Modeling airway resistance dynamics after tidal and deep inspirations

Using the forced oscillation technique, we tracked airway resistance continuously during quiet breathing (QB) and deep inspiration (DI), thus observing fluctuations in resistance that may reflect mechanisms of airway stretch and renarrowing. After DI, however, the resistance may be depressed for a period not related to volume changes. We hypothesized that this gradual increase in resistance after DI-induced dilation was determined by a simple time constant. Furthermore, to the extent that this effect reflects dynamic characteristics of airway renarrowing, the resistance change after each tidal inspiration should also be constrained by this temporal limit. A model relating resistance fluctuations to the breathing pattern, including both instantaneous and delayed effects, was developed and applied to data from 14 nonasthmatic and 17 asthmatic subjects (forced expiratory volume in 1 s = 103 +/- 13 and 83 +/- 12%, respectively, means +/- SD) after methacholine challenge (dose 145 +/- 80 and 3.0 +/- 3.4 micromol, respectively) that resulted in respective forced expiratory volume in 1 s reductions of 16 +/- 7 and 24 +/- 6% from baseline. Resistance was measured continuously for 1 min of QB, a DI, followed by a further minute of QB. Resistance values at end expiration (Ree) and end inspiration were calculated. We found that the sequence of Ree after DI was best modeled by a power-law function of time rather than an exponential decay (r2 = 0.82 +/- 0.18 compared with 0.63 +/- 0.16; P < 0.01). Furthermore, the coefficient characterizing this "renarrowing function" was close to equal to the coefficient characterizing the equivalent function of resistance change between each resistance value at end inpiration and subsequent Ree during QB, particularly in the nonasthmatic subjects for whom the intraclass correlation was 0.66. This suggests that the same time-dependent factors determine renarrowing after both large and small breaths.