Study of tracheal collapsibility, compliance and stress by considering its asymmetric geometry

The shape of tracheal cartilage has been widely treated as symmetric in analytical and numerical models. However, according to both histological images and in vivo medical image, tracheal cartilage is of highly asymmetric shape. Taking the cartilage as symmetric structure will induce bias in calculation of the collapse behavior, as well as compliance and muscular stress. However, this has been rarely discussed. In this paper, tracheal collapse is represented by considering its asymmetric shape. For comparison, the symmetric shape, which is reconstructed by half of the cartilage, is also presented. A comparison of cross-sectional area, compliance of airway and stress in the muscular membrane, determined by asymmetric shape and symmetric shape is made. The result indicates that the symmetric assumption brings a small error, around 5% in predicting the cross-sectional area under loading conditions. The relative error of compliance is more than 10%. Particularly when the pressure is close to zero, the error could be more than 50%. The model considering the symmetric shape results in a significant difference in predicting stress in muscular membrane by either under- or over-estimating it. In conclusion, tracheal cartilage should not be treated as a symmetric structure. The results obtained in this study are helpful in evaluating the error induced by the assumption in geometry.