Fluid transport in branched structures with temporary closures: a model for quasistatic lung inflation

A model of the recruitment-derecruitment and volume of lung units in an excised lung as it is inflated-deflated between minimum and maximum lung volume

The role of the recruitment-derecruitment of small structures in the lung (lung units) as the lung increases and decreases in volume has been debated. The objective of this study was to develop a model to estimate the change in the number and volume of open lung units as an excised lung is inflated-deflated between minimum and maximum lung volume. The model was formulated based on the observation that the compliance of the slowly changing quasi-static pressure-volume (P-V) curve of an excised rat lung can differ from the compliance of a faster changing small sinusoidal pressure volume perturbations superimposed on the curve. In those regions of the curve where differences in compliance occur, the lung tissue properties exhibit nonlinear characteristics, which cannot be linearized using "incremental" or "small signal" analysis. The model attributes the differences between the perturbation and quasi-static compliance to an additional nonlinear compliance term that results from the sequential opening and closing of lung units. Using this approach, it was possible to calculate the normalized average volume and the normalized number of open units as the lung is slowly inflated-deflated. Results indicate that the normalized average volume and the normalized number of open units are not linearly related to normalized lung volume, and at equal lung volumes the normalized number of open units is greater and the normalized average lung unit volume is smaller during lung deflation when compared to lung inflation. In summary, a model was developed to describe the recruitment-derecruitment process in excised lungs based on the differences between small signal perturbation compliance and quasi-static compliance. Values of normalized lung unit volume and the normalized number of open lung units were shown to be nonlinear functions of both transpulmonary pressure and normalized lung volume.

Airway reopening through catastrophic events in a hierarchical network

When you reach with your straw for the final drops of a milkshake, the liquid forms a train of plugs that flow slowly initially because of the high viscosity. They then suddenly rupture and are replaced with a rapid airflow with the characteristic slurping sound. Trains of liquid plugs also are observed in complex geometries, such as porous media during petroleum extraction, in microfluidic two-phase flows, or in flows in the pulmonary airway tree under pathological conditions. The dynamics of rupture events in these geometries play the dominant role in the spatial distribution of the flow and in determining how much of the medium remains occluded. Here we show that the flow of a train of plugs in a straight channel is always unstable to breaking through a cascade of ruptures. Collective effects considerably modify the rupture dynamics of plug trains: Interactions among nearest neighbors take place through the wetting films and slow down the cascade, whereas global interactions, through the total resistance to flow of the train, accelerate the dynamics after each plug rupture. In a branching tree of microchannels, similar cascades occur along paths that connect the input to a particular output. This divides the initial tree into several independent subnetworks, which then evolve independently of one another. The spatiotemporal distribution of the cascades is random, owing to strong sensitivity to the plug divisions at the bifurcations.

Transport of wetting liquid plugs in bifurcating microfluidic channels

A plug of wetting liquid is driven at constant pressure through a bifurcation in a microchannel. For a plug advancing in a straight channel, we find that the viscous dissipation in the bulk may be estimated using Poiseuille's law while Bretherton and Tanner's laws model the additional dissipation occurring at the rear and front interfaces. At a second stage, we focus on the behavior of the plug flowing through a T-junction. Experiments show the existence of a threshold pressure, below which the plug remains blocked at the entrance of the junction. Above this required pressure, the plug enters the bifurcation and either ruptures or splits into two daughter plugs, depending on the applied pressure and on the initial length of the plug. By means of geometrical arguments and the previously cited laws, we propose a global model to predict the transitions between the three observed behaviors.

Relating airway diameter distributions to regular branching asymmetry in the lung

We study the distribution Pi(n)(D) of airway diameters D as a function of generation N in asymmetric airway trees of mammalian lungs. We find that the airway bifurcations are self-similar in four species studied. Specifically, the ratios of diameters of the major and minor daughters to their parent are constants independent of N until a cutoff diameter is reached. We derive closed form expressions for Pi(N)(D) and examine the flow resistance of the tree based on an asymmetric flow division model. Our findings suggest that the observed diameter heterogeneity is consistent with an underlying regular branching asymmetry.

Acoustic evidence of airway opening during recruitment in excised dog lungs

The aim of this study was to test the hypothesis that the mechanism of recruitment and the lower knee of the pressure-volume curve in the normal lung are primarily determined by airway reopenings via avalanches rather than simple alveolar recruitments. In isolated dog lung lobes, the pressure-volume loops were measured, and crackle sounds were recorded intrabronchially during both the first inflation from the collapsed state to total lobe capacity and a second inflation without prior degassing. The inflation flow contained transients that were accompanied by a series of crackles. Discrete volume increments were estimated from the flow transients, and the energy levels of the corresponding crackles were calculated from the sound recordings. Crackles were concentrated in the early phase of inflation, with the cumulative energy exceeding 90% of its final value by the lower knee of the pressure-volume curve. The values of volume increments were correlated with crackle energy during the flow transient for both the first and the second inflations ( r2 = 0.29–0.73 and 0.68–0.82, respectively). Because the distribution of volume increments followed a power law, the correlation between crackle energy and discrete volume increments suggests that an avalanche-like airway opening process governs the recruitment of collapsed normal lungs.

Perimeter growth of a branched structure: application to crackle sounds in the lung

We study an invasion percolation process on Cayley trees and find that the dynamics of perimeter growth is strongly dependent on the nature of the invasion process, as well as on the underlying tree structure. We apply this process to model the inflation of the lung in the airway tree, where crackling sounds are generated when airways open. We define the perimeter as the interface between the closed and opened regions of the lung. In this context we find that the distribution of time intervals between consecutive openings is a power law with an exponent beta approximately 2. We generalize the binary structure of the lung to a Cayley tree with a coordination number Z between 2 and 4. For Z=4, beta remains close to 2, while for a chain, Z=2 and beta=1, exactly. We also find a mean field solution of the model.