Session EL: Bio-Fluids: Lungs

Clearance of a Mucus Plug

Mucus plugging may occur in pulmonary airways in asthma, chronic obstructive pulmonary disease (COPD) and cystic fibrosis. How to clear the mucus plug is essential and of fundamental importance. Mucus is known to have a yield stress and a mucus plug behaves like a solid plug when the applied stresses are below its yield stress $\tau _{y}$. When the local stresses reaches $\tau _{y}$, the plug starts to move and can be cleared out of the lung. It is then of great importance to examine how the mucus plug deforms and what is the minimum pressure required to initiate its movement. The present study used the finite element method (FEM) to study the stress distribution and deformation of a solid mucus plug under different pressure loads using ANSYS software. The maximum shear stress is found to occur near the rear transition region of the plug, which can lead to local yielding and flow. The critical pressure increases linearly with the plug length and asymptotes when the plug length is larger than the half channel width. Experimentally a mucus simulant is used to study the process of plug deformation and critical pressure difference required for the plug to propagate. Consistently, the fracture is observed to start at the rear transition region where the plug core connects the films. However, the critical pressure is observed to be dependent on not only the plug length but also the interfacial shape.   

The effect of viscoelasticity on the stability of the lung's liquid layer

The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid which is modeled here as a Jeffreys fluid. To examine the role of mucus alone, we model a single layer of a visco-elastic fluid. Nonlinear evolution equations are derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Solutions of the nonlinear evolution equations reveal that the closure time, defined to be the time required for a plug to form, decreases with increasing film thickness and viscoelasticity. Some results obtained from direct numerical simulations are also presented and compared with the lubrication theory model.   

Liquid Plug Propagation in a Flexible Microchannel: Experimental and Numerical Studies

The lung's small airways can close due to the formation of a liquid plug bridge, or airway wall collapse or a combination of both in diseases such as chronic obstructive pulmonary disease (COPD) and respiratory distress syndrome (RDS), and in the external instillation of therapeutical drugs or surfactants.~ The propagation of a formed plug can produce high pressure, high shear stress, and large gradients of each, which may damage the cells lining the airway walls. This study is motivated by an interest in the effect of wall flexibility on the plug propagation and its resulting wall stresses in small airways. We fabricated a flexible microchannel to mimic the flexible small airways using soft lithography. As the plug propagates along the flexible microchannels, the local wall deformation is observed in the plug core region, which increases with plug speed but slightly increases with plug length. The pressure drop across the plug is measured and observed to increase with plug speed and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with the experimental measurement.   

Motion of a semi-infinite bubble in a liquid filled channel using the level set method

The study of plug propagation in lung airways is of interest in the treatment of medical conditions such as asthma and in drug delivery. The problem of a semi-infinite bubble steadily displacing a liquid in a 2D channel (planar Bretherton problem) is computed using a fractional-step method on a Cartesian grid to solve the Navier-Stokes equations and a level-set formulation for resolving the air-liquid interface. We matched with available literature the geometry of the front and rear menisci of this semi-infinite bubble, stresses on the channel walls, and the maximum pressure drop as a function of the Capillary number -- the ratio of viscous to surface tension effects. Furthermore, we present preliminary results for flows within tapered walls to address area expansion near airway bifurcations.   

Particle Deposition for Flow over a Wedge

Particle transport and deposition associated with flow over a wedge is investigated as a model for particle transport and flow at an airway bifurcation. Using matched asymptotics, a uniformly valid solution is obtained to represent the high Reynolds number flow over a wedge which considers both the viscous boundary layer near the wedge and the outer inviscid region, and is then used to solve the particle transport equations. The phenomenon of boundary layer shielding is investigated and is characterized by a positive normal velocity component near the wall that pushes particles in the boundary layer away from the wall and prevents particle impaction. Additionally, deposition efficiency and relative distribution of impacted particles are presented. The present model compares well to more complex ones that consider the three dimensional structure of an airway, but is advantageous in that the boundary layer phenomena can be closely investigated.   

Anomalous bubble propagation in elastic tubes

Airway reopening is an important physiological event, as exemplified by the first breath of an infant that inflates highly collapsed airways by driving a finger of air through its fluid-filled lungs. Whereas fundamental models of airway reopening predict the steady propagation of only one type of bubble with a characteristic rounded tip, our experiments reveal a surprising selection of novel bubbles with counter-intuitive shapes that reopen strongly collapsed, liquid-filled elastic tubes. We characterize these bubbles in terms of their dimensionless speed and the initial level of tube collapse, and find sub-critical exchanges of stability between them. Moreover, our multiple bubbles are associated with a discontinuous relationship between bubble pressure and speed that sets exciting challenges for modellers.   

Reopening of a microfluidic airway tree in the presence of liquid plugs

Many respiratory diseases are associated with the occlusion of pulmonary airways with liquid plugs, which are generally assumed to cause the collapse of the airways. Previous work has shown that the reopening of the airways proceeds through avalanches occurring over several generations, although measurements on real lungs are limited to single point measurements at the trachea. Here, we present a microfluidic model airway tree which consists of five generations of bifurcations that are partially occluded with liquid plugs. The initial distribution of the plugs in the tree displays high sensitivity to initial conditions with evidence of chaotic distribution. The reopening is achieved by applying a constant pressure or constant flow rate at the root of the tree and cascades of different types are observed in the two cases: While the constant pressure forcing is found to open the whole tree, a constant flow rate forcing opens only a single path. Finally we observe that the elasticity of the airways is not a necessary ingredient for the cascades to occur.   

Numerical analysis of the formation process of aerosols in the alveoli

For a successful diagnosis of lung diseases through an analysis of non-volatile molecules in the exhaled breath, an exact understanding of the aerosol formation process is required. This process is modeled using Computational Fluid Dynamics (CFD). The model shows the interaction of the boundary surface between the streamed airway and the local epithelial liquid layer. A 2-D volume mesh of an alveolus is generated by taking into account the connection of the alveoli with the sacculi alveolares (SA). The Volume of Fluid (VOF) Method is used to model the interface between the gas and the liquid film. The non-Newtonian flow is modeled by the implementation of the Ostwald de Waele model. Surface tension is a function of the surfactant concentration. The VOF-Method allows the distribution of the concentration of the epithelial liquid layer at the surface to be traced in a transient manner. The simulations show the rupturing of the liquid film through the drop formation. Aerosol particles are ejected into the SA and do not collide with the walls. The quantity, the geometrical size as well as the velocity distributions of the generated aerosols are determined. The data presented in the paper provide the boundary conditions for future CFD analysis of the aerosol transport through the airways up to exhalation.