Analysis of Airway Narrowing Based on Dynamic Buckling Model

In order to elucidate the mechanism of airway narrowing in asthma, dynamic buckling analysis was performed for basement membrane. The basement membrane was treated as two-dimensional circular thin-walled viscoelastic shell of Voigt model and contraction of smooth muscle was replaced by inward transmural pressure applied to the basement membrane. Governing equations for the dynamic buckling was derived and wave number of buckling mode obtained were compared with numerical simulation results by non-linear FEM and with experimental results. The non-dimensional parameters are thickness radius ratio, non-dimensional increasing speed of inward transmural pressure, non-dimensional retardation time and Poisson ratio. Wave number of buckling mode is determined as the number having maximum amplification from initial imperfection mode. The wave number of buckling mode increases with increase in non-dimensional increasing speed of inward transmural pressure and it decreases with increase in non-dimensional retardation time. It has been known that wave number of buckling mode decreases due to thickening and hardening of basement membrane caused by the remodeling in asthma. This fact is originated from decrease in non-dimensional increasing speed of inward transmural pressure due to the remodeling. In the dynamic buckling analysis the damping effect of the basement membrane is necessary to take into consideration, because the primary component of the basement membrane is collagen having damping characteristics.