# Rotatory Chair Testing in Otology: Biomechanical Modeling and Numerical Simulation

Manon Blaise, Daniel Baumgartner, Anne Charpiot

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Manon Blaise, Daniel Baumgartner, Anne Charpiot. Rotatory Chair Testing in Otology: Biomechanical Modeling and Numerical Simulation. Congrès Français de Mécanique, 2022, Association Française de Mécanique (AFM), Aug 2022, Nantes, France. hal-04219693

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# Rotatory chair testing in otology: biomechanical modeling and numerical simulation

M. BLAISEª, D. BAUMGARTNERᵇ, A. CHARPIOTᶜ

a. Laboratoire ICube, UMR 7357 CNRS et Université de Strasbourg –
   manon.blaise@etu.unistra.fr

b. Laboratoire ICube, UMR 7357 CNRS et Université de Strasbourg –
   daniel.baumgartner@unistra.fr

c. Hôpitaux Universitaires de Strasbourg, Pôle Tête-Cou, Service ORL –
   anne.charpiot@chru-strasbourg.fr

## Abstract:

Rotational chair testing is one of the clinical gold standards for assessing vestibular function in case of dizziness and vertigo. To ensure the body balance control within space, the vestibule of the inner ear senses head acceleration. The vestibule detects the deflection of some ciliated cells during head movements. Deflection and strain of cilia are induced by the interactions between inner ear fluids – endolymph and perilymph– and thin structures that are the membranous labyrinth of the vestibule and the cupula. The present work aimed to study these interactions by developing a finite element (FE) model of a part of the human vestibule called the lateral semicircular canal. While several models in the literature use an approach with a rigid canal, the present work explores the results of rotational testing with the influence of the membranous labyrinth modeled as flexible and the cupula following a viscoelastic behaviour. When compared to literature, results show similar transversal deformation trends of the cupula. Values of the maximal displacement of the cupula differ depending on simulations and mainly because of different assumptions that are mentioned.

**Keywords:** Biomechanics, Balance, Inner ear, Finite Element Method, Fluid-Structure Interaction

## 1 Introduction

In vertebrates, sense of balance is vital and primitive. Combined with vision and proprioception, the vestibular apparatus is one of the three inputs attributed to the postural control system. The labyrinth is filled with endolymph and immersed in perilymph, both waterlike fluids. The soft membranous labyrinth is comprised of two saclike structures and three semicircular canals (SCC) dedicated to linear and angular acceleration measurement of the head [1]. The three SCC –each about 6 mm in diameter– form a quasi-orthogonal basis, so that head motion is detected in any direction. A sensory area of interest is retrieved in each membranous duct with a transversal gelatinous diaphragm called the cupula which overlays at its base a layer of sensory hair cells. During head movements, the cupular diaphragm is deformed by endolymph flow and cilia embedded in the cupula are elongated targeting
mechanotransduction mechanisms up to vestibular nerve fibers (see Figure 1-Right). By neural pathways, the brain thus receives and handles accurate data on head position allowing to move and control body orientation in space. On the contrary, in case of a vestibular disorder, the brain can receive information from the vestibule, the eyes and the muscles that do not match: this is when the conflicting information triggers vertigo and dizziness. From a clinical point of view, it is therefore necessary to study the physiological and pathological functioning of the inner ear sensors in order to make a targeted diagnosis on the origin of balance disorders. Rotational chair testing (RCT) is thus commonly used to assess vestibular function [2]–[4].

The smallness and the fragility of the vestibular organ makes understanding the interactions between the fluids and the thin tissue structures incomplete, delicate and challenging. While compartmentalization of both inner ear fluids is ensured by the membranous labyrinth, and the balance of fluid pressure and volume provides physiological deformations of the cupula, several models in the literature use an approach with SCC constrained as rigid walls [5]–[7] and cupula modeled as linear elastic material. To the best of our knowledge, the present work is the first to study the influence of the surrounding structures on the response of the cupula deformation by modelling the perilymphatic compartment and the membranous labyrinth as a soft material, with cupula following a viscoelastic constitutive law. For this purpose, a finite element (FE) model of a lateral SCC was developed and used to simulate RCT. Deformation and behaviour of the cupula were studied and compared with similar works in the literature.

# 2 Materials and Methods

## 2.1 Finite Element (FE) Model

<figure><img src="image_2.png" /><figcaption>Figure 1. Left: Top view of the semicircular canal FE model. “U” and “C” represent the utricle region and canal entrance respectively. Scale bar=1 mm. Right: Diagram of the cupular zone in a semicircular canal.</figcaption></figure>

A 3D FE model of a 50-µm slice of a lateral SCC was built using Altair Hyperworks™ software. The anatomical dimensions and geometry were extracted from Curthoys and Oman [8]. Six continuously meshed parts describe the two fluids –endolymph and perilymph– and four tissue structures –labyrinth membrane, cupula, crista and bone– of a human lateral SCC, resulting in a whole model of 10,338 hexahedral elements (see Figure 1-Left). The membranous labyrinth, forming biologically a small tube with an enlarged part called the utricle, contains the endolymph and bathes in the perilymph. Thus, to represent it in section, the edge which separates the two liquids was meshed in orange, while the other
edge was confused with the bone in grey because strictly attached to it (see Figure 1). Properties of water were assigned to both fluids (density of 1,000 kg.m⁻³, kinematic viscosity of 8.5 e-04 Pa.s) [9]. An innovative feature of the current model was that solid tissues were assumed to be quasi-incompressible, linear elastic following Hooke's law, except the cupula which followed a viscoelastic behaviour law [10]. The viscoelastic model used was that of a generalized Kelvin-Voigt model, also known as Zener model, and consists of a first spring (E) put in series with a second spring (E₁) working in parallel with a Navier dashpot (η₁) (see Figure 2). The instantaneous modulus E refers to the initial elastic response and the equilibrium modulus E₀, referring to the long-term elastic response, is obtained from E and E₁ as follows:

$$E0 = \frac{E * E1}{E + E1}$$

<figure><img src="image_3.png" /><figcaption>Figure 2. Representation of the viscoelastic Zener model attributed to the cupula.</figcaption></figure>

Concerning mechanical and physical properties of the cupula, very few direct experiments on animals have been performed and none on humans due to the consistency, smallness and fragility of this small organ. Selva et al. [10] computed from both mathematical and FE model an estimation of the cupula's Young's modulus at 5.4 Pa, a value that has been adopted by most of FE models in the literature [7], [11]–[13]. Because it is mainly composed of water and soft gelatinous glycoproteins, the cupula is assumed to behave as hydrogel thus viscoelastic material [10], [14], [15]. In our model, the long-term Young's modulus E₀ was equal to 5.0 Pa, in accordance to literature. The parameters used in the model are summarized in Table 1.

<table><caption>Table 1. Mechanical properties and parameters used in the model.</caption><thead><tr><th>PARTS of the FE model</th><th>Young's modulus (Pa)</th><th>Density (kg.m<sup>-3</sup>)</th><th>Viscosity (Pa.s)</th><th>Poisson's ratio</th></tr></thead><tbody><tr><td>Labyrinth membrane</td><td>100</td><td>1,000</td><td>-</td><td>0.48</td></tr><tr><td>Crista</td><td>1.0 e+06</td><td>1,000</td><td>-</td><td>0.48</td></tr><tr><td>Bone</td><td>2.0 e+10</td><td>1,500</td><td>-</td><td>0.48</td></tr><tr><td>Cupula</td><td>E=50; E1=5</td><td>1,000</td><td>-</td><td>0.48</td></tr><tr><td>Endolymph</td><td>-</td><td>1,000</td><td>8.5 e-04</td><td>-</td></tr><tr><td>Perilymph</td><td>-</td><td>1,000</td><td>8.5 e-04</td><td>-</td></tr></tbody></table>

All nodes of the model were constrained in the normal direction (to prevent from fluid leakage) and the bony part received boundary conditions to prevent its deformation. In this way, the SCC was controlled by the bony part as a rigid body. Solicitations imposed to this rigid body are described in the next subpart.

## 2.2 Rotational Chair Testing

Rotatory chair testing (RCT) is considered as a clinical test of reference to assess vestibular function and particularly bilateral vestibular weakness and lateral SCC response [2], [3]. Physiologically, head movements are detected in the vestibule which transmits electric information by the vestibular nerve
up to the brain. Then the central nervous system coordinates a response by sending efferent signals to the eye muscles in order to keep stable the image on the retina, i.e. to coordinate the movement of the eyes in function of the movement of the head. In practice, for every head movement in one direction, there is eye movement in the opposite direction. This adaptation is called the Vestibulo-Ocular Reflex (VOR) and is at the basis of the rotational chair testing. In clinical practice, the patient seats on a rotating chair and wears a video headset. The chair undergoes sinusoidal trajectories around its vertical axis between 0.01 and 6 Hz, while eye movements are recorded by the headset. The extinction of the eyes movement detected by this video-oculography indicates the time it takes for the cupula to return to its initial and resting position. This time constant assures the proper functioning of the vestibular system.

In this way, five RCT were simulated by imposing to the model a horizontal sinusoidal movement at 0.64, 1, 2, 4 and 6 Hz with a maximal angular velocity of 25°.s⁻¹ (see Figure 3). Rotations of the 3D slice were exclusively reduced to the horizontal plan so that the normal vector of the slice met the vector of gravity, named then as the “vertical axis”. The center of rotation was placed at an offset point from the canal center to represent the foramen magnum. The movement was stopped in each case after one period of sine to assess the return of the cupula. The angular velocity, i.e. the amplitude of the function, was in accordance with the clinical practice and was also chosen to allow comparison with the results of Shen’s study [7].

In these RCT simulations, maximal transverse displacement, deformation trend, shear strain as well as Von Mises stress of the cupula were analyzed.

<figure><img src="image_4.png" /><figcaption>Figure 3. Angular velocity profiles for sinusoidal solicitations.</figcaption></figure>

# 3 Results

Initial considerations allowed to identify a similar trend of cupula deformation (see Figure 4) found in each test undertaken, namely:

(i) the first stages of the rotation of the canal led to a bulging of the cupula in its center;

(ii) the deformation was in the opposite sense to the movement;

(iii) maximal shear strain and stress were found at the top of the crista, i.e. at the base of the cupula, where the ciliated sensory cells are located.
<table><caption>Table 2. Cupula displacement, delay between maximum amplitude and maximal displacement, maximal Von Mises stress and maximal strain in different simulations.</caption><thead><tr><th>Solicitation</th><th>Maximal displacement<br>of N1 node in the<br>cupula (μm)</th><th>Maximal<br>shear strain<br>(e-02)</th><th>Maximal<br>Von Mises<br>stress<br>(Pa)</th><th>Time delay<br>between<br>displacement of<br>head and cupula<br>(s)</th></tr><tr><th></th><th colspan="4">Utricle / Canal side</th></tr></thead><tbody><tr><td>0.64 Hz</td><td>19</td><td>23</td><td>2.47</td><td>0.20</td><td>0.335</td></tr><tr><td>1.0 Hz</td><td>21</td><td>25</td><td>3.47</td><td>0.28</td><td>0.225</td></tr><tr><td>2.0 Hz</td><td>24</td><td>27</td><td>3.67</td><td>0.52</td><td>0.130</td></tr><tr><td>4.0 Hz</td><td>24</td><td>28</td><td>3.53</td><td>0.86</td><td>0.075</td></tr><tr><td>6.0 Hz</td><td>23</td><td>26</td><td>3.17</td><td>0.99</td><td>0.055</td></tr></tbody></table>

Results of the five simulations in terms of cupula displacement, shear stress and strain are listed in Table 2. Starting the clockwise angular movement, the cupula always first deflected to the utricle, i.e. to the opposite movement direction (see Figure 4). Then it relaxed toward initial position due to its viscoelastic behaviour and moved –after a recorded delay– to the canal side after finally completely relaxing. The maximal transverse displacements plotted in Figure 5-Left associated with the corresponding data in Table 2 show that the expansion of the cupula, i.e. the amplitude of the motion, is globally the same from 0.64 to 6 Hz and around 25 µm (min=19 µm, max=28 µm). However during the second part of the movement, when the canal rotates anti-clockwise deflecting the cupula towards the canal side, the amplitude is slightly higher than clockwise (26 vs 22 µm on average). Both towards the utricle and towards the canal, the curves at 2 Hz and 4 Hz show equal and slightly higher values than in the three other frequencies. The Von Mises shear stress and shear strain were in all five configurations maximal at the top of the crista, where the cilia from the cell layer are embedded into the cupula. According to the cupular displacement, highest values of shear strain are retrieved in 2 Hz and 4 Hz simulations. However, Von Mises stresses increase with frequency. Lastly, it was observed that the motion of the cupula did not occur simultaneously with the canal rotation but after a lapse of time. This delay was recorded as shown in Figure 5-Right and reported in Table 2, to conclude that this parameter decreases linearly with the period of the sine.
<figure><img src="image_5.png" /></figure>

Figure 5. View of the shear stress (Von Mises) repartition in the cupula at t=0,075 s of the 4 Hz sinusoidal simulation. Maximal stress is located at the base of the cupula (colored elements), on the top of the crista (grey elements). White star represents the node N1 where the maximal transverse displacements are recorded. Displacement of the cupula has been enlarged for a better visual appreciation.

<figure><img src="image_6.png" /></figure>

Figure 4. Left: Transversal displacement of N1 node in the cupula (see Fig. 4) in different RCT: negative values describe the utricular direction, positive values the canalar direction. Right: Transversal displacement of N1 (blue curve) compared to the displacement of the whole canal (red curve) in RCT at 2 Hz: the change of direction of deformation of the cupula occurred 130 ms after the canal movement toward this direction.

# 4 Discussion and conclusion

RCT remains the gold standard to diagnose bilateral vestibular weakness [3] in particular at low frequencies between 0.01 and 1 Hz. The complementary classical video Head Impulse Test (vHIT) has a predominant frequency at 2.5 Hz, and in clinical examination a head rotation covering 15-30° is performed at 1 to 2 Hz. Finally, frequencies ranging from 2 to 6 Hz corresponds to common head motions [4]. This test is useful for assessing the VOR and therefore vestibular function by comparing the speed of the rotating chair, i.e. the speed of the head, and the speed of the eye movement.
Direct experimental studies that document the mechanical properties of the cupula and its biomechanical behaviour in specific situations such as in RCT are still lacking. While waiting for these experiments, the development of FE models allows us to deepen our knowledge and hypotheses of the functioning of the cupula in relation to its environment, its stresses and its solicitations. In particular, the originality of this work is (i) the modeling of the perilymphatic compartment traditionally absent from FE vestibule modeling [5], [7], [11], [12], [16], but also (ii) the viscoelastic behaviour of the cupula and (iii) the placement of the rotation axis (see [6]).

In Shen et al. [7], similar sinusoidal solicitations at 0.5, 1, 2, 4 and 6 Hz are imposed to a bilateral model of the vestibule including the three SCC with rigid membranes containing their cupulae and the endolymph. When rotated at 2 Hz for a maximal angular velocity of 25°.s⁻¹, the lateral cupula deflects towards the canal side up to 3.74 µm and then anticlockwise towards the utricle up to 3.64 µm. The trend was the same in the present study, differing in magnitude, which here was 24 and 27 µm towards the utricle and the canal side respectively (see Table 2). Both studies found a quasi equal response of the cupula motion at 2 and 4 Hz rotations. In Selva et al. [5], a constant angular velocity of π/2 rad.s⁻¹ is rapidly imposed in 0.2 s to a 3D model of a lateral SCC in which membranes are considered as rigid boundary conditions. The maximal displacement found in the cupula was 15 µm, which has the same order of magnitude as the response found in the current study. The concentration of shear strain at the top of the crista, in accordance to the mechanotransduction mechanisms, has also been observed and pointed by Wu et al. [12] and by Baumgartner et al. [17] in a previous study.

Concerning the cupular displacement, a relatively free and unconstrained movement would be expected from a thin diaphragm of viscoelastic material with a low Young's modulus of about 5 Pa. Considering this remark, the results found in this study –around 20 µm– seem physiologically consistent with the size, shape and properties of the cupula.

To conclude, a total of five rotational tests were simulated with the model of the right lateral SCC, including viscoelastic cupula, flexible membranous labyrinth and perilymphatic compartment bordering this membrane. The results obtained are consistent with what is observed and predicted clinically, namely that cupula is deflected by following the head motion when it is rotated and returns to its initial position with decreasing speed if it does not undergo further acceleration or deceleration. Further studies should complete the model by including the three canals as a whole as well as the two otolith structures and enlarge the solicitations to explore.

## References

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