A nonlinear model of respiratory mechanics in emphysematous lungs

Existing mechanical models of chronic obstructive lung disease have failed to explain a number of experimental findings of airway obstruction, e.g., the varying manners of frequency dependence of resistance (FDR). Departing from the parallel-unit concept and attempting to account for the "check-valve" mechanism in the emphysematous lung, we proposed a single-compartment lung model with a nonlinear pressure-flow relationship: P + P* = LV + K1V + K3(V +/- V*)3 + V/c, where P* = K3V*, V* is a constant. The plus and minus signs in the cubic term indicate the expiratory and inspiratory check valves, respectively. The choice of an asymmetric P - V relation reflects several properties of emphysematous lungs such as airflow limitation and higher expiratory resistance. Implementation of the above equation using sine wave, white noise, and step inputs resulted in various forms of FDR at frequencies between 0 and 40 Hz depending on the type of input used. Resistance was most sensitive to changes in input pressure amplitude. The model's results suggest that the P - V nonlinearity can have a significant influence on the impedance construct in obstructed lung disease.