Biomedical Engineering Reference
In-Depth Information
Fig. 10.5.
LD-RBC shape evolution at different
N
c
(number of particles in LD-RBC model) and
stretching forces
vectors of two RBCs with their center line. The RBC normal vector is defined as
=
∑
v
k
×
v
k
+
1
,
v
k
=
x
k
−
.
n
c
x
c
(10.32)
N
c
Here,
x
k
is the position of the
k
th particle in each RBC,
x
c
is the position of the
center of mass, and
N
c
is the number of particles in each RBC. The center line
v
ci j
of
two RBCs (cell
i
and cell
j
)isdefinedas
x
ci
−
x
cj
. The angle formed by the normal
vector of one cell with the center line is determined by their dot product
n
ci
n
ci
·
v
ci j
d
i
=
v
ci j
.
(10.33)
The Morse interaction is turned on if
d
i
>
d
c
and
d
j
>
d
c
, otherwise, it is kept off.
(
π
/
)
The critical value,
d
c
, is chosen to be equal to
cos
4
, i.e., the critical angle (
θ
c
)
to turn on/off the aggregation interaction is
π
/
4. This value is found to be suitable
to induce rouleaux formation, but exclude the disordered aggregation. The proposed
aggregation algorithm can be further illustrated by a sketch in Fig. 10.6, where the
aggregation between two neighbor RBCs is decided to be on/off according to their
relative orientation.
10.2.5 Scaling of model and physical units
The dimensionless constants and variables in the DPD model must be scaled with
physical units. The superscript
M
denotes that a quantity is in “model” units, while
P
identifies physical units (SI units). We define the length scale as follows
D
0
D
0
r
M
=
m
,
(10.34)
