Modeling the Progression of Epithelial Leak Caused by Overdistension

Abstract

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.

Keywords: Alveolar Stretch; Lung Injury; Spring Network Model.

FIGURE 1

Configuration of hexagonal network. (a) The outer boundary is fixed after the network is stretched biaxially with force F_s. Each cell contains a network of springs connecting inner nodes to cell–cell junctions. (b) The junctions on the cell borders can separate to form leaks between the cells if the resultant force from the attached springs in one cell exceeds the threshold value for that node.

FIGURE 2

Leak progression in the 45-cell network. The panels (a–f) show how the leak caused by the applied stretch force F_s = 0.07 forms. Only one node fails at a time; nf indicates how many nodes have failed in each panel. The shading represents the value of the maximum spring force within each cell. Spring stiffness k = 1, force threshold F_t = 0.2, and cell edge length h = 1.

FIGURE 3

Model behavior with increasing stretch force, F_s, and increasing network size. (a) Leak area, A_leak, normalized by the total network area before stretching and cell–cell junction failure, A₀, at end-inspiration and end-expiration. (b) Number of junction failures; note that the number of failures does not continue to increase with F_s. (c) Total number of leaks formed for each stretch force and network size; fewer leaks are formed in the larger networks.

FIGURE 4

Sensitivity to parameters k (stiffness), h (edge length), and F_t (force threshold) in 45-cell network. (a) Leak area, A_leak, normalized by the total network area before stretching and cell–cell junction failure, A₀, is plotted against the stretch force F_s. (b) Change in F_s at leak onset from the baseline case is shown for ±10%, ±25%, and ±50% changes in k, h, and F_t. For a 50% decrease in F_t and a 50% increase in k or h, all values of F_s formed a leak. (c) All cases are plotted on nondimensional axes, with the end-inspiration curves following the left-hand axis and the end-expiration curves following the right-hand axis. F_spring is the maximum internal spring force in the network before cell–cell junction failures occur.

FIGURE 5

Stretch force F_s that initiates leak. The uniform case (dotted line) is compared to the cases with increasing variation in k (stiffness) and F_t in the 45-cell network. k and F_t were chosen from normal distributions with μ_k = 1 and σ_k =0.05, 0.1, and 0.15 and μ_Ft = 0.2 and σ_Ft = 0.01, 0.02, 0.03, respectively. Bars represent mean and SD (n = 50). All means significantly different from each other except ^a and ^b (p ≤ 0.01).

FIGURE 6

Sensitivity to inhomogeneous k (stiffness) and F_t (force threshold) in 45-cell network. (a) Mean leak area, A_leak, normalized by the total network area before stretching and cell–cell junction failure, A₀ and (b) mean number of leaks are plotted with increasing stretch force, F_s. Shading represents standard deviation bounds (n = 50). k and F_t were chosen from normal distributions with μ_k = 1 and σ_k =0.05, 0.1, and 0.15 and μ_Ft = 0.2 and σ_Ft = 0.01, 0.02, 0.03, respectively.