Continuum-kinetic-microscopic model of lung clearance due to core-annular fluid entrainment

Abstract

The human lung is protected against aspirated infectious and toxic agents by a thin liquid layer lining the interior of the airways. This airway surface liquid is a bilayer composed of a viscoelastic mucus layer supported by a fluid film known as the periciliary liquid. The viscoelastic behavior of the mucus layer is principally due to long-chain polymers known as mucins. The airway surface liquid is cleared from the lung by ciliary transport, surface tension gradients, and airflow shear forces. This work presents a multiscale model of the effect of airflow shear forces, as exerted by tidal breathing and cough, upon clearance. The composition of the mucus layer is complex and variable in time. To avoid the restrictions imposed by adopting a viscoelastic flow model of limited validity, a multiscale computational model is introduced in which the continuum-level properties of the airway surface liquid are determined by microscopic simulation of long-chain polymers. A bridge between microscopic and continuum levels is constructed through a kinetic-level probability density function describing polymer chain configurations. The overall multiscale framework is especially suited to biological problems due to the flexibility afforded in specifying microscopic constituents, and examining the effects of various constituents upon overall mucus transport at the continuum scale.

Figures

Fig. 1

Waves induced in an annular liquid layer by core air flow at low, 30 l/m (top) and high, 60 l/m (bottom) volume flow rates in a vertical tube of 1 cm diameter. At the low flow rate ripples form on the surface accumulating into an advancing front that transports mass. At the high flow rate irregular waves are observed. (Photographs courtesy of Jeffrey Oleander, Roberto Camassa, UNC Joint Applied Mathematics & Marine Science Fluids Lab)

Fig. 2

Schematic of complex, polymeric structure of a typical mucin

Fig. 3

Schematic of overall mucus-air model. Cross-linkages are formed between micelles arising from mucins modeled as telechelic chains. Hydrophobic ends denoted by red disks, water-soluble middle segment denoted by a line. Force in the network is preponderently carried by the cross-links (thick, green lines). Some of the chains form closed loops onto the same network node and do not carry any appreciable network load. Other chains have a dangling free end that potentially can form additional cross linkages. The friction coefficient of the solvent with free nodes at the end of a dangling chain is ζfree, that with the larger micelle nodes is ζnode, ζnode > ζfree. The mucins are surrounded by water solvent molecules (blue disks). The mucus layer forms an interface with an adjacent air region (black circles).

Fig. 4

Lattice sites, continuum control volumes and directions D of D2Q9 lattice Boltzmann model.

Fig. 5

Branch and junction segments along an airway.

Fig. 6

Face (F) and volume centered (C) quantities in an airway segment Sa,b along branch Ba, and a junction Jc. Rectangles show extent of lattice used in kinetic-level simulations.

Fig. 7

Succession of steps in multiscale computation of airway core-annular flow to advance continuum-level parameters Q from time tn to tn+1.

Fig. 8

Four-generation Hofman-Koblinger airway [20].

Fig. 9

Air-only flow in the vicinity of the first airway junction (carina)

Fig. 10

Air-only flow in airway generations 2–4. Strong secondary flows are induced by the junctions.

Fig. 11

Sequence of interface shaped between core gas and annular mucus flows, at time interval ΔT = 0.2 sec during peak expiration, V̇ = 35 liter/min flow rate, small active mucin link lifetime.

Fig. 12

Sequence of interface shapes as in Fig. 11, but with long active mucin link lifetime.

Fig. 13

Sequence of interface shapes at high flow rates.