Fluid Jet Stimulation of Auditory Hair Bundles Reveal Spatial Non-uniformities and Two Viscoelastic-Like Mechanisms.

Hair cell mechanosensitivity resides in the sensory hair bundle, an apical protrusion of actin-filled stereocilia arranged in a staircase pattern. Hair bundle deflection activates mechano-electric transduction (MET) ion channels located near the tops of the shorter rows of stereocilia. The elicited macroscopic current is shaped by the hair bundle motion so that the mode of stimulation greatly influences the cell's output. We present data quantifying the displacement of the whole outer hair cell bundle using high-speed imaging when stimulated with a fluid jet. We find a spatially non-uniform stimulation that results in splaying, where the hair bundle expands apart. Based on modeling, the splaying is predominantly due to fluid dynamics with a small contribution from hair bundle architecture. Additionally, in response to stimulation, the hair bundle exhibited a rapid motion followed by a slower motion in the same direction (creep) that is described by a double exponential process. The creep is consistent with originating from a linear passive system that can be modeled using two viscoelastic processes. These viscoelastic mechanisms are integral to describing the mechanics of the mammalian hair bundle.

In situ motions of individual inner-hair-cell stereocilia from stapes stimulation in adult mice.

In vertebrate hearing organs, mechanical vibrations are converted to ionic currents through mechanoelectrical-transduction (MET) channels. Concerted stereocilia motion produces an ensemble MET current driving the hair-cell receptor potential. Mammalian cochleae are unique in that the tuning of sensory cells is determined by their mechanical environment and the mode of hair-bundle stimulation that their environment creates. However, little is known about the in situ intra-hair-bundle motions of stereocilia relative to one another, or to their environment. In this study, high-speed imaging allowed the stereocilium and cell-body motions of inner hair cells to be monitored in an ex vivo organ of Corti (OoC) mouse preparation. We have found that the OoC rotates about the base of the inner pillar cell, the hair bundle rotates about its base and lags behind the motion of the apical surface of the cell, and the individual stereocilia move semi-independently within a given hair bundle.

A two-photon FRAP protocol to measure the stereociliary membrane diffusivity in rat cochlear hair cells.

Fluorescence recovery after photobleaching (FRAP) has been widely used to monitor membrane properties by measuring the lateral diffusion of fluorescent particles. This protocol describes how to perform two-photon FRAP on the stereocilia of live cochlear inner hair cells using a lipophilic dye, di-3-ANEPPDHQ, to assess the stereociliary membrane diffusivity. We also detail two-photon FRAP microscope setup and calibration, as well as FRAP parameter setting and data analysis. For complete details on the use and execution of this protocol, please refer to George et al. (2020).

Rat Auditory Inner Hair Cell Mechanotransduction and Stereociliary Membrane Diffusivity Are Similarly Modulated by Calcium.

The lipid bilayer plays a pivotal role in force transmission to many mechanically-gated channels. We developed the technology to monitor membrane diffusivity in order to test the hypothesis positing that Ca2+ regulates open probability (P o) of cochlear hair cell mechanotransduction (MET) channels via the plasma membrane. The stereociliary membrane was more diffusive (9x) than the basolateral membrane. Elevating intracellular Ca2+ buffering or lowering extracellular Ca2+ reduced stereociliary diffusivity and increased MET P o. In contrast, prolonged depolarization increased stereociliary diffusivity and reduced MET P o. No comparable effects were noted for soma measurements. Although MET channels are located in the shorter stereocilia rows, both rows had similar baseline diffusivity and showed similar responses to Ca2+ manipulations and MET channel blocks, suggesting that diffusivity is independent of MET. Together, these data suggest that the stereociliary membrane is a component of a calcium-modulated viscoelastic-like element regulating hair cell mechanotransduction.

Unraveling the mystery of hearing in gerbil and other rodents with an arch-beam model of the basilar membrane.

The mammalian basilar membrane (BM) consists of two collagen-fiber layers responsible for the frequency-to-place tonotopic mapping in the cochlea, which together form a flat beam over at least part of the BM width. The mechanics of hearing in rodents such as gerbil pose a challenge to our understanding of the cochlea, however, because for gerbil the two layers separate to form a pronounced arch over the remaining BM width. Moreover, the thickness and total width normally thought to determine the local stiffness, and tonotopic mapping in turn, change little along the cochlear length. A nonlinear analysis of a newly developed model, incorporating flat upper and arched lower fiber layers connected by ground substance, explains the initial plateau and subsequent quadratic increase found in measured stiffness vs. deflection curves under point loading, while for pressure loading the model accurately predicts the tonotopic mapping. The model also has applicability to understanding cochlear development and to interpreting evolutionary changes in mammalian hearing.

Cochlear Outer-Hair-Cell Power Generation and Viscous Fluid Loss.

Since the discovery of otoacoustic emissions and outer hair cell (OHC) motility, the fundamental question of whether the cochlea produces mechanical power remains controversial. In the present work, direct calculations are performed on power loss due to fluid viscosity and power generated by the OHCs. A three-dimensional box model of the mouse cochlea is used with a feed-forward/feed-backward approximation representing the organ of Corti cytoarchitecture. The model is fit to in vivo basilar membrane motion with one free parameter for the OHCs. The calculations predict that the total power output from the three rows of OHCs can be over three orders of magnitude greater than the acoustic input power at 10 dB sound pressure level (SPL). While previous work shows that the power gain, or the negative damping, diminishes with intensity, we show explicitly based on our model that OHC power output increases and saturates with SPL. The total OHC power output is about 2 pW at 80 dB SPL, with a maximum of about 10 fW per OHC.

Cytoarchitecture of the mouse organ of corti from base to apex, determined using in situ two-photon imaging.

The cells in the organ of Corti are highly organized, with a precise 3D microstructure hypothesized to be important for cochlear function. Here we provide quantitative data on the mouse organ of Corti cytoarchitecture, as determined using a new technique that combines the imaging capabilities of two-photon microscopy with the autofluorescent cell membranes of the genetically modified mTmG mouse. This combination allowed us to perform in situ imaging on freshly excised tissue, thus minimizing any physical distortions to the tissue that extraction from the cochlea and chemical fixation and staining might have caused. 3D image stacks of the organ of Corti were obtained from base to apex in the cochlear duct, from which 3D lengths and relative angles for inner and outer hair cells, Deiters' cells, phalangeal processes, and inner and outer pillars were measured. In addition, intercellular distances, diameters, and stereocilia shapes were obtained. An important feature of this study is the quantitative reporting of the longitudinal tilts of the outer hair cells towards the base of the cochlea, the tilt of phalangeal processes towards the apex, and Deiters' cells that collectively form a Y-shaped building block that is thought to give rise to the lattice-like organization of the organ of Corti. The variations of this Y-shaped element along the cochlear duct and between the rows of outer hair cells are shown with the third row morphologically different from the other rows, and their potential importance for the cochlear amplifier is discussed.

The importance of the hook region of the cochlea for bone-conduction hearing.

For the most part, the coiled shape of the cochlea has been shown to have only minor importance for air-conducted hearing. It is hypothesized, however, that this coiled shape may play a more significant role for the bone-conducted (BC) route of hearing, through inertial forces exerted by the middle ear and cochlear fluid, and that this can be tested by comparing the results of applying BC stimuli in a variety of different directions. A three-dimensional finite element model of a human middle ear coupled to the inner ear was formulated. BC excitations were simulated by applying rigid-body vibrations normal to the surface of the basilar membrane (BM) at 0.8 (d(1)), 5.8 (d(2)), 15.6 (d(3)), and 33.1 (d(4)) mm from the base of the cochlea, such that relative motions of the fluid within the cochlea produced excitations of the BM. The vibrational direction normal to the BM surface at the base of the cochlea (d(1)) produced the highest BM velocity response across all tested frequencies-higher than an excitation direction normal to the BM surface at the nonbasal locations (d(2)-d(4)), even when the stimulus frequency matched the best frequency for each location. The basal part of the human cochlea features a well-developed hook region, colocated with the cochlear vestibule, that features the largest difference in fluid volume between the scala vestibuli (SV) and scala tympani (ST) found in the cochlea. The proximity of the hook region to the oval and round windows, combined with it having the biggest fluid-volume difference between the SV and ST, is thought to result in a maximization of the pressure difference between the SV and ST for BC stimuli normal to the BM in this region, and consequently a maximization of the resulting BM velocity.

Superior-semicircular-canal dehiscence: effects of location, shape, and size on sound conduction.

The effects of a superior-semicircular-canal (SSC) dehiscence (SSCD) on hearing sensitivity via the air-conduction (AC) and bone-conduction (BC) pathways were investigated using a three-dimensional finite-element (FE) model of a human middle ear coupled to the inner ear. Dehiscences were modeled by removing a section of the outer bony wall of the SSC and applying a zero-pressure condition to the fluid surface thus exposed. At each frequency, the basilar-membrane velocity, vBM, was separately calculated for AC and BC stimulation, under both pre- and post-dehiscence conditions. Hearing loss was calculated as the difference in the maximum magnitudes of vBM between the pre- and post-dehiscence conditions representing a change in hearing threshold. In this study, BC excitations were simulated by applying rigid-body vibrations to the model along the directions of the (arbitrarily defined) x, y, and z axes of the model. Simulation results are consistent with previous clinical measurements on patients with an SSCD and with results from earlier lumped-element electrical-circuit modeling studies, with the dehiscence decreasing the hearing threshold (i.e., increasing vBM) by about 35 dB for BC excitation at low frequencies, while for AC excitation the dehiscence increases the hearing threshold (i.e., decreases vBM) by about 15 dB. A new finding from this study is that the initial width (defined as the width of the edge of the dehiscence where the flow of the fluid-motion wave from the oval window meets it for the first time) on the vestibular side of the dehiscence has more of an effect on vBM than the area of the dehiscence. Analyses of dehiscence effects using the FE model further predict that changing the direction of the BC excitation should have an effect on vBM, with vBM being about 20 dB lower due to BC excitation parallel to the longitudinal direction of the BM in the hook region (the x direction) as compared to excitations in other directions (y and z). BC excitation in the x direction and with a 'center' dehiscence located midway along the length of the SSC causes a reduction in the anti-symmetric component of the fluid pressure across the BM, as compared to the other directions of BC excitation, which results in a decrease in vBM at high frequencies. This article is part of a special issue entitled "MEMRO 2012".

Rationale, design and clinical performance of the mechanical response tissue analyser: a non-invasive technology for measurement of long bone bending stiffness.

Prediction of osteoporotic fractures is currently an imperfect science and new tools are desperately needed to identify at-risk patients at an earlier stage in the disease process. The mechanical response tissue analyser (MRTA) is a novel, non-invasive, radiation-free device that measures the bending stiffness of long bones in vivo, an indicator of a bone's ability to resist deformation under a given load and a strong predictor of long bone structural integrity and strength. Bone bending stiffness measured with the MRTA has been consistently shown to be a stronger predictor of post-mortem and ex vivo bone breaking strength compared to bone mineral measured with dual-energy X-ray absorptiometry. Bone bending stiffness measured with MRTA also decreases with advanced age and disease states and increases with chronic physical activity, independent of bone mineral changes. The MRTA measures different parameters than DXA (bone quality vs bone mineral content and density) and may be a more robust tool for identifying those at risk for fracture. Research initiatives focused on improving long-term repeatability and optimizing the signal-to-noise ratio of the measurement are currently underway to further advance the clinical usefulness of this technology.

Von Békésy and cochlear mechanics.

Georg Békésy laid the foundation for cochlear mechanics, foremost by demonstrating the traveling wave that is the substrate for mammalian cochlear mechanical processing. He made mechanical measurements and physical models in order to understand that fundamental cochlear response. In this tribute to Békésy we make a bridge between modern traveling wave observations and those of Békésy, discuss the mechanical properties and measurements that he considered to be so important, and touch on the range of computational traveling wave models.

Feed-forward and feed-backward amplification model from cochlear cytoarchitecture: an interspecies comparison.

The high sensitivity and wide bandwidth of mammalian hearing are thought to derive from an active process involving the somatic and hair-bundle motility of the thousands of outer hair cells uniquely found in mammalian cochleae. To better understand this, a biophysical three-dimensional cochlear fluid model was developed for gerbil, chinchilla, cat, and human, featuring an active "push-pull" cochlear amplifier mechanism based on the cytoarchitecture of the organ of Corti and using the time-averaged Lagrangian method. Cochlear responses are simulated and compared with in vivo physiological measurements for the basilar membrane (BM) velocity, V(BM), frequency tuning of the BM vibration, and Q10 values representing the sharpness of the cochlear tuning curves. The V(BM) simulation results for gerbil and chinchilla are consistent with in vivo cochlea measurements. Simulated mechanical tuning curves based on maintaining a constant V(BM) value agree with neural-tuning threshold measurements better than those based on a constant displacement value, which implies that the inner hair cells are more sensitive to V(BM) than to BM displacement. The Q10 values of the V(BM) tuning curve agree well with those of cochlear neurons across species, and appear to be related in part to the width of the basilar membrane.

Isokinetic resistance training increases tibial bending stiffness in young women.

Bone mineral content (BMC) and bone mineral density (BMD) are common but imperfect surrogate measures of bone strength. The mechanical response tissue analyzer is a device that measures long bone bending stiffness (EI), which strongly predicts bone breaking strength. We hypothesized that isokinetic resistance training of the knee flexor and extensor muscles would increase tibial EI, BMC, and BMD in young women. Fifty-two women, aged 18-26 years, performed concentric (CON, n = 30) or eccentric (ECC, n = 22) isokinetic resistance training with the nondominant leg three times per week for 20 weeks. Before and after the training period, subjects were tested for CON and ECC peak torque of the knee flexor and extensor muscles with isokinetic dynamometry, tibial BMC and BMD using dual-energy X-ray absorptiometry, and tibial EI using mechanical response tissue analysis. Both training groups increased CON (15-21%) and ECC (17-31%) peak torque vs. the untrained leg. Tibial EI increased in the entire cohort (26%) and in each training group (CON 34%, ECC 16%) vs. the untrained tibia. Tibial BMC and BMD increased in the trained and untrained tibiae, with no significant differences between limbs. No differential tibial EI or bone mineral outcomes were observed between the CON and ECC training groups. In summary, CON and ECC isokinetic resistance training increased tibial EI, but not BMC or BMD, in young women.

A COCHLEAR MODEL USING THE TIME-AVERAGED LAGRANGIAN AND THE PUSH-PULL MECHANISM IN THE ORGAN OF CORTI.

In our previous work, the basilar membrane velocity V(BM) for a gerbil cochlea was calculated and compared with physiological measurements. The calculated V(BM) showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the V(BM) for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase.

A MULTISCALE MODEL OF THE ORGAN OF CORTI.

The organ of Corti is the sensory epithelium in the cochlea of the inner ear. It is modeled as a shell-of-revolution structure with continuous and discrete components. Our recent work has been on the inclusion of the viscous fluid. Measurements from various laboratories provide the opportunity to refocus on the elastic properties. The current detailed model for the organ of Corti is reasonably consistent with diverse measurements. Most components have little stiffness in the propagation direction. However, the isotropic stiffness of the pillar heads is found to offer an explanation for the difference in point load and pressure measurements. The individual rows of inner hair cell stereocilia with tip links and the Hensen stripe are included, since these details are important for the determination of the neural excitation. The results for low frequency show a phase of tip link tension similar to auditory nerve measurements. The nonlinearity of fluid in the small gaps is considered. A result is that as amplitude increases, because of the near contact with the Hensen stripe, the excitation changes polarity, similar to the peak-splitting neural behavior sometimes observed.

Finite element modeling of acousto-mechanical coupling in the cat middle ear.

The function of the middle ear is to transfer acoustic energy from the ear canal to the cochlea. An essential component of this system is the tympanic membrane. In this paper, a new finite element model of the middle ear of the domestic cat is presented, generated in part from cadaver anatomy via microcomputed tomographic imaging. This model includes a layered composite model of the eardrum, fully coupled with the acoustics in the ear canal and middle-ear cavities. Obtaining the frequency response from 100 Hz to 20 kHz is a computationally challenging task, which has been accomplished by using a new adaptive implementation of the reduced-order matrix Padé-via-Lanczos algorithm. The results are compared to established physiological data. The fully coupled model is applied to study the role of the collagen fiber sublayers of the eardrum and to investigate the relationship between the structure of the middle-ear cavities and its function. Three applications of this model are presented, demonstrating the shift in the middle-ear resonance due to the presence of the septum that divides the middle-ear cavity space, the significance of the radial fiber layer on high frequency transmission, and the importance of the transverse shear modulus in the eardrum microstructure.

Isokinetic training increases ulnar bending stiffness and bone mineral in young women.

Numerous studies have investigated the effects of physical activity on bone health; however, little is known about the effects of isokinetic strength training on bone. While bone mineral density (BMD) is widely used to assess bone health and fracture risk, there are several limitations of this measure that warrant new technology development to measure bone strength. The mechanical response tissue analyzer (MRTA) assesses bone strength by measuring maximal bending stiffness (EI). We hypothesized that isokinetic strength training of the elbow flexors and extensors would increase ulnar EI, BMD, and bone mineral content (BMC) in young women. Fifty-four women trained the nondominant arm 3 times per week for 20 weeks; 32 trained concentrically (CON) and 22 trained eccentrically (ECC). Subjects were assessed for the following variables pre- and post-training: CON and ECC peak torque of the elbow flexors and extensors with isokinetic dynamometry, ulnar mineral content and density using dual-energy X-ray absorptiometry, and ulnar EI using MRTA. Isokinetic training increased CON (17%) and ECC (17%) peak torque, even when controlling for changes in the untrained arm. Eccentric training increased CON and ECC peak torque while CON training improved CON peak torque only. Isokinetic training increased ulnar EI 28%, which was statistically greater than the untrained arm. Ulnar EI increased 25% with CON training and 32% with ECC training. Both training modes resulted in greater EI gains compared to the untrained limb. Isokinetic training increased ulnar BMC (2.7%) and BMD (2.3%), even when controlling for untrained ulna changes. Both training modalities resulted in BMC and BMD increases; however, only CON training yielded gains when controlling for changes in the untrained limb. In conclusion, isokinetic strength training increases ulnar EI, BMC, and BMD in young women; no statistical differences were noted between CON and ECC training modes.

Intracochlear pressure and derived quantities from a three-dimensional model.

Intracochlear pressure is calculated from a physiologically based, three-dimensional gerbil cochlea model. Olson [J. Acoust. Soc. Am. 103, 3445-3463 (1998); 110, 349-367 (2001)] measured gerbil intracochlear pressure and provided approximations for the following derived quantities: (1) basilar membrane velocity, (2) pressure across the organ of Corti, and (3) partition impedance. The objective of this work is to compare the calculations and measurements for the pressure at points and the derived quantities. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic basilar membrane with dimensional and material property variation along its length. The arrangement of outer hair cell forces within the organ of Corti cytoarchitecture is incorporated by adding the feed-forward approximation to the passive model as done previously. The intracochlear pressure consists of both the compressive fast wave and the slow traveling wave. A Wentzel-Kramers-Brillowin asymptotic and numerical method combined with Fourier series expansions is used to provide an efficient procedure that requires about 1 s to compute the response for a given frequency. Results show reasonably good agreement for the direct pressure and the derived quantities. This confirms the importance of the three-dimensional motion of the fluid for an accurate cochlear model.

The discordant eardrum.

At frequencies above 3 kHz, the tympanic membrane vibrates chaotically. By having many resonances, the eardrum can transmit the broadest possible bandwidth of sound with optimal sensitivity. In essence, the eardrum works best through discord. The eardrum's success as an instrument of hearing can be directly explained through a combination of its shape, angular placement, and composition. The eardrum has a conical asymmetrical shape, lies at a steep angle with respect to the ear canal, and has organized radial and circumferential collagen fiber layers that provide the scaffolding. Understanding the role of each feature in hearing transduction will help direct future surgical reconstructions, lead to improved microphone and loudspeaker designs, and provide a basis for understanding the different tympanic membrane structures across species. To analyze the significance of each anatomical feature, a computer simulation of the ear canal, eardrum, and ossicles was developed. It is shown that a cone-shaped eardrum can transfer more force to the ossicles than a flat eardrum, especially at high frequencies. The tilted eardrum within the ear canal allows it to have a larger area for the same canal size, which increases sound transmission to the cochlea. The asymmetric eardrum with collagen fibers achieves optimal transmission at high frequencies by creating a multitude of deliberately mistuned resonances. The resonances are summed at the malleus attachment to produce a smooth transfer of pressure across all frequencies. In each case, the peculiar properties of the eardrum are directly responsible for the optimal sensitivity of this discordant drum.

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth.

Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tip-growing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.