Biomedical Engineering Reference
In-Depth Information
is terminated when a bond is formed. Finally, the forces of all remaining bonds are
calculated and applied.
Note that this algorithm permits only a single bond per ligand, while receptors
may establish several bonds if several ligands are free within their reaction radius.
This provides an additional capability for the adhesive dynamics model compared
with that employing one-to-one interactions between receptors and ligands. Also,
this assumption appears to furnish a more realistic representation of adhesive inter-
actions of Pf-RBCs with a coated surface. Pf-RBCs display a number of parasitic
nanometer-size protrusions or knobs on the membrane surface [55, 56, 57], where
receptors that mediate RBC adherence are clustered.
10.2.4 Low-Dimensional RBC (LD-RBC) model
Here, we will employ the DPD formulation presented in Sect. 10.2.2. The LD-RBC
is modelled as a ring of 10 colloidal DPD particles connected by wormlike chain
(WLC) springs. The intrinsic size of colloidal particle is determined by the radius of
the sphere effectively occupied by a single DPD particle [46], which is defined by
the distribution of its surrounding solvent particles.
To construct the cell model, however, we allow particles in the same RBC to over-
lap, i.e., the colloidal particles in the same cell still interact with each other through
the soft standard DPD linear force (see Eq. (10.2)). The radius,
a
, of each colloidal
particle is chosen to be equal to the radius of the ring, and hence the configuration
of RBC is approximately a closed-torus as shown in Fig. 10.4.
The WLC spring force interconnecting all cell particles in each RBC is given by
r
ij
l
m
k
B
T
p
1
1
4
+
F
WLC
=
2
−
,
(10.30)
r
ij
l
m
)
4
(
1
−
where
r
ij
is the distance between two neighboring beads,
p
is the persistence length,
and
l
m
is the maximum allowed length for each spring. Since the cell has also bend-
Fig. 10.4.
LD-RBC: A sketch of the low-dimensional closed-torus like RBC model
