ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

dimensionless frequency . With the above definitions, the dimensionless advectiondiffusion-reaction
equation at constant temperature and low density of ligands can be
written [12]:
At the cells surface (0 < x < 1, y = 0), we considered a first order two ways reaction for
ligands binding the receptors on the cell membrane [13]:
where B is the surface concentration of bound receptors normalized by total number of
receptors (RT), is the dimensionless association rate, K is the dimensionless binding
affinity.
We considered ligands as autologous and secreted at a constant rate. Therefore,
boundary conditions on the reactive surface were defined as:
where is the dimensionless secretion rate.
(2)
(3)
, for (4)
The boundary conditions at the chamber entrance, downstream end and channel ceiling,
were respectively given by [14]:
, , (5)
This model was implemented in COMSOL 4.2a (COMSOL Inc, Palo Alto, USA).
Physiological constant values were used as input data [9, 15, 16]:
(L = 6.1mm, h = 0.25 mm), (V = 4.9 mm/s), D = 100 µm 2 /s, , =
20 nM (K = 100), = 3 10 4 M -1 s -1 ( 3.75 10 -3 ), CT = 2 10 -7 mol/m 3 , = 15.7 10 -3 .
The stationary no-flow (Pe = 0) solution for infinite epithelia (L = ∞) was taken as
initial condition and set as reference state:
For the oscillatory flow, four values of frequency were considered: 0.1, 0.5, 1 and 2 Hz.
(6)
(7)
(8)