Biomedical Engineering Reference
In-Depth Information
t=0.1
t=10
t=20
1
0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
t=30
t=40
t=50
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
t=60
t=70
t=80
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Fig. 3
Snapshots of cell activation and subsequent movement at t
D
0:1;
;80. Tangential
anchoring energy is enforced in the diffuse interface between the membrane and cortical layer
with (˛
1
D
0:1;˛
2
D
0). The cell migrates to the direction where the cortex lay is activated
We first simulate the cell movement under the influence of local activation of
the nematic phase in the cortical layer without explicitly enforcing an anchoring
boundary condition at the membrane (the diffuse interface). The activation affects
both the membrane and the interface between the cortical layer and the interior
cytoplasma/cytosol region. Both outward and inward protrusion of the cortical layer
are shown in Fig.
2
. We then repeat the simulation with the same set of model
parameters while allowing for tangential anchoring energy at the membrane. The
protrusion is reduced in magnitude. However, the inward invasion nearly disappears
while the cell membrane bulges slightly on both sides of the prominent protrusion.
This is depicted in Fig.
3
with a few selected snapshots. In the third numerical
experiment, we impose the tangential anchoring condition at the membrane with
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