Biomedical Engineering Reference
In-Depth Information
4
Ht = 0.15
Ht = 0.3
Ht = 0.45
3.5
3.5
Ht = 45%
3
3
experiments
simulations
2.5
2.5
2
Ht = 30%
2
1.5
1.5
1
Experiment
Simulation (LD−RBC)
Simulation (MS−RBC)
0.5
1
0
10
0
10
1
10
2
10
3
0.5
0
5
10
15
20
25
30
35
40
45
50
Tube diameter (
m)
(a)
μ
(b)
μ
Tube diameter ( m)
Fig. 10.15.
Flow resistance in healthy blood: (a) Relative apparent viscosity compared with ex-
perimental data [72] for various hematocrit values and tube diameters. The inset plot is a snapshot
of RBCs in Poiseuille flow in a tube of a diameter
D
=
20μmat
H
t
=
0
.
45. (b) Comparison of
MS-RBC and LD-RBC models; the lines are the empirical correlation by Pries et al. [72] (from
[51, 61])
the models and the experimental data represented by an empirical fit; however, it is
clear that for vessels with diameter below 15
−
20 microns the LD-RBC model fails
as the membrane rheology becomes important, which the low-dimensional model
does not account for.
RBCs in Poiseuille flow migrate to the tube center forming a core in the flow. The
inset of Fig. 10.15 shows a sample snapshot of RBCs flowing in a tube of diameter
D
m. A RBC core formation is established with a thin plasma layer next to the
tube walls called the
cell-free
layer (CFL) [73]. The thickness of the CFL is directly
related to the Fahraeus and the Fahraeus-Lindqvist effects, both of which were ac-
curately captured by the DPD model, see [73]. To determine the CFL thickness we
computed the outer edge of the RBC core, which is similar to CFL measurements
in experiments [74, 75]. Fig. 10.16 shows a sample CFL edge from simulations for
H
t
=
=
20
μ
m and local CFL thickness distribution, which is constructed
from a set of discrete local measurements of CFL thickness taken every 0
0
.
45 and
D
=
20
μ
m along
the
x
(flow) direction. The fluid viscosity of the CFL region is much smaller than that
of the tube core populated with RBCs providing an effective lubrication for the core
to flow.
.
5
μ
10.4.2.2 Aggregation and Rouleaux formation
Here, we present simulations in a wide range of shear rate values including the
low shear rate regime with and without the aggregation models described in
Sects. 10.2.3.4 and 10.2.4.2. The viscosity was derived from simulations of plane
Couette flow using the Lees-Edwards periodic boundary conditions in which the
shear rate and the density of cells were verified to be spatially uniform. The ex-
perimental viscosities of well-prepared erythrocytes without rouleaux and of whole
blood were measured at hematocrit 45 % and at temperature 37
◦
C by [76, 77, 78] us-
ing rotational Couette viscometers. At the same conditions for both the MS-RBC and
