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Comparative Study
. 2012 Jul;113(1):124-9.
doi: 10.1152/japplphysiol.01578.2011. Epub 2012 Apr 12.

Continuum vs. spring network models of airway-parenchymal interdependence

Baoshun Ma  1 , Jason H T Bates
Affiliations
Comparative Study

Continuum vs. spring network models of airway-parenchymal interdependence

Baoshun Ma et al. J Appl Physiol (1985). 2012 Jul.

Abstract

The outward tethering forces exerted by the lung parenchyma on the airways embedded within it are potent modulators of the ability of the airway smooth muscle to shorten. Much of our understanding of these tethering forces is based on treating the parenchyma as an elastic continuum; yet, on a small enough scale, the lung parenchyma in two dimensions would seem to be more appropriately described as a discrete spring network. We therefore compared how the forces and displacements in the parenchyma surrounding a contracting airway are predicted to differ depending on whether the parenchyma is modeled as an elastic continuum or as a spring network. When the springs were arranged hexagonally to represent alveolar walls, the predicted parenchymal stresses and displacements propagated substantially farther away from the airway than when the springs were arranged in a triangular pattern or when the parenchyma was modeled as a continuum. Thus, to the extent that the parenchyma in vivo behaves as a hexagonal spring network, our results suggest that the range of interdependence forces due to airway contraction may have a greater influence than was previously thought.

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Figures

Fig. 1.
Fig. 1.
A: hexagonal spring network (HSN) model. B: continuum mechanics finite-element model. Network-to-airway size ratio (L/D) is 9.5 for both models.
Fig. 2.
Fig. 2.
Normalized force (F/Fmax) in parenchyma due to airway contraction in the HSN model and normalized van Mises stress based on continuum mechanics model. Models at the two L/D values have the same airway size but different overall network size. Ratio of maximum force (L/D = 9.5 vs. 27.3) is 7.8, and ratio of maximum stress is 0.97 for the two L/D values.
Fig. 3.
Fig. 3.
Comparison of displacement and force fields for linear and nonlinear springs in the HSN model, with L/D = 9.5 in both cases. Δr/Δrmax, normalized displacement of the parenchyma caused by airway contraction.
Fig. 4.
Fig. 4.
Normalized displacement in parenchyma in continuum mechanics and HSN models.
Fig. 5.
Fig. 5.
Curve-fitting to normalized parenchymal displacement vs. normalized distance from airway centroid for continuum mechanics (A) and HSN (B) models.
See this image and copyright information in PMC

References

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