Airway Surface Liquid and Respiratory Mucus - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 780

Table 12.7. Simulation domain of the airway surface liquid constituted by a periciliary fluid and
a mucus layer (Source: [ 1594 ]).

Subdomain Features

Ciliated epithelium Rigid, straight, smooth interface

Periciliary liquid Cell-surface-anchored mucins immersed in water

Newtonian fluid
Constant physical properties
(mass density, dynamic viscosity)
Layer thickness 5 m

Mucus layer Mucin mesh

Non-Newtonian gel
Variable physical properties
(mass density, dynamic viscosity)
Layer thickness 2.5

m

Air Convective transport

Oscillatory flow (frequency 0.20-0.25 Hz)
Incompressible, Newtonian fluid

12.7 Mucus Transport Modeling

Numerical investigations have been carried out on interactions between mucus
motion and air flow at the microscopic scale [ 1592 ]. Mucus displacement is driven
by respiratory epithelium cilia, but not markedly by air stream.
A quasi-steady Stokes flow of fluid with spatially variable viscosity has been sim-
ulated over a moving boundary [ 1593 ]. A second-order elliptic partial differential
equation is non-linearly coupled to a first-order hyperbolic equation that describes
the cilium beating, which takes into account the actin polymerization via a model of
elastic beams of variable modulus.
The simulation domain of the airway surface liquid is defined in Table 12.7 .Ina
preliminary study, 2 cilia states are only considered: a rest (without contact with the
mucus layer) and an erected state, partly penetrating the mucus layer. In the former,
the cilium lies parallel to the airway wall, immersed in the periciliary fluid, pointing
in the direction of mucus flow. A cilium is modeled by a succession of constant
radius spheres separated by a constant distance. When the cilium is straight, all the
sphere centers are aligned. A random process is used to provide cilium positions at
rest. A stiffening mechanism based on angle between 3 successive spheres along the
cilium models the cilium beating cycle. Model parameters and their values are listed
in Table 12.8 . In the preliminary work, mucus is assumed to be Newtonian (constant
dynamic viscosity

1) and the air-mucus interface is flat.
From a macroscopic point of view, mucus is a thixotropic gel that behaves as:
(1) an elastic solid at low shear and (2) a viscous liquid at high shear. The dynamical

μ =