Dynamic visco-elastic buckling analysis of an in vitro airway model: prediction of circumferential and axial buckling mode numbers

The purpose of the research reported here was to elucidate the mechanism of formation of the various lobes observed in asthmatic airways by both theoretical and experimental analysis employing an in vitro airway model. The rationale is that the elucidated mechanism will facilitate the development of new diagnostic methods and treatment regimens for asthma. Lobe formation was analyzed on the basis of an assumption of cross-sectional buckling of the airway. Here, we propose a dynamic visco-elastic buckling model analysis of the airway for the prediction of circumferential and axial buckling mode numbers. The calculated circumferential buckling mode numbers were in reasonably good agreement with those measured in the dynamic buckling experiment using the in vitro airway model. The calculated axial buckling mode numbers were in qualitative agreement with those observed in the experiment. The non-dimensional parameters related to the remodeling and the consequent pathologies occurring in asthmatic airways were also shown, and the influence of changes in the non-dimensional parameters on the circumferential and axial buckling mode numbers was also calculated. The circumferential and axial buckling mode numbers decreased due to thickening and stiffening of the basement membrane. Thickening of the tissues surrounding the basement membrane and the increase in the mucus secreted in the airway lumen were modeled as an increase in the added mass on the basement membrane. The results of calculation showed that the circumferential and axial buckling mode numbers increased because of the thickening of the surrounding tissues and the increase in mucus secretion. We suggest that it may be possible to diagnose the severity of asthma by using the results of the calculation of the changes in the buckling mode numbers caused by the changes in the strength of the remodeling. The physiological reality of the in vitro airway model reported here is discussed using the non-dimensional parameters.