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Christopher Bergevin
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SIAM 2016

Advances in mathematical models of hearing

  Mini-Symposium at the:
  SIAM Conference on the Life Sciences
  Boston, MA USA              July 11-14, 2016

  Date: Wednesday, July, 13 2016
  Time: 10:30 AM – 6 PM
  Location: Boston Westin Waterfront
  Flyer: pdf

Organizer: Christopher Bergevin (Dept. of Physics & Astronomy, York University)
Questions? → cberge [at] yorku.ca

Overview

The inner ear is an active system, using energy to biomechanically improve and extend its dynamic range of operation. Theoretical study of these processes has been challenging, given limited physiological data due to the difficulty of direct measurement. Recent advancements in measurement technology however have provided crucial new empirical insights that inform and place important constraints on theory. The theme of this symposium is twofold: explore these recent theoretical developments of active auditory function, as well as how such models motivate new directions in applied mathematics (e.g., emergent dynamics from coupled nonlinear oscillators).

Speakers

Schedule

(abstracts provided below)

  • 10:30 Introduction
  • 10:35 – Bergevin & Shera – Dynamics of Hearing: The Active Ear
  • 11:00 – O Maoileidigh, Salvi, & Hudspeth – Bifurcations of a Noisy Biological Oscillator Are Associated with Function
  • 11:30 – Wang, Steele, & Puria – Calculation of Cochlear Viscous Fluid Loss and Outer-Hair Cell Power Generation based on 3D WKB Method
  • 12:00 – Zhou & Nam – Consequences of Organ of Corti Micro-Mechanics
  • 12:30 – Discussion & (long) Break
  • 4:00 – Meaud & Bowling – Investigating the Spontaneous Emission of Sounds by the Mammalian Ear Using a Computational Model
  • 4:30 – Chadwick & Lamb – Mode Conversion in the Cochlea
  • 5:00 – Olson – Intracochlear Pressure and Voltage Measurements Support Dual-Mode Cochlear Models
  • 5:30 – Discussion
  • 6:00 – End

   ⇒ Complete schedule can be accessed here

Abstracts

  • Dynamics of the Active Ear
    • Authors: Christopher Bergevin & Christopher Shera
    • Abstract: As a biological detector, the vertebrate ear exhibits a remarkable variety of dynamical behavior that provides fertile ground for mathematical study. The goal of this talk is two-fold. First, general background on the ear will be provided to set a basis for the the talks comprising the symposium. Second, we will explore a remarkable aspect of hearing: The ear not only responds to sound, but generates and coherently emits it as well. These sounds, called otoacoustic emissions (OAEs), provide crucial insight into inner ear function. To explore the biophysical processes possibly giving rise to spontaneous emissions (SOAEs), we will focus on a theoretical framework based upon coupled active nonlinear oscillators. To help constrain such an SOAE model, we also report recent empirical data that characterize SOAE dynamics and their perturbations due to external transient stimuli.
  • Bifurcations of a noisy biological oscillator are associated with function
    • Authors: Daibhid O Maoileidigh, Joshua Salvi, AJ Hudspeth
    • Abstract: Hair bundles actively transduce mechanical stimuli into electrical signals in the auditory, vestibular, and lateral-line systems of vertebrates. Theory predicts that a bundle’s function is dictated by whether it operates near particular types of bifurcation. We confirmed these predictions by employing a feedback system to change the operating point of individual hair bundles. We identified two kinds of bifurcation, despite the presence of substantial environmental noise, associated with three distinct types of signal detector.
  • Calculation of Cochlear Viscous Fluid Loss and Outer-Hair Cell Power Generation based on 3D WKB Method
    • Authors: Yanli Wang, Charles Steele, Sunil Puria
    • Abstract: Ever since the discovery of the active mechanisms in living cochleae and the motility of the OHCs, there has been heated discussion as to whether or not the cochlea provides mechanical power. De Boer and Nuttall [1] conclude that there is power amplification of the traveling wave, while van der Heijden and Versteegh [2] recently claim evidence against this. Despite decades of intense effort, direct experimental support for cochlear power gain is still lacking due to the difficulties in measuring energy flow, since both velocity and pressure measurements are required. Approximations of the pressure by measuring the BM velocity and using an assumed local BM impedance have been attempted, however such formulations and calculations have been shown to be misleading. An innovative method has been to approximate the BM displacement by calculating the spatial pressure gradient at multiple locations. Experiments have also been performed to measure the BM displacement and pressure in the SV simultaneously. However, these experimental results are inconclusive for power gain.
          The current work presents a direct calculation of the net power on the cross section of the cochlea, energy loss in the fluid space due to viscosity, and power output by OHCs. This forward calculation is based on a 3-dimensional (3D) box model of the cochlea with physiological relevant parameters, such as variation of geometry, fluid viscosity, and consideration made to the cytoarchtecture of the OoC. The fluid structure interaction between the cochlear fluid and the basilar membrane is solved using WKB solution method [3]. The calculation of power employs numerical integration with the 3D distribution of fluid velocity and pressure obtained from the model. The details of the model formulation are described elsewhere [4]. In agreement with previous work, we show a positive net power gain basal to the best frequency (BF) location at lower sound pressure levels (SPLs). In addition to net power gain, our work is the first to separate the OHC power output and energy dissipation from the net change of power. From calculations based on our model, at a low input level such as 10 dB SPL near the threshold of hearing, the mechanical power provided by the three rows of OHCs is more than three orders of magnitude larger than the input acoustic input power at the stapes. We show quantitatively based on our model, for the first time, that as the input SPL increases, the absolute power provided by the OHCs continues to grow and eventually saturates, even though the relative power output of the OHCs decreases with respect to the acoustic input.

         [1] de Boer, E.; Nuttall, A. L.: The ‘inverse problem’ solved for a three-dimensional model of the cochlea. III. Brushing-up the solution method. J. Acoust. Soc. Am. Vol 105, pp 3410–3420, 1999.
         [2] van der Heijden, M. ; Versteegh, C. P. C. : Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave. J. Assoc. Res. Otolaryngol. Vol 16, pp 581–597, 2015.
         [3] Steele, C. R. & Taber, L. A. Comparison of WKB calculations and experimental results for three‐dimensional cochlear models. J. Acoust. Soc. Am. Vol 65, pp 1007–1018, 1979.
         [4] Wang, Y.; Steele, C. R.; Puria S.: Cochlear Outer-Hair-Cell Power Generation and Viscous Fluid Loss. Scientific Reports 6, 19475.
  • Consequences of organ of Corti micro-mechanics
    • Authors: Wenxiao Zhou, Jong-Hoon Nam
    • Abstract: In the mammalian cochlea, small vibrations of the sensory epithelium are amplified due to the active mechanical feedback of the outer hair cells. It has been consistently observed that high frequency sounds encoded in the basal cochlea are amplified more than low frequency sounds. Although this location-dependent amplification has been a characteristic used to validate theoretical models, different models rely on different mechanisms to achieve the location-dependent amplification. For example, earlier studies have considered greater active feedback force toward the base. As physiological evidence does not support this assumption, more recent theoretical studies explored alternative mechanisms such as tonotopically varying mechano-transduction properties of the outer hair cells. We have developed a computational model of the cochlea featuring continuum mechanics-based organ of Corti mechanics, and realistic physiological properties of the outer hair cell (e.g., active force capacity, mechano-transduction properties, and membrane RC time constant). Using the computational model, we show that the organ of Corti micro-mechanics can explain the location-dependent amplification. Specifically, outer hair cell’s active force leads its length change by 90 degrees in the basal locations, but the force and the length change are in phase in the apical locations. Our results show that this phase difference is determined by the passive mechanics. To support the conclusion, we present: 1) the power flux along the cochlear length, 2) the spatial pattern of outer hair cell power generation, 3) the effect of local inhibition of outer hair cell force, and 4) the effect of the RC time constant of outer hair cell membrane. Supported by NIH R01 014685
  • Investigating the spontaneous emission of sounds by the mammalian ear using a computational model
    • Presenter: Julien Meaud, Thomas Bowling
    • Abstract: The mammalian cochlea can sometimes spontaneously emit sounds, called spontaneous otoacoustic emissions (SOAEs). In this work, we investigate the generation of SOAEs using a physiologically-based computational model of the mammalian cochlea. Using our computational framework, linear stability analysis and nonlinear time-domain simulations are used to analyze the emergence of linearly unstable modes and of limit cycle oscillations. Our simulations give insights into the role of key micromechanical parameters on the generation of SOAEs.
  • Mode Conversion in the Cochlea
    • Authors: Richard Chadwick, Jessica Lamb
    • Abstract: Mode conversion is a wave phenomenon studied in other fields such as plasma physics, geophysics, and optics. It occurs when the wave numbers of two nonorthogonal modes approach each other, and coincides with a breakdown of the WKB energy conservation equation. In the dual wave model of the cochlea, this occurs when both eigenvectors approach (-i,1), Here the identities of the modes can become confused and they may exchange energy, and also cause a reflection.
  • Intracochlear Pressure and Voltage Measurements Support Dual-Mode Cochlear Models
    • Author: Elizabeth Olson
    • Abstract: Recent measurements of pressure and voltage at the basilar membrane in the gerbil cochlea (Dong and Olson 2013 Biophysical J 105:1067-1078) revealed a meaningful phase relationship: At the local frequency for which nonlinearity commenced, the voltage phase underwent a transition relative to pressure. At the low frequency side of the transition, voltage was ~ in phase with pressure and at the high frequency side, voltage led pressure by ~ 0.3 cycle. Based on the known phase relationships between BM pressure and BM velocity, and between OHC voltage and OHC force (Frank, Hemmert and Gummer 1999 PNAS 96: 4420 – 4425), at frequencies above the transition the OHC force would be phased to pump energy into the traveling wave. Thus, the phase transition was interpreted as the activation of the cochlear amplifier. The present work has to do with the source of the significant phase transition. The voltage phase transition and accompanying amplitude variation are hypothesized to be based in OHC stimulation arising from the differencing of two modes of motion (for example, basilar membrane – tectorial membrane). Recent dual-mode models of the cochlea (Lamb and Chadwick 2014 PLOS ONE 9: e85969; Cormack, Liu, Nam and Gracewski 2015 JASA 137: 1117-1125) were used for guidance. Features of the voltage data at frequencies close to the phase transition emerged from the differencing of two traveling waves, and such a differencing is naturally available from the dual-mode models.