Abstracts Physics

Airway mechanics and pulmonary function tests

by Ulrich Holzhäuser

Methods of engineering mechanics were applied to further the theoretical understanding of the elastic deformation of some specific components of the tracheobronchial tree when subject to a transmural pressure difference. The contribution of the epithelial basement membrane to airway collapse was analysed. The well-known approach based on the physics of a shell was extended to investigate the influence of a non-homogeneous stiffness of the basement membrane on airway collapse. Results were obtained for the fundamental "two-lobe" collapse. These indicate that the critical pressure at which collapse starts depends on the location of the region of maximal stiffness. A method was presented for analysing asymmetric stress-strain behaviour when the Young modulus of a material is different in compression than in tension. Results indicated that, if the basement membrane were stiffer in compression than in tension, the resulting collapsed structure would be slightly stiffer than in the case of no stiffness difference and thus the airway would be less narrowed and less compliant. The deformation of the trachea was analysed by using the same theory as used in the study of the folding of the epithelial membrane. Computations were made to investigate (i) a semi-circular "base-shape" as well as more complex, non-circular shapes, (ii) the effect of shortening of the posterior membrane, (iii) localised weakening of the cartilage ring. Good agreement between model predictions and published MRI microscopy data from rabbit tracheas was obtained. The concepts of fluid mechanics in elastic tubes were used to analyse the effects of airway remodelling on forced expiratory airflow and resistance to airflow. The tracheobronchial tree was modeled as a system of branching, elastic tubes. Flow behaviour through that system of tubes was analysed which allowed the simulation of pulmonary function tests, in particular forced expiration and response to a muscle agonist. Effects of thickening of the airway wall components (adventita, smooth muscle and the submucosa) on exiratory flow and airways resistance, were investigated. Results showed that thickening of the smooth muscle had the strongest effect on expiratory airflow and airway resistance, followed by thickening of the submucosal area. Model results were within a physiologically feasible range.