Dennis M. Freeman

Longitudinally propagating traveling waves of the mammalian tectorial membrane.

Sound-evoked vibrations transmitted into the mammalian cochlea produce traveling waves that provide the mechanical tuning necessary for spectral decomposition of sound. These traveling waves of motion that have been observed to propagate longitudinally along the basilar membrane (BM) ultimately stimulate the mechano-sensory receptors. The tectorial membrane (TM) plays a key role in this process, but its mechanical function remains unclear. Here we show that the TM supports traveling waves that are an intrinsic feature of its visco-elastic structure. Radial forces applied at audio frequencies (2–20 kHz) to isolated TM segments generate longitudinally propagating waves on the TM with velocities similar to those of the BM traveling wave near its best frequency place. We compute the dynamic shear storage modulus and shear viscosity of the TM from the propagation velocity of the waves and show that segments of the TM from the basal turn are stiffer than apical segments are. Analysis of loading effects of hair bundle stiffness, the limbal attachment of the TM, and viscous damping in the subtectorial space suggests that TM traveling waves can occur in vivo. Our results show the presence of a traveling wave mechanism through the TM that can functionally couple a significant longitudinal extent of the cochlea and may interact with the BM wave to greatly enhance cochlear sensitivity and tuning.

Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching

Image registration algorithms based on piecewise linear inter- polators (spatiotemporal gradients or block matching) are analyzed to determine subpixel registration accuracy. Results reveal not only random errors due to image noise but also systematic bias present even if the images are noise free. If the displacement between the images is small, bias is small. However, if the displacement between the images is larger than about 1/25 pixel, the bias component of the registration error ex- ceeds the random component for most imaging conditions. Bias also depends on image content: it is generally larger for images with higher spatial frequency content than for images with lower spatial frequency content. We have developed a reduced-bias registration algorithm that takes advantage of the nearly linear relation between image displace- ment and bias that results for small displacements. The new algorithm is direct (noniterative), increases computational costs by approximately a factor of 4, and reduces the bias by approximately a factor of 4. This improvement is large compared to improvement obtained with averag- ing. For our applications, in which imaging noise is typically 50 dB smaller than the signal, registration errors using the new algorithm are smaller than 1/50 pixel.

Using a light microscope to measure motions with nanometer accuracy

A system for measuring nanometer motions of microscopic structures is demonstrated. Stop-action images of a target are obtained with a light microscope, CCD camera, and stroboscopic illuminator. Mo- tions are determined directly from measured images using algorithms from computer vision. The accuracy of motion measurements using the system is assessed using a moving target with calibrated displacements. Accuracy is determined for specimens viewed under our most optimal conditions as well as for a number of suboptimal conditions that illustrate important degradation mechanisms. Measured errors are compared to predictions based on computer simulations of theoretical models. Re- sults show that the most important hardware factors include substrate vibrations and camera imperfections. Measurement errors for the most optimal hardware conditions are primarily due to systematic bias in the computer vision algorithms. For our most optimal conditions, the system can resolve motions as small as nanometers. Thus, errors in motion measurements are small compared to both the wavelength of the light used to obtain the images and the pixel spacing of the video microscope.

Plastic masters—rigid templates for soft lithography

We demonstrate a simple process for the fabrication of rigid plastic master molds for soft lithography directly from (poly)dimethysiloxane devices. Plastics masters (PMs) provide a cost-effective alternative to silicon-based masters and can be easily replicated without the need for cleanroom facilities. We have successfully demonstrated the use of plastics micromolding to generate both single and dual-layer plastic structures, and have characterized the fidelity of the molding process. Using the PM fabrication technique, world-to-chip connections can be integrated directly into the master enabling devices with robust, well-aligned fluidic ports directly after molding. PMs provide an easy technique for the fabrication of microfluidic devices and a simple route for the scaling-up of fabrication of robust masters for soft lithography.

Multi-image gradient-based algorithms for motion estimation

image registration algorithms based on gradient methods provide quantitative motion measurements from sequences of video images. Although such measurements can be degraded by image noise, larger degradations typically result from systematic bias in the algorithms that is present even if the images are noise-free. To improve the accuracy of motion measurements, we develop a new class of multi-image algorithms based on multidimensional digital filters. The new algorithms provide better estimates of spatial and temporal gradients and also compensate for motion blur caused by the nonzero acquisition time of the imager. We optimize filters to measure arbitrary motions, and we illustrate the results when those filters are used to estimate constant velocity movements. We also show results for filters that are optimized for harmonic analysis of periodic motions. Using these algorithms, systematic bias in the amplitude of sinusoidal motion is less than 0.001 pixels for motions smaller than 1 pixel in amplitude. This represents a hundredfold decrease in bias compared to existing methods.

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.

Static material properties of the tectorial membrane: a summary

The tectorial membrane (TM) is a polyelectrolyte gel. Hence, its chemical, electrical, mechanical, and osmotic properties are inextricably linked. We review, integrate, and interpret recent findings on these properties in isolated TM preparations. The dimensions of the TM in alligator lizard, chick, and mouse are sensitive to bath ion concentrations of constituents normally present in the cochlear fluids - an increase in calcium concentration shrinks the TM, and an increase in sodium concentration swells the TM in a manner that depends competitively on the calcium concentration. The sodium-induced swelling is specific; it does not occur with other alkali metal cations. We interpret these findings as due to competitive binding of sodium and calcium to TM macromolecules which causes a change in their conformation that leads to a change in mechanical properties. In mouse TM, decreasing the bath pH below 6 or increasing it above 7 results in swelling of the TM. Electric potential measurements are consistent with the notion that the swelling is caused by a pH-driven increase in positive fixed charge at low pH and an increase in the magnitude of the negative fixed charge at high pH which is consistent with the known protonation pattern of TM macromolecules. Increasing the osmotic pressure of the bathing solution with polyethylene glycol shrinks the TM and decreasing the ionic strength of the bathing solution swells the TM. Both results are qualitatively consistent with predictions of a polyelectrolyte gel model of the TM.

Tectorial membrane travelling waves underlie abnormal hearing in Tectb mutant mice

Remarkable sensitivity and exquisite frequency selectivity are hallmarks of mammalian hearing, but their underlying mechanisms remain unclear. Cochlear insults and hearing disorders that decrease sensitivity also tend to broaden tuning, suggesting that these properties are linked. However, a recently developed mouse model of genetically altered hearing (Tectb−/−) shows decreased sensitivity and sharper frequency selectivity. In this paper, we show that the Tectb mutation reduces the spatial extent and propagation velocity of tectorial membrane (TM) travelling waves and that these changes in wave propagation are likely to account for all of the hearing abnormalities associated with the mutation. By reducing the spatial extent of TM waves, the Tectb mutation decreases the spread of excitation and thereby increases frequency selectivity. Furthermore, the change in TM wave velocity reduces the number of hair cells that effectively couple energy to the basilar membrane, which reduces sensitivity. These results highlight the importance of TM waves in hearing.

Nanometer resolution of three-dimensional motions using video interference microscopy

An interferometric video system for measuring microelectromechanical systems (MEMS) with nanometer resolution is demonstrated. Interferograms are generated by combining light reflected from the target with light reflected from a reference mirror. Motions are determined from sequences of stop-action interferograms obtained with stroboscopic illumination. The system was used to measure motions of a microfabricated accelerometer. In-plane motions were determined by analysis of brightfield images using gradient methods with subpixel resolution. Results are compared for brightfield images obtained by blocking light from the reference arm of the interferometer and for brightfield images reconstructed from interferograms. Out-of-plane motions are determined by analyzing interferograms obtained with different positions of the reference mirror. Results demonstrate nanometer resolution of in-plane motions and subnanometer resolution of out-of-plane motions.

Hydrodynamic forces on hair bundles at low frequencies

We have analyzed a model for the motion of hair bundles of hair cells at low frequencies. In the model, hair-cell organs are represented as a system of rigid mechanical structures surrounded by fluid. A rigid body, that represents a hair bundle, is hinged to a vibrating plate that represents the sensory epithelium. These structures are surmounted by a second vibrating plate that represents a tectorial structure. The analysis shows that both viscous and inertial properties of the fluid are important even at asymptotically low frequencies. The relative importance of these properties depends critically on the presence and mode of motion of the tectorial plate. As a result, the angular displacement of the body at low frequencies can be proportional to basal plate displacement, velocity, acceleration, or to no simple integral of its motion; the functional relation depends upon the disposition of the tectorial plate.