William J Doyle1. 1. Department of Otolaryngology, University of Pittsburgh, School of Medicine, Pittsburgh, PA, USA. Electronic address: Cuneyt.alper@chp.edu.
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)∑P(ҚPs(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: 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)∑P(ҚPs(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.