A simplified model of airway narrowing due to bronchial mucosal folding

Bronchial mucosal folding during bronchoconstriction can be a significant phenomenon, and a number of previous studies have provided models which examine a number of aspects of this important problem. Previous approaches include finite-element analyses, fluid-structure interaction, linear elasticity models, geometrical computer optimisation, and more. These models have focused on changes to the elastic properties of the airways due to mucosal folding, rather than airway narrowing, and suffer from too great a degree of computational complexity for use in multiscale, spatially distributed models of the lung now being developed. We propose a simplified, geometrical model of airway folding under the assumptions of fixed airway wall area, fixed basement membrane perimeter during constriction, specified shape and number of folds, and liquid filling of the mucosal folds, in the context of determining effective airway radius and hence airway impedance. We show that this model generates predictions in good agreement with existing models while being vastly simpler to solve.