Mathematical analysis of atelectasis formation in middle ears with sealed ventilation tubes

Aim: A mathematical model was developed to identify time periods of atelectasis induction in middle ear (ME) ventilated via ventilating tubes (VT). Atelectatic ears are characterized by a total gas pressure lower than 760 mmHg. Methods: Ventilating tubes 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 cleft. This results in initially a total ME pressure rise followed by a decrease in subatmospheric pressures. Time periods for atelectasis reformation was determined once ME pressure crossed the 760 mmHg value and continued to decline as the atelectasis reached higher grades. Results: Time periods calculated by the model varied from 18 to 125 min in ME cavities ranging in volume from 0.5 to 3.5 mL, respectively. These results were calculated for conditions of venous blood in the lining mucosa blood and are consistent with prior clinical tests that measured an induced return to previous atelectasis state following the closure of the VT in 33 tested ears within 25-120 min (43 min on average). Conclusions: The model demonstrates that under the above conditions, diffusive gas transfer in relation to blood gas content is the leading mechanism to alterations in ME pressure and volume. It may be used as a tool to determine ME physiological cavity volume of ears with VT.