Workshop 8: The Auditory System

(June 25,2007 - June 28,2007 )

Organizers


David Mountain
Biomedical Engineering, Boston University

The human auditory system from the inner ear to the auditory cortex is a complex multilevel pathway of sound information processing. One of the early stages of sound processing occurs in the cochlea, where the vibration pattern of the basilar membrane encodes the frequency and amplitude of incoming sound signals. Though well-known partial differential equations (PDEs) in classical mechanics provide a solid foundation for describing these mechanical activities, additional nonlinearities must be modeled to capture responses such as tonal suppressions and the observed frequency selectivity.

The workshop aims to explore the mathematical models of the ear at a number of different levels, ranging from PDE models of the mechanics of the basilar membrane, to biophysical models of the outer hair cells, to signal processing applications in industry and health sciences.

Specific workshop topics would be:

  • Cochlea: models and mechanics.
  • Hair cells: biophysics and active feedback.
  • Applications of signal processing methods to hearing aids, ear implants and speech recognition.

Accepted Speakers

Jont Allen
Dept. of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign
Richard Chadwick
Chief Section on Auditory Mechanics, National Institutes of Health
Egbert De Boer
Academic Medical Center, Universiteit van Amsterdam
Karl Grosh
Mechanical Engineering and Biomedical Engineering, University of Michigan
James Harte
Centre for Applied Hearing Research, Technical University of Denmark
Elizabeth Olson
Otolaryngology, Head and Neck Surgery, Columbia University
Robert Shannon
Auditory Implants and Perception Research, House Ear Institute
Christopher Shera
Otology & Laryngology, Harvard Medical School
Alexander Spector
Biomedical Engineering and Mechanical Engineering, Johns Hopkins University
Charles Steele
Division of Mechanics and Computation, Stanford University
Marcel Van der Heijden
Dept Neuroscience, RSM Erasmus University
Jack Xin
Department of Mathematics, University of California, Irvine
Monday, June 25, 2007
Time Session
11:15 AM
12:00 PM
Kuni Iwasa - The biological roles of hair bundle motility and electromotility

Short talk: While hair cells are the mechanoreceptor cells in the ear, reverse transduction in these cells, which provides feedback to the senosory process, is shown to be essential for the sensitivity and frequency selectivity of the ear. One such reverse transduction in hair bundles and is known as fast adaptation. Another reverse transduction in the cell body of outer hair cells is called electromotility. Previously we examined the effectiveness of electromotility by comparing it with viscous drag due to shear motion in the gap between the reticular lamina and the tectorial membrane that is associated with basilar membrane vibration (Ospeck et al, Biiophys. J 2003). It showed that electromotility can counteract viscous drag up to about 10 kHz without any enhancing mechanism. Using a similar method, here we attempt to evaluate the effectiveness of fast adaptation by estimating the mechanical work it does in response to steady sinusoidal stimulation with small amplitudes and then comparing the work with the viscous loss at the gap. We found that "twitch," which is re-closure of the transducer channel due to Ca entry, leads to a gain in the mechanical energy, whereas "release," which is relaxation due to Ca entry, does not. Our calculation leads to a frequency limit, up to which fast adaptation can counteract the viscous drag. The limiting frequency that we estimated for twitch was about 100 Hz, quite low compared with the auditory frequency of mammals. However, the limiting frequency that we obtained for avian ear is higher than their auditory frequency range (~2 kHz), indicating that we can explain the auditory range of the avian ear, which depends on fast adaptation alone. These results are therefore consistent with the assumption that the reverse transduction in the mammalian ear is primarily due to electromotility.


Work done in collaboration with B. Sul.

03:30 PM
04:15 AM
Charles Steele - Asymptotic-numerical solution for cochlear model with full organ of Corti

Our focus is on physically based modeling. For basic three-dimensional models for the fluid - elastic waves in the cochlea, direct numerical computation requires many hours of super computer time. In contrast the combination of asymptotic and numerical methods requires seconds on a small computer for a given frequency. For validation, several life-sized models of the human cochlea have been fabricated by micromachining. The direct measurements of response and computation produce reasonable agreement, sufficient to justify the efficient computational procedure. The need for the full three-dimensional fluid model is clarified by the measurements of Olson, which show a rapid decay of the pressure with the distance perpendicular to the basilar membrane. The calculations show the similar decay. Olson recently extended the measurement of the nonlinear distortion products, and the computations show qualitative agreement.


A more elaborate model includes what may be the most important cellular features of the OC. The model is multiscale, from ciliary tip links with diameter of a few nanometers to the basilar membrane with features on the scale of millimeters. The validation for the extended model is from measurements by Ulfendahl and colleagues with confocal microscopy of the details of the motion of the cross section of the OC. The full organ of Corti model is extended for the computation of high frequency, for which the longitudinal traveling waves are of significance.

Tuesday, June 26, 2007
Time Session
09:00 AM
09:45 AM
Christopher Shera - Laser with a twist: Traveling-wave propagation and gain functions from throughout the choclea

Except at the handful of sites explored by the inverse method, the characteristics---indeed, the very existence---of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are determined by quantities known as propagation and gain functions. The properties of these functions, and their variation along the length of the cochlea, are central to an understanding of cochlear mechanics. We outline a method for deriving propagation and gain functions from measurements of basilar-membrane (BM) mechanical transfer functions. By applying the method to indirect estimates of near-threshold BM responses obtained from (1) Wiener-kernel analysis of chinchilla auditory-nerve responses to noise (Recio-Spinoso et al. 2005; Temchin et al. 2005) and (2) zwuis analysis of cat auditory-nerve responses to complex tones (van der Heijden and Joris 2003; 2006), we derive and interpret propagation and gain functions throughout the cochlea in sensitive, undamaged preparations.



 
10:30 AM
11:15 AM
Egbert De Boer - Waves in cochlear fluids

At least two types of fluid waves in the cochlea can be distinguished: compression waves and surface waves, both play a part in cochlear mechanics. Usually, the part played by compression waves is neglected but in explaining bone conduction they are essential. The measurements of von Bekesy on cadaver ears have been superceded by more accurate measurements in living and anesthetized animals. It was discovered that the frequency response of the basilar membrane is considerably sharper than thought before, and depends very much on the physiological condition of the animal studied. The waves in the cochlea can be further divided into long and short waves, the region of the strongest response is the region where short waves prevail. In theories of cochlear mechanics an amplification mechanism has been conceived which enhances the response and increases the sharpness of tuning. The same mechanism, being of physiological origin and thus extremely vulnerable, is also the (main) site of cochlear nonlinearity. A model of the cochlea that includes these types of waves and the physiological amplification mechanism can quantitatively explain nearly all linear and nonlinear phenomena that the real cochlea exhibits. There remain a few problem areas in global cochlear mechanics, most of these have to do with otoacoustic emissions. In a study directed at the origin of Distortion Product Otoacoustic Emissions (DPOAEs), it has been discovered that waves in the fluid of the cochlea do not exactly behave as in the theory. Several explanations of this aberrant behavior have been put forward, these range from consideration of compression waves, via investigation of non-classical models, to a reconsideration of the phenomenon of coherent reflection. It is perhaps too early to attempt a synthesis of all sub-models but that a definitive progress has been made is certain.



 
11:15 AM
12:00 PM
Tilak Ratnanather - A few unresolved, if not peripheral, questions on the auditory periphery from the periphery!

Short talk: Despite focusing on the central auditory pathway, the auditory periphery continues to be fascinating. Personal observations from the periphery raise a few unresolved questions with a mathematical flavor as follows:



  1. Is the OHC turgor pressure 1kPa?

  2. Do localized stresses caused by fluid jets impinging on the OHC lateral wall result in pore formation and thus an increase in OHC hydraulic conductivity increase from 2x10-4 cm/s to 2x10-3 cm/s?

  3. Why does the phase for an isolated OHC at acoustic frequencies in response to stimuli change to around 100 degrees and well below 180 degrees?

  4. Is the effective mass of the isolated OHC in response to stimuli at acoustic frequencies 0.06?

02:00 PM
02:45 PM
Jont Allen - Wave power flux in inhomogeneous media

See below

03:30 PM
04:15 PM
Richard Chadwick - The whispering gallery effect in the mammalian cochlea: A boost for low frequencies

The spiral shape of the mammalian cochlea not only helps acoustic energy reach the apex of the cochlea, but also induces a radial pressure gradient that increases toward the outer wall. The resulting asymmetric loading of the cochlear partition boosts the sensitivity to low frequency sounds. The mathematics and physics of the effect are explained using wave propagation and wave tracing approaches. Behavioral and morphometric data in both land and sea mammals are presented to support the theory.


Work done in collaboration with Daphne Manoussaki, Emilios Dimitriadis, and Darlene Ketten.

Wednesday, June 27, 2007
Time Session
09:00 AM
09:45 AM
Marcel Van der Heijden - Group delays in the apex of the cochlea

Are cochlear traveling waves genuine waves? This is not a semantic issue. There is physics behind it. Waves carry energy. In a unidirectional wave the energy is propagating in a single direction. The energy flow can be visualized by varying (modulating) the intensity of the stimulus that drives the wave. These intensity fluctuations do not cause instantaneous variations in the intensity of the wave. Instead the fluctuations are propagated at a finite speed that need not match the phase velocity of the wave. Mathematically, the travel speed of intensity fluctuations is described by the group velocity. The resulting travel time to a given location is the group delay. Obviously, in a unidirectional wave the group delay will grow monotonically with distance. Other systems, such as an array of uncoupled resonators, generally lack this monotonic growth of group delay.


To analyze how group delay varies along the cochlea - and to test whether it obeys the monotonic growth demanded by a unidirectional traveling wave - one needs to know how phase varies with stimulus frequency and with cochlear location. We derived these phase patterns in the apex of the cochlea from our auditory nerve measurements, and analyzed them in terms of group delays. Joint work with Philip X. Joris.


 

10:30 AM
11:15 AM
Elizabeth Olson - The passive substrate for active cochlear tuning

Stapes vibration launches a traveling wave down the cochlear partition that peaks at frequency dependent locations along the cochlear spiral. The traveling wave and peaking occur in both healthy (active) and dead (passive) cochleae. However, in an active cochlea, at locations where in a passive cochlea the traveling wave exhibits a broadly tuned peak, the wave instead continues to grow and attains a relatively sharp and much higher peak a short distance apical of the passive peak place.


The physical basis for even these very basic observations of cochlear tuning remains uncertain. Organ of Corti mass, resistance, and longitudinal coupling have all been employed in cochlear models although their true nature is not known. I will explore their possible roles in passive and active cochlear mechanics, and discuss how they can be measured in the lab. Role of organ of Corti mass in frequency tuning: The basis of the passive peak is not certain, with some models employing significant organ of Corti mass, in which case the concept of local organ of Corti resonance is important, while other models get by with zero organ of Corti mass. We have performed measurements of traveling wave wavelength that are designed to probe the significance of organ of Corti mass.


Traveling wave resistance and the cochlear amplifier: Robust observations of basilar membrane response timing indicate that the cochlear amplifier works as a negative resistance that is large enough to overcome positive (normal) resistance over a limited longitudinal extent. Within that extent more power flows into the traveling wave due to the amplifier than flows out due to damping. Thus, the important impedance that must be overcome by the amplifier is resistance. We are making direct measurements of organ of Corti frequency-dependent impedance to measure resistance.


Longitudinal coupling is generally not good for cochlear models as it works against well-established observations of cochlear mechanics, in particular the sharp apical drop-off in phase and amplitude. However, several models of active cochlear mechanics employ longitudinal coupling. Also, measurements of passive stiffness indicate a significant cellular component, which suggests the existence of significant longitudinal coupling. We are beginning studies to eliminate cells of the organ of Corti in order to look for changes in traveling wave wavelength that will help identify the role of longitudinal coupling in cochlear mechanics.

11:15 AM
12:15 PM
Monty Escabi - Distinct roles for onset and sustained activity in the neuronal code for temporal periodicity and acoustics envelope shape

Short talk: Periodic patterns in natural sounds are an important acoustic attribute that contributes rhythm and pitch perception. Although numerous studies have examined the neuronal representation of periodic stimuli the mechanisms responsible for encoding the shape of a stimulus envelope concurrently in with periodic information are not well understood. Traditionally, it is assumed that temporal patterns in acoustic signals are represented by either the average neuronal discharge rate or temporal synchrony to the sound envelope. Compelling evidence for a pure rate or synchrony neuronal code, however, is lacking. Here we demonstrate that neurons in the auditory midbrain of cats employ two complementary mechanisms that enable them to efficiently encode temporal periodicity and envelope shape information. We recorded single unit activity in the central nucleus of the inferior colliculus (ICC) and compared neuronal responses to periodic noise bursts and sinusoidally modulated noise. We develop a shuffled correlation technique that allows us to systematically characterize the temporal periodicity response pattern for onset and sustained responses. Neurons with sustained responses faithfully encode the envelope shape at low modulation rates but deteriorate and fail to account for timing and envelope information at high rates. In contrast, onset neuronal responses accurately entrain to the stimulus repetition and provide a means of encoding repetition information at rates exceeding 1000Hz. These results argue against conventional rate or synchrony based codes and provides two independent but complementary mechanisms by which ICC neurons simultaneously encode envelope shape and repetition information in complex. (supported by NIDCD R01DC006397-01A1)



 
11:15 AM
12:15 PM
Craig Atencio - Laminar Organization of Spectrotemporal Processing in the Primary Auditory Cortex of the Cat

Short talk: A fundamental problem in auditory cortex is how to determine a neuron's receptive field. In previous work spectrotemporal receptive fields (STRFs), which are calculated through the spike triggered average (STA), have been used successfully to determine the modulation preferences and stimulus selectivity properties of auditory cortex neurons. While informative, STRFs may be biased by stimulus correlations and they do not characterize neural sensitivity to multiple stimulus dimensions. In this study we overcame these limitations by using a model in which a neuron is selective for two dimensions in a high dimensional stimulus space. To derive the model, single neuron responses were recorded in response to a dynamic moving ripple stimulus in the primary auditory cortex (AI) of the cat. Each relevant dimension was then determined by maximizing the mutual information between the neural response and the projection of the stimulus onto directions in the stimulus space. This process removes the effects of stimulus correlations from the estimates of the dimensions. After the relevant dimensions were determined we calculated the nonlinear, memory-less input-output function that relates spiking probability to the stimulus projection. For all neurons we found that the nonlinearities of the STA and the first relevant dimension were monotonic and highly correlated. The nonlinearity of the second relevant dimension was usually symmetric. When the nonlinearities of the spike triggered average and the first dimension were plotted against depth the layers that received thalamic input had the most asymmetric nonlinearities. The two-dimensional nonlinearity for the first and second relevant dimensions also varied with layer, with the most separable nonlinearities in layers that receive thalamic input. This implies that the processing by the two dimensions may be dissociated in thalamic input layers though this approximation is not appropriate at further positions in the AI microcircuit. These results argue for a hierarchical model of spectrotemporal processing in the AI microcircuit.


Work done incollaboration with Tatyana Sharpee and Christoph E. Schreiner.

02:00 PM
02:45 PM
Alexander Spector - Outer Hair Cell" From Molecular Motors to Cochlear Mechanics

Outer hair cells are critical to the amplification and sharp frequency selectivity of the mammalian cochlea. Outer hair cell has a unique form of motility (electromotility) driven by changes in the cell's transmembrane potential. The major features of the electromotile cell are length changes, active force production, and electric charge transfer. We will discuss the modeling of these three interrelated phenomena at the molecular, cellular, and organ levels with a particular focus on high-frequency conditions. The membrane protein (motor) prestin is a crucial molecular component of active hearing. We will present a mathematical model describing the prestin-related transfer of an electric charge across a portion of the membrane under high-frequency conditions. We will also discuss how the outer hair cell can overcome the mechanical (viscous) and electrical (capacitive) high-frequency filtering in the cochlear environment and produce an active force significant to the cochlear amplification.



 
03:30 PM
04:15 PM
Karl Grosh - Electromotility and Electrical Conduction in the Cochlea

The cells and structures of the organ of Corti are hypothesized to act in an electromechanical feedback system boosting the mechanical response of cochlea, such as the basilar membrane, to low-level acoustic input. A physiological model based on this hypothesis predicts key aspects of the electromechanical cochlear response to both acoustical and electrical stimulation. The model explicitly couples mechanical, electrical and fluidic domains including a piezoelectric model of the OHC soma. A method for including hair bundle motility is presented along with preliminary results indicating a subsidiary role for hair bundle motility. The electrical stimulation and response of the cochlea has grown in importance. This is in part because electrical stimulation provides a means for interrogating the response of the cochlea and testing hypothesis of cochlear function. Further, electrical stimulation is the final output of cochlear prosthesis. Finally, as we contemplate combined electrical and mechanical hearing prosthesis for patients with partially functional cochlea, the interaction of injected electrical disturbances in the cochlear fluids with those arising form normally functioning cells becomes more central.



 
Thursday, June 28, 2007
Time Session
10:30 AM
11:15 AM
James Harte - Modelling the role of compression in the auditory system: From bio- to psycho-physics

It is the purpose of this talk to present a system's framework for interpreting effective or phenomenological models of the auditory periphery. The auditory system can be modelled with varying degrees of abstraction away from the underlying physiological processes, where the degree of complexity required in a given model is dependent on its intended purpose. The greater complexity in modelling a biophysical process in detail may not be necessary, and indeed may cloud the interpretability of results. Using phenomenological models, designed to incorporate particular dynamic features or phenomena of the real system, may allow a simplified framework to interpret its role in the auditory system as a whole.


It is well known that the mammalian cochlea is nonlinear, which manifests in the mechanical response of the basilar membrane (BM). For sinusoidal excitation the BM displays a compressive nonlinearity, conventionally described using an input-output level curve. This displays a slope of 1 dB/dB at low levels and a slope m < 1 dB/dB at higher-levels. Detailed biophysical models containing physiologically realistic active mechanisms and BM dynamics exist that can explain this simple representation of auditory compression. However, debate is still prevalent as to the exact mechanisms and important anatomical and physiological features. By using simpler phenomenological models for compression, inspired from the more detailed biophysical models, one can obtain a useful framework to explain a variety of experimental physiological data, i.e. BM compression. Two classes of nonlinear systems will be considered in this talk as models of BM compression, one class with static power-law nonlinearity and one class with level-dependent properties (using either an automatic gain control or a Van der Pol oscillator). By carefully choosing their parameters, it will be shown that all models can produce level curves that are similar to those measured on the BM. As well as this, links will be made with investigations on otoacoustic emission nonlinearity, and also to psychophysical measures of dynamic range compression and perceptual data. Thus demonstrating the high degree of generality these simple phenomenological models can be made to have. The complementary nature of biophysical models to phenomenological and even more abstract psycho-physical models will be discussed.

02:00 PM
02:45 PM
Robert Shannon - Auditory prostheses and neuroscience: electrical stimulation of the human cochlea, cochlear nucleus and inferior colliculus

Cochlear implants are in widespread use (>100,000 patients worldwide) and provide a level of hearing restoration that allows most recipients to converse by telephone. However, cochlear implants are not useful for patients with no remaining auditory nerve, so new prosthetic devices have been designed to stimulate the cochlear nucleus in the brainstem and the inferior colliculus in the midbrain, using both surface and penetrating electrodes. We will present psychophysical results and speech recognition results from cochlear implants and from surface and penetrating electrodes at the level of the cochlear nucleus and inferior colliculus. Surprisingly, many psychophysical measures of temporal, spectral and intensity resolution are similar across stimulation sites and electrode types. Excellent speech recognition and modulation detection are observed in cochlear implants and in some patients with stimulation of the cochlear nucleus, but not in patients who lost their auditory nerve from vestibular schwannomas. Quantitative comparison of results from electrical stimulation of the auditory system at different stages of neural processing, and across patients with different etiologies can provide insights into auditory processing mechanisms.



 
Name Email Affiliation
Aguda, Baltazar bdaguda@gmail.com MBI - Long Term Visitor, Bioinformatics Institute, Singapore
Ahmadi, Mahnaz ahmadi.6@osu.edu Speech and Hearing Science, The Ohio State University
Allen, Jont jontalle@uiuc.edu Dept. of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign
Atencio, Craig craig@phy.ucsf.edu Otolaryngology-Head and Neck Surgery, W.M. Keck Center for Integrative Neuroscience
Bergevin, Christopher dolemite@MIT.EDU HST - Speech and Hearing Biosciences, Massachusetts Institute of Technology
Best, Janet jbest@mbi.osu.edu
Chadwick, Richard chadwick@helix.nih.gov Chief Section on Auditory Mechanics, National Institutes of Health
De Boer, Egbert deboere@ohsu.edu Academic Medical Center, Universiteit van Amsterdam
Dembele, Bassidy bdembele@mbi.osu.edu Department of Mathematics, Howard University
Deng, Li deng@microsoft.com Speech Technology Group, Microsoft Research
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Dome, Claudia dome.10@osu.edu Otolaryngology/Speech and Hearing, The Ohio State University
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Escabi , Monty escabi@engr.uconn.edu Electrical & Computer Engineering, University of Connecticut
Feth, Lawrence feth.1@osu.edu Speech and Hearing Science, The Ohio State University
Fletcher, Patrick patrick.allen.fletcher@gmail.com Mathematics, University of British Columbia
Frijns , Johan j.h.m.frijns@lumc.nl ENT Department, Rijksuniversiteit te Leiden
Goldwyn, Joshua jgoldwyn@amath.washington.edu Applied Mathematics, University of Washington
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Green, Edward egreen@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Grosh , Karl grosh@umich.edu Mechanical Engineering and Biomedical Engineering, University of Michigan
Harte, James jha@oersted.dtu.dk Centre for Applied Hearing Research, Technical University of Denmark
Iwasa , Kuni kiwasa@helix.nih.gov Chief, Biophysics Section, NIDCD, National Institutes of Health
Kao, Chiu-Yen kao.71@osu.edu MBI - Long Term Visitor, The Ohio State University
Karunanayaka, Prasanna kar4rp@cchmc.org Dept. of Radiology, Cincinnati Children's Hospital Medical Center
Kim, Yangjin ykim@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
King, Wayne M. king.812@osu.edu Speech and Hearing Sciences, The Ohio State University
Knight, Kim knight.224@osu.edu Speech/Hearing, The Ohio State University
Krishnamurthy, Ashok ashok@osc.edu Electrical and Computer Engineering, The Ohio State University
Ku, Emery ek@isvr.soton.ac.uk Institute of Sound and Vibration Research, University of Southampton
Liu, Yi-Wen liuy@boystown.org Center for Hearing Research, Boys Town National Research Hospital
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Mountain, David dcm@bu.edu Biomedical Engineering, Boston University
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Olson, Elizabeth eao2004@columbia.edu Otolaryngology, Head and Neck Surgery, Columbia University
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Patra, Hari patra.3@osu.edu Speech and Hearing Science, The Ohio State University
Poling, Gayla poling.75@osu.edu Hearing Science, The Ohio State University
Poole, Kristi poole.105@osu.edu Speech and Hearing, The Ohio State University
Raphael, Robert rraphael@rice.edu Bioengineering, Rice University
Ratnanather , Tilak tilak@cis.jhu.edu Center for Imaging Science and Institute for Computational Medicine, Johns Hopkins University
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Seeman, Scott seeman.1@osu.edu Speech and Hearing Science, The Ohio State University
Shannon, Robert bshannon@hei.org Auditory Implants and Perception Research, House Ear Institute
Shera, Christopher shera@mit.edu Otology & Laryngology, Harvard Medical School
Spector, Alexander aspector@jhu.edu Biomedical Engineering and Mechanical Engineering, Johns Hopkins University
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Steele, Charles chasst@stanford.edu Division of Mechanics and Computation, Stanford University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Sun, Shuying ssun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Thaler, Lore thaler.11@osu.edu Psychology, The Ohio State University
Thomas, Evelyn ethomas@mbi.osu.edu Department of Mathematics, Howard University
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Van der Heijden , Marcel m.vanderheyden@erasmusmc.nl Dept Neuroscience, RSM Erasmus University
Weisenberger, Jan weisenberger.21@osu.edu College of Social and Behavioral Sciences, The Ohio State University
Woodruff, John woodruff.95@osu.edu Computer Science and Engineering, The Ohio State University
Xin, Jack jxin@math.uci.edu Department of Mathematics, University of California, Irvine
Zhang, Yanyan zhang.736@osu.edu Department of Mathematics, University of Houston
Wave power flux in inhomogeneous media

See below

Laminar Organization of Spectrotemporal Processing in the Primary Auditory Cortex of the Cat

Short talk: A fundamental problem in auditory cortex is how to determine a neuron's receptive field. In previous work spectrotemporal receptive fields (STRFs), which are calculated through the spike triggered average (STA), have been used successfully to determine the modulation preferences and stimulus selectivity properties of auditory cortex neurons. While informative, STRFs may be biased by stimulus correlations and they do not characterize neural sensitivity to multiple stimulus dimensions. In this study we overcame these limitations by using a model in which a neuron is selective for two dimensions in a high dimensional stimulus space. To derive the model, single neuron responses were recorded in response to a dynamic moving ripple stimulus in the primary auditory cortex (AI) of the cat. Each relevant dimension was then determined by maximizing the mutual information between the neural response and the projection of the stimulus onto directions in the stimulus space. This process removes the effects of stimulus correlations from the estimates of the dimensions. After the relevant dimensions were determined we calculated the nonlinear, memory-less input-output function that relates spiking probability to the stimulus projection. For all neurons we found that the nonlinearities of the STA and the first relevant dimension were monotonic and highly correlated. The nonlinearity of the second relevant dimension was usually symmetric. When the nonlinearities of the spike triggered average and the first dimension were plotted against depth the layers that received thalamic input had the most asymmetric nonlinearities. The two-dimensional nonlinearity for the first and second relevant dimensions also varied with layer, with the most separable nonlinearities in layers that receive thalamic input. This implies that the processing by the two dimensions may be dissociated in thalamic input layers though this approximation is not appropriate at further positions in the AI microcircuit. These results argue for a hierarchical model of spectrotemporal processing in the AI microcircuit.


Work done incollaboration with Tatyana Sharpee and Christoph E. Schreiner.

Are Basilar-Membrane Traveling Waves Necessary for Long OAE Delays?

Short talk: The long latencies associated with mammalian otoacoustic emissions (OAEs) are generally attributed to delays arising from basilar-membrane (BM) traveling waves. If traveling waves are responsible for OAE latencies, one might expect significantly shorter OAE latencies in species lacking a tuned or flexible BM. To test this hypothesis, we examine stimulus frequency otoacoustic emissions (SFOAEs) evoked using low-level stimuli in a wide range of species including human, cat, guinea pig, chicken, gecko, and frog. SFOAE phase gradients imply emission latencies of 1 ms or longer in all species, a delay significantly longer than can be accounted for by middle-ear transmission and energy propagation via fluid compression. Therefore, basilar-membrane traveling waves are not necessary for significant OAE latencies. To explain the long latencies, we hypothesize that OAE latencies reflect delays associated with mechanical tuning. To test this hypothesis, we compare SFOAE latencies with ANF-based measures of tuning sharpness and find a correlation in all species except the frog. Our results suggest that in most species OAE latencies reflect the presence of mechanical frequency selectivity that may or may not be associated with traveling waves. [work performed with C.A. Shera and D.M. Freeman]

The whispering gallery effect in the mammalian cochlea: A boost for low frequencies

The spiral shape of the mammalian cochlea not only helps acoustic energy reach the apex of the cochlea, but also induces a radial pressure gradient that increases toward the outer wall. The resulting asymmetric loading of the cochlear partition boosts the sensitivity to low frequency sounds. The mathematics and physics of the effect are explained using wave propagation and wave tracing approaches. Behavioral and morphometric data in both land and sea mammals are presented to support the theory.


Work done in collaboration with Daphne Manoussaki, Emilios Dimitriadis, and Darlene Ketten.

Waves in cochlear fluids

At least two types of fluid waves in the cochlea can be distinguished: compression waves and surface waves, both play a part in cochlear mechanics. Usually, the part played by compression waves is neglected but in explaining bone conduction they are essential. The measurements of von Bekesy on cadaver ears have been superceded by more accurate measurements in living and anesthetized animals. It was discovered that the frequency response of the basilar membrane is considerably sharper than thought before, and depends very much on the physiological condition of the animal studied. The waves in the cochlea can be further divided into long and short waves, the region of the strongest response is the region where short waves prevail. In theories of cochlear mechanics an amplification mechanism has been conceived which enhances the response and increases the sharpness of tuning. The same mechanism, being of physiological origin and thus extremely vulnerable, is also the (main) site of cochlear nonlinearity. A model of the cochlea that includes these types of waves and the physiological amplification mechanism can quantitatively explain nearly all linear and nonlinear phenomena that the real cochlea exhibits. There remain a few problem areas in global cochlear mechanics, most of these have to do with otoacoustic emissions. In a study directed at the origin of Distortion Product Otoacoustic Emissions (DPOAEs), it has been discovered that waves in the fluid of the cochlea do not exactly behave as in the theory. Several explanations of this aberrant behavior have been put forward, these range from consideration of compression waves, via investigation of non-classical models, to a reconsideration of the phenomenon of coherent reflection. It is perhaps too early to attempt a synthesis of all sub-models but that a definitive progress has been made is certain.



 
Distinct roles for onset and sustained activity in the neuronal code for temporal periodicity and acoustics envelope shape

Short talk: Periodic patterns in natural sounds are an important acoustic attribute that contributes rhythm and pitch perception. Although numerous studies have examined the neuronal representation of periodic stimuli the mechanisms responsible for encoding the shape of a stimulus envelope concurrently in with periodic information are not well understood. Traditionally, it is assumed that temporal patterns in acoustic signals are represented by either the average neuronal discharge rate or temporal synchrony to the sound envelope. Compelling evidence for a pure rate or synchrony neuronal code, however, is lacking. Here we demonstrate that neurons in the auditory midbrain of cats employ two complementary mechanisms that enable them to efficiently encode temporal periodicity and envelope shape information. We recorded single unit activity in the central nucleus of the inferior colliculus (ICC) and compared neuronal responses to periodic noise bursts and sinusoidally modulated noise. We develop a shuffled correlation technique that allows us to systematically characterize the temporal periodicity response pattern for onset and sustained responses. Neurons with sustained responses faithfully encode the envelope shape at low modulation rates but deteriorate and fail to account for timing and envelope information at high rates. In contrast, onset neuronal responses accurately entrain to the stimulus repetition and provide a means of encoding repetition information at rates exceeding 1000Hz. These results argue against conventional rate or synchrony based codes and provides two independent but complementary mechanisms by which ICC neurons simultaneously encode envelope shape and repetition information in complex. (supported by NIDCD R01DC006397-01A1)



 
Electromotility and Electrical Conduction in the Cochlea

The cells and structures of the organ of Corti are hypothesized to act in an electromechanical feedback system boosting the mechanical response of cochlea, such as the basilar membrane, to low-level acoustic input. A physiological model based on this hypothesis predicts key aspects of the electromechanical cochlear response to both acoustical and electrical stimulation. The model explicitly couples mechanical, electrical and fluidic domains including a piezoelectric model of the OHC soma. A method for including hair bundle motility is presented along with preliminary results indicating a subsidiary role for hair bundle motility. The electrical stimulation and response of the cochlea has grown in importance. This is in part because electrical stimulation provides a means for interrogating the response of the cochlea and testing hypothesis of cochlear function. Further, electrical stimulation is the final output of cochlear prosthesis. Finally, as we contemplate combined electrical and mechanical hearing prosthesis for patients with partially functional cochlea, the interaction of injected electrical disturbances in the cochlear fluids with those arising form normally functioning cells becomes more central.



 
Modelling the role of compression in the auditory system: From bio- to psycho-physics

It is the purpose of this talk to present a system's framework for interpreting effective or phenomenological models of the auditory periphery. The auditory system can be modelled with varying degrees of abstraction away from the underlying physiological processes, where the degree of complexity required in a given model is dependent on its intended purpose. The greater complexity in modelling a biophysical process in detail may not be necessary, and indeed may cloud the interpretability of results. Using phenomenological models, designed to incorporate particular dynamic features or phenomena of the real system, may allow a simplified framework to interpret its role in the auditory system as a whole.


It is well known that the mammalian cochlea is nonlinear, which manifests in the mechanical response of the basilar membrane (BM). For sinusoidal excitation the BM displays a compressive nonlinearity, conventionally described using an input-output level curve. This displays a slope of 1 dB/dB at low levels and a slope m < 1 dB/dB at higher-levels. Detailed biophysical models containing physiologically realistic active mechanisms and BM dynamics exist that can explain this simple representation of auditory compression. However, debate is still prevalent as to the exact mechanisms and important anatomical and physiological features. By using simpler phenomenological models for compression, inspired from the more detailed biophysical models, one can obtain a useful framework to explain a variety of experimental physiological data, i.e. BM compression. Two classes of nonlinear systems will be considered in this talk as models of BM compression, one class with static power-law nonlinearity and one class with level-dependent properties (using either an automatic gain control or a Van der Pol oscillator). By carefully choosing their parameters, it will be shown that all models can produce level curves that are similar to those measured on the BM. As well as this, links will be made with investigations on otoacoustic emission nonlinearity, and also to psychophysical measures of dynamic range compression and perceptual data. Thus demonstrating the high degree of generality these simple phenomenological models can be made to have. The complementary nature of biophysical models to phenomenological and even more abstract psycho-physical models will be discussed.

The biological roles of hair bundle motility and electromotility

Short talk: While hair cells are the mechanoreceptor cells in the ear, reverse transduction in these cells, which provides feedback to the senosory process, is shown to be essential for the sensitivity and frequency selectivity of the ear. One such reverse transduction in hair bundles and is known as fast adaptation. Another reverse transduction in the cell body of outer hair cells is called electromotility. Previously we examined the effectiveness of electromotility by comparing it with viscous drag due to shear motion in the gap between the reticular lamina and the tectorial membrane that is associated with basilar membrane vibration (Ospeck et al, Biiophys. J 2003). It showed that electromotility can counteract viscous drag up to about 10 kHz without any enhancing mechanism. Using a similar method, here we attempt to evaluate the effectiveness of fast adaptation by estimating the mechanical work it does in response to steady sinusoidal stimulation with small amplitudes and then comparing the work with the viscous loss at the gap. We found that "twitch," which is re-closure of the transducer channel due to Ca entry, leads to a gain in the mechanical energy, whereas "release," which is relaxation due to Ca entry, does not. Our calculation leads to a frequency limit, up to which fast adaptation can counteract the viscous drag. The limiting frequency that we estimated for twitch was about 100 Hz, quite low compared with the auditory frequency of mammals. However, the limiting frequency that we obtained for avian ear is higher than their auditory frequency range (~2 kHz), indicating that we can explain the auditory range of the avian ear, which depends on fast adaptation alone. These results are therefore consistent with the assumption that the reverse transduction in the mammalian ear is primarily due to electromotility.


Work done in collaboration with B. Sul.

The passive substrate for active cochlear tuning

Stapes vibration launches a traveling wave down the cochlear partition that peaks at frequency dependent locations along the cochlear spiral. The traveling wave and peaking occur in both healthy (active) and dead (passive) cochleae. However, in an active cochlea, at locations where in a passive cochlea the traveling wave exhibits a broadly tuned peak, the wave instead continues to grow and attains a relatively sharp and much higher peak a short distance apical of the passive peak place.


The physical basis for even these very basic observations of cochlear tuning remains uncertain. Organ of Corti mass, resistance, and longitudinal coupling have all been employed in cochlear models although their true nature is not known. I will explore their possible roles in passive and active cochlear mechanics, and discuss how they can be measured in the lab. Role of organ of Corti mass in frequency tuning: The basis of the passive peak is not certain, with some models employing significant organ of Corti mass, in which case the concept of local organ of Corti resonance is important, while other models get by with zero organ of Corti mass. We have performed measurements of traveling wave wavelength that are designed to probe the significance of organ of Corti mass.


Traveling wave resistance and the cochlear amplifier: Robust observations of basilar membrane response timing indicate that the cochlear amplifier works as a negative resistance that is large enough to overcome positive (normal) resistance over a limited longitudinal extent. Within that extent more power flows into the traveling wave due to the amplifier than flows out due to damping. Thus, the important impedance that must be overcome by the amplifier is resistance. We are making direct measurements of organ of Corti frequency-dependent impedance to measure resistance.


Longitudinal coupling is generally not good for cochlear models as it works against well-established observations of cochlear mechanics, in particular the sharp apical drop-off in phase and amplitude. However, several models of active cochlear mechanics employ longitudinal coupling. Also, measurements of passive stiffness indicate a significant cellular component, which suggests the existence of significant longitudinal coupling. We are beginning studies to eliminate cells of the organ of Corti in order to look for changes in traveling wave wavelength that will help identify the role of longitudinal coupling in cochlear mechanics.

A few unresolved, if not peripheral, questions on the auditory periphery from the periphery!

Short talk: Despite focusing on the central auditory pathway, the auditory periphery continues to be fascinating. Personal observations from the periphery raise a few unresolved questions with a mathematical flavor as follows:



  1. Is the OHC turgor pressure 1kPa?

  2. Do localized stresses caused by fluid jets impinging on the OHC lateral wall result in pore formation and thus an increase in OHC hydraulic conductivity increase from 2x10-4 cm/s to 2x10-3 cm/s?

  3. Why does the phase for an isolated OHC at acoustic frequencies in response to stimuli change to around 100 degrees and well below 180 degrees?

  4. Is the effective mass of the isolated OHC in response to stimuli at acoustic frequencies 0.06?

Auditory prostheses and neuroscience: electrical stimulation of the human cochlea, cochlear nucleus and inferior colliculus

Cochlear implants are in widespread use (>100,000 patients worldwide) and provide a level of hearing restoration that allows most recipients to converse by telephone. However, cochlear implants are not useful for patients with no remaining auditory nerve, so new prosthetic devices have been designed to stimulate the cochlear nucleus in the brainstem and the inferior colliculus in the midbrain, using both surface and penetrating electrodes. We will present psychophysical results and speech recognition results from cochlear implants and from surface and penetrating electrodes at the level of the cochlear nucleus and inferior colliculus. Surprisingly, many psychophysical measures of temporal, spectral and intensity resolution are similar across stimulation sites and electrode types. Excellent speech recognition and modulation detection are observed in cochlear implants and in some patients with stimulation of the cochlear nucleus, but not in patients who lost their auditory nerve from vestibular schwannomas. Quantitative comparison of results from electrical stimulation of the auditory system at different stages of neural processing, and across patients with different etiologies can provide insights into auditory processing mechanisms.



 
Laser with a twist: Traveling-wave propagation and gain functions from throughout the choclea

Except at the handful of sites explored by the inverse method, the characteristics---indeed, the very existence---of traveling-wave amplification in the mammalian cochlea remain largely unknown. Uncertainties are especially pronounced in the apex, where mechanical measurements lack the independent controls necessary for assessing damage to the preparation. At a functional level, the form and amplification of cochlear traveling waves are determined by quantities known as propagation and gain functions. The properties of these functions, and their variation along the length of the cochlea, are central to an understanding of cochlear mechanics. We outline a method for deriving propagation and gain functions from measurements of basilar-membrane (BM) mechanical transfer functions. By applying the method to indirect estimates of near-threshold BM responses obtained from (1) Wiener-kernel analysis of chinchilla auditory-nerve responses to noise (Recio-Spinoso et al. 2005; Temchin et al. 2005) and (2) zwuis analysis of cat auditory-nerve responses to complex tones (van der Heijden and Joris 2003; 2006), we derive and interpret propagation and gain functions throughout the cochlea in sensitive, undamaged preparations.



 
Outer Hair Cell" From Molecular Motors to Cochlear Mechanics

Outer hair cells are critical to the amplification and sharp frequency selectivity of the mammalian cochlea. Outer hair cell has a unique form of motility (electromotility) driven by changes in the cell's transmembrane potential. The major features of the electromotile cell are length changes, active force production, and electric charge transfer. We will discuss the modeling of these three interrelated phenomena at the molecular, cellular, and organ levels with a particular focus on high-frequency conditions. The membrane protein (motor) prestin is a crucial molecular component of active hearing. We will present a mathematical model describing the prestin-related transfer of an electric charge across a portion of the membrane under high-frequency conditions. We will also discuss how the outer hair cell can overcome the mechanical (viscous) and electrical (capacitive) high-frequency filtering in the cochlear environment and produce an active force significant to the cochlear amplification.



 
Asymptotic-numerical solution for cochlear model with full organ of Corti

Our focus is on physically based modeling. For basic three-dimensional models for the fluid - elastic waves in the cochlea, direct numerical computation requires many hours of super computer time. In contrast the combination of asymptotic and numerical methods requires seconds on a small computer for a given frequency. For validation, several life-sized models of the human cochlea have been fabricated by micromachining. The direct measurements of response and computation produce reasonable agreement, sufficient to justify the efficient computational procedure. The need for the full three-dimensional fluid model is clarified by the measurements of Olson, which show a rapid decay of the pressure with the distance perpendicular to the basilar membrane. The calculations show the similar decay. Olson recently extended the measurement of the nonlinear distortion products, and the computations show qualitative agreement.


A more elaborate model includes what may be the most important cellular features of the OC. The model is multiscale, from ciliary tip links with diameter of a few nanometers to the basilar membrane with features on the scale of millimeters. The validation for the extended model is from measurements by Ulfendahl and colleagues with confocal microscopy of the details of the motion of the cross section of the OC. The full organ of Corti model is extended for the computation of high frequency, for which the longitudinal traveling waves are of significance.

Group delays in the apex of the cochlea

Are cochlear traveling waves genuine waves? This is not a semantic issue. There is physics behind it. Waves carry energy. In a unidirectional wave the energy is propagating in a single direction. The energy flow can be visualized by varying (modulating) the intensity of the stimulus that drives the wave. These intensity fluctuations do not cause instantaneous variations in the intensity of the wave. Instead the fluctuations are propagated at a finite speed that need not match the phase velocity of the wave. Mathematically, the travel speed of intensity fluctuations is described by the group velocity. The resulting travel time to a given location is the group delay. Obviously, in a unidirectional wave the group delay will grow monotonically with distance. Other systems, such as an array of uncoupled resonators, generally lack this monotonic growth of group delay.


To analyze how group delay varies along the cochlea - and to test whether it obeys the monotonic growth demanded by a unidirectional traveling wave - one needs to know how phase varies with stimulus frequency and with cochlear location. We derived these phase patterns in the apex of the cochlea from our auditory nerve measurements, and analyzed them in terms of group delays. Joint work with Philip X. Joris.