A mathematical model for gas exchange in the human middle ear

A mathematical model was developed to identify time periods of atelectasis induction in middle ears (ME) ventilated via ventilating tubes (VT). VT´s were deliberately sealed and ME gas content changed in the presence of a preset blood gas pressure. Once sealed, CO₂ rapidly diffuses out of the blood via lining tissues into the ME. This results in initially a total ME pressure rise followed by decrease to sub atmospheric pressures. Time periods for atelectasis reformation were determined once ME pressure crossed the 760 mmHg value and continued to decline as the atelectasis reached higher grades. Time periods calculated by the model varied from 28 min to 165 min in ME cavities ranging in volume from 0.5 mL to 3 mL respectively. Blood gas pressure in the lining mucosa was altered between arterial gas composition to venal blood composition in a first order fashion. These results are consistent with prior clinical tests that measured an induced return to previous atelectasis state following the closure of the VT´s in 33 tested ears within 25-120 min (43 min on average). The model demonstrates that increase in blood flow rate alter the exchange rate of CO₂ and N₂ between the ME and blood to be perfusion limited whereas that of O₂ remains diffusion limited. The model may be used as a tool to determine ME physiological cavity volume of ears with VT´s.