Fig 1.
(A) Schematic representation of a Human Bronchial Epithelial (HBE) cell culture. (B) HBE cell culture geometry. (C) combination DIC with fluorescent labeled mucus of mouse airway section. Scale bar 7 um. Image courtesy of Camille Ehre, UNC Marsico Lung Institute. (D) HBE cell culture in cylindrical coordinates and reduction from 3D cylinder to 2D rectangular region based on the axisymmetric assumption.
Fig 2.
Demonstration of rotational mucus transport in HBE cell cultures.
(A) Traces of 1 mm fluorescent micro-spheres at the culture surface from a 5 second time lapse exposure. (B) Linear velocities of the particles versus distance from the center of rotation. Data extrapolated from [25].
Fig 3.
(A) Experimental data of storage (G’) and loss (G”) moduli for 2.5 wt% HBE mucus across a frequency range (symbols), together with the corresponding fit to 5 UCM modes (lines). (B) Viscosity vs. shear rate data (symbols) for 2.5 wt% HBE mucus and corresponding fit to a sum of 5 Giesekus modes (line). The curve shown is the best fit under the condition 0 ≤ α ≤ 0.5. Model parameters are given in Table 1. Data courtesy of Jeremy Cribb and David Hill, UNC-CH.
Table 1.
Parameters for five-mode Giesekus model.
Table 2.
Imposed boundary conditions.
Fig 4.
The oscillatory driving condition f(t) imposed at the bottom plate to mimic cilia power and return strokes and given by Eq (5).
Table 3.
The value used for the angular velocity is the same as the largest angular velocity of the oscillatory driving condition given by Eq (5).
Fig 5.
Transient snapshots of the flow field for a Newtonian fluid.
The velocity field in the plot is the secondary flow (ur vs uz) and the color map in the background is the primary flow (uθ). Note that the length scales in these plots differ by one order of magnitude, as z is given in microns and r in millimeters. Geometric parameters used in this simulation are given in Table 3. The imposed driving condition for swirling flow is ω0 = 0.0157 Rad/s.
Fig 6.
Transient snapshots of the flow field for a single mode UCM model.
Times are selected to capture the formation and evolution of a vortex in the upper right hand side of the domain. Geometric and model parameters used in this simulation are given in Table 3. The imposed driving condition for swirling flow is ω0 = 0.0157 Rad/s.
Fig 7.
Transient snapshots of the flow field for a single mode Giesekus model with mobility parameter α = 0.3.
Geometric and model parameters used in this simulation are given in Table 3. The imposed driving condition for swirling flow is ω0 = 0.0157 Rad/s.
Fig 8.
Transient snapshots of the flow field for a 5-mode Giesekus model with parameters specified in Table 1.
Geometric and other model parameters used in this simulation are given in Table 3. The imposed driving condition for swirling flow is ω0 = 0.0157 Rad/s.
Fig 9.
Steady state surface shape is shown for the different models used in this study.
Geometric and model parameters used in this simulation are given in Table 3. The imposed driving condition for swirling flow is ω0 = 0.0157 Rad/s.
Fig 10.
Mass transport flux rate across the θ = 0 plane for the different models used in this study.
Calculation of the mass flux is discussed in the text. Parameters in this simulation correspond to those used in Fig 9.
Fig 11.
Velocity time series for a 5-mode Giesekus model.
Parameters are given in Tables 1–3 and the oscillatory driving condition is given by Eq (5).
Fig 12.
Mass transport flux rate across the θ = 0 plane.
The oscillatory driving condition is given by Eq (5) and model parameters are given in Tables 1–3.
Fig 13.
Results for a 5-mode Giesekus model simulation.
(A) Displacement along the angular direction at the edge of the cell culture at three different heights, (B) angular velocity at the edge of the cell culture as a function of height, (C) comparison of resulting velocity profiles with those reported in [14]. Parameters are given in Tables 1–3.
Fig 14.
(A) shear stress vs shear rate and (B) shear stress vs shear strain at different positions of the cell culture.
Fig 15.
(A) Storage modulus G′, and (B) loss modulus G″, everywhere in the cell culture for a 5-mode Giesekus model. Note that since this is considered to be in the linear regime, this is equivalent to a 5-mode UCM model.
Fig 16.
(A) shear strain and(B) shear stress across the gap at r = 0.5R with R = 5 mm. The aspect ratio of the mucus layer is 100, as compared to Fig 15 where the aspect ratio is 200.
Fig 17.
LAOS analysis for nonlinear viscoelasticity.
Values are given for r = 0.4R and z = 0.4H with R = 5 mm. Fig adapted from output of MITlaos software [58].
Fig 18.
Third harmonic Chebyshev coefficients.
(A) e3 (elastic stress) and (B) υ3 (viscous stress) at r = 0.5R and h = 0.5H for different mean driving velocities (uθ) and aspect ratio (R/H).
Fig 19.
Initial distribution of drug concentration at the air-mucus interface.
The distribution is shown in red. (A) Disk of radius 1mm and (B) strip whose width varying as a function of the radius: 2πr/100. (C) Area to measure absorption at the bottom plate.
Fig 20.
The percentages of the drug concentration absorbed at the bottom plate on the outer section exterior to the domain of initial concentration (Fig 19A) versus Peclet number. (B) The time it takes for 95% of the drug concentration deposited at the surface in a small disk at the center (Fig 19A) to be absorbed on the outer section at the bottom plate versus Peclet number Pe.
Fig 21.
Percentage of a drug concentration deposited at the surface in the rectangular domain in Fig 19B that is absorbed on the circular sector in Fig 19C at the bottom plate vs. Peclet number.