Epithelial cell deformation during surfactant-mediated airway reopening: a theoretical model

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Abstract
A theoretical model is presented describing the reopening by an advancing air bubble of an initially liquid-filled collapsed airway lined with deformable epithelial cells. The model integrates descriptions of flow-structure interaction (accounting for nonlinear deformation of the airway wall and viscous resistance of the airway liquid flow), surfactant transport around the bubble tip (incorporating physicochemical parameters appropriate for Infasurf), and cell deformation (due to stretching of the airway wall and airway liquid flows). It is shown how the pressure required to drive a bubble into a flooded airway, peeling apart the wet airway walls, can be reduced substantially by surfactant, although the effectiveness of Infasurf is limited by slow adsorption at high concentrations. The model demonstrates how the addition of surfactant can lead to the spontaneous reopening of a collapsed airway, depending on the degree of initial airway collapse. The effective elastic modulus of the epithelial layer is shown to be a key determinant of the relative magnitude of strains generated by flow-induced shear stresses and by airway wall stretch. The model also shows how epithelial-layer compressibility can mediate strains arising from flow-induced normal stresses and stress gradients.