Basilar membrane and tectorial membrane stiffness in the CBA/CaJ mouse

Abstract

The mouse has become an important animal model in understanding cochlear function. Structures, such as the tectorial membrane or hair cells, have been changed by gene manipulation, and the resulting effect on cochlear function has been studied. To contrast those findings, physical properties of the basilar membrane (BM) and tectorial membrane (TM) in mice without gene mutation are of great importance. Using the hemicochlea of CBA/CaJ mice, we have demonstrated that tectorial membrane (TM) and basilar membrane (BM) revealed a stiffness gradient along the cochlea. While a simple spring mass resonator predicts the change in the characteristic frequency of the BM, the spring mass model does not predict the frequency change along the TM. Plateau stiffness values of the TM were 0.6 ± 0.5, 0.2 ± 0.1, and 0.09 ± 0.09 N/m for the basal, middle, and upper turns, respectively. The BM plateau stiffness values were 3.7 ± 2.2, 1.2 ± 1.2, and 0.5 ± 0.5 N/m for the basal, middle, and upper turns, respectively. Estimations of the TM Young's modulus (in kPa) revealed 24.3 ± 25.2 for the basal turns, 5.1 ± 4.5 for the middle turns, and 1.9 ± 1.6 for the apical turns. Young's modulus determined at the BM pectinate zone was 76.8 ± 72, 23.9 ± 30.6, and 9.4 ± 6.2 kPa for the basal, middle, and apical turns, respectively. The reported stiffness values of the CBA/CaJ mouse TM and BM provide basic data for the physical properties of its organ of Corti.

FIG. 1

The sensor used for the stiffness measurements consisted of an insect needle pin, sensor bimorph, driver bimorph, and a glass rod. All components were attached to each other with cyanoacrylate. The sensor tip diameter was about 10 μm.

FIG. 2

Sensor response voltage measured from the sensor bimorph is plotted versus the sensor tip displacement. Voltage decreased linearly with a slope of 0.082 V/μm until the sensor’s noise floor of 1 mV (dashed line) was reached.

FIG. 3

Cantilever tips of an atomic force microscope (50-μm wide, 450-μm long, and 2–5-μm thick) were chosen to test the sensor’s validity by measuring a known stiffness. The cantilever stiffness provided by the manufacturer was between 0.2 and 1.6 (N/m), dependent on the cantilever. The measured stiffness values were similar to the provided stiffness values. Differences were not statistically significant (paired t test, p < 0.05).

FIG. 4

Cochlear cross-sectional view in the apical turn of a CBA/CaJ mouse hemicochlea. The short arrows indicate the sites of sensor tip positioning for stiffness measurements at the BM and TM. Notice that the tip is approximately at the middle of the pectinate zone of the BM or at the middle of the upper surface of the TM. Radial and longitudinal directions within the cochlea are indicated by long arrows.

FIG. 5

A Sketch of the sensor system and its systematic approach to the target tissue. For each step of the measurement, the base to which the stiffness sensor is mounted is advanced by 1 μm (Δx _base-static  = 1 μm). If the tip of the stiffness sensor does not touch any object, the tip will also advance by 1 μm and Δx _tip-static = 1 μm. In case the tip touches tissue, the base still will advance by 1 μm (Δx _base-static), but the tip will advance less Δx _tip-static = 1 μm- x _{deflect-dynamic}. The deflection of the stiffness sensor equals the amount the tip advancement will be less than the base advancement or, in other words, the tip advancement plus the deflection are same as the base advancement (Δx _tip-static  + x _{deflect-dynamic} =Δx _base-static). B shows a representative example of the point stiffness as a function of sensor base and sensor tip position. C shows the increase in point stiffness with the advancement of the sensor. The stiffness increases from the noise floor over a small range to a plateau. Beyond the plateau, the stiffness increases in a non-linear fashion. Data are fitted to the function k(x) = k _plateau + A(x − x _offset)² (see also text) to determine the value for the plateau stiffness.

FIG. 6

Indentation of the measuring sensor in the BM. In the left column, the measuring sensor is shown at different distances from the BM and after indentation. The middle column is the difference of the image in the left column and the first image in the left column. If no displacement occurred, the image is gray or white. The darkened areas show the displacements of the sensor or tissue structures in the difference images. The right column provides the corresponding sensor responses. Filled circles show at which point during the advancement of the sensor base the image has been taken.

FIG. 7

Indentation of the measuring sensor in the TM. In the left column, the measuring sensor is shown at different distances from the TM and after indentation. The middle column is the difference of the image in the left column and the first image in the left column. If no displacement occurred, the image is gray or white. The darkened areas show the displacements of the sensor or tissue structures in the difference images. The right column provides the corresponding sensor responses. Filled circles show at which point during the advancement of the sensor base the image has been taken.

FIG. 8

A shows all measured Young’s modulus values of the BM in CBA/CaJ mice. Values were obtained for the basal, middle, and apical turns of the cochlea. B depicts all Young’s modulus data for the TM, obtained at the same longitudinal cochlear position as in described in A.

FIG. 9

A and B show basic driving point stiffness measurements obtained at the BM and TM in CBA/CaJ mice. The green graphs show recordings from the apical turn, the blue and red graphs depict measurements from the middle and basal turn, respectively. C and D show all the corresponding plateau stiffness values from the recordings shown in A and B. Plateau stiffness was determined as described in methods and Figure 5c.

FIG. 10

The square root of the driving point stiffness obtained at the BM is plotted together with the best-frequency neural map of Müller et al. (2005).