Elsevier

Hearing Research

Volume 354, October 2017, Pages 73-85
Hearing Research

Research Paper
A formal description of middle ear pressure-regulation

https://doi.org/10.1016/j.heares.2017.08.005Get rights and content

Highlights

  • A mathematical description of middle-ear pressure-regulation as a flow-regulated process.

  • This mathematical model is developed from standard diffusion and air-flow equations.

  • The model accurately predicts the middle-ear pressure-trajectories reported for past clinical observations and experiments.

  • Operation of the model explains the generation of the measured higher than expected middle-ear N2 pressures.

  • The model predicts the increase in middle-ear pressure that was misinterpreted as gas production by the middle-ear mucosa.

Abstract

Introduction

Middle ear (ME) pressure-regulation (MEPR) is a homeostatic mechanism that maintains the ME-environment pressure-gradient (MEEPG) within a range optimized for “normal” hearing.

Objective

Describe MEPR using equations applicable to passive, inter-compartmental gas-exchange and determine if the predictions of that description include the increasing ME pressure observed under certain conditions and interpreted by some as evidencing gas-production by the ME mucosa.

Methods

MEPR was modeled as the combined effect of passive gas-exchanges between the ME and: perilymph via the round window membrane, the ambient environment via the tympanic membrane, and the local blood via the ME mucosa and of gas flow between the ME and nasopharynx during Eustachian tube openings. The first 3 of these exchanges are described at the species level using the Fick's diffusion equation and the last as a bulk gas transfer governed by Poiseuille's equation. The model structure is a time-iteration of the equation: PMEg(t=(i+1)Δt) = ∑s(PMEs(t=iΔt)+(1/(βMEsVME)∑PPs(PCs(t=(iΔt)-PMEs(t=(iΔt))). There, PMEg(t=iΔt) and PMEs(t=iΔt) are the ME total and species-pressures at the indexed times, PCs(t=iΔt) is the species-pressure for each exchange-compartment, βMEsVME is the product of the ME species-capacitance and volume, ҚPs is the pathway species-conductance, and ∑S and ∑P are operators for summing the expression over all species or exchange pathways.

Results

When calibrated to known values, the model predicts the empirically measured ME species-pressures and the observed time-trajectories for total ME pressure and the MEEPG under a wide variety of physiologic, pathologic and non-physiologic conditions.

Conclusions

Passive inter-compartmental gas exchange is sole and sufficient to describe MEPR.

Introduction

The middle ear (ME) is a relatively non-collapsible, biological gas pocket that is usually closed to direct communication with the ambient environment (Sade and Ar, 1997). For hearing, the middle-ear (ME) functions to detect the near-continuous, low-magnitude, high-frequency, environmental pressure fluctuations associated with perceived “sound”, represent that flux as a pressure-time signal conditioned for effective gas-fluid coupling and present the conditioned pressure-time signals to the cochlear perilymph (Hawkins, 1964, Mason, 2016, Wilson, 1987). The sensory unit for this mechanism, the tympanic membrane (TM), functions like the diaphragm of a differential pressure-sensor. Consequently, optimal signal extraction requires that the ME medium be matched to that of the environment (i.e., gas-gas coupling) and that the ME “reference” pressure be maintained at near atmospheric levels. However, those requisite conditions are intrinsically unstable as environmental pressure independently fluctuates with changes in altitude and the movement of weather fronts and ME pressure is independently changed by diffusive gas transfers between the ME and adjacent anatomical compartments (Doyle, 2000). A ME-environment mismatch in pressure and/or media dampens TM responsiveness causing a conductive “hearing loss”.

In otherwise healthy MEs, hearing efficiency is inversely related to the absolute magnitude of the ME-environment gas-pressure gradient (MEEPG) measured at a standard ME volume (Austin, 1978, Lildholt, 1983, Tonndorf, 1964, Wright, 1970, Zwislocki and Feldman, 1970). Moreover, at an approximate MEEPG of −300 daPa, the accompanying mucosal-ME hydrostatic pressure gradient causes the ME gas pocket to “collapse” with fluids transferred from the local blood to the ME cavity (Alper et al., 1997, Flisberg, 1970, Swarts et al., 1995). That pathologic condition is associated causally with a moderate to severe conductive hearing loss (Dobie and Berlin, 1979, Roland et al., 1989).

Biological homeostasis is the maintenance of a quasi-stable physiologic state by mechanisms that counter those processes that drive a system toward instability and, ultimately, functional failure (Recordati and Bellini, 2004). For the ME, homeostasis refers to those mechanisms that maintain a negligible MEEPG (i.e. system regulators) by countering the effects of other processes that drive the development of non-zero MEEPGs (i.e. system stressors). This biofeedback mechanism is referred to as ME pressure-regulation (MEPR) (Doyle, 2000).

It is well accepted that the risks for certain types of conductive hearing loss and ME pathologies are inversely related to MEPR efficiency (Bluestone and Klein, 2007, Dobie and Berlin, 1979, Kitahara et al., 1994, Roland et al., 1989, Truswell et al., 1979). Consequently, there is a continuing interest in developing medical and/or surgical interventions that improve MEPR efficiency in certain “at risk” populations (Kanemaru et al., 2005, Kanemaru et al., 2013, Kanemaru et al., 2004, Llewellyn et al., 2014, Yung, 1998). In application, this requires that the physiology of MEPR be well understood from a mechanistic perspective. Currently, a number of conceptually distinct mechanisms for MEPR have been described, with stable MEEPGs being volume-regulated, temperature-regulated, pressure-regulated, flow-regulated or regulated by some combinations of these mechanisms (Adams, 1954, Bluestone, 2005, Csakanyi et al., 2014, Doyle, 2000, Fooken Jensen and Gaihede, 2016, Gaihede et al., 2010, Hergils and Magnuson, 1988, Paduariu et al., 2015).

Traditional descriptions of MEPR are based on a flow-regulated model that for efficient function requires a balance in the volume of gas supplied to the ME during Eustachian tube (ET) openings with the volume removed from the ME by passive trans-barrier diffusive exchange with adjacent compartments. Here, a formal, mathematical model of flow-regulated MEPR that incorporates standard equations for passive inter-compartmental gas-exchange is developed (Ranade et al., 1980) and then used to test the hypothesis that a flow-regulated description of MEPR is sole and sufficient to explain the behaviors of ME pressure known from observation and experiment. To that end, the model was parameterized and evaluated for accuracy in predicting the empirically measured ME gas composition and the MEEPG trajectories observed under physiologic and non-physiologic conditions. Included in the latter are those that favor an increasing ME pressure over short time intervals, a phenomenon often attributed to gas-production by the ME mucosa (MEM) (Buckingham, 1990, Buckingham and Ferrer, 1980, Kanemaru et al., 2004, Kanemaru et al., 2005). Abbreviations and symbols used in the text and equations are presented in Table 1.

Section snippets

Exchange system structure

The functional ME is a temperature stable, relatively fixed-volume, gas-filled, bony cavity located within the petrosal portion of the temporal bone. That cavity is divided into two primary subcompartments, the anterior, ME proper and the posterior, mastoid air-cell system (MACS) (Bluestone, 2005). These subcompartments are continuous in the gas-phase via a fixed-diameter open channel, the mastoid antrum, and share a continuous mucosa consisting of a single layer of epithelial cells overlying a

Calculations

Using these equations, a compartment-level, computational model describing MEPR was constructed for use in simulating MEEPG trajectories under defined conditions. That model treats ME gas-exchange as simultaneous, gradient-driven, trans-barrier diffusive molar species-exchanges between the ME and three fixed-volume, homogenous, mixed-gas compartments, the atmosphere, perilymph and MEM blood, and the intermittent bolus gas-flows between the ME and NP during active and passive ET openings.

Contribution of trans-TM/RWM species-exchange to MEPR

The model was calibrated using the standard values for the parameters listed in Table 2, Table 3, Table 4 and a 10-h simulation was run under the conditions of no active ET openings (FETO = 0) and: 1) no trans-TM or trans-RWM gas-exchange (ҚTMs and ҚRWMs = 0) but trans-MEM gas-exchange set to its standard value, 2) gas-exchange across those membranes are set to their standard values but trans-MEM gas-exchange is ignored (ҚMEMs = 0), and 3) gas-exchange across all three trans-barrier pathways.

Discussion

Efficient ME function requires that the TM be maintained at maximum compliance with approximately equal ME and ambient total gas pressures. Because the ME is not in direct communication with the environment, ME and environmental pressures vary independently over time which causes significant MEEPGs. Dissipation of those gradients is accomplished by a homeostatic mechanism, MEPR, that has a very narrow tolerance for hearing efficiency, MEEPG range from approximately −100 to 100 daPa, and a

Conclusions

A mathematical model of flow-regulated MEPR was developed and formalized. All processes included in the model have a well-established physiology that can be represented using simple mathematical equations. Thermodynamic considerations show that the included processes are energetically favorable as they obey the 2nd law and reduce the free energy of the system to a local minimum. When linked within a formal model and calibrated to extant conditions, operation of those processes predicts observed

Funding

NIH Grant DC007667.

Financial disclosure information

The author has no financial disclosures.

Conflict of interest

The author has no conflicts to disclose.

Acknowledgements

This study was supported in part by a grant from the National Institutes of Health (P50 007667). Corresponding author Cuneyt M. Alper, M.D. would like to acknowledge Ellen M. Mandel, M.D. for her help in editing and preparation of revised manuscript, after the passing of William J. Doyle, Ph.D.

References (66)

  • B. Ars et al.

    Middle ear pressure balance under normal conditions. Specific role of the middle ear structure

    Acta Otorhinolaryngol. Belg

    (1994)
  • D.F. Austin

    Sound conduction of the diseased ear

    J. Laryngol. Otol.

    (1978)
  • C.D. Bluestone

    Eustachian Tube Structure, Function, Role in Otitis Media

    (2005)
  • C.D. Bluestone et al.

    Otitis Media in Infants and Children

    (2007)
  • C.A. Buchman et al.

    Influenza A virus–induced acute otitis media

    J. Infect. Dis.

    (1995)
  • R.A. Buckingham

    Middle ear gas generation in myringoplasties

    Ann. Otol. Rhinol. Laryngol.

    (1990)
  • R.A. Buckingham et al.

    Observations of middle ear pressures. Commentary with movie

    Ann. Otol. Rhinol. Laryngol. Suppl.

    (1980)
  • E.I. Cantekin et al.

    Airflow through the eustachian tube

    Ann. Otol. Rhinol. Laryngol.

    (1979)
  • E.I. Cantekin et al.

    Dilation of the eustachian tube by electrical stimulation of the mandibular nerve

    Ann. Otol. Rhinol. Laryngol.

    (1979)
  • E.I. Cantekin et al.

    Effect of surgical alterations of the tensor veli palatini muscle on eustachian tube function

    Ann. Otol. Rhinol. Laryngol.

    (1980)
  • M.L. Casselbrant et al.

    Experimental paralysis of tensor veli palatini muscle

    Acta Otolaryngol.

    (1988)
  • U. Cinamon et al.

    Mastoid and tympanic membrane as pressure buffers: a quantitative study in a middle ear cleft model

    Otol. Neurotol.

    (2003)
  • Z. Csakanyi et al.

    Middle ear gas pressure regulation: the relevance of mastoid obliteration

    Otol. Neurotol.

    (2014)
  • R.A. Dobie et al.

    Influence of otitis media on hearing and development

    Ann. Otol. Rhinol. Laryngol. Suppl.

    (1979)
  • W. Doyle

    Middle ear pressure regulation

  • W.J. Doyle et al.

    Pressure chamber tests of eustachian tube function document lower efficiency in adults with colds when compared to without colds

    Acta Otolaryngol.

    (2014)
  • W.J. Doyle et al.

    Sensitivity and specificity of eustachian tube function tests in adults

    JAMA Otolaryngol. Head. Neck Surg.

    (2013)
  • J.U. Felding et al.

    Gas composition of the normal and the ventilated middle ear cavity

    Scand. J. Clin. Lab. Invest Suppl.

    (1987)
  • M. Gaihede et al.

    Middle ear pressure regulation–complementary active actions of the mastoid and the Eustachian tube

    Otol. Neurotol.

    (2010)
  • J.E. Hawkins

    Hearing

    Annu. Rev. Physiol.

    (1964)
  • S. Hellstrom et al.

    The pressure equilibrating function of pars flaccida in middle ear mechanics

    Acta Physiol. Scand.

    (1983)
  • L. Hergils et al.

    Regulation of negative middle ear pressure without tubal opening

    Arch. Otolaryngol. Head. Neck Surg.

    (1988)
  • L. Hergils et al.

    Human middle ear gas composition studied by mass spectrometry

    Acta Otolaryngol.

    (1990)
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