High-Frequency Force Generation in the Constrained Cochlear Outer Hair Cell: A Model Study

Abstract

Cochlear outer hair cell (OHC) electromotility is believed to be responsible for the sensitivity and frequency selectivity of the mammalian hearing process. Its contribution to hearing is better understood by examining the force generated by the OHC as a feedback to vibration of the basilar membrane (BM). In this study, we examine the effects of the constraints imposed on the OHC and of the surrounding fluids on the cell's high-frequency active force generated under in vitro and in vivo conditions. The OHC is modeled as a viscoelastic and piezoelectric cylindrical shell coupled with viscous intracellular and extracellular fluids, and the constraint is represented by a spring with adjustable stiffness. The solution is obtained in the form of a Fourier series. The model results are consistent with previously reported experiments under both low-and high-frequency conditions. We find that constrained OHCs achieve a much higher corner frequency than free OHCs, depending on the stiffness of the constraint. We analyze cases in which the stiffness of the constraint is similar to that of the BM, reticular lamina, and tectorial membrane, and find that the force per unit transmembrane potential generated by the OHC can be constant up to several tens of kHz. This model, describing the OHC as a local amplifier, can be incorporated into a global cochlear model that considers cochlear hydrodynamics and frequency modulation of the receptor potential, as well as the graded BM stiffness and OHC length.

Contribution of outer hair cell bending to stereocilium deflection in the cochlea

“…For the constrained OHC of length 30 lm (with K = 0.05 N/m), our results (about 0.5 nm/mV) are somewhat smaller than those (about 0.8 nm/mV) given by Liao et al (2005b). The differences in the values are probably due to the different lateral wall models (one-layered membrane model) and parameters used in their models.…”

“…For the isolated OHC of length 60 lm (with K = 0), our results are close to those given by Tolomeo and Steele (1998). For the isolated OHC of length 30 lm (with K = 0), our results (about 4.5 nm/mV at low frequencies) are larger than those (about 3 nm/mV at low frequencies) given by Liao et al (2005b). 5 e x h P (nN/lm/mV) À2.16 · 10 À3 À0.87 · 10 À3 E P h P (nN/lm) 1 e h h P (nN/lm/mV) À2.02 · 10 À3 À0.81 · 10 À3 m P 0.9 G xh (nN/lm 2 ) 6.3933 6.3933 Tolomeo and Steele (1998) and Fig.…”

“…3, the amplitude remains almost unattenuated up to 10 kHz. This is in accordance with the finding that stiffness-constrained OHCs achieve higher corner frequencies than freely isolated OHCs (Liao et al, 2005b). The phase values in Fig.…”

“…2, the results from our model are compared with the reported frequency responses of the OHC for the axisymmetric mode (Tolomeo and Steele, 1998;Liao et al, 2005b). For the beam-bending mode, no reported results are available for comparison.…”

“…5 e x h P (nN/lm/mV) À2.16 · 10 À3 À0.87 · 10 À3 E P h P (nN/lm) 1 e h h P (nN/lm/mV) À2.02 · 10 À3 À0.81 · 10 À3 m P 0.9 G xh (nN/lm 2 ) 6.3933 6.3933 Tolomeo and Steele (1998) and Fig. 3b in Liao et al (2005b).…”