A Nonlinear Model Combining Pulmonary Mechanics and Gas Concentration Dynamics

To elucidate the various mechanisms by which pulmonary mechanics affect the distribution of gas species throughout the lungs, a multicompartment model relating pressure differences, flows, volumes, and gas species concentrations has been developed. The alveolar regions of the model are nonlinearly elastic and the pressure-flow relation of their associated small airways is volume dependent. Various combinations of parameter values were chosen, including cases in which the model was mechanically uniform (normal) and nonuniform (obstructive). Computer solutions of model equations were obtained for both piecewise-exponential and sinusoidal transpulmonary pressure inputs. Clinical measures of mechanical uniformity and gas concentration homogeneity were evaluated along with unobservable indexes. Results indicate how the distribution of mechanical variables affects the distribution of gas species concentration within the lungs. For the nonuniform (obstructive) model, the gas is distributed more inhomogeneously at higher frequencies and lower lung volumes. The distribution of initial dead space gas to the compartments as well as pendelluft tend to decrease this inhomogeneity. Dynamic compliance for the non-uniform model was frequency dependent at each of the three volume operating points investigated, whereas the semilog nitrogen washout curve was essentially linear for some frequencies and volumes while nonlinear for others. Consequently, inferences about distributions of mechanical parameters and intrapulmonary gas may require that clinical measurements be obtained together at several frequencies and volume operating points.