Mechanical interactions between adjacent airways in the lung

Abstract

The forces of mechanical interdependence between the airways and the parenchyma in the lung are powerful modulators of airways responsiveness. Little is known, however, about the extent to which adjacent airways affect each other's ability to narrow due to distortional forces generated within the intervening parenchyma. We developed a two-dimensional computational model of two airways embedded in parenchyma. The parenchyma itself was modeled in three ways: 1) as a network of hexagonally arranged springs, 2) as a network of triangularly arranged springs, and 3) as an elastic continuum. In all cases, we determined how the narrowing of one airway was affected when the other airway was relaxed vs. when it narrowed to the same extent as the first airway. For the continuum and triangular network models, interactions between airways were negligible unless the airways lay within about two relaxed diameters of each other, but even at this distance the interactions were small. By contrast, the hexagonal spring network model predicted that airway-airway interactions mediated by the parenchyma can be substantial for any degree of airway separation at intermediate values of airway contraction forces. Evidence to date suggests that the parenchyma may be better represented by the continuum model, which suggests that the parenchyma does not mediate significant interactions between narrowing airways.

Keywords: airway mechanics; finite element model; mechanical heterogeneity; parenchymal mechanics; spring network model.

Fig. 1.

Schematic of computational domain and details of model geometry. The continuum model (bottom left) consists of a triangular mesh representing the parenchyma with two circular holes representing the airways, while in the hexagonal network model the parenchyma is represented by elastic alveolar walls with some walls removed to create the airways (bottom middle). The triangular spring network model was created by adding one point at the center of each hexagon and forming six triangles inside the hexagon. The two airways shown here have identical relaxed sizes and are placed symmetrically about the vertical center line. Simulations were also performed for two airways of different sizes (results not shown).

Fig. 2.

Time courses of narrowing of the two airways in the hexagonal spring network model. The isometric contraction forces were identical for the two airways, but the initial maximum contraction speed of Airway 2 was twice that of Airway 1.

Fig. 3.

Lumen area of Airway 1 in the hexagonal spring network model when both airways contracted vs. when only Airway 1 contracted, for two values of isometric contraction force (A: F₀ = 0.005; B: F₀ = 0.01).

Fig. 4.

Ratio of Airway 1 lumen areas (only Airway 1 contracts vs. both airways contract) as a function of isometric contraction force (F₀) in the hexagonal network model. The near-field data were obtained for a separation distance of 2.6 relaxed airway diameters (i.e., in the decreasing region of the plots in Fig. 3), while the far-field data were obtained for a separation distance of 10 diameters (i.e., in the plateau region of the plots in Fig. 3).

Fig. 5.

Comparison of Airway 1 lumen area in the continuum model when both airways contracted vs. when only Airway 1 contracted.

Fig. 6.

Ratio of Airway 1 lumen areas (only Airway 1 contracts vs. both airways contract) as a function of radial contraction force in the continuum model. The near-field data were obtained for a separation distance of 2.4 relaxed airway diameters (i.e., in the increasing region of the plots in Fig. 5), while the far-field data were obtained for a separation distance of 10 diameters (i.e., in the plateau region of the plots in Fig. 5).

Fig. 7.

Comparison of Airway 1 lumen area in the triangular spring network model when both airways are contracted vs. when only Airway 1 is contracted.