On morphometric measurement of oxygen diffusing capacity in middle ear gas exchange

An accurate mathematical model of transmucosal gas exchange is prerequisite to understanding middle ear (ME) physiology. Current models require experimentally measured gas species time constants for all extant conditions as input parameters. However, studies on pulmonary gas exchange have shown that a morphometric model that incorporates more fundamental physiochemical and anatomic parameters accurately simulates transport from which the species time constants can be derived for all extant conditions. Here, we implemented a variant of that model for ME gas exchange that requires the measurement of diffusional length (tau) for the ME mucosa. That measure contributes to the mucosal diffusing capacity and reflects the resistance to gas flow between air space and capillary. Two methods for measuring tau have been proposed: linear distance between the air-mucosal boundary and capillary and the harmonic mean of all contributing pathway lengths. Oxygen diffusing capacity was calculated for different ME mucosal geometries by using the two tau measures, and the results were compared with those predicted by a detailed, two-dimensional finite element analysis. Predictive accuracy was improved by incorporating the harmonic tau measure, which captures important information regarding variations in capillary shape and distribution. However, compared with the oxygen diffusing capacity derived from the finite element analysis, both measures yielded nonlinear, positively biased estimates. The morphometric techniques underestimate diffusion length by failing to account for the curvilinear gas flow pathways predicted by the finite element model.