Continuum vs. spring network models of airway-parenchymal interdependence

Ma, Baoshun; Bates, Jason H. T.

doi:10.1152/japplphysiol.01578.2011

Cited by 22 publications

(32 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results of the present investigation build on our previous modeling studies of airwayparenchymal interdependence in which we showed that the distribution of displacements and forces within the parenchyma surrounding a contracting airway are rather different depending on whether the parenchyma is modeled as a hexagonal network of springs, a triangular network (Ma and Bates, 2012;Ma et al, 2013), or a continuum model (Breen et al, 2012). In all cases the parenchymal distortion is greatest next to the airway wall and decreases with radial distance (Figs.…”

Section: Discussionsupporting

confidence: 78%

“…4), similar to the predictions of the Lai-Fook theory (LaiFook, 1979b;Lai-Fook et al, 1977a;Lauzon et al, 1992), which is based on continuum mechanics. We attribute these differences in predicted behavior to the differences in resistance to shear exhibited by the hexagonal versus the triangular spring networks (Ma and Bates, 2012). Without the diagonal struts that form the triangular network, the hexagonal network of springs more easily undergoes shear deformation.…”

Section: Discussionmentioning

confidence: 97%

“…Since the pioneering work of Mead et al (Mead et al, 1970) that brought attention to the physiological importance of airway-parenchymal interdependence, there have been numerous studies of this phenomenon (Adler and Bates, 2000;Adler et al, 1998;Benjamin et al, 1974;Dandurand et al, 1993;Khan et al, 2010;Lai-Fook, 1979b;Lai-Fook and Hyatt, 1979;Lai-Fook et al, 1977a;Lai-Fook and Kallok, 1982;Ma and Bates, 2012;Noble et al, 2005;Smith et al, 1984;Wilson, 1972). All theoretical studies to date have assumed the parenchyma to be homogeneous, yet it is well known that substantial heterogeneity and anisotropy can develop in the lung parenchyma in disease (Chapman et al, 2012;Ito et al, 2004;Ito et al, 2007;Kaczka et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Influence Of Parenchymal Heterogeneity On Airway-Parenchymal Interdependence

Ma¹,

Bates²

2012

B29. The Lung on the Border Between Order and Chaos

Self Cite

View full text Add to dashboard Cite

To estimate the influence of parenchymal heterogeneities on airway-parenchymal interdependence, we considered a circular airway embedded within elastic parenchyma modeled as 1) a hexagonal spring network, 2) a triangular spring network, or 3) a continuum. The deformation in the parenchyma due to active airway contraction was simulated using the finite element method. Random perturbations of elastic moduli in the parenchyma did not significantly affect the overall pattern of force transmission. By contrast, when elastic moduli were increased along a path projecting radially outward from the airway, the hexagonal spring network model predicted significantly increased force along this line as the airway contracted, but this was not observed in other two models. These results indicate that tissue heterogeneities generally have minimal effect on the global nature of airway-parenchymal interdependence. However, in the exceptional circumstance of scar tissue aligned radially from the airway wall, parenchymal distortion forces may propagate much farther from the airway wall than was previously thought.

show abstract

Section: Discussionsupporting

confidence: 78%

Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence Of Parenchymal Heterogeneity On Airway-Parenchymal Interdependence

Ma¹,

Bates²

2012

B29. The Lung on the Border Between Order and Chaos

Self Cite

View full text Add to dashboard Cite

show abstract

“…We represented the alveolar walls in the parenchyma as pin-joined springs arranged in a repeating hexagonal pattern, as this represents the conventional idealization of the appearance of a thin slice of lung tissue (Mead et al, 1970; Wilson, 1972). We found, somewhat unexpectedly, that such a network produces long-range transmission of forces in response to the distortion produced by the narrowing of the embedded airway (Ma and Bates, 2012; Ma et al, 2013a). By contrast, when the springs are arranged in a repeating triangular pattern, or the parenchyma is represented as an elastic continuum, the elastic forces fall off rapidly with distance from the airway wall (Ma and Bates, 2012), in apparent accord with existing theory about airway-parenchymal interdependence (Lai-Fook, 1979; Wilson, 1972).…”

Section: Introductionmentioning

confidence: 77%

Resistance to alveolar shape change limits range of force propagation in lung parenchyma

Smith

Bates

2015

Respiratory Physiology & Neurobiology

Self Cite

View full text Add to dashboard Cite

We have recently shown that if the lung parenchyma is modeled in 2 dimensions as a network of springs arranged in a pattern of repeating hexagonal cells, the distortional forces around a contracting airway propagate much further from the airway wall than classic continuum theory predicts. In the present study we tested the hypothesis that this occurs because of the negligible shear modulus of a hexagonal spring network. We simulated the narrowing of an airway embedded in a hexagonal network of elastic alveolar walls when the hexagonal cells of the network offered some resistance to a change in shape. We found that as the forces resisting shape change approach about 10% of the forces resisting length change of an individual spring the range of distortional force propagation in the spring network fell of rapidly as in an elastic continuum. We repeated these investigations in a 3-dimensional spring network composed of space-filling polyhedral cells and found similar results. This suggests that force propagation away from a point of local parenchymal distortion also falls off rapidly in real lung tissue.

show abstract

“…We developed custom software based on the finite element method, adapted from our previously described model of airway-parenchymal interdependence, 18–21 that solves a system of force equilibrium equations for a planar spring network. 40 Each spring was assumed to be a bar element with baseline length x 0 .…”

Section: Methodsmentioning

confidence: 99%

Modeling the Progression of Epithelial Leak Caused by Overdistension

Hamlington

Smith

et al. 2016

Cel. Mol. Bioeng.

Self Cite

View full text Add to dashboard Cite

Mechanical ventilation is necessary for treatment of the acute respiratory distress syndrome but leads to overdistension of the open regions of the lung and produces further damage. Although we know that the excessive stresses and strains disrupt the alveolar epithelium, we know little about the relationship between epithelial strain and epithelial leak. We have developed a computational model of an epithelial monolayer to simulate leak progression due to overdistension and to explain previous experimental findings in mice with ventilator-induced lung injury. We found a nonlinear threshold-type relationship between leak area and increasing stretch force. After the force required to initiate the leak was reached, the leak area increased at a constant rate with further increases in force. Furthermore, this rate was slower than the rate of increase in force, especially at end-expiration. Parameter manipulation changed only the leak-initiating force; leak area growth followed the same trend once this force was surpassed. These results suggest that there is a particular force (analogous to ventilation tidal volume) that must not be exceeded to avoid damage and that changing cell physical properties adjusts this threshold. This is relevant for the development of new ventilator strategies that avoid inducing further injury to the lung.

show abstract

Continuum vs. spring network models of airway-parenchymal interdependence

Cited by 22 publications

References 30 publications

Influence Of Parenchymal Heterogeneity On Airway-Parenchymal Interdependence

Influence Of Parenchymal Heterogeneity On Airway-Parenchymal Interdependence

Resistance to alveolar shape change limits range of force propagation in lung parenchyma

Modeling the Progression of Epithelial Leak Caused by Overdistension

Contact Info

Product

Resources

About