The estimation of lung mechanics parameters in the presence of pathology: a theoretical analysis

Mechanical lung function is frequently assessed in terms of lung resistance (R (L)), lung elastance (E (L)), and airway resistance (R (aw)). These quantities are determined by measuring input impedance at various oscillation frequencies, and allow lung tissue resistance (R (t)) to be estimated as the difference between R (L) and R (aw). These various parameters change in characteristic ways in the presence of lung pathology. In particular, the ratio R (t)/E (L) (known as hysteresivity, (eta) has been shown both experimentally and in numerical simulations to increase when regional heterogeneities in mechanical function develop throughout the lung. In this study, we performed an analytical investigation of a two-compartment lung model and showed that while heterogeneity always leads to an increase in E (L), eta will increase only initially. When heterogeneity becomes extreme, eta stops increasing and starts to decrease. However, there are no experimental reports of eta decreasing under conditions in which heterogeneity would be expected to exist. We speculate that this is because liquid bridges invariably form across airway lumen that narrow to a certain point, thereby preventing them from achieving arbitrarily small non-zero radii. We also show that recruitment of closed lung units during lung inflation may lead to variables responses in both eta and E (L).