A new geometrical and mechanical relation in the respiratory system with airflow limitation—From the perspective of analytical respiratory mechanics

Classic respiratory mechanics is a branch of vectorial mechanics, which aims to recognize all forces acting on the respiratory system. Another branch of mechanics, analytical mechanics, has been used for analyzing the motions of complicated systems with constraints through equilibrium among scalar quantities such as kinetic energy and potential energy. However, until now, there have not been any studies concerning about analytical respiratory mechanics. In this paper, the author has obtained two types of motion equations (linear and nonlinear) for the airflow limitation from formulation of the analytical respiratory mechanics. Reconstructed flow-volume trajectories of the linear equation revealed a new relationship among the slope of the linear portion of trajectory, the coefficient of the dissipation function and the coefficient of the potential function. Reconstructed trajectories of the nonlinear equation suggested that a curved flow-volume trajectory would be caused by the emergence of regional hypoventilated clusters with airtrapped lobules. In conclusion, analytical respiratory mechanics will provide the basis for analyzing the mechanical properties of the respiratory system concerning pulmonary functional images made by newly developed technologies.