Fluid-Mechanical Model for Sound-Induced Vertigo B. Grieser, D. Obrist, Professorship L. Kleiser

Superior Canal Dehiscence Patients with a superior canal dehiscence (SCD) in the inner ear (Fig. 1) suffer from events of dizziness and vertigo in response to sound [1], also known as Tullio phenomenon (TP). So far, the mechanisms behind TP remained obscure.

Hypothesis

In accordance with the third window theory, we assume that the vibrating stapes causes abnormal perilymph pulsations towards the pathologic ‘window’ (SCD) in the organ of balance (Fig. 2). Based on this assumption, we hypothesize that the (elastic) membranous canal acts as a waveguide, with wave speeds far below the acoustic wave speed. These waves interact with the endolymph, thereby causing a rapidly pulsating flow with a non-zero mean component, also known as steady streaming. TP patients interpret such a flow as a motion of the head and respond by a countermotion of the eye through the vestibulo-ocular reflex (VOR).

Fluid-Mechanical Model

We developed a computational model (Fig. 2) to simulate fluid-structure-interactions between perilymph, endolymph and the elastic membranous canal. Since we expect a nonlinear phenomenon in the endolymph, it is solved with the Navier-Stokes equations in the Arbitrary Lagrangian Eulerian (ALE) formulation. The numerical coupling procedure uses the Aitken relaxation and follows a so-called ‘Dirichlet-Neumann’ approach. The solver was implemented using the software library OpenFOAM.

Results

The results confirmed the traveling-wave hypothesis as well as the existence of steady streaming (Fig. 3) in response to sound stimuli. A series of simulations was carried out to assess the influence of various parameters – such as sound frequency, sound volume, membranous canal stiffness, SCD size and SCD location – on the intensity of TP. Using dimensional analysis, we were able to empirically derive a dimensionless relationship between these para-meters [4]. The results reveal a ‘sweet spot’ for TP within the audible spectrum (Fig. 4) which largely agrees with patient data. We found that steady streaming primarily originates from Reynolds stresses in the fluid, which are weakest in the lower sound spectrum. Additionally, natural variations in the stiffness of the membranous canal and the stapes motility are observed to shift the sweet spot. Sound frequencies above the ring frequency [2] do not invoke vestibular reactions (Fig. 4).

If ways can be found to artificially stiffen the membranous canals, it should be possible to alleviate the symptoms for patients with SCD – according to our model predictions. This could pose a less harmful alternative to the surgical interventions which currently feature a high relapse rate.

Figure 1 Inner ear with a superior canal dehiscence. (A) CT reconstruction from [3]. (B) Source: http://www.earsite.com/.

Figure 2 Computational model for the Tullio phenomenon.

Figure 3 Mean flow profiles within the endolymph: Eulerian (black) and Lagrangian mean (red), Stokes drift (blue).

Figure 4 Contour plot of the pathological eye velocity in response to harmonic sound of frequency f at sound pressure level SPL. The red line denotes the ring frequency [2] of the membranous canal with stiffness E=20kPa.

References

[1] Minor, L.B., et al., Arch Otolaryngol Head Neck Surg, 124(3):249-58, 1998

[2] Gautier, F., et al., Acta Acustica, 93:333-44, 2007 [3] Hegemann, S.C., and Carey, J.P., Otolaryngol Clin N Am,

44:377-82, 2011 [4] Grieser, B., Dissertation ETH Zurich, No. 22681, 2015

12 Introduction

latter value was used by Obrist (2008) to derive a volumetric stiffness of13GPa/m3.

Figure 1.8: Superior canal dehiscence: schematic visualization of thepathoanatomy. Part of the temporal bone along the roof of the supe-rior canal is dehiscent and opens up to the dura mater (shown in blue)which covers the cranial cavity. Retrieved on January 12, 2015, fromhttp://www.earsite.com/what-is-superior-canal-dehiscence.

1.3 Superior canal dehiscence

The superior canal dehiscence (SCD) syndrome is a pathological condi-tion of the inner ear which remained unidentified until Minor et al. (1998)connected it to vestibular symptoms in response to sound and pressurestimuli. It refers to an abnormal absence or disruption of the tempo-ral bone which separates the inner-ear fluids from the cranial cavity, cf.Fig. 1.8. Predominantly affected due to its protuberant position withinthe temporal bone is the superior canal (SC), although dehiscences ofhorizontal (HC) and, even less likely, posterior canals (PC) have been re-ported as well (Chien et al., 2011; Cremer et al., 2000a; Erdogan et al.,2011; Krombach et al., 2006).

Section 1.3.1 gives a detailed description of the SCD pathophysiology,along with diagnostic and therapeutic measures to identify and poten-tially cure SCD patients. The so-called third-window theory is intro-duced in Section 1.3.2 and draws a connection to the fluid and solidmechanics of the semicircular canals (SCC), based on which a separatediscussion on the influence of the SCD on the stapes motility follows inSection 1.3.3.

30 Physical Modeling

Figure 3.1: Left : Physical model for sound-induced vertigo due to a dehiscence ofbone above the superior canal (SC) in the vestibular system. Upper right : Straight-ened model of the SC with concentric, circular cross-sections of endolymph (EL) andperilymph (PL), confined between the ampulla and the utricle, and separated bythe elastic membranous labyrinth (ML). Center right: Fluid-structure interactionbetween the one-dimensionally modeled PL/ML and the axisymmetric model of theEL. Lower right: Volume-based cupula model.

harmonics, it will most likely be present in more complex acoustic wave-forms, too. Therefore the stapes motion is modeled as a perfect sinusoid,well-defined by its amplitude (velocity Us) and the sound frequency f .

As the stapes vibrates, at least two oscillating fluid columns formin the perilymph (density ρf): one leads towards the round window viathe cochlear scalae, and the other(s) towards the dehiscence along thesemicircular canals (SCC).

Our physical model will only consider the shortest vestibular pathwaywhose centerline coordinate is denoted by x. It passes first the ampulla(x = 0) of the superior canal (SC) and then leads directly to the de-hiscence along the narrow duct (Fig. 3.1). The frequency-dependentadmittance φ of the cochlea in presence of an SCD is considered bypredictions from Kim et al. (2013), cf. Fig. 1.12. Apart from that, wedo not expect further implications on the balance sense which originatefrom the cochlear pathway.

We assume that the effects of the dehiscence on the stapes motility

92 Results and Discussion

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Figure 5.20: Axial mean of the endolymph velocity, ue, viewed from an (a) Eulerianand (b) Lagrangian perspective, along with the resulting (c) Stokes drift. (d) Cross-sectional profiles of the axial mean velocities. Simulated for sound frequency f=1kHz,Young’s modulus E=40 kPa and perilymph velocity amplitude Up=2.6mm/s. Dataacquisition and post-processing by Benner (2015).

5.3 Eye response to sound stimuli 105

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Figure 5.28: Activity map of the Tullio phenomenon for the virtual patient ➁ of theprevious figure. Contour plots of the predicted slow-phase eye velocity αt correspondto our model (5.29)-(5.33), and are shown as a function of the sound frequency fand the sound pressure level SPL. The dashed line (red) corresponds to the ringfrequency fπ (5.4), marking the onset of a stop band region for acoustic plane wavesaccording to Gautier et al. (2007). Physical parameters are given in Tab. 4.3.

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Figure 5.28: Activity map of the Tullio phenomenon for the virtual patient ➁ of theprevious figure. Contour plots of the predicted slow-phase eye velocity αt correspondto our model (5.29)-(5.33), and are shown as a function of the sound frequency fand the sound pressure level SPL. The dashed line (red) corresponds to the ringfrequency fπ (5.4), marking the onset of a stop band region for acoustic plane wavesaccording to Gautier et al. (2007). Physical parameters are given in Tab. 4.3.

Author's personal copy

the inner ear and intracranial space as the patient aged. This effect might occur if theelasticity of the dura changed with age, or if the pressure gradients between the innerear and intracranial space changed. Another possibility is that the patient experiencedthe loss of some central compensatory mechanism that had minimized the symptomsin childhood. However, the immediate recovery from all symptoms shortly after theoperation argues against a central process that might have slowly deteriorated,because a slow readaptation to the new (plugged) state would then be expected.Instead, the instant resolution of symptoms with the correction of the peripheral defectsuggests strongly that some change in the physiology of the dehiscence explained theworsening of symptoms in adulthood. The nature of this change has not beendetermined.This case raises the possibility that SCDS symptoms may be present in childhood

and go unrecognized. Increased awareness of this diagnosis may help identify morecases of children experiencing symptoms of SCDS. Clinicians evaluating youngpatients experiencing dizziness should maintain a high degree of suspicion ofSCDS. Symptoms such as autophony and hearing one’s own body sounds mayseem so unusual to children that they may not spontaneously share these complaintswith their parents or clinicians. A careful history is essential to diagnosing SCDS, andclinicians may have to inquire about apparent agoraphobia to determine if it is really

Fig. 1. Cervical vestibular evokedmyogenic potential thresholds before (A) and after (B) plug-ging of the superior canal. The threshold is determined by a linear regression through theamplitudes of the potentials at different stimulus intensities. This technique is a very roughway to determine the threshold, but because the change in amplitudewith stimulus intensityis usually linear, the authors oftenuse only two stimulus intensities if the threshold has normalvalues. As can be seen, even with four intensities used in (A) for the threshold of the rightsacculus, the amplitudes are close to the linear regression and the threshold is at approxi-mately 46 decibels above normal adult hearing level (dB nHL), which is considerably belownormal (75 dB nHL in the authors’ laboratory). After plugging, the vestibular evokedmyogenic potential threshold is normal on both sides, between 80 and 90 dB nHL. The ampli-tude at 90 dB nHL is almost identical on both sides. The value of 176 mV at 95 dB nHL may bea little high, but even taking the value of the first measurement (131 mV) would result ina normal threshold.

Fig. 2. (A) CT reconstruction in the plane of the right superior semicircular canal. A largedehiscence in the upper part of the semicircular canal can be seen. (B) The dehiscence intra-operatively. Scale ticks are 1 mm.

SCD Congenital or Aquired 381

A B