A fibrous dynamic continuum model of the tympanic membrane

Abstract

The geometry and anisotropic ultrastructure of the tympanic membrane are used in combination with curvilinear shell equations to formulate a general continuum model describing its dynamic behavior. Primary terms appearing in the model are associated with shell membrane restoring forces, bending-type structural damping, and transverse inertia. Since the model is based extensively on the physical characteristics of the membrane, it is relatively easy to account for differences between species as well as pathological conditions. The fibrous structure and cone-shaped geometry, readily apparent in mammalian eardrums, introduce several small parameters into the model that are exploited in order to construct a closed-form asymptotic solution. The solution includes the coupling to the three-dimensional motion of the ossicular chain and it includes the frequency-dependent pressure distribution in the auditory canal. When applied to the cat eardrum, this asymptotic solution is shown to reproduce a large manifold of experimentally observed frequency and excitation-dependent vibrational shapes. In addition to the shapes, transient amplitude and phase data for the cat are reproduced.

Outer and Middle Ears

“…The decrease in motion results because the malleus, together with the attached ossicles and cochlea, loads the parts of the membrane that are "coupled" to the manubrium but have less effect on more "distant" parts of the membrane (Funnell and Laszlo 1977; Shaw and Stinson 1983; Rabbitt and Holmes 1986;Funnell, Decraemer, and Khanna 1987). The attachment of the malleus to the tympanic membrane varies among species (Funnell and Laszlo 1982).…”

Time-domain “wave” model of the human tympanic membrane

“…Distributed models may be used to accurately simulate more complex anatomical structures of the TM. Typically, those models rely on a finite elements analysis (FEA), or an asymptotic approach (Funnel and Laszlo, 1978;Rabbitt and Holmes, 1986;Funnel et al, 1987). A clear strength of FEA models is that they can account for complex mechanical and physical constraints by their detailed representations of the eardrum structure.…”

Computer-integrated finite element modeling of human middle ear

“…Several quantitative middle ear models, including an analytical model (Rabbitt and Holmes 1986), analog circuit model (Hudde and Weistenhöfer 1997) and multibody model (Eiber et al 2000) sought to predict normal and pathological mechanics in the middle ear. Yet, the finite element (FE) method, a general numerical procedure, has distinct advantages in modeling complex biological systems when compared to other methods.…”