Modeling stochastic and spatial heterogeneity in a human airway tree to determine variation in respiratory system resistance

Abstract

Asthma is a variable disease with changes in symptoms and airway function over many time scales. Airway resistance ( Raw) is variable and thought to reflect changes in airway smooth muscle activity, but just how variation throughout the airway tree and the influence of gas distribution abnormalities affect Raw is unclear. We used a multibranch airway lung model to evaluate variation in airway diameter size, the role of coherent regional variation, and the role of gas distribution abnormalities on mean Raw ( R̄aw) and variation in Raw as described by the SD ( SDRaw). We modified an anatomically correct airway tree, provided by Merryn Tawhai (The University of Auckland, New Zealand), consisting of nearly 4,000 airways, to produce temporal and spatial heterogeneity. As expected, we found that increasing the diameter variation by twofold, with no change in the mean diameter, increased SDRaw more than fourfold. Perhaps surprisingly, R̄aw was proportional to SDRaw under several conditions—when either mean diameter was fixed, and its SD varied or when mean diameter varied, and SD was fixed. Increasing the size of a regional absence in gas distribution (ventilation defect) also led to a proportionate increase in both R̄aw and SDRaw. However, introducing regional dependence of connected airways strongly increased SDRaw by as much as sixfold, with little change in R̄aw. The model was able to predict previously reported Raw distributions and correlation of SDRaw on Raw in healthy and asthmatic subjects. The ratio of SDRaw to R̄aw depended most strongly on interairway coherent variation and only had a slight dependence on ventilation defect size. These findings may explain the linear correlation between variation and mean values of Raw but also suggest that regional alterations in gas distribution and local coordination in ventilation amplify any underlying variation in airway diameters throughout the airway tree.