Drive mechanisms to the inner and outer hair cell ...

Drive mechanisms to the inner and outer hair cell stereocilia Nima Maftoon, Hamid Motallebzadeh, John J. Guinan, and Sunil Puria

Citation: AIP Conference Proceedings 1965, 120002 (2018); doi: 10.1063/1.5038510 View online: https://doi.org/10.1063/1.5038510 View Table of Contents: http://aip.scitation.org/toc/apc/1965/1 Published by the American Institute of Physics

Drive Mechanisms to the Inner and Outer Hair Cell Stereocilia Nima Maftoon1,2, b), Hamid Motallebzadeh1,2, John J. Guinan Jr.1,2,3, and Sunil Puria1,2,3, a) 1

Eaton-Peabody Laboratory, Massachusetts Eye and Ear Department of Otolaryngology, Harvard Medical School 3 Speech and Hearing Bioscience and Technology, Harvard University Graduate School of Arts and Sciences 2

a)

Corresponding author: [email protected] b) [email protected]

Abstract. It has been long believed that inner hair cell (IHC) stimulation can be gleaned from the classic ter-Kuile shear motion between the reticular lamina (RL) and tectorial membrane (TM). The present study explores this and other IHC stimulation mechanisms using a finite-element-model representation of an organ of Corti (OoC) cross section with fluidstructure interaction. A 3-D model of a cross section of the OoC including soft tissue and the fluid in the sub-tectorial space, tunnel of Corti and above the TM was formulated based on anatomical measurements from the gerbil apical turn. The outer hair cells (OHCs), Deiter’s cells and their phalangeal processes are represented as Y-shaped building-block elements. Each of the IHC and OHC bundles is represented by a single sterocilium. Linearized Navier-Stokes equations coupled with linear-elastic equations discretized with tetrahedral elements are solved in the frequency domain. We evaluated the dynamic changes in the OoC motion including sub-tectorial gap dimensions for 0.1 to 10 kHz input frequencies. Calculations show the classic ter-Kuile motion but more importantly they show that the gap-height changes which produce oscillatory radial flow in the subtectorial space. Phase changes in the stereocilia across OHC rows and the IHC are also observed.

INTRODUCTION For over a century, the dominant view about how inner-hair-cell (IHC) and outer-hair-cell (OHC) stereocilia are deflected has been the shear model of ter Kuile (1900). In this model, transverse motion of the basilar membrane (BM) due to the pressure difference between the scala tympani and scala vestibuli causes transverse movement of the organ of Corti (OoC) and radial shear between the reticular lamina (RL) and the tectorial membrane (TM). This shear in turn causes deflection of the hair bundles, all in phase. However, several experimental studies cast doubt about the validity of this ingrained assumption. In a series of studies of the TM, Freeman & coworkers showed that the TM deforms and can carry traveling waves of radial motion (e.g., Ghaffari et al., 2007; Gu et al., 2008). Karavitaki & Mountain (2007) showed, with electrical stimulation, that OHC motility makes the deformations in the OoC much more complicated than the ter Kuile conceptualization. Nowotny and Gummer (2006, 2011) demonstrated that AC-current-induced motion of OHCs causes oscillating changes in the height of the subtectorial gap between the RL and the TM. Recent measurements by Ren et al. (2016) and Lee et al. (2016) in unopened cochleae revealed that in acoustic stimulation the RL and TM generally move more than the BM does at low to moderate stimulus levels. To gain an understanding of how OoC motion and deformation lead to deflection of OHC and IHC stereocilia, we are developing 3-D finite-element models of a “thin-slice” 24 µm radial cross section of the OoC in the longitudinal direction. Our present focus is to study RL and TM motions and how they produce fluid flow in the subtectorial space that drives IHC stereocilia for passive mechanics (e.g., without OHC motility). To the Ear and Back Again - Advances in Auditory Biophysics AIP Conf. Proc. 1965, 120002-1–120002-6; https://doi.org/10.1063/1.5038510 Published by AIP Publishing. 978-0-7354-1670-3/$30.00

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METHODS We developed a 3-D fluid-solid interaction model of the thin-slice cross section that includes one row of hair cells from the apex of the gerbil cochlea. The main geometrical features of the model are based on the image of the gerbil hemicochlea reported by Edge et al. (1998). We supplement the Edge et al. data with geometrical data from Karavitaki & Mountain (2007) and Soons et al. (2015). Our first model included the TM, BM, inner sulcus, endolymphatic space, as well as stereocilia for the IHC and each of the three rows of OHCs, but without the cytoarchitecture between the RL and BM (Maftoon et al., 2017).

FIGURE 1. Cross-section model of the organ of Corti incorporating inner and outer hair-cell bodies, Deiters’ cells (including phalangeal processes), pillar cells (red) and Hensen’s cell body area (yellow) surrounded by a fluid environment (cyan).

We continue to improve this model with increasing realism. In this paper, we present results from a more detailed version of the model in which the bulk of the soft tissue representing the OoC in the first version is replaced by detailed representations of inner and outer hair cell bodies, Deiters’ cells (including their phalangeal processes), and pillar cells (Fig.1). The arcuate zone (AZ) and pectinate zone (PZ) have different properties. Figure 2 shows close-up details of the hair bundles in the subtectorial space and the connection of the stereocilia bundles to the cell bodies using embedded rootlets. TABLE 1. Material properties used in the model (text inside the parentheses indicates colors of the corresponding elements in Figs. 1 and 2) Young’s modulus (Pa)

Organ of Corti (yellow) Pillar cells (red) Tectorial membrane (magenta) Deiters’ cells (green) Phalangeal processes (light blue) OHC (blue) IHC (light green) Inner Sulcus cells (brown) Reticular lamina (dark blue) Cuticular plates (dark blue) Rootlets (orange) Sterocilia (red) BM arcuate zone (gray) BM pectinate zone (black)

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10×103 1×106 30×103 1×106 1×106 200×103 10×103 10×103 20×103 20×103 1×106 1×106 1×106 200×106

Cochlear fluid was modeled as viscous water using the linearized Navier-Stokes equation. Solid structures were modeled as nearly incompressible linear elastic material using best estimates of the mechanical properties from the literature (Table 1). All soft tissues were modeled with a density of 1100 kg/m3 with 15% structural damping. The arch in the PZ of the basilar membrane was not morphologically included in the model. However, to include its stiffening effect (Kapuria et al., 2017), the PZ was modeled 200 times stiffer than the AZ. The model was excited by applying on the BM a spatially-uniform sinusoidally-varying sound pressure of 1 Pa (94 dB SPL) from 100 Hz to 10 kHz on the scala-tympani side. The following boundary conditions were incorporated in the model: (1) The BM was clamped at its two end faces, (2) The tectorial membrane and inner sulcus were clamped at their interface with the spiral limbus, and (3) Anti-periodic boundary condition was applied at the two faces of the cochlea slice.

Tectorial membrane

Rootlet Reticular lamina Inner hair cell

OHC

(a)

(b)

FIGURE 2. Close up detailed views of Fig. 1. (a) Three OHCs and one IHC with their hair bundles represented as stereocilia in the subtectorial space, (b) The hair cell stereocilia are connected to the cell bodies using embedded rootlets. Very fine mesh was used to correctly represent geometry of the rootlets. The stiffness of each hair-cell’s stereocilium has been made equivalent to the whole-bundle stiffness.

RESULTS We compared our model results at the BM and near the RL to the Optical Coherence Tomography (OCT) vibrometry measurements near the RL in cadaveric gerbils (Dong et al., 2017). Both the experimental (Fig. 3-A) and model results (Fig. 3-B) have comparable low-pass-like displacement magnitudes. The model has a corner frequency of about 2 kHz which is slightly higher than the measured corner frequency of about 1.5 kHz in the second turn of the cochlea. The model drive pressure of 94 dB SPL on the BM is approximately equivalent to 60 dB SPL sound pressure in the ear canal considering the gerbil middle-ear pressure gain.

FIGURE 3. Displacement magnitude (in nm) vs. frequency (in kHz) responses (A) post mortem measured near the RL (dotted green line) and noise floor (dashed-dot black line) using OCT in the second turn of the gerbil cochlea with 60 dB SPL ear canal pressure (Dong et al., 2017), (B) from the model near the RL corresponding to the measurement location in (A) and for comparison at the BM near the middle Deiters’ cell.

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Model animations show (Fig. 4-A shows two snap shots at different phases of the motion) that at low frequencies, for example 100 Hz, there are similarities to the ter Kuile model in terms of in-phase motions of the RL, TM and OHC bundles and gross motion of the OoC and BM (not shown). However, in contrast to the ter Kuile conceptualization, the subtectorial gap height changed (inset figure) leading to oscillatory radial fluid flow in the subtectorial space. The IHC stereocilia deflection slightly leads the OHC stereocilia motion. This suggests that the IHC stereocilia motion does not follow the motion predicted by the ter Kuile model.

FIGURE 4. Motions in the subtectorial space at three frequencies: (A) 100 Hz, (B) 2000 Hz and (C) 6000 Hz. The black and light magenta outlines show snap shots at or near extremes of the motion. The motion amplitude has been exaggerated for presentation clarity. Motions were magnified 25, 30 and 300 times at 100 Hz, 2000 Hz and 6000 Hz, respectively. Important motion features are highlighted by arrows. The inset figures show the motion of the IHC bundle. Within each panel, the green-bar fiduciary markers are the same length and help to see the gap changes.

Figure 4-B shows motions near the corner frequency of 2 kHz. At this frequency, the OHC and IHC bundles were in phase with each other. The subtectorial gap height changed and produced oscillatory radial fluid flow, exciting the IHC bundle. Furthermore, animations indicate signs of TM deformation (not shown). Figure 4-C shows motions above the corner frequency at 6 kHz. At this frequency, the OHC bundles were not in phase with each other. The subtectorial gap height changed in a complex and radially dependent manner. Fluid inertia did not prevent subtectorial gap height changes even at high frequencies (up to our simulation limit of 10 kHz, not shown). The TM showed apparent deformation.

DISCUSSION AND CONCLUSIONS The results of this developing model to date already indicate that IHC stereocilia are driven by more than just radial shear between the RL and the TM. IHC bundle deflections are also produced by the change in the subtectorial gap height that produces oscillatory radial fluid motion as previously hypothesized (Steele and Puria, 2005; Nowotny and Gummer, 2006, 2011; Guinan 2012).

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The relative contributions of these mechanisms are location and frequency dependent and are likely altered by the OHC motility in the active cochlea. It has been thought that changes in the subtectorial gap height are diminished as frequency increases due to viscous damping and fluid inertia (Chadwick, et at., 1996). However, the model shows that the gap-height changes even at the highest frequencies investigated (10 kHz). It appears that the high inertia of the fluid in the gap does not prevent this fluid from moving at high frequencies.

ACKNOWLEDGMENTS This work was supported in part by grant R01 DC07910 by the NIDCD of NIH.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Chadwick, R.S., Dimitriadis, E.K., Iwasa, K.H., (1996). Active control of waves in a cochlear model with subpartitions. Proceedings of the National Academy of Sciences, 93, 2564-9. Dong, W., Oghalai, J. S., Xia, A. & Puria S. (2017). Optical Coherence Tomography (OCT) Measurements of in Vivo Organ of Corti Vibration Within the Gerbil Cochlear Apex, ARO midwinter meeting, Baltimore, MD. Edge, R. M., Evans, B. N., Pearce, M., Richter, C.-P., Hu, X., & Dallos, P. (1998). Morphology of the unfixed cochlea. Hearing Research, 124(1–2), 1–16. Ghaffari, R., Aranyosi, A. J., & Freeman, D. M. (2007). Longitudinally propagating traveling waves of the mammalian tectorial membrane. Proceedings of the National Academy of Sciences, 104(42), 16510. Gu, J. W., Hemmert, W., Freeman, D. M., & Aranyosi, A. J. (2008). Frequency-dependent shear impedance of the tectorial membrane. Biophysical journal, 95(5), 2529–2538. Guinan, J.J., Jr., (2012). How are inner hair cells stimulated? Evidence for multiple mechanical drives. Hear Res. 292, 35-50. Kapuria, S., Steele, C. R., & Puria, S. (2017). Unraveling the mystery of hearing in gerbil and other rodents with an arch-beam model of the basilar membrane. Scientific Reports, 7(1), 228. Karavitaki, K. D., & Mountain, D. C. (2007). Imaging electrically evoked micromechanical motion within the organ of corti of the excised gerbil cochlea. Biophysical journal, 92(9), 3294–3316. ter Kuile, E. (1900). Die Uebertragung der Energie von der Grundmembran auf die Haarzellen. Archiv für die gesamte Physiologie des Menschen und der Tiere, 79(3–4), 146–157. Lee, H. Y., Raphael, P. D., Park, J., Ellerbee, A. K., Applegate, B. E., & Oghalai, J. S. (2015). Noninvasive in vivo imaging reveals differences between tectorial membrane and basilar membrane traveling waves in the mouse cochlea. Proceedings of the National Academy of Sciences, 112(10), 3128–3133. Maftoon, N., Guinan, J. J., Jr., and Puria, S. (2017). Relative contributions of oscillatory shear and fluid motions at the inner hair cell bundle in a cross-section model of the cochlea. Presented at ARO (Baltimore, MD). Nowotny, M., & Gummer, A. W. (2006). Nanomechanics of the subtectorial space caused by electromechanics of cochlear outer hair cells. Proceedings of the National Academy of Sciences of the United States of America, 103(7), 2120–2125. Nowotny, M., & Gummer, A. W. (2011). Vibration responses of the organ of Corti and the tectorial membrane to electrical stimulation. The Journal of the Acoustical Society of America, 130(6), 3852–3872. Ren, T., He, W., & Kemp, D. (2016). Reticular lamina and basilar membrane vibrations in living mouse cochleae. Proceedings of the National Academy of Sciences, 113(35), 9910–9915. Soons, J. A. M., Ricci, A. J., Steele, C. R., & Puria, S. (2015). Cytoarchitecture of the Mouse Organ of Corti from Base to Apex, Determined Using In Situ Two-Photon Imaging. JARO: Journal of the Association for Research in Otolaryngology, 16(1), 47–66. Steele, C. R., Puria, S. (2005). Force on inner hair cell cilia. International Journal of Solids and Structures, 42, 5887-5904.

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COMMENTS & QUESTIONS [Online Forum] Domenica Karavitaki: The anatomical parameters are formulated based on anatomical measurements in the gerbil apical turn. The model is run to 10 kHz which seems to be well above the CF of the gerbil apex. Please clarify in the text the relevance of the observations at these highest frequencies. Author: Running the model at frequencies much higher than the characteristic frequency of the cross section enabled us to study effects of the fluid inertia on the motions in the subtectorial space. Although the model is for an apical cross section, many aspects will also be true for a basal, high frequency cross section. For instance, our observation of gap-height changes for up to the highest frequencies tested (10 kHz) indicates that the gap fluid inertia does not prevent gap-height changes at such high frequencies. This should also be relevant for the high-frequency, basal cochlea. Aritra Sasmal: How would you include the effect of the longitudinal wave number in this model? Have you included the different properties of the TM (like the Marginal band, anisotropy etc) in this simulation? It might be interesting to see how that affects the stimulation of the IHC stereocilia. Author: The model, with its current setup, cannot capture the longitudinal waves in the cochlea. Soft tissues were modeled as isotropic materials. Effects of anisotropy and the marginal band on the results should be explored in subsequent studies. [Post-Talk Q&A] Jont Allen: Is viscosity included in the model and how do the effects show up as vorticity in the subtectorial space as the flow in this space should be viscous dominated? Author: The model includes viscosity and we did observe vortices in the subtectorial space, but these were not described due to space limitations. Jonathan B. Sellon: Does apparent contact between the Hensen strip and the tip of inner hair cell stereocilia seen in the animations seem realistic? Author: That was a visualization artifact due to magnification. If the motions are not magnified there is no appearance of contact between the Hensen strip and the tip of the stereocilia. Marcel van der Heijden: Can the model capture the longitudinal wave in the cochlea? Author: The current model representation is for a thin-slice (24 µm) radial cross section of the cochlea and thus is not meant to incorporate longitudinal cochlear waves.

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