Surfactant-Mediated Airway and Acinar Interactions in a Multi-Scale Model of a Healthy Lung

Abstract

We present a computational multi-scale model of an adult human lung that combines dynamic surfactant physicochemical interactions and parenchymal tethering between ~16 generations of airways and subtended acini. This model simulates the healthy lung by modeling nonlinear stress distributions from airway/alveolar interdependency. In concert with multi-component surfactant transport processes, this serves to stabilize highly compliant interacting structures. This computational model, with ~10 k degrees of freedom, demonstrates physiological processes in the normal lung such as multi-layer surfactant transport and pressure-volume hysteresis behavior. Furthermore, this model predicts non-equilibrium stress distributions due to compliance mismatches between airway and alveolar structures. This computational model provides a baseline for the exploration of multi-scale interactions of pathological conditions that can further our understanding of disease processes and guide the development of protective ventilation strategies for the treatment of acute respiratory distress syndrome (ARDS).

Keywords: acute respiratory distress syndrome; biofluid mechanics; fluid–structure interactions; high-performance computing; multi-scale modeling; surfactant.

Figure 1

Schematic of a “simple” lung unit with one terminal airway attached to an acinus.

Figure 2

Schematic flow chart of the of system evolution for the simulation model.

Figure 3

Distribution relationships for the computational model of a half-lung. (A) The Weibel generation of the terminal airways connecting to acinar regions, (B) the residual volume of the acini connecting to the terminal airways.

Figure 4

Tube law through the Weibel 6th generation. Airways smaller than the 6th generation are assumed to have the same tube law as the 6th generation. Experimental data is shown for the first 3 generations.

Figure 5

Example hysteresis loop of an alveolus. Γ₁ is inversely proportional to the interfacial area. The primary layer begins to collapse when Γ₁ ≥ Γ_∞, forming a secondary layer between the bulk and primary layer. When Γ₁ < Γ_∞, the secondary layer dynamically respreads, which stabilizes the surface tension.

Figure 6

Dynamic surface tension of the lung. (A) Specific time points during breathing cycle. (B) 3-D figure of the half-lung at four time points. The color scale in the legend denotes the surface tension. Statistical variation is documented in Figure 8.

Figure 7

Pressure vs. volume curve of the entire lung. The points (a), (b), (c), and (d) relate to Figure 6. Note, this figure demonstrates a portion of the total PV curve for volumes between end-inspiration and end-expiration for normal tidal volume breathing (~0.82 L).

Figure 8

Average acinar global forcing vs. local forcing. (A) PV relationship, (B) pressure vs. time, global (−P_PL, red), local (ΔP_AC = P_AC−P_PL, blue). Airway resistance leads to the hysteresis area difference between global and local forcing shown in (A) and the pressure time lag shown in (B), contributes to the global PV hysteresis behavior.

Figure 9

Surface tension behavior of model elements. (A) Average surface-tension vs. volume of acinar units. Statistical variation of these element is provided in Figure 10A. (B) Representative surface-tension vs. normalized surface area of airways demonstrating variations in behavior. The acinar and airway surface tension hysteresis behavior is similar to the isolated model in Figure 5 and contributes to the PV hysteresis behavior of the entire lung. Surface tension variation of airways corresponds to observations in Figure 6.

Figure 10

(A) Average acinar surface tension with standard deviation. Secondary layer respreading stabilizes surface tension near γ_∞. Low surface tension demonstrates surfactant collapse behavior. (B) The average maximum and minimum surface tension of each airway generation together with standard deviation by Horsfield generation. The minimum surface tension decreases with more compliant (smaller) airways. The secondary layer respreading stabilizes the maximum surface tension near γ_∞.

Figure 11

(A) Acinar residual volume plotted against the minimum surface tension. Regressions of (1) symmetrical (a = 1.58 and b = 6.56, reduced chi-square=0.22) and (2) asymmetrical acini (a = 0.66 and b = 6.16, reduced chi-square = 0.28) show that the surface tension is lower in asymmetrical acini. (B) Minimum surface tension plotted against the flow path length to the trachea. No correlation exists.

Figure 12

Acinar (A) and representative airways, (B) surface tension after a deep sigh. The secondary layer respreading stabilizes the surface tension around γ_∞. In airways, secondary layer depletion can be seen where the surface tension rises rapidly again after being stabilized around γ_∞ for a short period. Compared to the stationary tidal breathing state, the additional surfactant in the primary layer by respreading from the secondary layer and adsorption from the bulk during sigh leads to a lower surface tension at end-expiration. The representative airways are the same as those shown in Figure 9.

Figure 13

(A) Predictions of terminal airway radius with and without parenchymal tethering. Parenchymal hole radius R_H (green), airway radius with parenchymal tethering, $R_{AW,\frac{w}{P}}$ (red), and predicted airway radius without parenchymal tethering, $R_{AW,\frac{w}{o}P}$ (blue). This figure demonstrates the important feature that in this healthy lung model, $R_H>R_{AW,\frac{w}{o}P}$. This implies that parenchyma provides an outwardly directed mechanical stress that stabilizes compliant airways. (B) The average maximum and minimum strain deviation of each Horsfield airway generation. Bars represent the standard deviation.

Figure 14

Dynamic strain deviation in the lung model. (A) Specific time points during breathing cycle, (B) 3-D figure of the airway network at four time points, with color representing the strain deviation from the equilibrium parenchymal state.