Mechanical properties of the respiratory system derived from morphologic insight

This paper aims to provide the mechanical parameters of the respiratory airways (resistance, inertance, and compliance) from morphological insight, in order to facilitate the correlations of fractional-order models with pathologic changes. The approach consists of taking into account wall thickness, inner radius, tube length, and tissue structure for each airway level to combine them into a set of equations for modeling the pressure drop, flow, wall elasticity, and air velocity (axial and radial). Effects of pulmonary disease affecting the inner radius and elastic modulus of bronchial tree are discussed. A brief comparison with the circulatory system, which poses similarities with the respiratory system, is also given. The derived mechanical parameters can serve as elements in a transmission line equivalent, whose structure preserves the geometry of the human respiratory tree. The mechanical parameters derived in this paper offer the possibility to evaluate input impedance by altering the morphological parameters in relation to the pulmonary disease. In this way, we obtain a simple, yet accurate, model to simulate and understand specific effects in respiratory diseases; e.g., airway remodeling. The final scope of the research is to relate the variations in airway structure with disease to the values of fractional-order model parameters.