Computer-assisted time-averaged holograms of the motion of the surface of the mammalian tympanic membrane with sound stimuli of 0.4–25 kHz

https://doi.org/10.1016/j.heares.2009.03.010Get rights and content

Abstract

Time-averaged holograms describing the sound-induced motion of the tympanic membrane (TM) in cadaveric preparations from three mammalian species and one live ear were measured using opto-electronic holography. This technique allows rapid measurements of the magnitude of motion of the tympanic membrane surface at frequencies as high as 25 kHz. The holograms measured in response to low and middle-frequency sound stimuli are similar to previously reported time-averaged holograms. However, at higher frequencies (f > 4 kHz), our holograms reveal unique TM surface displacement patterns that consist of highly-ordered arrangements of multiple local displacement magnitude maxima, each of which is surrounded by nodal areas of low displacement magnitude. These patterns are similar to modal patterns (two-dimensional standing waves) produced by either the interaction of surface waves traveling in multiple directions or the uniform stimulation of modes of motion that are determined by the structural properties and boundary conditions of the TM. From the ratio of the displacement magnitude peaks to nodal valleys in these apparent surface waves, we estimate a Standing Wave Ratio of at least 4 that is consistent with energy reflection coefficients at the TM boundaries of at least 0.35. It is also consistent with small losses within the uniformly stimulated modal surface waves. We also estimate possible TM surface wave speeds that vary with frequency and species from 20 to 65 m/s, consistent with other estimates in the literature. The presence of standing wave or modal phenomena has previously been intuited from measurements of TM function, but is ignored in some models of tympanic membrane function. Whether these standing waves result either from the interactions of multiple surface waves that travel along the membrane, or by uniformly excited modal displacement patterns of the entire TM surface is still to be determined.

Introduction

Sound-induced motion of the tympanic membrane (TM) is the first stage in the transformation of airborne environmental sound into the hydro-mechanical stimulus to the sensory cells within the auditory inner ear. While there are a multitude of detailed models of TM function (e.g. Funnell and Laszlo, 1977, Rabbitt and Holmes, 1986, Rabbitt, 1988, Funnell and Decraemer, 1996, Gan et al., 2002, Koike et al., 2002, Fay et al., 2005, Fay et al., 2006, Parent and Allen, 2007) there is a relative paucity of data describing sound-induced motion of the entire TM, especially at frequencies above 8 kHz. The most detailed descriptions of the motion of the mammalian TM to date come from time-averaged holograms collected in cats (Khanna and Tonndorf, 1972), cadaveric humans (Tonndorf and Khanna, 1972, Bally, 1978, Fritze et al., 1978), cadaveric dogs (Naito, 1990, Okano, 1990, Suehiro, 1990, Maeta, 1991) and live humans (Løkberg et al., 1979). These data generally provide good qualitative descriptions of the magnitude of sound-induced motions of the mammalian TM surface. There are also more modern quantitative measurements that use either speckle holography (Wada et al., 2002) or scanning laser Doppler vibrometry (Konrádsson et al., 1987, Huber et al., 1997, Decraemer et al., 1999) to study the sound-induced motion of the surface of the TM but the published data using these techniques are few.

Because of the lack of published data, we have not been able to answer fundamental questions of TM function. One major question that has been the subject of differing opinions in the literature is how the TM contributes to high-frequency hearing. Several older reports (Tonndorf and Khanna, 1970, Tonndorf and Khanna, 1972, Shaw and Stinson, 1983) suggest that the complex patterns of TM motion observed with stimulus frequencies above 4 kHz indicate a ‘break-up’ of the TM similar to the complex motion patterns of microphone diaphragms and loudspeaker cones with sounds above the high-frequency limit of effective sound transduction in these devices (Fletcher, 1992). A more recent report opines that the complexity is due to a plethora of modes with closely spaced natural frequencies that can sum to provide efficient TM response to high-frequency stimulation (e.g. Fay et al., 2006). A second major question is whether surface waves on the TM contribute to sound conduction by the middle ear, specifically whether predictions of the transmission of TM surface waves from the periphery to the center contributes to observations of ‘middle-ear delay’ (Puria and Allen, 1998, Olson, 1998, Parent and Allen, 2007). A third major question is whether the observations or predictions of wave-like phenomena on the TM surface (e.g. Puria and Allen, 1998, Fay et al., 2005) result from traveling transverse surface waves, or are the consequence of uniformly driven modal motions in a lossy membrane; a complication to this distinction is that equations describing modal behavior can be used to describe traveling waves and vice-versa. While, the data we present do not directly answer these questions, they place limits on the answers.

Over the last two years our group – including personnel from the Worcester Polytechnic Institute (WPI) and the Massachusetts Eye and Ear Infirmary (MEEI) – has worked to apply modern computer-assisted high-speed opto-electronic holography (OEH) to the study of the vibration of the TM (Furlong et al., 2006, Rosowski et al., 2007, Furlong et al., in press, Hernández-Montes et al., in press). The main benefits of OEH are that the holographic interference patterns are recorded by a digital camera, and the computation of the reconstructed holographic images is accelerated by the use of computer-controlled variations in the length of the optical path of one of the interfering beams (Furlong and Pryputniewicz, 1995, Furlong and Pryputniewicz, 1998). We have used OEH to produce time-averaged holograms (TAHs) that describe the magnitude of the sound-induced motion of the surface of the TM of cadaveric and live animals to tones of varied frequency and level, where the digital-optical processing techniques (described below) allow independent computations of surface motion patterns at rates of 10 holograms per second. We use these TAHs to quantify patterns of TM surface motion produced by sound frequencies between 0.4 and 25 kHz. Two advantages of OEH derived time-averaged holography are (1) the high spatial resolution of the measurement; we image the whole surface of the TM with a pixel size equivalent to an area of (45 μm)2; (2) the optical measurements, holographic computations and display occur at video rates. Therefore, one can sweep frequency or level and observe real-time changes in the displacement pattern of the entire TM.

A unique feature of our results is the demonstration of ‘ordered’ modal displacement patterns on the surface of the TM at frequencies above 8 kHz. The observation of these patterns depends on the high-spatial resolution of the OEH technique. The displacement patterns produced by sound frequencies above 2 kHz describe clear nodes (regions where the motion is minimal) on the TM surface that are indicative of strong modal patterns, e.g. standing waves, on the TM surface. Such modal patterns are not a primary feature of several existing models of TM surface displacement (Fay et al., 2005, Fay et al., 2006, Parent and Allen, 2007). The recognition of the presence of modes or standing waves, and descriptions of their frequency dependence and associated wave-propagation velocities and TM losses will lead to refinements of our understanding of TM motion.

Section snippets

Computer-assisted laser holography

Computer-assisted opto-electronic holography (OEH) uses a digital camera synchronized with an optical phase shifter to capture multiple interference images while stepping the optical phase of one of the interfering beams in cyclic steps of 90° (Furlong and Pryputniewicz, 1995, Furlong and Pryputniewicz, 1998). The optical interference images captured by the digital camera describe variations in the optical path length between a beam of coherent light that is reflected from a moving object (the

Variations in TAHs with stimulus frequency

Fig. 4 shows TAHs of the sound-induced TM displacements of a cadaveric human (left-most column), a cadaveric chinchilla (second to the left), live chinchilla (third from the left) and cadaveric cat (right column), at selected frequencies from about 400 Hz (the top row of TAHs) to near 20 kHz (the bottom row). The stimulus intensities (in dB SPL) were selected to produce a moderate level of TM motion in each TAH. At the top of each column is a cartoon depicting the orientation of the exposed TM

Comparison to previous studies

The time-averaged holograms in Fig. 4 show similarities and differences with TAHs that have been previously described. The best-described set of TAH data is that of Khanna and Tonndorf (1972) in cat and Tonndorf and Khanna (1972) in human temporal bone. In those groundbreaking studies Khanna and Tonndorf described simple patterns of TM surface displacement that occurred at frequencies of less than 2 kHz, where the displacement patterns were consistent with in-phase displacement of the entire

Significance and conclusions

The ordered patterns of displacements we describe in time-averaged holograms measured at stimulus frequencies above 8 kHz are unique: They have not been described before, except for some preliminary reports (Furlong et al., 2006, Rosowski et al., 2007, Furlong et al., in press). The description of standing wave-like modal patterns on the TM, is not new (e.g. Khanna and Tonndorf, 1972, Funnell and Laszlo, 1977) but the existence of such standing-waves on the TM surface is not generally

Acknowledgements

We thank the staff of the Eaton-Peabody Laboratory (EPL) at the Massachusetts Eye and Ear Infirmary (MEEI) and the Center for Holographic Studies and Laser micro-mechaTronics (CHSLT) at the Worcester Polytechnic Institute (WPI) for their support in our work. Special thanks goes to Mr. Christopher Scarpino an engineer at the EPL who was a student at WPI who initiated the contacts between our two groups, and assisted in the fabrication of the holography and sound-delivery system. Some of the

References (53)

  • J. Fay et al.

    Three approaches for estimating the elastic modulus of the tympanic membrane

    J. Biomech.

    (2005)
  • G.von. Bally

    Holographic vibration analysis of the tympanic membrane (in German)

    Larng. Rhinol.

    (1978)
  • L. Brillouin

    Wave Propagation and Group Velocity

    (1960)
  • W. Chien et al.

    Measurements of human middle- and inner-ear mechanics with dehiscence of the superior semicircular canal

    Otol. Neurotol.

    (2007)
  • Decraemer, W.F., Khanna, S.M., Funnell, W.R.J., 1999. Vibrations at a fine grid of points on the cat tympanic membrane...
  • W.F. Decraemer et al.

    Anatomical and mechanical properties of the tympanic membrane

  • W. Dong et al.

    Middle ear forward and reverse transfer function

    J. Neurophysiol.

    (2006)
  • J.P. Fay et al.

    The discordant eardrum

    PNAS

    (2006)
  • N.H. Fletcher

    Acoustic Systems in Biology

    (1992)
  • W. Fritze et al.

    Holographic investigations of the mode of vibration of the human eardrum (in German)

    Arch. Otorhinolaryngol.

    (1978)
  • W.R.J. Funnell et al.

    On the incorporation of moiré shape measurements in finite-element models of the cat eardrum

    J. Acoust. Soc. Am.

    (1996)
  • W.R.J. Funnell et al.

    Modeling of the cat eardrum as a thin shell using the finite-element method

    J. Acoust. Soc. Am.

    (1977)
  • W.R.J. Funnell et al.

    A critical review of experimental observations on ear-drum structure and function

    ORL

    (1982)
  • C. Furlong et al.

    Opto-mechanical study and optimization of a cantilever plate dynamics

    SPIE

    (1995)
  • C. Furlong et al.

    Hybrid computational and experimental approach for the study and optimization of mechanical components

    Opt. Eng.

    (1998)
  • Furlong, C., Ravicz, M.E., Rodgers, M.T., Rosowski, J.J., 2006. Real-time opto-electronic holographic measurements of...
  • Furlong, C., Rosowski, J.J., Hulli, N., Ravicz, M.E., in press. Preliminary analyses of tympanic-membrane motion from...
  • R.Z. Gan et al.

    Three-dimensional modeling of middle-ear biomechanics and its applications

    Otol. Neurotol.

    (2002)
  • R.L. Goode et al.

    New knowledge about the function of the human middle ear: development of an improved analog model

    Am. J. Otol.

    (1994)
  • J.J. Guinan et al.

    Middle-ear characteristics of anesthetized cats

    J. Acoust. Soc. Am.

    (1967)
  • Hernández-Montes, M.d.S., Furlong, C., Rosowski, J.J., Hulli, N., Harrington, E., Cheng, J.T., Ravicz, M.E., Santoyo,...
  • A. Huber et al.

    The vibration pattern of the tympanic membrane after placement of a total ossicular replacement prosthesis (TORP)

  • S.M. Khanna et al.

    Tympanic membrane vibrations in cats studied by time-averaged holography

    J. Acoust. Soc. Am.

    (1972)
  • L.E. Kinsler et al.

    Fundamentals of Acoustics

    (1982)
  • T. Koike et al.

    Modeling of the human middle ear using the finite-element method

    J. Acoust. Soc. Am.

    (2002)
  • K. Konrádsson et al.

    Computerized laser Doppler interferometric scanning of the vibrating tympanic membrane

    Scand. Audiol.

    (1987)
  • Cited by (0)

    View full text