An Analysis of the Acoustic Input Impedance of the Ear

Abstract

Ear canal acoustics was examined using a onedimensional lossy transmission line with a distributed load impedance to model the ear. The acoustic input impedance of the ear was derived from sound pressure measurements in the ear canal of healthy human ears. A nonlinear least squares fit of the model to data generated estimates for ear canal radius, ear canal length, and quantified the resistance that would produce transmission losses. Derivation of ear canal radius has application to quantifying the impedance mismatch at the eardrum between the ear canal and the middle ear. The length of the ear canal was found, in general, to be longer than the length derived from the one-quarter wavelength standing wave frequency, consistent with the middle ear being mass-controlled at the standing wave frequency. Viscothermal losses in the ear canal, in some cases, may exceed that attributable to a smooth rigid wall. Resistance in the middle ear was found to contribute significantly to the total resistance. In effect, this analysis "reverse engineers" physical parameters of the ear from sound pressure measurements in the ear canal.

Non-invasive estimation of middle-ear input impedance and efficiency

“…Data from all studies are consistent with the ME being stiffness dominated through 1 kHz, as evidenced by jZ ED j decreasing at a rate of $3 dB/ octave (power units) and a negative /Z ED . Other work has similarly demonstrated the stiffness dominance of Z ED at low frequencies in humans and other mammals (Zwislocki, 1962;Shaw and Stinson, 1981;Rabinowitz, 1981;Lynch et al, 1994;Voss and Allen, 1994;Huang et al, 2000a;Withnell and Gowdy, 2013). FIG.…”

“…6). The resonances and anti-resonances in Z ED from Margolis et al (1999) are likely due to the impedances of the ossicles (Withnell and Gowdy, 2013) and ME air space (Zwislocki, 1962;Stepp and Voss, 2005;Keefe, 2015), whereas those in Z ED from Voss et al (2001b) and O'Connor and Puria (2008) may be due primarily to the ossicles (as these studies subtracted the impedance of the ME air space from Z ED ). Had the ME model used in the current work been extended to include either the ME air space or additional mass-elements for the ossicles, the estimated Z ED might have more closely approximated that from the other studies.…”

“…Data from Voss et al (2001b) was obtained only to 4 kHz and so further comparison with that study is not possible. Recent modeling work in living ears from Withnell and Gowdy (2013) suggests that Z ED becomes mass-dominated above 4 kHz (also see Shaw, 1977 andKringlebotn, 1988). Indeed, the form of Z ED above 4 kHz remains an area of uncertainty and likely is influenced by the particular ME model used to derive the estimate.…”

“…Multiple magnitude fluctuations accompanied by small phase shifts were evident in Z ED , especially between 1 and 5 kHz. Presumably, these magnitude and phase fluctuations are associated with the acoustics of the ossicles and/or middle-ear air space (Stepp and Voss, 2005;Withnell and Gowdy, 2013). Z ED was stiffness dominated through at least 12 kHz.…”

“…Previous work transforming Z EC to Z ED have relied on a model of the residual canal space where the cross-sectional area was fixed (Rabinowitz, 1981;Voss and Allen, 1994;Margolis et al, 1999;Withnell and Gowdy, 2013). However, the area of the canal changes across its length (e.g., Stinson and Lawton, 1989;Farmer-Fedor and Rabbitt, 2002;Rasetshwane and Neely, 2011) with the effect that a portion of the forward-propagating sound pressure may be reflected before reaching the eardrum (as occurs in an acoustic horn, Rasetshwane et al, 2012).…”