Mathematical model of chest wall mechanics: a phenomenological approach

Abstract

A mathematical model of chest wall mechanics, based on a phenomenological approach to force balances, provides a quantitative framework for analyzing many types of chest wall movements by using orthogonal displacement coordinates. The moveable components of the ventilatory system include the rib cage, diaphragm, and abdomen. A distinction is made between the lung-apposed and diaphragm-apposed actions on the rib cage. The model equations are derived from "pressure" balances and geometrical relations of the compartments; the stress-displacement relations are hyperbolic. With this model we simulated stiff and flaccid chest wall behavior under normal and constrained conditions associated with abdominal compression, a Mueller maneuver, and a diaphragmatic isometric inspiration. We also examined situations that produce paradoxical as well as orthodox inspiratory movements. The results of these simulations were quantitatively consistent with available data from the literature. A phenomenon predicted by the stiff-wall model during quasi-static inspiration is that the rib cage displacement is negligible near residual volume, but then increases dramatically with lung volume. Since this mathematical model has a sound physical basis and is more comprehensive than previous models, it can be used to predict and analyze the behavior of the chest wall under a wide variety of circumstances.