A micromechanical model of airway-parenchymal interdependence

Abstract

The forces of parenchymal interdependence in the lung are potent inhibitors of airway smooth muscle shortening, as evidenced by the marked dependence of bronchial responsiveness on lung volume. In this study we developed a mathematical-computer model of the effects of parenchymal interdependence on airway smooth muscle shortening. A three-dimensional network of cuboidal alveolar walls was tethered at its boundaries and surrounded a single airway with mechanical properties identical to the alveolar parenchyma. The walls were assigned highly nonlinear properties so that the pressure-volume behavior of the model matched that measured in dogs. Constriction of the airway was achieved by increasing the circumferential tension in the airway wall, and then solving the force-balance equations of the model to calculate the equilibrium configurations of the airway wall and all the interconnecting alveolar walls. The changes in airway resistance predicted by the model at various transpulmonary pressures (P(tp)) were compared to those obtained by the alveolar capsule oscillator technique in dogs during induced bronchoconstriction at various P(tp) (Balassy et al., J. Appl. Physiol. 78:875-880, 1995). The model matched the data reasonably well at P(tp) values above about 0.5 kPa, but was too responsive at lower P(tp). We were able to make the model match the data at all P(tp) by including an additional stiffness term, such as might conceivably arise from the airway wall itself.