A mathematical model of trans-mucosal gas exchanges

Abstract

Problem: Gas exchanges in the middle ear (ME) are thought to be the cornerstone in the development of atelectasis and cholesteatoma. The purpose of the current study was to validate a mathematical model of trans-mucosal gas exchanges based on ME volume variations. Methods: According to Fick’s law of diffusion, the rate of diffusion of a gas is proportional to the partial pressure difference of the gas between the 2 sides of the diffusion barrier, the solubility and diffusion coefficient of the gas in the diffusion barrier, and the surface area available for diffusion − and inversely proportional to the thickness L of the diffusion barrier. In a first step, we designed an experimental rat model for exclusive study of trans-mucosal gas exchanges. In a second step, a mathematical model of trans-mucosal gas exchanges for N2 was developed. In order to validate both models, 2 assumptions were tested. First, linearity of gas volume variations should be verified, ie, being constant. Second, the effective thickness of the diffusion barrier that can be deduced from Fick’s law should correspond to the actual thickness. Results: First, normal rat ME gas volume variations exhibited a linear decrease ( = -0.130μL min-1 ± 0.03) which lasted 31.1min ± 8.5 SD. Second, the effective thickness Le of the diffusion barrier was 71.4 μm, which is in accordance with that of histologic studies reported in the literature for rats where the thickness of mucosa varies between 9 and 150 μm. Conclusion: Since both assumptions were checked for validity, it is now possible to estimate the variation of effective blood flow surrounding the ME in experimental conditions using this mathematical model and knowing the thickness. Significance: Further studies in inflamed ears may bring informative data on the ME circulation and the role of the ME mucosa in gas exchanges in pathologic conditions. Support: No support