Wally Grant

Computational models of hair cell bundle mechanics: III. 3-D utricular bundles

Six utricular hair bundles from a red-eared turtle are modeled using 3-D finite element analysis. The mechanical model includes shear deformable stereocilia, realignment of all forces during force load increments, and tip and lateral link inter-stereocilia connections. Results show that there are two distinct bundle types that can be separated by mechanical bundle stiffness. The more compliant group has fewer total stereocilia and short stereocilia relative to kinocilium height; these cells are located in the medial and lateral extrastriola. The stiff group are located in the striola. They have more stereocilia and long stereocilia relative to kinocilia heights. Tip link tensions show parallel behavior in peripheral columns of the bundle and serial behavior in central columns when the tip link modulus is near or above that of collagen (1x10(9) N/m(2)). This analysis shows that lumped parameter models of single stereocilia columns can show some aspects of bundle mechanics; however, a distributed, 3-D model is needed to explore overall bundle behavior.

Computational models of hair cell bundle mechanics: II. Simplified bundle models

Simplified versions of hair cell bundles are mechanically modeled. The influence of various geometric and material combinations on bundle stiffness, link tensions and deformation shape are examined. Three models are analyzed within this paper: two stereocilia connected by one link, two stereocilia connected by a biologically realistic set of links, and a column of stereocilia connected by realistic links. Stereocilia are modeled using a distributed parameter model [J. Biomech. Eng. 122, 44]. Some fundamental rules for linking bundles emerge from these tests: (1) Links must have a threshold stiffness value for the bundle to deform as a whole. Beyond this value, the stereocilia are perfectly linked and variations in link stiffness do not significantly effect the bundle stiffness or link tension. (2) Decreasing the relative heights of successive stereocilia may increase link tension while decreasing bundle stiffness. (3) When lateral links exist, the top most lateral links carry the majority of tension. Lower links in single column model appear mechanically insignificant. (4) Extending the length of the bundle in a column does not increase the stiffness once the column reaches a certain length.

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

SUMMARY Vestibular hair cell bundles in the inner ear contain a single kinocilium composed of a 9+2 microtubule structure. Kinocilia play a crucial role in transmitting movement of the overlying mass, otoconial membrane or cupula to the mechanotransducing portion of the hair cell bundle. Little is known regarding the mechanical deformation properties of the kinocilium. Using a force-deflection technique, we measured two important mechanical properties of kinocilia in the utricle of a turtle, Trachemys (Pseudemys) scripta elegans. First, we measured the stiffness of kinocilia with different heights. These kinocilia were assumed to be homogenous cylindrical rods and were modeled as both isotropic Euler–Bernoulli beams and transversely isotropic Timoshenko beams. Two mechanical properties of the kinocilia were derived from the beam analysis: flexural rigidity (EI) and shear rigidity (kGA). The Timoshenko model produced a better fit to the experimental data, predicting EI=10,400 pN μm2 and kGA=247 pN. Assuming a homogenous rod, the shear modulus (G=1.9 kPa) was four orders of magnitude less than Youngs modulus (E=14.1 MPa), indicating that significant shear deformation occurs within deflected kinocilia. When analyzed as an Euler–Bernoulli beam, which neglects translational shear, EI increased linearly with kinocilium height, giving underestimates of EI for shorter kinocilia. Second, we measured the rotational stiffness of the kinocilium insertion (κ) into the hair cells apical surface. Following BAPTA treatment to break the kinocilial links, the kinocilia remained upright, and κ was measured as 177±47 pN μm rad–1. The mechanical parameters we quantified are important for understanding how forces arising from head movement are transduced and encoded by hair cells.

Quantifying utricular stimulation during natural behavior.

The use of natural stimuli in neurophysiological studies has led to significant insights into the encoding strategies used by sensory neurons. To investigate these encoding strategies in vestibular receptors and neurons, we have developed a method for calculating the stimuli delivered to a vestibular organ, the utricle, during natural (unrestrained) behaviors, using the turtle as our experimental preparation. High-speed digital video sequences are used to calculate the dynamic gravito-inertial (GI) vector acting on the head during behavior. X-ray computed tomography (CT) scans are used to determine the orientation of the otoconial layer (OL) of the utricle within the head, and the calculated GI vectors are then rotated into the plane of the OL. Thus, the method allows us to quantify the spatio-temporal structure of stimuli to the OL during natural behaviors. In the future, these waveforms can be used as stimuli in neurophysiological experiments to understand how natural signals are encoded by vestibular receptors and neurons. We provide one example of the method, which shows that turtle feeding behaviors can stimulate the utricle at frequencies higher than those typically used in vestibular studies. This method can be adapted to other species, to other vestibular end organs, and to other methods of quantifying head movements.

Computational models of hair cell bundle mechanics: I. Single stereocilium.

A distributed parameter model for describing the response of a stereocilium to an applied force is presented. This model is based on elasticity theory, plus the geometry and material properties of the stereocilium. The stereocilia shaft above the taper is not assumed to be perfectly rigid. It is assumed to be deformable and that two separate mechanisms are involved in its deformation: bending and shear. The influence of each mode of deformation is explored in parametric studies. Results show that the magnitude of tip deflection depends on the shear compliance of the stereocilium material, the degree of base taper, and stereocilium height. Furthermore, the deformation profiles observed experimentally will occur only if there are constraints on the geometry and material properties of the stereocilium.

Otoliths - Accelerometer and seismometer; Implications in Vestibular Evoked Myogenic Potential (VEMP)

ABSTRACT Vestibular otolithic organs are recognized as transducers of head acceleration and they function as such up to their corner frequency or undamped natural frequency. It is well recognized that these organs respond to frequencies above their corner frequency up to the 2–3 kHz range (Curthoys et al., 2016). A mechanics model for the transduction of these organs is developed that predicts the response below the undamped natural frequency as an accelerometer and above that frequency as a seismometer. The model is converted to a transfer function using hair cell bundle deflection. Measured threshold acceleration stimuli are used along with threshold deflections for threshold transfer function values. These are compared to model predicted values, both below and above their undamped natural frequency. Threshold deflection values are adjusted to match the model transfer function. The resulting threshold deflection values were well within in measure threshold bundle deflection ranges. Vestibular Evoked Myogenic Potentials (VEMPs) today routinely uses stimulus frequencies of 500 and 1000 Hz, and otoliths have been established incontrovertibly by clinical and neural evidence as the stimulus source. The mechanism for stimulus at these frequencies above the undamped natural frequency of otoliths is presented where otoliths are utilizing a seismometer mode of response for VEMP transduction. HIGHLIGHTSMechanics theory for seismic instruments is applied to the otolith organs.Otoliths are accelerometers below the natural frequency and seismometers above.In seismometer mode the otoconial layer is at rest and the base is in motion.In seismometer mode otoliths report neuro‐epithelial base displacement.High frequency Bone Conducted Vibration (BCV) results in striolar region stimulus.

Biomechanical Measurement of Kinocilium

Vestibular hair cell bundles in the inner ear each contain a single kinocilium that has the classic 9+2 axoneme microtubule structure. Kinocilia transmit movement of the overlying otoconial membrane mass and cupula to the mechanotransducing portion of the hair cell bundle. Here, we describe how force-deflection techniques can be used to measure turtle utricle kinocilium shaft and base rotational stiffness. In this approach, kinocilia are modeled as homogenous cylindrical rods and their deformation examined as both isotropic Euler-Bernoulli beams (bending only) and transversely isotropic Timoshenko beams (combined shear and bending). The measurements fit the transversely isotropic model much better with flexural rigidity EI=10,400 pN μm(2) (95% confidence interval: 7182-13,630) and shear rigidity kGA=247 pN (180-314), resulting in a shear modulus (G=1.9 kPa) that was four orders of magnitude less than Youngs modulus (E=14.1 MPa), indicating that significant shear deformation occurs within deflected kinocilia. The base rotational stiffness (κ) was measured following BAPTA treatment to break the kinocilial links that bind the kinocilium to the bundle along its shaft, and κ was measured as 177±47 pN μm/rad. These parameters are important for understanding how forces arising from head movement are transduced and encoded.