Deformations of the isolated mouse tectorial membrane produced by oscillatory forces

Mechanical properties of the isolated tectorial membrane (TM) of the mouse were measured by applying oscillatory shear forces to the TM with a magnetic bead (radius approximately 10 mcm). Sinusoidal forces at 10 Hz with amplitudes from 5 to 33 nN were applied tangentially to the surfaces of 11 TMs. The ratio of force to bead displacement ranged from 0.04 to 0.98 N/m (median: 0.18 N/m, interquartile range: 0.11-0.30 N/m, n=90). Increasing frequency from 10 to 100 Hz decreased the magnitude of the displacement of the magnetic bead by 6-7.3 dB/decade. The phase of the displacement lagged that of the stimulus current by approximately 27-44 degrees across frequencies. Displacement of the adjacent tissue decreased as the distance from the magnetic bead increased. Space constants were of the order of tens of micrometers. Forces with equal amplitude and frequency were applied radially and longitudinally. Longitudinal displacements in response to longitudinal forces were 1-10 times as large as radial displacements in response to radial forces in 85% of 560 paired measurements. These results suggest that the following mechanical properties of the TM are important. (1) Viscoelasticity: The frequency dependence of TM displacement lies between that of a purely viscous and a purely elastic material, suggesting that both are important. (2) Mechanical coupling: Space constants indicate that hair bundles could interact mechanically with adjacent hair bundles via the TM. (3) Anisotropy: The mechanical impedance is greater in the radial direction than it is in the longitudinal direction. This mechanical anisotropy correlates with anatomical anisotropies, such as the radially oriented fibrillar structure of the TM.