Physical dimensions influence the functional property of the semicircular canal

The functional dependence of the semicircular canal upon its physical dimensions was evaluated by measuring the internal radius (r), the radius of curvature (R) and the cupula radius (rC) of the posterior canal in 10 freshly dissected frog labyrinths. These values have been compared to the same parameters of the cat labyrinth. The coefficients I, B, K in the Steinhausen equation were determined for both animals. The A ratio between cupula deflection and endolymph displacement was also calculated by utilizing the Bernard equation. The A ratio is three times larger in the frog than in the cat. It follows that if the same acceleration produces similar endolymph displacements in the posterior canal of both animals, the cupula deflection will be larger in the frog. The solution of the Steinhausen equation in the presence of a constant acceleration, however, reveals that the same stimulus intensity will result in a larger endolymph displacement in the cat posterior canal; similarly, the endolymph displacement directly depends on the duration of the stimulating period in both animals. Contrary to the Bernard assumption, these effects generate a G ratio (psi frog/psi cat) which is less than the Q ratio (A frog/A cat). Moreover, G decreases on increasing the duration of the stimulating period. For stimuli of short duration the semicircular canal of a small animal is expected to exhibit a higher sensitivity than that of a larger one. However, the definitive primary afferent discharge will be largely controlled by the receptor/generator potential properties.     

A poroelastic continuum model of the cupula partition and the response dynamics of the vestibular semicircular canal.

Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.     

A mathematical model of the response of semicircular canal and otolith to head rotation under gravity

The mathematical model of the system composed of two sensors: semicircular canal and sacculus, is presented. The system is described by three series of blocks: biomechanical block, mechanoelectrical transduction mechanism and hair cell ionic currents and membrane potential dynamics. The response of the aforecited system to various stimuli (head rotation under gravity and falling) was investigated. The identification of the model parameters was fulfilled for the experimental data, obtained for the axolotle (Ambystoma tigrinum) in Institute of Physiology, Autonomous University of Puebla, Mexico. The comparative analysis of canal and sacculus membrane potential was realized.     

The responses of primary and secondary sensory hair cells in the squid statocyst to mechanical stimulation

Summary Intracellular recordings were obtained from primary and secondary sensory hair cells in the anterior transverse crista segment of the squid (Alloteuthis subulata) statocyst during imposed displacements of the overlying cupula. The secondary sensory hair cells were depolarized by ventral movements of the cupula and hyperpolarized by dorsal cupula movements. The displacement/response curve was asymmetric around the zero position and sigmoidal in shape, similar to that already described for vertebrate hair cells. The cells are estimated to have a sensitivity of at least 0.5 mV per degree angle of cilia displacement. The responses showed pronounced adaptation and could be blocked by bath applied alcohols, such as heptanol or octanol, or by high concentrations of aminoglycosides.The primary sensory hair cells were depolarized by dorsal movements of the cupula, usually responding with a burst of action potentials. The displacement/response curve was also sigmoidal in shape and the firing pattern showed strong adaptation to maintained displacements of the cupula.The cupula itself appeared to be irregular in shape, extending much further into the statocyst cavity in its central part than at its edges. This is likely to result in differences in the responses of the underlying hair cells along the length of the crista ridge.     

Temperature dependency of cupular mechanics and hair cell frequency selectivity in the fish canal lateral line organ

The mechanical frequency selectivity of the cupula located in the supraorbital lateral line canal and the frequency selectivity of the hair cells driven by the cupula were measured simultaneously in vivo. Laser interferometry was used to measure cupular mechanics and extracellular receptor potentials were recorded to determine hair cell frequency selectivity. Results were obtained from two teleost fish species, the ruffe (Acerina cernua L.), a European temperate zone freshwater fish, and the tropical African knife fish (Xenomiystus nigri). In both species cupular displacement grows with increasing frequency of canal fluid displacement, reaching a maximum at 115 Hz in the ruffe and at 460 Hz in the African knife fish. Cupular best frequencies were independent of temperature. Cut-off frequencies of hair cell frequency selectivity were found to depend on temperature with a Q10 of 1.75, ranging from 116 Hz (4 degrees C) to 290 Hz (20 degrees C), as established in the ruffe. At normal habitat temperatures of the two fish species (ruffe, 4 degrees C; African knife fish, 28 degrees C), this results in hair cell cut-off frequencies that match the two different cupular best frequencies remarkably well. This match suggests adjusted signal transfer in these two peripheral stages of canal lateral line transduction.     

Quantitative analysis of benign paroxysmal positional vertigo fatigue under canalithiasis conditions

In our daily life, small flows in the semicircular canals (SCCs) of the inner ear displace a sensory structure called the cupula which mediates the transduction of head angular velocities to afferent signals. We consider a dysfunction of the SCCs known as canalithiasis. Under this condition, small debris particles disturb the flow in the SCCs and can cause benign paroxysmal positional vertigo (BPPV), arguably the most common form of vertigo in humans. The diagnosis of BPPV is mainly based on the analysis of typical eye movements (positional nystagmus) following provocative head maneuvers that are known to lead to vertigo in BPPV patients. These eye movements are triggered by the vestibulo-ocular reflex, and their velocity provides an indirect measurement of the cupula displacement. An attenuation of the vertigo and the nystagmus is often observed when the provocative maneuver is repeated. This attenuation is known as BPPV fatigue. It was not quantitatively described so far, and the mechanisms causing it remain unknown. We quantify fatigue by eye velocity measurements and propose a fluid dynamic interpretation of our results based on a computational model for the fluid–particle dynamics of a SCC with canalithiasis. Our model suggests that the particles may not go back to their initial position after a first head maneuver such that a second head maneuver leads to different particle trajectories causing smaller cupula displacements.     

Topography and mechanics of the cupula in the fish lateral line. I. Variation of cupular structure and composition in three dimensions.

The cupula of the supraorbital neuromast in the lateral line canal of the clown knifefish contains vertical columns. In the central region of the cupula overlying the macula, these columns are densely packed, are relatively constant in size, and run from the base of the cupula to the surface of the cupula which is exposed to canal fluid. There are two types of columns, dark and light, which form elliptical compartments in planes of section that cut across the columns; the cupula therefore has the appearance of mosaic tile in such sections. The dark compartments contain tubules that extend from the base of the cupula at the junction with the macula to the top of the cupula. Each tubule is associated with the kinocilium of a single hair cell. The lateral parts of the cupula, not overlying the macula, also contain compartments, but these compartments differ in size and structure from those in the central region. In addition to the compartments, the central region of the cupula also contains spherical aggregates of droplets. These small aggregates, termed mora, are found principally in a layer within the central region of the cupula, but are also found outside this layer. Because of their light-reflecting properties, the mora can be used for noninvasive optical measurements in vivo of the motion of the cupula.     

Numerical modeling of the cupular displacement and motion of otoconia particles in a semicircular canal

Balance is achieved and maintained by a balance system called a labyrinth that is composed of three semicircular canals and the otolith organs that sense linear gravity and acceleration. Within each semicircular canal, there is a gelatinous structure called the cupula, which is deformed under the influence of the surrounding endolymph. One of the balance disorders is benign paroxysmal positional vertigo, and one of the pathological conditions that have been identified as possible causes of this syndrome is canalithiasis—disturbance of the endolymph flow and cupular displacement caused by the free-moving otoconia particles within the lumen of the canal. Analysis of phenomena occurring within the semicircular canal can help to explain some balance-related disorders and the response of the vestibular system to external perturbations under various pathological conditions. Numerical simulations allow a study of the influence of a wide range of factors, without the need to perform experiments and clinical examinations. In case of canalithiasis, an accurate explanation and tracking of the motion of otoconia particles in vivo is obviously nearly impossible. In this study, a numerical model was developed to predict the motion of otoconia particles within the semicircular canal and the effect of the endolymph flow and particles on the deformation of the cupula.     

Morphology of the Hagfish Inner Ear

The inner ear of five species of hagfishes was examined with different light and electron microscopical techniques. In all species, the labyrinth contains a single macula and two cristae, in a single semicircular canal. The macula consists of a horizontal, a middle vertical and a posterior horizontal component. Each component is covered by numerous round statoconia. The ring-shaped cristae have very long kinocilia, but lack a proper cupula. The sensory epithelia show signs of regeneration, indicated by the presence of mitoses and apoptotic hair cells.     

Functional morphology of the crista ampullaris: with special interests in sensory hairs and cupula: a review.

The functional significance of the ciliary interconnections and cupula has been reviewed. The ciliary interconnecting systems are divided into 2 types, i.e. side links and tip links. The side links acts to maintain the regular distance between the cilia thereby keeping the geometrical arrangement of the entire sensory hair bundle intact as well as to prevent close contact between neighbouring cilia. The tip links, stretching upwards from the tips of the shorter stereocilia to their taller neighbouring shafts, are actually involved in mechanoelectrical transduction. The cupula is composed of the cupula and subcupular meshwork. The subcupular meshwork consists of long branching filaments cross-bridged to one another. The cupula would function as a rigid plate and equally distribute the shear force of the cupula to all the ciliary bundles. The subcupular meshwork may play a role in the transmission of the shear strain force of the cupula to the ciliary bundle and may also exert an additional damping effect in order to prevent unwanted vibrations.     

A mouse model for benign paroxysmal positional vertigo with genetic predisposition for displaced otoconia

Abnormal formation of otoconia, the biominerals of the inner ear, results in balance disorders. The inertial mass of otoconia activates the underlying mechanosensory hair cells in response to change in head position primarily during linear and rotational acceleration. Otoconia associate exclusively with the two gravity receptors, the utricle and saccule. The cristae sensory epithelium is associated with an extracellular gelatinous matrix known as cupula, equivalent to otoconia. During head rotation, the inertia of endolymphatic fluids within the semicircular canals deflects the cupula of the corresponding crista and activates the underlying mechanosensory hair cells. It is believed that detached free‐floating otoconia particles travel ectopically to the semicircular canal and cristae and are the culprit for benign paroxysmal positional vertigo (BPPV). The Slc26a4 mouse mutant harbors a missense mutation in pendrin. This mutation leads to impaired transport activity of pendrin and to defects in otoconia composition and distribution. All Slc26a4 ^loop/loop homozygous mutant mice are profoundly deaf but show inconsistent vestibular deficiency. A panel of behavioral tests was utilized in order to generate a scoring method for vestibular function. A pathological finding of displaced otoconia was identified consistently in the inner ears of mutant mice with severe vestibular dysfunction. In this work, we present a mouse model with a genetic predisposition for ectopic otoconia with a clinical correlation to BPPV. This unique mouse model can serve as a platform for further investigation of BPPV pathophysiology, and for developing novel treatment approaches in a live animal model.     

Cupular response and functional anatomy to pressure application in the pigeon.

In this study, horizontal semicircular canal of the pigeon was inserted with a microfill, 164 micrometers in outer diameter, to gauge the pressure change in the canal and to clarify two things. One is whether the endolymph passes through the crista ampullaris or not. The other is as to the space where the endolymph passes through in the crista ampullaris if the endolymph goes through the crista. The pressure applications were performed by using Evans blue solution and as a result three pressure groups, i.e., 1) high, 2) moderate and 3) low were discriminated. Our results suggest that the endolymphatic fluid passes through the subcupular space or the top of the crista ampullaris when the pressure is enough small like the head rotates in daily life. Accordingly we present a new hypothesis as to the functional anatomy of the cupula in contrast to current hypotheses e.g. drum membrane or revolving door.     

Hydrodynamic detection by cupulae in a lateral line canal: functional relations between physics and physiology

In the present review, signal-processing capabilities of the canal lateral line organ imposed by its peripheral architecture are quantified in terms of a limited set of measurable physical parameters. It is demonstrated that cupulae in the lateral line canal organ can only partly be described as canal fluid velocity detectors. Deviation from velocity detection may result from resonance, and can be characterized by the extent to which a single dimensionless resonance number, N _r , exceeds 1. This number depends on four physical parameters: it is proportional to cupular size, cupular sliding stiffness and canal fluid density, and inversely proportional to the square of fluid viscosity. Situated in a canal, a cupula may benefit from its resonance by compensating for the limited frequency range of water motion that is efficiently transferred into the lateral line canal. The peripheral transfer of hydrodynamic signals, via canal and cupula, leads to a nearly constant sensitivity to outside water acceleration in a bandwidth that ranges from d.c. to a cut-off frequency of up to several hundreds of Hertz, significantly exceeding the cut-off frequency of the lateral line canal. Threshold values of hydrodynamic detection by the canal lateral line organ are derived in terms of water displacement, water velocity, water acceleration and water pressure gradients and are shown to be close to the detection limits imposed by hair cell mechano-transduction in combination with the physical constraints of peripheral lateral line signal transfer. The notion that the combination of canal- and cupular hydrodynamics effectively provides the lateral line canal organ with a constant sensitivity to water acceleration at low frequencies so that it consequently functions as a low-pass detector of pressure gradients, supports the appropriateness of describing it as a sense organ that “feels at a distance” (Dijkgraaf in Biol Rev 38:51–105, 1963)     

Ultrastructure of free neuromasts of Bathygobius fuscus (gobiidae) and canal neuromasts of Apogon cyanosoma (apogonidae)

Light and electron microscopic observations were made on the lateral line organs of the free neuromasts of the goby Bathygobius fuscus and the canal neuromasts of the cardinal fish Apogon cyanosoma. As in other lateral line systems, each neuromast consists of hair cells, supporting cells and mantle supporting cells, the whole being covered by a cupula. In B. fuscus the free neuromasts are mounted on papillae and have hair cells with stereocilia up to 2.5 μm long and a single kinocilium at least 25 μm long. Each neuromast is covered by a vane-like cupula that can be divided into two regions. The central region over the sensory area contains columns of myelin-like figures. These figures are absent from the outer region covering the mantle. The canal neuromasts of A. cyanosoma are diamond-shaped with up to 1,500 hair cells. The cupula is unusual in having a channel that lies over the sensory region. The hair cells have up to 45 stereocilia, the tallest reaching 2.5 μm, and a kinocilium at least 5 μm long. Tip links are shown for the first time between rows of stereocilia of the hair cells of lateral line neuromasts. The presence of tip links has now been demonstrated for all acousticolateral hair cell systems.     

Rapid responses of the cupula in the lateral line of ruffe (<Emphasis Type="Italic">Gymnocephalus cernuus</Emphasis>)

Displacements of cupulae in the supraorbital lateral line canal in ruffe (Gymnocephalus cernuus) have been measured using laser interferometry and by applying transient as well as sinusoidal fluid stimuli in the lateral line canal. The cupular displacement in response to impulses of fluid velocity shows damped oscillations at approximately 120 Hz and a relaxation time-constant of 4.4 ms, commensurate with a quality factor of approximately 1.8. These values are in close agreement with the frequency characteristics determined via sinusoidal fluid stimuli, implying that the nonlinearity of cupular dynamics imposed by the gating apparatus of the sensory hair cells is limited in the range of cupular displacements and velocities measured (100–300 nm; 100–300 m/s). The measurements also show that cupular displacement instantaneously follows the initial waveform of transient stimuli. The functional significance of the observed cupular dynamics is discussed.     

Experimental measurement of the stiffness of the cupula.

An experimental procedure is described which consists of cutting the canal duct, inserting a micropipette and administering known volumetric displacements to the cupula. The cupula is made visible by dying the endolymph. Known displacements are administered to the cupula, and the time constant of the return to its equilibrium position is measured. With this information, the stiffness of the cupula is calculated. The experiment was successfully carried out on five White King pigeons. The mean stiffness found in somewhat less than other results reported in the literature, and reasons for this discrepancy are noted.     

Functional physiology of the semicircular canal ampulla.

Physiology of the semicircular canal (sc) was studied by applying different manipulations to the isolated frog sc. Function of the cupula was investigated by mapping out the mechanical sensitivity on the cupular surface and by removing and replacing the cupula. The cupula was found to be most essential for effective activation of sc receptors. Responses of sc receptors to direct temperature change were studied. The sc nerve discharge increased and decreased due to cool and warm temperature change respectively. This suggests a possibility of direct temperature effect as one of the mechanisms of caloric response.     

A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV

Benign paroxysmal positional vertigo (BPPV) is a mechanical disorder of the vestibular system in which calcite particles called otoconia interfere with the mechanical functioning of the fluid-filled semicircular canals normally used to sense rotation. Using hydrodynamic models, we examine the two mechanisms proposed by the medical community for BPPV: cupulolithiasis, in which otoconia attach directly to the cupula (a sensory membrane), and canalithiasis, in which otoconia settle through the canals and exert a fluid pressure across the cupula. We utilize known hydrodynamic calculations and make reasonable geometric and physical approximations to derive an expression for the transcupular pressure DeltaPc exerted by a settling solid particle in canalithiasis. By tracking settling otoconia in a two-dimensional model geometry, the cupular volume displacement and associated eye response (nystagmus) can be calculated quantitatively. Several important features emerge: (1) a pressure amplification occurs as otoconia enter a narrowing duct; (2) an average-sized otoconium requires approximately 5 s to settle through the wide ampulla, where DeltaPc is not amplified, which suggests a mechanism for the observed latency of BPPV; and (3) an average-sized otoconium beginning below the center of the cupula can cause a volumetric cupular displacement on the order of 30 pL, with nystagmus of order 2 degrees/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.     

Models of membrane resonance in pigeon semicircular canal type II hair cells

Pigeon vestibular semicircular canal type II hair cells often exhibit voltage oscillations following current steps that depolarize the cell membrane from its resting potential. Currents active around the resting membrane potential and most likely responsible for the observed resonant behavior are the Ca⁺⁺-insensitive, inactivating potassium conductance I _A (A-current) and delayed rectifier potassium conductance I _K. Several equivalent circuits are considered as representative of the hair cell membrane behavior, sufficient to explain and quantitatively fit the observed voltage oscillations. In addition to the membrane capacitance and frequency-independent parallel conductance, a third parallel element whose admittance function is of second order is necessary to describe and accurately predict all of the experimentally obtained current and voltage responses. Even though most voltage oscillations could be fitted by an equivalent circuit in which the second order admittance term is overdamped (i.e., represents a type of current with two time constants, one of activation and the other of inactivation), the sharpest quality resonance obtained with small current steps (around 20 pA) from the resting potential could be satisfactorily fit only by an underdamped term.     

The model of cupular dynamics in the case of the difference of the cupula and endolymph densities

The function of semicircular canals (SC) is based on the precise equality of densities of the cupula and endolymph. Otherwise the information provided by SC would depend on the orientation of both the gravity vector relative to canal plane and the axis of rotation. It would also depend on the distance between the axis of rotation and the center of the SC. We believe that the equality of densities is approximate and expect that due to the high sensitivity of the SC, even the small differences of densities (approximately 10(-4) g/cm3) can influence the SC dynamics, and this influence depends on the conditions of canal stimulation. The work aims to examine this hypothesis and analyze the parameters of the SC and mechanical stimulation under which the effect of the difference of densities on the SC functioning could be observed.