Biomedical Engineering Reference
In-Depth Information
cytometry and from the response of single RBC in shear flow. In all cases we run
corresponding DPD simulations in order to compare and match the experimentally
observed responses. In the following, we describe details of this procedure and we
also demonstrate that while the parameters can be estimated in a relatively narrow
regime, we can then predict accurately the single RBC mechanics, dynamics and
rheology over a much wider range of operating conditions.
10.3.1 Shear modulus using optical tweezers
To mimic the optical tweezers experiments of [9] a modelled RBC undergoes stretch-
ing by applying a stretching force on both ends of the cell. The total stretching force
f
M
is applied to
N
−
and
N
+
N
v
) along the negative and the
positive directions, respectively. These vertices cover a near-spherical area on the
RBC surface with
vertices (
N
−
=
N
+
=
ε
02 which corresponds to the contact diameter of the attached
silica bead with diameter 2
ε
=
0
.
m used in experiments [9]. Note that the viscous prop-
erties of the membrane and of the suspending medium do not affect final stretching
since the RBC response is measured after convergence to the equilibrium stretched
state is achieved for given force.
Fig. 10.7 (left) compares the simulated axial and transverse RBC diameters with
their experimental counterparts [9] for different coarse-graining levels starting from
the spectrin-level (
N
v
=
μ
500.
Excellent correspondence between simulations and experiments is achieved for
μ
0
=
27344) to the highly coarse-grained network of
N
v
=
N/m independently of the level of coarse-graining.
The small discrepancy between simulated and experimental transverse diameters is
probably a consequence of the optical measurements being performed from only
a single observation angle. Numerical simulations showed that RBCs subjected to
stretching tend to rotate in y-z plane, and therefore measurements from a single ob-
6
.
3
μ
N/m and
Y
=
18
.
9
μ
Experiment
Nv = 500
Nv = 1000
Nv = 3000
Nv = 9128
Nv = 27344
20
25
Experiment, healthy
Simulation (MS-RBC), healthy
Simulation (LD-RBC), healthy
Experiment, schizont
Simulation (MS-RBC), schizont
Simulation (LD-RBC), schizont
18
x
x
x
x
x
x
x
x
x
x
16
20
A
xia
l
14
D
x
A
x
x
12
15
x
x
x
10
x
8
x
10
x
x
x
x
x
x
x
x
x
x
x x
x
x
x
x
x
6
4
5
D
T
Transverse
2
0
0
0
50
100
150
200
0
50
100
150
200
force (pN)
force (pN)
Fig. 10.7.
MS-RBC (left): Stretching response of a healthy RBC for different coarse-graining lev-
els. MS-RBC vs. LD-RBC (right): Stretching response of a healthy RBC and a Pf-RBC (schizont
stage) with the experiments of [9].
D
A
and
D
T
refer to the axial and transverse diameters (from
[51, 61])
