stroboscopic holography measurements that quantify the sound-induced displacement at over 500 000 points on the TM surface, but only along a single measurement direction (Cheng et al, 2010;Cheng et al, 2013;Cheng et al, 2015).…”