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.     

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.     

Adenylate cyclase and carbonic anhydrase in the semicircular canal epithelium of the frog Rana esculenta

Summary Because the secretion of endolymph has been localized in the ampullar part of the frog semicircular canal, we attempted to determine by cytochemical methods the ultrastructural localization of two enzymes that are assumed to play a role in endolymph secretion: carbonic anhydrase and adenylate cyclase. Functionally, the epithelium of the frog semicircular canal can be schematically divided into three areas: sensory (crista ampullaris), secretory (dark cells), and non-sensory and nonsecretory (transitional and undifferentiated cells) areas. Carbonic anhydrase activity was widely distributed in dark cells. Dark cell labeling disappeared in the presence of acetazolamide. The other cells of the canal did not show any carbonic anhydrase labeling except for the supporting cells of the sensory cells. Adenylate cyclase activity was found on the basolateral and apical membranes of dark cells, and on the apical membrane of sensory cells; weak labeling was also observed in the other epithelial cells. In the apical membrane of the dark cells, adenylate cyclase labeling was dependent on the presence of vasotocin, the frog antidiuretic hormone. The dark cells of the frog semicircular canal thus possess the enzyme equipment needed for the secretion of endolymph and its possible hormonal regulation.     

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.     

An analysis of the mechanical forces in each semicircular canal of the cat under single and combined rotations

The vector equation for the general motion of a body in an inertial system is used to analyze the accelerations in the semicircular canals of the cat when the head undergoes rotation about a vertical axis only, rotation about the naso-occipital axis only, and both rotations simultaneously. The corresponding mean forces and mean pressures in the endolymph are calculated by means of a closed line integral along each canal circumference. The importance of the area of the semicircular canal and of its orientation in space become evident. One can see through this mathematical analysis that the input pattern received by the labyrinthine system depends on a set of well-specified geometrical and mechanical conditions, which must be precisely evaluated in order to interpret the nystagmic outputs.     

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.     

Semicircular duct and ampulla dimensions in cat,guinea pig and man

Predictions from the classic theory of semicircular canal operation, the torsion pendulum model, depend upon labyrinthine dimensions and the physical properties of the endolymph. The dimensions of the semicircular canal, duct and ampulla in cat, guinea pig and man were determined from measurements of magnified sections of decalcified temporal bones. Estimates of the effect of shrinkage were obtained from measures in fresh material and it appears shrinkage is probably only a fairly small factor. The dimensions so obtained were used to provide new estimates of the short time constant and other mechanical parameters of the torsion pendulum model in the three species.     

Intraspecific variation in the domestic cat bony labyrinth revealed by different measurement techniques

The knowledge of intraspecific variation is important to make assumptions on an interspecific level. To study intraspecific variation in the bony labyrinth morphology of the domestic cat, eleven specimens of Felis silvestris catus and two additional subspecies (F. s. lybica, F. s. ornata) were investigated. The sample comprises skulls of adult males and females, as well as juvenile cats. Each bony labyrinth endocast was virtually reconstructed based on µCT scans. To estimate the radius of curvature of each inner ear semicircular canal, three different approaches were tested. The comparison of the different methods resulted in different absolute values for the measured radii. The assumed best structure to precisely characterize the size of a semicircular canal is the inner perimeter. Within the tested sample, the anterior semicircular canal is always the largest, while the posterior semicircular canal is the second largest and the lateral semicircular canal the smallest in most cases. The coefficient of variation lies below 10% for all bony labyrinth measurements within the sample. The inner perimeter values of each semicircular canal are similar within all investigated specimens, even though the skull length of adult cats is twice as long as that of juvenile cats. Thus, inner ear biometry of the domestic cat seems stable throughout growth series and can therefore be used for systematic and ecological studies and the inclusion of juvenile individuals is reasonable. It is noteworthy that the inner perimeter values of the semicircular canals do not vary as much as the values of the angles spanned between the three canals within the sample. The inner ear within the cat skull is oriented about 25° to 31° to the palate (angle between the plane anchored to the lateral semicircular canals (SC) and the plane anchored to the palate). The cochlea coils between 3.00 and 3.25 turns in the investigated sample.     

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.     

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.     

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.     

Semicircular canal radii of curvature (R) in cat,guinea pig and man

The radii of curvature (R) of the horizontal (Rh), anterior (Ra) and posterior (Rp) semicircular canals were measured by a new technique (called ROTA) for cat, guinea pig and man. For each canal, data points from the ossecus canal were rotated and plotted by computer such that the plane of the sheet of computer plot corresponded to the plane best fitting that canal. The radius of each osseous canal was determined and where necessary, the radius of the are of data points was corrected for thickness of the absent tissue. For cat, guinea pig and man there are differences in R between canals within a labyrinth suggesting that if other things are equal there could be differences in the average mechanical sensitivity of the canals, which is consistent with physiological recordings from primary vestibular neurons in the cat, The Rs determined by ROTA are compared with Rs determined by conventional histological means.     

The semicircular canals of the hagfish Myxine glutinosa

The internal radius (r) and radius of curvature (R) of the single semicircular canals of Myxine glutinosa have unusual dimensions. In mammals and fish the increase in dimension of r and R with respect to body weight is small; in fish r is larger than in mammals of equivalent weight in order to increase the sensitivity of the canals to angular rotation and R increases correspondingly (Jones & Spells, 1963). In Myxine r is larger than in fish or mammals yet R is smaller. It is argued that the large internal radius is the result of the need to increase the sensitivity of a single canal which has to signal rotation in three planes while the small radius of curvature follows from the absence of a cupula. In order to verify that the cristae of the canals do respond to rotational velocity, recordings were obtained from the nerves serving the canals during rotation in the horizontal plane. The frequency response of several afferents recorded simultaneously at sinusoidal rotations between 0.25 and 2.0 Hz was in the form of a sine wave 90 in advance of head position, as would be expected of a velocity transducer. The gain of single afferents was an order of magnitude less than those reported for other vertebrates.     

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.     

Mechanics of Coriolis stimulus and inducing factors of motion sickness.

To specify inducing factors of motion sickness comprised in Coriolis stimulus, or cross-coupled rotation, the sensation of rotation derived from the semicircular canal system during and after Coriolis stimulus under a variety of stimulus conditions, was estimated by an approach from mechanics with giving minimal hypotheses and simplifications on the semicircular canal system and the sensory nervous system. By solving an equation of motion of the endolymph during Coriolis stimulus, rotating angle of the endolymph was obtained, and the sensation of rotation derived from each semicircular canal was estimated. Then the sensation derived from the whole semicircular canal system was particularly considered in two cases of a single Coriolis stimulus and cyclic Coriolis stimuli. The magnitude and the direction of sensation of rotation were shown to depend on an angular velocity of body rotation and a rotating angle of head movement (amplitude of head oscillation when cyclic Coriolis stimuli) irrespective of initial angle (center angle) of the head relative to the vertical axis. The present mechanical analysis of Coriolis stimulus led a suggestion that the severity of nausea evoked by Coriolis stimulus is proportional to the effective value of the sensation of rotation caused by the Coriolis stimulus.     

Possible functional properties of the labyrinth in Brachiosaurus brancai]

The dimensions of the semicircular canals and the respective ampullae of a complete labyrinth caste of Brachiosaurus Brancai were determined. Using the equation of motion and the dimensions of the semicircular canals the behaviour of the endolymph displacement of the Brachiosaurus labyrinth was calculated. The time constants of the system were found to be between the values 4 sec and 13 sec for T1 and 0.2 sec and 0.5 sec for T2. From these results it was concluded, that the head movements of the animal occurred in a range between 0.02 and 0.1 cps.     

NMDA receptors in afferent synapses of frog semicircular canals

The effects of competitive (2-amino-phosphonovaleric acid) and noncompetitive (Mg²⁺, ketamine, kynurenic acid) antagonists of N-methyl-D-aspartate (NMDA) receptors on synaptic transmission were studied in afferent synapses of the frog semicircular canals. All of these antagonists reduced the rate of background activity in the nerve of posterior semicircular canal by 30–50%, which confirms the presence of glutamate NMDA receptors in the hair cell synapses in the frog semicircular canals.Neurofiziologiya/Neurophysiology, Vol. 25, No. 3, pp. 168–169, May–June, 1993.     

MRI magnetic field stimulates rotational sensors of the brain

Vertigo in and around magnetic resonance imaging (MRI) machines has been noted for years [1, 2]. Several mechanisms have been suggested to explain these sensations [3, 4], yet without direct, objective measures, the cause is unknown. We found that all of our healthy human subjects developed a robust nystagmus while simply lying in the static magnetic field of an MRI machine. Patients lacking labyrinthine function did not. We use the pattern of eye movements as a measure of vestibular stimulation to show that the stimulation is static (continuous, proportional to static magnetic field strength, requiring neither head movement nor dynamic change in magnetic field strength) and directional (sensitive to magnetic field polarity and head orientation). Our calculations and geometric model suggest that magnetic vestibular stimulation (MVS) derives from a Lorentz force resulting from interaction between the magnetic field and naturally occurring ionic currents in the labyrinthine endolymph fluid. This force pushes on the semicircular canal cupula, leading to nystagmus. We emphasize that the unique, dual role of endolymph in the delivery of both ionic current and fluid pressure, coupled with the cupula's function as a pressure sensor, makes magnetic-field-induced nystagmus and vertigo possible. Such effects could confound functional MRI studies of brain behavior, including resting-state brain activity.     

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.