Biomedical Engineering Reference
In-Depth Information
treading transition to higher shear rates. Fig. 10.10 (right) shows the average RBC
tank-treading angle and the swinging amplitude. The values are consistent with ex-
perimental data [14] and appear to be not very sensitive to the membrane viscosity.
Note that the swinging frequency is equal to twice the tank-treading frequency.
In conclusion, the RBC model accurately captures membrane dynamics in shear
flow, while the theoretical models can predict RBC dynamics
at most
qualitatively.
The theoretical models assume ellipsoidal RBC shape and a fixed (ellipsoidal) RBC
tank-treading path. Our simulations showed that a RBC is subject to deformations
along the tank-treading axis. In addition, modelled RBCs show substantial shape
deformations (buckling) in a wide range around the tumbling-to-tank-treading tran-
sition. A degree of these deformations depends on the F oppl-von Karman number
κ
k
c
,where
R
0
=
A
tot
0
defined as
YR
0
/
. As an example, if the RBC bend-
ing rigidity is increased by a factor of five, the aforementioned shape deformations
become considerably smaller, while if the RBC bending rigidity is increased by a
factor of ten, the shape deformations practically subside. The theoretical models do
not take the bending rigidity into consideration, while experimental data are not con-
clusive on this issue. This again raises the question about the magnitude of bending
rigidity of healthy RBCs since our simulations (TTC and RBC dynamics in shear
flow) indicate that the RBC bending rigidity may be several times higher than the
widely used value of
k
c
=
/
(
4
π
)
10
−
19
J
.
2
.
4
×
10.4 Validation
In the previous section we demonstrated how we can use experimental data from
single-cell measurements to extract the input parameters for the models, but also, to
partially validate the simulated biophysical behaviour of single RBCs. In this sec-
tion, we extend this validation further by comparing simulation results based on
the MS-RBC model as well as on the LD-RBC model with different experiments.
First, we consider data from microfluidic experiments in channels with very small
cross-sections, i.e., comparable to the smallest capillaries. We also compare with
experimental results from the dynamic response of RBCs going though properly mi-
crofabricated geometric constrictions. Subsequently, we present simulation results
for whole blood in terms of the flow resistance in tubes and compare against well
known experimental results. Finally, we demonstrate how these multiscale simula-
tions can be used as a “virtual rheometer” to obtain the human blood viscosity over
a wide range of shear rate values. This includes the low shear rate regime, where the
formation of rouleaux is shown to determine the strong non-Newtonian behaviour
of blood.
10.4.1 Single RBC: comparison with microfluidic experiments
Microfabrication techniques allow manufacturing of channels with dimensions com-
parable to the smallest blood vessels. In recent years, microfluidic experiments have
become popular in measuring properties of RBCs and other cells. Even though, at
