Abstract
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 con cerning pulmonary functional images made by newly developed technologies.
Highlights
Since Newton laid the solid foundation of dynamics by formulating the laws of motion, the science of mechanics has developed along two main lines
Leibniz is the originator of the second branch of mechanics which usually called analytical mechanics, which bases the entire study of equilibrium and motion on two fundamental scalar quantities, kinetic energy and work function [1]
Lanczos compared the difference between Newtonian mechanics and analytical mechanics [1], and summarized four principal viewpoints: 1) vectorial mechanics isolates the particle and considers it as an individual, but analytic mechanics considers the system as a whole; 2) vectorial mechanics constructs a separate acting force for each moving particle, but analytical mechanics considers one single function the work function; 3) if strong forces maintain a definite relation between the coordinates of a system, and that relation is empirically given, the analytical treatment takes the given relation for granted, without requiring knowledge of the forces which maintain it; and 4) in the analytical method, the entire set of equations of motion can be developed from one unified principle of least action
Summary
Since Newton laid the solid foundation of dynamics by formulating the laws of motion, the science of mechanics has developed along two main lines. One branch, which we shall call vectorial mechanics, starts directly from Newton’s laws of motion. Leibniz is the originator of the second branch of mechanics which usually called analytical mechanics, which bases the entire study of equilibrium and motion on two fundamental scalar quantities, kinetic energy and work function (this is frequently replaceable by the potential energy) [1]. We encounter problems of mechanics for which the work function is a function of the position of particles and of the time For such systems, the law of conservation of energy does not hold. It is demanded that physiologists reconstruct analytical respiratory mechanics based on SPLs in place of the classical vectorial, which will help us to accurately understand new pulmonary functional images produced by new technologies. Reconstructed trajectories have revealed a new relationship among mechanical properties of the respiratory system in airflow limitation, and suggested a close relationship between the shapes of flowvolume trajectories and the emerged regional air-trapping in the lung
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