Frequency-dependent shear impedance of the tectorial membrane

Microscale mechanical probes were designed and bulk-fabricated for applying shearing forces to biological tissues. These probes were used to measure shear impedance of the tectorial membrane (TM) in two dimensions. Forces were applied in the radial and longitudinal directions at frequencies ranging from 0.01-9 kHz and amplitudes from 0.02-4 μN. The force applied was determined by measuring the deflection of the probes' cantilever arms. TM impedance in the radial direction had a magnitude of 63 ± 28 mN·s/m at 10 Hz and fell with frequency by 16 ± 0.4 dB/decade, with a constant phase of -72 ± 6°. In the longitudinal direction, impedance was 36 ± 9 mN·s/m at 10 Hz and fell by 19 ± 0.4 dB/decade, with a constant phase of -78 ± 4°. Impedance was nearly constant as a function of force except at the highest forces, for which it fell slightly. These results show that the viscoelastic properties of the TM extend over a significant range of audio frequencies, consistent with a poroelastic interpretation of TM mechanics. The shear modulus G′ determined from these measurements was 17-50 kPa, which is larger than in species with a lower auditory frequency range. This value suggests that hair bundles cannot globally shear the TM, but most likely cause bulk TM motion.