Mechanics of compartmental models of the chest wall

Standard methods for describing the mechanical properties of a linear elastic system are applied to the two- and three-compartment models of the chest wall. The compliance matrix and the experiments required to determine the entries in this matrix and thereby to describe the mechanical properties of the relaxed chest wall are described. The effective forces exerted by external loads and muscle tension are defined. The formal theory is used to identify relations among variables. From the definition of effective force, it follows that the ratio of the forces exerted by the diaphragm on the rib cage and abdomen is the same as the ratio of the dependence of diaphragm length on rib cage and abdominal volumes. As an example of relations among variables that follow from the symmetry of the compliance matrix, it is shown that the change of gastric pressure caused by raising pleural pressure is related to the change in lung volume caused by changing stomach volume.