Surfactant Effects on Fluid-Elastic Instabilities of Liquid-Lined Flexible Tubes: A Model of Airway Closure

• Published in: Journal of biomechanical engineering 1993-08, Vol.115 (3), p.271-277
• Main Authors: Halpern, D, Grotberg, J. B
• Format: Article
• Language: English
• Subjects: Adolescent; Adult; Age Factors; Aged; Air; Air breathing; Airway Obstruction - physiopathology; Biological and medical sciences; Bronchi - physiology; Child; Elasticity; Fundamental and applied biological sciences. Psychology; Humans; Lung Compliance; Lung Volume Measurements; Mathematics; Models, Biological; Pulmonary Surfactants - physiology; Respiratory system: anatomy, metabolism, gas exchange, ventilatory mechanics, respiratory hemodynamics; Rheology; Stress, Mechanical; Surface Tension; Time Factors; Vertebrates: respiratory system; Viscosity
• ISSN: 0148-0731; 1528-8951
• DOI: 10.1115/1.2895486

A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, εc, decreases with increasing mean surface-tension or wall compliance. Surfactant increases εc by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.