Figure 11. Circuit diagram.

Middle ear modeled as a succession of mass/stiffness elements in a transmission line. Masses (M) are in g and stiffness (K) in dyn/cm. The first sub-circuit corresponds to the manubrium, which because of its flexibility has properties of both mass (M_man) and stiffness (K_man). The second sub-circuit corresponds to the malleus (M_m) and malleus-incus joint (K_mij). The third sub-circuit corresponds to the incus (M_i) and incus-stapes junction (K_is). The stapes mass is terminated by the cochlear input impedance, Z_C. The values for Z_C and the masses were informed by values in the literature, see text for details. The stapes footplate area, A_fp is also in the literature. We used an impedance matching assumption to find the K values, as follows (see text): $Z_c{A}_{fp}^2=\sqrt{K_{\mathit{man}}{M}_{\mathit{man}}}=\sqrt{K_{\mathit{mij}}{M}_m}=\sqrt{K_{is}{M}_i}$. The parameter values used in the model are:

$$\begin{array}{l}{M}_{st}=1.16\times {10}^{-4}g,M_i=1.055\times {10}^{-4}g,M_m=1.27\times {10}^{-4}g,M_{\mathit{man}}=6.36\times {10}^{-5}g\\ K_{is}=1.4\times {10}^7\mathit{dyne}/cm,K_{\mathit{mij}}=1.16\times {10}^7\mathit{dyne}/cm,K_{\mathit{man}}=2.32\times {10}^7\mathit{dyne}/cm\\ A_{fp}=6.2\times {10}^{-3}{cm}^2,Z_c=1\times {10}^6\mathit{dyne}·s/c{m}^5\end{array}$$