Biomedical Engineering Reference
In-Depth Information
between rows of obstacles, making it easier to enter the next opening. As a result,
the particular design of this device lessens the dependence of the cell velocity on
membrane viscosity.
10.4.2 Whole healthy blood
Next, we present simulation results for whole blood modelled as a suspension of
healthy RBCs using the two RBC models without changing the parameters that we
have established from single-cell measurements. We first consider flow in a tube in
order to assess flow resistance in microvessels, and subsequently, we focus on Cou-
ette flow in order to compare the predicted blood viscosity from rheometric mea-
surements.
10.4.2.1 Flow resistance
Here, we simulate blood flow in tubes of diameters ranging from 10
m. In
case of the MS-RBC model, it is important to model carefully the excluded volume
(EV) interactions among cells, which are often implemented through a repulsive
force between membrane vertices of different cells. A certain range (force cutoff
radius) of the repulsive interactions may impose a non-zero minimum allowed dis-
tance between neighboring RBC membranes, which will be called “screening dis-
tance” between membranes. The choice of a smaller cutoff radius may result in over-
lapping of cells, while a larger one would increase the screening distance between
cells, which may be unphysical and may strongly affect the results at high volume
fractions of RBCs. A better approach is to enforce EV interactions among cells by
employing reflections of RBC vertices on the membrane surfaces of other cells yield-
ing essentially a zero screening distance between two RBC surfaces. In addition, we
employ a
net repulsion
of RBCs from the wall by properly setting the repulsive force
coefficient between the wall particles and the cell vertices.
Fig. 10.15 shows plots of the apparent blood viscosity with respect to the plasma
viscosity. The apparent viscosity is defined as follows
μ
mto40
μ
η
app
=
πΔ
PD
4
P
is the
pressure difference,
Q
is the flow rate, and
L
is the length of the tube. It increases for
higher
H
t
values since higher cell crowding yields larger flow resistance. It is more
convenient to consider the relative apparent viscosity defined as
128
QL
,where
Δ
η
app
η
s
η
rel
=
,where
η
s
is the plasma viscosity. Fig. 10.15(a) shows the simulated
η
rel
values in compari-
son with the empirical fit to experiments [72] for the tube diameter range 10-40
m
and
H
t
values in the range 0.15-0.45. Excellent agreement between simulations and
experiments is obtained for the proper EV interactions for all cases tested. The pres-
sure gradients employed here are 2
μ
10
5
,1
10
5
, and 6
10
4
Pa
.
633
×
.
316
×
.
582
×
/
m
for tubes of diameters 10, 20, and 40
μ
m, respectively. In the case of low hematocrit
.
H
t
(e.g., 0
15) the velocity profiles closely follow parabolic curves in the near-wall
region. In the central region of the tube a substantial reduction in velocity is found for
all volume fractions in comparison with the parabolic profiles indicating a decrease
in the flow rate [73]. Fig.10.15(b) shows results from both the MS-RBC and LD-
RBC models for a wider range of tube diameters. The agreement is good between
