A mathematical and graphical analysis of inspiratory muscle action

In this paper a mathematical and graphical analysis is presented for the action of the diaphragm and the intercostal/accessory muscles of inspiration, in terms of the pressure developed, the volumes displaced and the work performed by each set of muscles. An analogous model is described which behaves according to the analysis. The critical variable by which the action of the diaphragm and intercostal/accessory muscles can be measured is the change in abdominal pressure Pab. When delta Pab = 0 it is assumed that the diaphragm has contracted isometrically and is acting as a fixator preventing an expiratory displacement of the abdomen. When delta Pab greater than 0 the diaphragm shortens and acts as an agonist. When delta Pab less than 0 the diaphragm lengthens as it contracts, performs negative work and the abdomen is displaced in an expiratory direction. For a given change in lung volume, as delta Pab diminishes, there is progressive recruitment of intercostal/accessory muscles and a progressive increase in the work of breathing over and above that required to produce the same change in lung volume by contraction of the diaphragm alone. For values of delta Pab greater than 0 the sum of diaphragm and intercostal/accessory muscle work is less than the total work, because of an increase in the elastic energy stored in the rib cage. For Pab less than 0 there is a decrease in the elastic energy stored in the rib cage leading to a marked increase in work performed and pressures developed by the intercostal/accessory muscles.