Stress distribution in a three dimensional, geometric alveolar sac under normal and emphysematous conditions

Abstract

Pulmonary emphysema is usually the result of chronic exposure to cigarette smoke in at risk individuals. To investigate the hypothesis that lung damage in emphysema results from coincident weakening in the structural properties of the tissue and increased mechanical forces--as one explanation of the continued development of pulmonary emphysema after smoking cessation--we developed a three dimensional, geometric dodecahedron-based acinar model. Using the model numerical analysis of the stress distribution in normal conditions could be compared with those resulting in emphysematous conditions. Finite element analysis was used to evaluate the model at a number of lung inflation levels, using quasi-static loading of the alveolar pressure. When internal alveolar pressure was increased along with the adjustment of the material properties to represent a weakening of one wall in the acinus, increased stress resulted at the perimeters of the weakened area. In particular this increased stress was localized at the junction points of the internal alveolar septa. It was also found that under the proposed simulated emphysematous conditions, a significant disruption in the stress distribution within the acinus model occurred at low, rather than high, lung volumes. This is supportive of the physiological observation that destruction of the diseased tissue can occur under less stress than those existing in the normal state.

Figure 1

The stacked rhombic dodecahedron alveolar sac model displayed from four different angles: an oblique view (A), a base view with a −15 degree x-axis rotation (B), a base view with a 15 degree x-axis rotation (C), and a base view with a 45 degree x-axis rotation (D).

Figure 2

The Young’s modulus for the emphysematous and normal tissue for the featured lung volumes. The destruction of the collagen and elastin fibers in the emphysematous tissue decrease the strength and the elastic recoil of the tissue, hence reducing the Young’s modulus. Abbreviations: TLC, total lung capacity.

Figure 3

The stress distributions for the normal alveolar sac models at two different lung volumes. The low lung volume (A) and the high lung volume (B) reveal a very similar stress distribution. Abbreviations: TLC, total lung capacity.

Figure 4

The stress distributions for the emphysematous alveolar sac models at two different lung volumes. A single area of the alveolar sac has the emphysematous material properties applied as highlighted in the figure. The low lung volume (A) and the high lung volume (B) reveal very different stress distributions. Specifically, very high stress levels are induced in the emphysematous area and the airway inlet at the low lung volume. Abbreviations: TLC, total lung capacity.

Figure 5

The external view of the alveolar sac model for the different disease states investigated at a mid lung volume of 60% total lung capacity. The states were: normal conditions (A), normal material properties with an elevated internal pressure (B), one simulated emphysematous alveolar wall with normal pressure (C), and finally a simulated emphysematous wall and elevated internal pressure (D). It can be seen from these external views that the stress distribution on the outer wall is disrupted for both emphysema models.

Figure 6

The internal view of the alveolar sac model at a lung volume of 60% total lung capacity showing the model sliced through the medial plane to reveal the inner wall of the emphysematous area. The states illustrated are: normal conditions (A), normal with an elevated internal pressure (B), a simulated emphysematous alveolar wall with normal pressure (C), and finally a simulated emphysemic wall and elevated internal pressure (D). These internal views highlight the elevated stress through out the internal emphysematous wall, with particularly high stresses at the wall junction sites.

Figure 7

A close up view of the simulated emphysematous wall incorporating the elevated internal pressure. Highlighted, is the significantly elevated stress levels at the internal junctions with the adjoining alveolar walls.