Effect of tube length on the buckling pressure of collapsible tubes

Background: The higher incidence of obstructive sleep apnea (OSA) in men than in women has been attributed to the upper airway being longer in men. The Starling resistor is the paradigm biomechanical model of upper airway collapse in OSA where a collapsible tube (representing the pharynx) is located between two rigid tubes (representing the nasal cavity and trachea). While the Starling resistor has been extensively studied due to its relevance to many physiological phenomena, the effect of tube length on tube collapsibility has not been quantified yet. Methods: Finite element analysis of a 3-dimensional collapsible tube subjected to a transmural pressure was performed in ANSYS Workbench. The numerical methods were validated with in vitro experiments in a silicone tube whose modulus of elasticity (361 +/- 28 kPa) and dimensions (length = 100 mm, diameter = 22.2 mm, and wall thickness = 1.59 mm) were selected so that tube compliance was similar to pharyngeal compliance in humans during sleep. The buckling pressure (transmural pressure at which the tube collapses) was quantified in tubes of three different diameters (10 mm, 16 mm, and 22.2 mm) and ten length-to-diameter ratios (L/D = 4 to 13), while keeping the wall-thickness-to-radius ratio constant at 0.143. Results: The absolute value of the buckling pressure decreased from 4.7 to 3.3 cmH2O (461-324 Pa) when L/D increased from 4 to 13. The buckling pressure was nearly independent from tube length for L/D > 10. Conclusions: Our finding that longer tubes are more collapsible than shorter tubes is consistent with the higher incidence of obstructive sleep apnea in males than females.