Biomedical Engineering Reference
In-Depth Information
bonds over the contact area at some instance of time, a Pf-RBC may be pulled to one
side. In addition, the hydrodynamic force on the RBC may be non-zero in
z
direction,
since the cell is not symmetric due to the local deformations shown in Fig. 10.21. The
RBC contact area in Fig. 10.23(b) is correlated with its displacement and velocity in
Fig. 10.22. Minima in the contact area coincide with maxima in the RBC velocity
corresponding to the stage of fast cell flipping from its one side to the other. The
cell contact area remains within the range of 10-50
m
2
, while the average value is
μ
m
2
.
To investigate the dependence of RBC adhesive dynamics on WSS, the velocity
of the upper plate is changed. Note that the shear rate is altered at the same time.
However, the WSS appears to be a key parameter which governs RBC adhesive
dynamics, since adhered RBCs are driven by fluid stresses and roll along the wall
with a much smaller velocity than that of the shear flow.
Several initial simulations with a varying WSS and other fixed parameters re-
vealed that a Pf-RBC may exhibit firm adhesion at a WSS lower than 0
.
equal to 38
6
μ
317
Pa
for
the case described above and can completely detach from the wall at higher WSS.
At low WSS, adhesion forces are strong enough to counteract the stress exerted on
the cell by the flow resulting in its firm sticking to the lower wall. On the contrary,
at high WSS existing bonds do not provide sufficiently strong adhesive interactions
which yields RBC detachment from the wall. RBC visualizations showed that its de-
tachment at high WSS occurs during the relatively fast motion of RBC flipping, since
the contact area at that step corresponds to its minimum. However, in experiments
[81] Pf-RBCs which moved on a surface coated with the purified ICAM-1 showed
persistent and stable rolling over long observation times and for a wide range of
WSS between 0
.
2
Pa
and 2
Pa
. This suggests that there must be a mechanism which
stabilizes rolling of infected RBCs at high WSS. This fact is not surprising since, for
example, leukocyte adhesion can be actively regulated depending on flow conditions
and biochemical constituents present [83, 84].
To stabilize RBC binding at high WSS we introduce adaptivity of the bond spring
constant (
k
s
) see Eq. (10.29). As the first approximation we assume a linear depen-
dence of
k
s
on the WSS, such that
k
s
is increased or decreased proportionally to an
increase or decrease in the WSS. Fig. 10.24 presents the average rolling velocity of
a Pf-RBC in comparison with experiments of cell rolling on a surface coated with
purified ICAM-1 [81]. The simulated average velocities for the “linear” case show
a near-linear dependence on the WSS and are in good agreement with experiments
up to some WSS value; the simulated value remains between the 10th and the 90th
percentiles found in experiments. However, the observed discrepancy at the highest
simulated WSS suggests that a further strengthening of cell-wall bond interactions
may be required. The dependence of the RBC rolling velocity on WSS found in ex-
periments is clearly non-linear. Therefore, the assumption of linear dependence of
k
s
on the WSS is likely to be an oversimplification. The simulation results marked
“non-linear” in Fig. 10.24 adopt a non-linear dependence of
k
s
on the WSS, and yield
excellent agreement with experiments.
In addition, there may be a change in bond association and dissociation kinetics
with WSS which would be able to aid in rolling stabilization of infected RBCs at
.
