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Cell Adhesion and Detachment in Shear Flow 219
Table 1. Simulation parameters.
Parameters Definition simulation value
R cell radius 4.0–5.0 µm
N r receptor number 780
N L ligand density 10 6 –10 8 /cm
λ equilibrium bond length 0.2 µm
σ spring constant 0.016 dyne/cm
µ viscosity 0.01–0.014 g/cm·s
ρ fluid density 1.0 g/cm 2
U max shear rate 20–80/s
H c cut-off length 0.4 µm
T temperature 310 K
kf 0 forward reaction rate 100.0/s
kr 0 reverse reaction rate 10.0/s
r 0 reactive compliance 0.02 µm
with the long semi-axis r a equal to 0.5 and the short semi-axis r b equal to
0.4. The velocity boundary conditions are as follows: a given constant on the
top boundary, zero on the bottom boundary, and periodicity in the horizontal
direction. The fluid and cells are at rest and the cells are in the contact region
initially (see Fig. 6(a)). We assume that the densities of fluid and cells are
1 g/cm 3 . The mesh size h for the flow field is 1/48 and the time step △t is
0.001 (unit: 0.1 second). The parameters used in the simulations are given in
Table 1.
We observed the simulations up to t = 100 (10 s), long enough for the flow
to be fully developed. The simulations were conducted at different shear rates
and dynamical viscosities, and the results are summarized in Table 2. From
the table, we can see, no cells were detached from the wall by the observed
time when the shear rate is 20/s for the dynamical viscosity of 0.01 g/cm-s;
while the detachment percentage increases from 10% to 40% when the shear
rate increases from 30/s to 40/s. All the 20 cells were detached from the wall
when the shear rate is greater than 80/s. Figure 5 shows the effect of shear
rate on cell detachment. This observation qualitatively agrees with the in
vitro experiment [SKE + 99]. We also observed that the detachment percentage
increases from 10% to 35% when the dynamical viscosity is increased from 0.01
to 0.014 (g/cm-s).
Figure 6 shows the snapshots of positions of 20 cells at t =0,5,5.35,
6.06, 9.49, and 10 (s), for the simulation with the dynamical viscosity equal
to 0.01 (g/cm-s) and the shear rate of 30 (/s). The snapshots quite clearly
depict the process of cell detachment from the wall. All the cells adhered to
the wall at t = 5 s; one cell was about to be detached at t =5.35 s; one cell
was completely detached from the layer at t =6.06 s. We found that during
the early stage of detachment the percentage of the detached cells is highly