Human Semicircular Canals Research Articles

Investigation on biomechanical responses in bilateral semicircular canals and nystagmus in vestibulo-ocular reflex experiments under different forward-leaning angles.

Different head positions affect the responses of the vestibular semicircular canals (SCCs) to angular movement. Specific head positions can relieve vestibular disorders caused by excessive stimulating SCCs. In this study, we quantitatively explored responses of human SCCs using numerical simulations of fluid-structure interaction and vestibulo-ocular reflex (VOR) experiments under different forward-leaning angles of the head, including 0°, 10°, 20°, 30°, 40°, 50°, and 60°. It was found that the horizontal nystagmus slow-phase velocity and corresponding biomechanical responses of the cupula in horizontal SCC increased with the forward-leaning angles of the head, reached a maximum when the head was tilted 30° forward, and then gradually decreased. However, no obvious vertical or torsional nystagmus was observed in the VOR experiments. In the numerical model of bilateral SCCs, the biomechanical responses of the cupula in the left anterior SCC and the right anterior SCC showed the same trends; they decreased with the forward-leaning angles, reached a minimum at a 40° forward tilt of the head, and then gradually increased. Similarly, the biomechanical responses of the cupula in the left posterior SCC and in the right posterior SCC followed a same trend, decreasing with the forward-leaning angles, reaching a minimum at a 30° forward tilt of the head, and then gradually increasing. Additionally, the biomechanical responses of the cupula in both the anterior and posterior SCCs consistently remained lower than those observed in the horizontal SCCs across all measured head positions. The occurrence of these numerical results was attributed to the consistent maintenance of mutual symmetry in the bilateral SCCs with respect to the mid-sagittal plane containing the axis of rotation. This symmetry affected the distribution of endolymph pressure, resulting in biomechanical responses of the cupula in each pair of symmetrical SCCs exhibiting same tendencies under different forward-leaning angles of the head. These results provided a reliable numerical basis for future research to relieve vestibular diseases induced by spatial orientation of SCCs.

Pathological Study of Light Cupula Syndrome on a Visual Bionic Semicircular Canal.

A type of persistent direction-changing positional nystagmus with a null point during head position deflection is known as light cupula syndrome (LCS) in the clinic. To date, the pathogenesis and biomechanical response of human semicircular canals with light cupula syndrome (LCS) (HSCs-LCS) are still unclear. In this study, based on the anatomical structure and size of the one-dimensional human semicircular canal (HSC) and imitating the pathological changes of the endolymph in HSC with LCS, a visual bionic semicircular canal (BSC) with LCS was fabricated using three-dimensional printing technology, hydrogel modification, and target tracking technology. Through theoretical derivation, mathematical models of the HSC-LCS perception process were established. By conducting in vitro experiments on the bionic model, the biomechanical response process of HSC-LCS was studied, and the mathematical models were validated. The results of pulse acceleration stimulation showed that the pathological changes in the density and viscosity of the endolymph could reduce the deformation of the cupula of the BSC-LCS and increase the time constant. The results of the sinusoidal acceleration stimulation showed that the amplitude-frequency gain of the BSC-LCS decreased and the phase difference increased. The BSC-LCS can be used as a tool for pathological research of the HSC-LCS. The results of this study can provide a theoretical basis for clinical diagnosis.

Design of an In Vitro Semicircular Canal Model and Its Use for the Study of Canalithiasis.

Canalithiasis is a common vestibular system disorder, which may lead to a specific form of vertigo known as BPPV or top-shelf vertigo. In this paper, based on the actual geometric parameters of the human semicircular canal, we designed a four-fold in vitro one-dimensional semicircular canal model using technologies such as three-dimensional printing, image processing, and target tracking. We investigated the essential characteristics of the semicircular canal, such as the time constant of the cupula and the relationship between the number, density, and size of the canalith and the cupular deformation during canalith settlement. The results showed a linear relationship between the number and size of the canalith and the amount of cupular deformation. We also found that when the number of canaliths reached a particular scale, the interaction between the canaliths exerted an additional disturbance on the cupular deformation ("Z" twist). In addition, we explored the latency time of the cupula during canalith settlement. Finally, we verified that the canaliths had little effect on the frequency characteristics of the semicircular canal by a sinusoidal swing experiment. All the results validate the reliability of our 4-fold in vitro one-dimensional semicircular canal model.

Study the biomechanical performance of the membranous semicircular canal based on bionic models

A BA (bionic ampulla) was designed and fabricated using an SMPF (Symmetric electrodes Metal core PVDF Fiber) sensor, which could imitate the sensory hair cells to sense the deformation of the cupula of the BA. Based on the BA, a bionic semicircular canal with membrane semicircular canal (MBSC) and a bionic semicircular canal without membrane semicircular canal (NBSC) were designed and fabricated. The biomechanical models of the MBSC and NBSC were established. The biomechanical models were verified through the perception experiments of the MBSC and the NBSC. The results showed that the SMPF could sense the deformation of the cupula. The MBSC and NBSC could sense the angular velocity and accelerations. What's more, it was speculated that in a human body, the endolymph probably had a function of liquid mass while the membranous semicircular canal and the cupula had a function similar to a spring in the human semicircular canal.

Development of Bionic Semicircular Canals and the Sensation of Angular Acceleration.

To study the sensing process of the human semicircular canals (HSCs) during head rotation, which is difficult to directly measure due to physiological reasons. A 1-BSC (one-dimensional bionic semicircular canal) and 3-BSC were prepared with soft SMPFs (symmetric electrode metal core polyvinylidene difluoride fibers), which could sense deformations similar to human sensory cells. Based on these models, experiments were carried out to study the principle of the HSCs. Deformations of the bionic ampulla (BA) depended on the angular acceleration. Gravity had a strong influence on the deformation of the BA in the vertical plane. When the 3-BSC was subjected to angular acceleration around one of its centerlines, the three BAs all deformed. The deformation of the BAs was linearly related to the angular acceleration. The deformation of the BA in the main semicircular canal was exactly three times that of the other two BAs.

Outcomes of the bionic semicircular canals support the "density hypothesis" and "circular hypothesis".

To date, there are three main hypotheses explaining why the human semicircular canals (HSCCs) cannot sense linear accelerations. To further study this issue, we designed a bionic ampulla (BA) instrumented with a symmetrical metal core polyvinylidene fluoride fiber as a bionic sensor, which imitates the structure and function of the human ampulla. The BA was confirmed to have a good sensing ability in experiments with a straight tube. Additionally, we designed a bionic semicircular canal model, a blocking model, and a square model. We compared the perception performance of these three models to test the "density hypothesis," the "closed loop hypothesis," and the "circular hypothesis." The outcomes of these experiments verified the "density hypothesis" and "circular hypothesis," but did not support the "closed loop hypothesis," shedding light on why the HSCC is sensitive to angular acceleration, but not to linear acceleration.

Quantitative analysis of the biomechanical response of semicircular canals and nystagmus under different head positions

The semicircular canals (SCCs) in the vestibular system can sense angular motion of the head, which performs a crucial role in maintaining the human's sense of balance. The different spatial orientations of the head affect the response of human SCCs to rotational movement. In this study, we combined the numerical model of bilateral human SCCs with vestibulo-ocular reflex experiments, and quantitatively investigated the responses of SCCs to constant angular acceleration when the head was in different left-leaning positions, including the head tilted 0°, 15°, 30°, 45°, 60°, 70°, 80°, and 90° to the left. The results showed that the vertical nystagmus slow-phase velocity (SPV) and the corresponding maximal cupula shear strain at the crista surface rose with an increase in the left-leaning angle of the head, reached a maximum at the position of the head tilted approximately 70° to the left, and then decreased gradually. Both the horizontal nystagmus SPV and the corresponding maximal cupula shear strain at the crista surface were the largest under the position of the head tilted 0° to the left, and decreased gradually as the left-leaning angle of the head increased. The numerical results of cupula shear strain at the crista surface in bilateral SCCs can quantitatively explain the combined effects of each SCC's excitation or inhibition on volunteers’ nystagmus SPV under different head positions. In addition, a fluid-structure interaction investigation revealed that different left-leaning head positions changed the endolymphatic pressure gradient distribution in SCCs, which determined the transcupular pressure, cupula shear strain at the crista surface, and nystagmus SPV.

Numerical modeling and verification by nystagmus slow-phase velocity of the function of semicircular canals.

The malfunctioning of semicircular canals (SCCs) in the vestibular system results in diseases that disrupt the individual's daily life. Vestibular diseases can be treated more effectively if the functioning of the SCCs is better understood. However, the SCC is difficult to dissect, because it is a complex structure buried deep in the inner ear. To thoroughly understand the function of SCCs and provide better treatment plans for vestibular diseases, we constructed a numerical model of human SCCs and validated it experimentally. Based on the principle of the vestibulo-ocular reflex, the cupula deformation deflects embedded sensory hair cell bundles, transmitting signals to the brain and inducing a slow compensatory eye movement. The slow-phase velocity (SPV) is the characteristic of the slow compensatory eye movement. We investigated the cupula deformation in the numerical model and the SPV under different conditions. The relationship between the cupula deformation and the SPV was quantified for three volunteers. It was observed that the maximal cupula deformation is proportional to the angular acceleration, while the SPV is changing nonlinearly with the angular acceleration. For three volunteers, the relationship between the cupula deformation and the SPV can be expressed by same type function of which the parameters are dependent on individual differences. These results validate the reliability of the numerical model.

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.

Finite element model of a human lateral semicircular canal of the inner ear

The human inner ear hosts a fundamental component of the mechanisms regulating balance and maintaining gaze: the vestibular system. It can detect motion thanks to three semicircular canals (SCC), w...

The Age-Related Orientational Changes of Human Semicircular Canals.

ObjectivesSome changes are found in the labyrinth anatomy during postnatal development. Although the spatial orientation of semicircular canals was thought to be stable after birth, we investigated the age-related orientational changes of human semicircular canals during development.MethodsWe retrospectively studied the computed tomography (CT) images of both ears of 76 subjects ranged from 1 to 70 years old. They were divided into 4 groups: group A (1–6 years), group B (7–12 years), group C (13–18 years), and group D (>18 years). The anatomical landmarks of the inner ear structures were determined from CT images. Their coordinates were imported into MATLAB software for calculating the semicircular canals orientation, angles between semicircular canal planes and the jugular bulb (JB) position. Differences between age groups were analyzed using multivariate statistics. Relationships between variables were analyzed using Pearson analysis.ResultsThe angle between the anterior semicircular canal plane and the coronal plane, and the angle between the horizontal semicircular canal plane and the coronal plane were smaller in group D than those in group A (P<0.05). The JB position, especially the anteroposterior position of right JB, correlated to the semicircular canals orientation (P<0.05). However, no statistically significant differences in the angles between ipsilateral canal planes among different age groups were found.ConclusionThe semicircular canals had tendencies to tilt anteriorly simultaneously as a whole with age. The JB position correlated to the spatial arrangement of semicircular canals, especially the right JB. Our calculation method helps detect developmental and pathological changes in vestibular anatomy.

Optimising the yaw motion cues available from a short stroke hexapod motion platform

AbstractThis paper presents findings from research conducted at the University of Liverpool aimed at optimising the motion cues available from a short-stroke hexapod motion platform. Piloted simulation experiments were conducted to gather both objective and subjective measures of pilot performance and motion fidelity for a typical helicopter low-speed yaw axis capture task. These measures included subjective ratings taken for the first time using a new motion fidelity rating scale. During the experiment four baseline configurations were presented to the pilot; – No motion, Rotational-only motion, Translational-only motion and Rotational + Translational motion, and within these baseline configurations various values of motion filter gains were examined. The key findings from the experiment show that the most acceptable motion fidelity was obtained when congruent cues were presented in both the rotational and translational axes. A possible explanation for this result is postulated to lie within the relative motion perception thresholds of the human semicircular canals. These results contrast with previous research which suggested that yaw axis motion cues were of less importance than translational motion cues.

The Human Semicircular Canals Orientation Is More Similar to the Bonobos than to the Chimpanzees

For some traits, the human genome is more closely related to either the bonobo or the chimpanzee genome than they are to each other. Therefore, it becomes crucial to understand whether and how morphostructural differences between humans, chimpanzees and bonobos reflect the well known phylogeny. Here we comparatively investigated intra and extra labyrinthine semicircular canals orientation using 260 computed tomography scans of extant humans (Homo sapiens), bonobos (Pan paniscus) and chimpanzees (Pan troglodytes). Humans and bonobos proved more similarities between themselves than with chimpanzees. This finding did not fit with the well established chimpanzee – bonobo monophyly. One hypothesis was convergent evolution in which bonobos and humans produce independently similar phenotypes possibly in response to similar selective pressures that may be associated with postural adaptations. Another possibility was convergence following a “random walk” (Brownian motion) evolutionary model. A more parsimonious explanation was that the bonobo-human labyrinthine shared morphology more closely retained the ancestral condition with chimpanzees being subsequently derived. Finally, these results might be a consequence of genetic diversity and incomplete lineage sorting. The remarkable symmetry of the Semicircular Canals was the second major finding of this article with possible applications in taphonomy. It has the potential to investigate altered fossils, inferring the probability of post-mortem deformation which can lead to difficulties in understanding taxonomic variation, phylogenetic relationships, and functional morphology.

Costimulation of the Horizontal Semicircular Canal during Skull Vibrations in Superior Canal Dehiscence Syndrome

A sound- and pressure-induced vestibuloocular reflex (VOR) has been described as vertical and torsional in superior canal dehiscence (SCD), and the rotational axes of induced VOR have been assumed to fit with the axis of the affected superior semicircular canal (SC). However, it has been difficult to characterize the pattern of vibration-induced VOR (ViVOR). We aimed to characterize the pattern of ViVOR by comparing the intensity and the axis of ViVOR with several clinical parameters of SCD. Ten symptomatic SCD patients were recruited. SCD size and location were measured on a reformatted image in the plane of the SC. Unilateral vibratory stimulation (100 Hz) was applied to the mastoid surface. ViVOR were recorded using 3D videooculography. The median 3D velocity of ViVOR was measured and the 3D vector trajectory plotted for reference against the axes of the human semicircular canals. A correlation between the magnitude of ViVOR and the size of SCD was evaluated. We also compared the location of SCD with the vertical-to-torsional component ratio of the ViVOR. ViVOR were present in 7 patients; 6 patients showed a substantial horizontal component in the excitatory direction in addition to strong torsional and weak vertical components. The computed rotational axes of ViVOR were located mostly between the axes of the ipsilateral SC and horizontal canal (HC) with a variable deviation to the axis of the ipsilateral posterior canal (PC). The magnitude of ViVOR was not related to the size of the SCD. The vertical-to-torsional component ratio of ViVOR tended to decline as the dehiscence was closer to the common crus. In SCD, mastoid vibration may stimulate the affected-side HC and PC as well as the SC. SCD can be suspected when excitatory horizontal torsional ViVOR direct to the side of the auditory symptoms.

Modeling the Effects of Gravity Transitions in the Vestibular System: Preliminary Findings (P06.042)

Objective: To demonstrate the effects of electromagnetic induction in a model of a human vestibular system. Background Humans are exposed to different geomagnetic gradients believed to produce physiological changes in balance and locomotion. Current investigations using magnetic field-dependent chemical reactions and magnetite have not properly explained such neuro-otologic disturbances happening in and out of Earth. The electromagnetic induction mechanism model may explain the vestibular side effects affecting balance and locomotion of people exposed to different geomagnetic fields. Design/Methods: We used Matlab custom-written scripts for modeling one semicircular canal of the vestibular system, which we exposed under eight different movement conditions, ranging from common walking on earth up to spaceflights in presence of static geomagnetic fields. The electrical resistance (R) for the semicircular canal was estimated to be 6.2 x 10-4 Ω. The induced electrical voltage and current was estimated according to Faraday9s: ∇x E = -∂B / ∂t; Kirchhoff9s: C ∂V / ∂t + V/R = 0, and Ohm9s law:I = V/R. Results: The induced vestibular voltage and current obtained with this computational model was of almost four orders of magnitude. It was approximately 6000 times or 76 decibels larger for the space shuttle - where the induced vestibular current was ∼ 1 A - compared to the baseline obtained while walking. Interestingly, such induced voltage and current started to be significant, approximately 150 times or 44 decibels larger at altitudes employed by commercial airplane flights. Conclusions: We found a new geomagnetic-side effect in the human semicircular canal due to fast aerospace motion, which starts to be significant at altitudes still used for human living. Such geomagnetic effects may play a role to induce balance, gait and locomotion abnormalities in people living in extreme environments. A closed system using an internal current loop present in the inner ear, is very likely to happen in humans. Supported by: Doctor Fidias E. Leon-Sarmiento was supported the Department of Defense ( USAMRAA, W81XWH-09-1-0467 ); Doctor Carlos V. Rizzo-Sierra was supported by the University of Pamplona (Research Grant No. 0012). Disclosure: Dr. Leon-Sarmiento has nothing to disclose. Dr. Rizzo-Sierra has nothing to disclose. Dr. Gonzalez has nothing to disclose.

Mechanical properties and motion of the cupula of the human semicircular canal

The mathematical model for the dynamics of the cupula-endolymph system of the inner ear semicircular canal, as elaborated by numerous investigators, remains a foundational tool in all of vestibular physiology. Most models represent the cupula as a linear spring-like element of stiffness K=DeltaP/DeltaV, where DeltaV is the volume displaced upon application of a pressure difference DeltaP. The parameter K directly influences the long time constant of the cupula-endolymph system. Given estimates of K based on experiments, we use thick and thin bending membrane theory, and also finite-element simulations based on more realistic cupula morphologies, to estimate the human cupula's Young's modulus E approximately 5.4 Pa. We show that for a model morphology, thick bending membrane theory and finite-element predictions are in good agreement, and conclude that the morphology of the attachment of the cupula to the slope of the crista should not greatly influence the volume displacement. We note, however, that other biological materials with very low E are hydrogels that have significant viscoelastic properties. Experiments to directly measure E and investigate potential viscoelastic behavior ultimately may be needed. In addition, based on experimental images we study two other different shapes for the cupula and quantify their impact on the deflection of the cupula. We also use a three-dimensional finite-element model to analyze both the shear strain distribution and its time evolution near the sensory epithelium. We conclude that stimulation of sensory hair cells probably begins at the centre of the crista and spreads toward the periphery of the cupula and down the sides of the crista. Thus, spatio-temporal variations in the shearing stimulus are predicted to impact subsequent transduction and encoding. Finally, modeling the fluid-filled vertical channels believed to lie within the cupula, we investigate the impact of different tube diameters on the transverse displacement field. We show that, for the assumed diameters and grid spacing, cupula displacements should be highly sensitive to the diameter of the tubes. Experiments to verify the existence of cupular channels and accurately measure their diameter and spacing are needed.

Three-Dimensional Reconstruction of the Human Semicircular Canals and Measurement of Each Membranous Canal Plane Defined by Reid's Stereotactic Coordinates

Equations for estimating the planar relationships of the human semicircular canals were devised by Blanks et al from a dissected bony labyrinth in a human skull. However, a similar study on the membranous semicircular canal planes has never been published. In this study, the angle between each membranous canal plane and Reid's stereotactic horizontal plane was measured on serial histologic sections of 7 temporal bones from Japanese adults. We reconstructed the 3 semicircular canals by computer-aided 3-dimensional analysis. The angles between each pair of both bony and membranous canal planes were measured. In the bony labyrinth, the angles between the 2 canal planes of the lateral-anterior, anterior-posterior, and lateral-posterior pairs were 90.51 degrees +/- 2.98 degrees (mean +/- SD), 91.70 degrees +/- 1.85 degrees, and 94.52 degrees +/- 3.32 degrees, respectively. The angles between the 2 membranous canal planes of the lateral-anterior, anterior-posterior, and lateral-posterior pairs were 90.05 degrees +/- 4.74 degrees, 91.03 degrees +/- 2.93 degrees, and 91.92 degrees +/- 5.22 degrees, respectively. The data from our study of the membranous labyrinth showed that the angles between each canal plane and the others were much closer to 90 degrees than was found by Blanks et al for the bony labyrinth.

Orientation of Human Semicircular Canals Measured by Three-Dimensional Multiplanar CT Reconstruction

Analysis of vestibulo-ocular reflex experiments requires knowledge of the absolute orientations (with respect to skull landmarks) of semicircular canals (SCC). Data relating SCC orientations to accessible skull landmarks in humans are sparse, apart from a classic study of 10 skulls, which concluded that the horizontal and anterior SCC are not mutually orthogonal (111 +/- 7.6 degrees). Multiple studies of isolated labyrinths have shown the inter-SCC angles are close to 90 degrees. We hypothesized that a larger sample would yield mean absolute SCC orientations closer to the mutual orthogonality demonstrated for isolated labyrinths. We measured canal orientations with respect to accessible skull landmarks using 3-D multiplanar reconstructions of computerized tomography scans of the temporal bones of 22 human subjects. Images were acquired with 0.5-mm thickness and reconstructed with in-plane resolution of 234 microm. There was no significant difference between the left and a mirror image of the right (p > 0.57 on multiway ANOVA of orientation vector coefficients), so data were pooled for the 44 labyrinths. The angle between the anterior and posterior SCC was 94.0 +/- 4.0 degrees (mean +/- SD). The angle between the anterior and horizontal SCC was 90.6 +/- 6.2 degrees. The angle between the horizontal and posterior SCC was 90.4 +/- 4.9 degrees. The direction angles between a vector normal to the left horizontal SCC and the positive Reid's stereotaxic X (+nasal), Y (+left), and Z (+superior) axes were 108.7 +/- 7.5 degrees, 92.2 +/- 5.7 degrees, and 19.9 +/- 7.0 degrees, respectively. The angles between a vector normal to the left anterior SCC and the positive Reid's stereotaxic X, Y, and Z axes were 125.9 +/- 5.2 degrees, 38.4 +/- 5.1 degrees, and 100.1 +/- 6.2 degrees, respectively. The angles between a vector normal to the left posterior SCC and the positive Reid's stereotaxic X, Y, and Z axes were 133.6 +/- 5.3 degrees, 131.5 +/- 5.1 degrees, and 105.6 +/- 6.6 degrees, respectively. The mean anterior SCC-contralateral posterior SCC angle was 15.3 +/- 7.2 degrees. The absolute orientations of human SCC are more nearly orthogonal than previously reported.

Three-dimensional Reconstruction and Measurement of the Human Membranous Semicircular Canal

The planar relationship of the human semicircular canals was determined by Blanks et al. at a series of points measured from the dissected bony labyrinth of the human skull. The relationship of membranous canal planes have not, however, been measured from the human temporal bone. We reconstructed 3 semicircular canals by computer-aided 3-dimensional analysis and measured the angles formed between pairs of 3 osseous and membranous canal planes of temporal bones. Five temporal bones in adults were used for this study. Results indicated angles formed between pairs of ipsi-lateral canal planes of both the bony and membranous labyrinth. Angles formed between the horizontal-anterior, anterior-posterior, and posterior-horizontal canal planes of the bony labyrinth were 89.64 +/- 1.82 (mean +/- SD), 90.95 +/- 1.25, and 94.02 +/- 3.77 degrees. The same angles measured from the membranous labyrinth were 90.12 +/- 2.64, 90.18 +/- 2.75, and 91.48 +/- 6.32 degrees. Differences between the angles formed between bony and membranous canal planes were 2.11, 6.05, and 3.26 degrees in the anterior, horizontal, and posterior canal. Pairs of membranous canal planes were nearly perpendicular without exception, but pairs of osseous canal planes had a larger deviation from 90 degrees. This suggested that membranous canals could successfully be constructed in adequate alignment for canal function in the large perilymphatic space within osseous semicircular canals.

Modal analysis of the diaphragm of the semicircular canal

The aim of this paper is to determine the domain of validity of calculated quasi-static deformations of the cupula and of ciliar deflections on the crista ampullaris. Several three-dimensional models of the isolated ampullar diaphragm of the human semicircular canal and of that of the frog are studied theoretically by modal analysis. The four first modes of vibration are determined for each structure. Numerical simulations prove that for the first mode of vibration, the cupular deformation has the same shape as that obtained by applying a static pressure difference across the ampullar diaphragm. We studied also the effect of the mechanical properties (Young's modulus and Poisson's coefficient) of the components of the ampullar diaphragm on the vibration modes and their frequencies. The condition, which must be satisfied by the cupular internal viscosity, to have resonance near the natural frequency of the ampullar diaphragm is determined.