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.     

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.     

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.     

Mechanical filtering by the boundary layer and fluid–structure interaction in the superficial neuromast of the fish lateral line system

A great diversity of aquatic animals detects water flow with ciliated mechanoreceptors on the body's surface. In order to understand how these receptors mechanically filter signals, we developed a theoretical model of the superficial neuromast in the fish lateral line system. The cupula of the neuromast was modeled as a cylindrical beam that deflects in response to an oscillating flow field. Its accuracy was verified by comparison with prior measurements of cupular deflection in larval zebrafish (Danio rerio). The model predicts that the boundary layer of flow over the body attenuates low-frequency stimuli. The fluid-structure interaction between this flow and the cupula attenuates high-frequency stimuli. The number and height of hair cell kinocilia and the dimensions of the cupular matrix determine the range of intermediate frequencies to which a neuromast is sensitive. By articulating the individual mechanical contributions of the boundary layer and the components of cupular morphology, this model provides the theoretical framework for understanding how a hydrodynamic receptor filters flow signals.     

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.     

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)     

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.     

In vitro model of a semicircular canal: Design and validation of the model and its use for the study of canalithiasis

We present an experimental model for a semicircular canal with canalithiasis. Canalithiasis is a pathological condition where free-floating particles disturb the flow field in the semicircular canals. It may lead to a specific form of vertigo known as BPPV or top-shelf vertigo. A careful scaling of the physical and geometrical parameters allows us to study the mechanics of this disease on an enlarged model of a single semicircular canal with laser vibrometry and video particle tracking. Early results confirm the proper operation of the model canal and support the current theories on the mechanisms of BPPV.     

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.     

Principles of Calcite Dissolution in Human and Artificial Otoconia

Human otoconia provide mechanical stimuli to deflect hair cells of the vestibular sensory epithelium for purposes of detecting linear acceleration and head tilts. During lifetime, the volume and number of otoconia are gradually reduced. In a process of degeneration morphological changes occur. Structural changes in human otoconia are assumed to cause vertigo and balance disorders such as benign paroxysmal positional vertigo (BPPV). The aim of this study was to investigate the main principles of morphological changes in human otoconia in dissolution experiments by exposure to hydrochloric acid, EDTA, demineralized water and completely purified water respectively. For comparison reasons artificial (biomimetic) otoconia (calcite gelatin nanocomposits) and natural calcite were used. Morphological changes were detected in time steps by the use of environmental scanning electron microscopy (ESEM). Under in vitro conditions three main dissolution mechanisms were identified as causing characteristic morphological changes of the specimen under consideration: pH drops in the acidic range, complex formation with calcium ions and changes of ion concentrations in the vicinity of otoconia. Shifts in pH cause a more uniform reduction of otoconia size (isotropic dissolution) whereas complexation reactions and changes of the ionic concentrations within the surrounding medium bring about preferred attacks at specific areas (anisotropic dissolution) of human and artificial otoconia. Owing to successive reduction of material, all the dissolution mechanisms finally produce fragments and remnants of otoconia. It can be assumed that the organic component of otoconia is not significantly attacked under the given conditions. Artificial otoconia serve as a suitable model system mimicking chemical attacks on biogenic specimens. The underlying principles of calcite dissolution under in vitro conditions may play a role in otoconia degeneration processes such as BPPV.     

The otoconia of the guinea pig utricle: internal structure, surface exposure, and interactions with the filament matrix

A unique feature of the vertebrate gravity receptor organs, the saccule and utricle, is the mass of biomineral structures, the otoconia, overlying a gelatinous matrix also called "otoconial membrane" on the surface of the sensory epithelium. In mammals, otoconia are deposits of calcium carbonate in the form of composite calcite crystals. We used quick-freezing, deep etching to examine the otoconial mass of the guinea pig utricle. The deep-etching step exposed large expanses of intact and fractured otoconia, showing the fine structure and relationship between their internal crystal structure, their surface components, and the filament matrix in which they are embedded. Each otoconium has a compact central core meshwork of filaments and a composite outer shell of ordered crystallites and macromolecular aggregates. A distinct network of 20-nm beaded filaments covers the surface of the otoconia. The otoconia are interconnected and secured to the gelatinous matrix by surface adhesion and by confinement within a loose interotoconial filament matrix. The gelatinous matrix is a dense network made of yet another type of filament, 22 nm in diameter, which are cross-linked by shorter filaments, characteristically 11 nm in diameter. Our freeze-etching data provide a structural framework for considering the molecular nature of the components of the otoconial complex, their mechanical properties, and the degree of biological versus chemical control of otoconia biosynthesis.     

Theoretical aspects of cupula deflection in semicircular canal

The deflection of the sensory hairs produced by a given volumetric displacement of endolymph (ΔV) is compared in the two usually-accepted models of the cupula behavior: the watertight hinged flap and the elastic diaphragm. Developing the mathematics of these two models, it appears that the elastic diaphragm engenders a larger deflection of sensory hairs than the hinged flap, the difference being about twice in magnitude. Whatever the model, the angle of the cupular deflection is always proportional to the relative angular displacement of the endolymph during natural stimulations.     

Biomechanical Analysis of Angular Motion in Association with Bilateral Semicircular Canal Function

The aim of this study was to characterize cupular deformation by calculating the degree of cupular expansion and cupular deflection using a finite element model of bilateral human semicircular canals (SCCs). The results showed that cupular deflection responses were consistent with Ewald’s II law, whereas each pair of bilateral cupulae simultaneously expanded or compressed to the same degree. In addition, both the degree of cupular expansion and cupular deflection can be expressed as the solution of forced oscillation during head sinusoidal rotation, and the amplitude of cupular expansion was approximately two times greater than that of cupular deflection. Regarding the amplitude frequency and phase frequency characteristics, the amplitude ratios among the horizontal SCC, the anterior SCC, and the posterior SCC cupular expansion was constant at 1:0.82:1.62, and the phase differences among them were constant at 0 or 180° at the frequencies of 0.5–6 Hz. However, both the amplitude ratio and the phase differences of the cupular deflection increased nonlinearly with the increase of frequency and tended to be constant at the frequency band between 2 and 6 Hz. The results indicate that the responses of cupular expansion might only be related to the mass and rigidity of three cupulae and the endolymph, but the responses of cupular deflection are related to the mass, rigidity, or damping of them, and these physical properties would be affected by vestibular dysfunction. Therefore, both the degree of cupular expansion and cupular deflection should be considered important mechanical variables for induced neural signals as these variables provide a better understanding of the SCCs system’s role in the vestibulo-ocular reflex during the clinical rotating chair test and the vestibular autorotation test. Such a numerical model can be further built to provide a useful theoretical approach for exploring the biomechanical nature underlying vestibular dysfunction.     

Gene targeting reveals the role of Oc90 as the essential organizer of the otoconial organic matrix

A critical part of the functional development of our peripheral balance system is the embryonic formation of otoconia, composite crystals that overlie and provide optimal stimulus input to the sensory epithelium of the gravity receptor in the inner ear. To date neither the functions of otoconial proteins nor the processes of crystal formation are clearly defined. Using gene targeting and protein analysis strategies, we demonstrate that the predominant mammalian otoconin, otoconin-90/95 (Oc90), is essential for formation of the organic matrix of otoconia by specifically recruiting other matrix components, which includes otolin, a novel mammalian otoconin that we identified to be in wildtype murine otoconia. We show that this matrix controls otoconia growth and morphology by embedding the crystallites during seeding and growth. During otoconia development, the organic matrix forms prior to CaCO3 deposition and provides optimal calcification efficiency. Histological and ultrastructural examinations show normal inner ear epithelial morphology but reduced acellular matrices, including otoconial, cupular and tectorial membranes, in Oc90 null mice, likely due to an absence of Oc90 and a profound reduction of otolin. Our data demonstrate the critical roles of otoconins in otoconia seeding, growth and anchoring and suggest mechanistic similarities and differences between otoconia and bone calcification.     

Cupular sense organs in Ciona (Tunicata: Ascidiacea)

The cupular organs of the atrial (exhalent) siphon of Ciona have been studied with scanning and transmission microscopy and are shown to resemble those of the vertebrate acoustico-lateralis system in several respects. The sensory cells are ciliated, and their cilia are apparently non-motile, having a modified inner tubular array. These cells lie amongst supporting cells that probably secrete the cupula, which is composed of polysaccharide and proteins as is the test. Ciona is sensitive to near-field vibrations, even after the brain has been removed; the significance of this observation and of the arrangement of the cupular organs is discussed. It is concluded that the tunicates show a suitable morphological starting point for the vertebrate acoustico-lateralis system.     

An Electrokinetic Model of Transduction in the Semicircular Canal

Transduction in the semicircular canal was studied by focusing an infrared beam on either side of exposed ampullae from the posterior canals of Rana pipiens. The direction of fluid movement resulting from a stimulus was inferred by observing the polarity of the change in afferent impulse mean rate relative to the spontaneous value. On the basis of the accepted functional polarization of this receptor, the results indicate that fluid moved toward the warmer side of the ampulla. Convection and thermal reception were shown to be unlikely explanations for these results. Morover, cupular displacements toward the warmer side would not be expected. Because thermo-osmosis can cause fluid to move toward the warmer side in a gelatin membrane, the results can be interpreted as evidence that thermo-osmosis occurred in the gelatinous cupula and influenced the transduction mechanism. Thermo-osmosis of liquids appears to be due to an electric field that is set up in a charged membrane; hence, the hair cells might have detected an electric field that occurred in the cupula during thermo-osmosis. Electroreception might be an important link in the transduction of physiological stimuli also. Rotational stimuli could result in weak electric fields in the cupula by the mechanoelectric effect. Cupular displacements could be important for large stimuli, but extrapolations to threshold stimuli suggest displacements of angstrom amplitudes. Therefore, electroreception by the hair cells could be an explanation of the great sensitivity that has been observed in the semicircular canal and other labyrinthine receptors.     

Cupular organs in two species of Corella (Tunicata: Ascidiacea)

Abstract. Simple cupular organs similar to those described in Ciona intestinalis were observed in Corella eumyota. They consist of a macula containing the cell bodies of 20–30 primary sensory neurons whose cilia project into a dome‐ or finger‐shaped structure, the cupula. Rather than being found in the mantle lining as in C. intestinalis, the organs were located on the atrial surface of the branchial sac. The sensory innervation was examined in whole‐mount preparations using anti‐tubulin immunohistochemistry. Sensory neurons in C. eumyota showed no immunoreactivity with antisera raised against gonadotropin‐releasing hormone (GnRH). A novel, elongated sense organ termed the cupular strand was found in Corella inflata. It has the same basic components as the simple type of cupular organ but consists of a single, long structure containing ～1500 sensory cells. Located on the atrial surface of the branchial sac, it extends along the midline of the dorsal fold, from the gonoduct openings almost as far as the brain. Preparations were examined using optical and electron microscopy. Nerves and cilia were visualized by anti‐tubulin immunofluorescence microscopy. It was possible to follow the sensory axons from the macula of the cupular strand to points where they joined branches of the visceral nerve, which enters a nerve root at the back of the brain. In C. inflata the sensory cell bodies and their axons were immunoreactive not only with anti‐tubulin but also with an antiserum raised against Tunicate I GnRH. There was no immunoreactivity, however, with Chicken II and catfish GnRH antisera. All three GnRH antisera labeled the dorsal strand plexus, a structure associated with production of GnRH in its role as a reproductive hormone. We concluded that the GnRH‐like molecule labeled in sensory neurons differs from the form of GnRH found in the dorsal strand plexus, and may have a different function, perhaps in the neural control of ciliary activity. The function of the cupular organs in species of Corella has not yet been investigated physiologically, but by analogy with such structures in other metazoans, cupular organs are probably hydrodynamic sensors registering local disturbances or changes in water flow through the atrial cavity.     

Settlement behavior of Chthamalus anisopoma larvae largely determines the adult distribution

Summary In the northern Gulf of California the adult distribution of the intertidal barnacle species, Chthamalus anisopoma, on exposed shores is approximately between 0.0 and 2.0 m above mean low water (MLW). The species is typically absent in protected (from wave splash) areas. In this study, I examined a series of alternative hypotheses relating to the factors that could be responsible for limiting the distribution. Post-settlement factors appear to be unimportant because settlement was largely restricted to areas within the adult distribution. Two processes could account for the high correlation between settlement and adult distributions. First, hydrodynamic factors could restrict deposition of larvae to sites that coincidently were in areas in which individuals could survive to maturity. Second, larvae may choose to settle only on sites where they can survive to maturity. Of the two, the later was supported as settlement could be induced on surfaces outside the adult distribution using transplanted adult conspecifics as cues. Thus, competent larvae were present outside the adult distribution of Chthamalus zone but did not settle under normal conditions. Also, there was no evidence that pre-emption of space by other sessile species, by itself, restricted the distribution of Chthamalus. Settlement within the existing adult distribution may be an evolutionary response to increased mortality for individuals settling outside the adult distribution compared to those settling within it.     

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.