Research PaperA formal description of middle ear pressure-regulation
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.
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Deceased author.