41
cell was transported from the V-shape structure to the chamber, the nDEP force was generated by
applying an electrical signal to the thick electrodes, and the cell stopped at an equilibrium position.
Figure 2.21 shows a HeLa cell capture dynamic process.
(a) (b) (c)
Figure 2.21: Single-cell capture, release, and trap experiments: (a) capture of one HeLa cell; (b) the
captured cell release by back ow; and (c) cell was kept by nDEP force.
2.6.3 3D ROTATION EXPERIMENT
3D cell rotation about X/Y/Z-axis can be achieved by applying dierent electrical signal congu-
rations.
(a) In-plane rotation mode
Figure 2.22 shows a HeLa cell rotating clockwise about the Z-axis at 270°/s (Vp-p = 6 V, f = 600
kHz). After changing the phase shift sequence of the four electrodes, the direction of rotation of
the cell was reversed, and the cell rotated counterclockwise about Z-axis.
(a)
(b)
Figure 2.22: A HeLa cell rotates about the Z-axis (Vp-p = 6 V, f = 600 kHz).
2.6 SINGLECELL 3D ROTATION EXPERIMENT
42
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
(b) Out-of-plane rotation mode
Figure 2.23 shows a HeLa cell rotating about Y-axis (Vp-p = 6 V, f = 600 kHz). By changing the
phase shift sequence of the electrical signals, the direction of rotation of the cells was changed.
(a)
(b)
Figure 2.23: A HeLa cells rotated about the Y-axis (Vp-p = 6 V, f = 600 kHz).
(c) X/Y/Z axis rotation
Figure 2.24 shows a 3D rotation of a HeLa cell (Vp-p = 6 V, f = 600 kHz). First, it rotated about
Z-axis, and then about X-axis, and nally about Y-axis.
(a)
(b)
(c)
Figure 2.24: A HeLa cell rotated about X/Y/Z-axis.
43
(d) Dierent rotation modes about X-axis when cells are inside and outside the chamber
When electrodes are congured to rotate the cell about X-axis, the cell will have dierent rotation
modes inside and outside the chamber (Figure 2.25).
θ=4 /3
θ=0
θ=0
X
B
θ=4 /3
θ=2 /3
Figure 2.25: Cell rotation state in dierent regions when cell rotates about the X-axis
When the cell ows to the chamber and has not yet reached the chamber, at the boundary
of bottom electrode, the cell rst rotates about Z-axis. When the cell ows into the chamber, the
rotation state of the cell is switched from in-plane rotation to out-of-plane rotation about X-axis.
is result can be conrmed by simulation analysis. Under the conguration of the out-of-plane
rotation about X-axis, outside the left boundary of the bottom electrode is in-plane rotational elec-
tric eld (Figure 2.26(a)). Figure 2.26(b) shows that one B cell rotating about Z-axis and X-axis
(Vp-p = 6 V, f = 600 kHz) across the boundary of bottom electrode.
(b)(a)
Surface: Voltage (V) Arrow: Electric Field (V/m)
160
120
80
40
0
-40
-80
-120
-160
10
8
6
4
2
0
-2
-4
-6
-8
-10
-200 200-100 1000
In-Plane RotationOut-of-Plane Rotation
Figure 2.26: e rotation state of cells at the boundary of bottom electrode under the signal congura-
tion for rotation about X-axis; (a) electric eld simulation; and (b) B cell rotation experiment.
2.6 SINGLECELL 3D ROTATION EXPERIMENT
44
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
After exiting the electrode chamber, the cell can also rotate in the gap between the thick
electrodes and the bottom electrode. If the cell is in a conical region (as shown by the dashed boxed
area in Figure 2.25), it will make out-of-plane rotation about the axis perpendicular to the surface
of the thick electrodes. Figure 2.27 shows that one HeLa cell adsorbed on the electrode surface
under pDEP force (Vp-p = 6 V, f = 2 MHz) and doing out-of-plane rotation about the axis per-
pendicular to the electrode surface.
t=0 s
10 µm
t=0.2 s t=0.4 s t=0.6 s
Figure 2.27: Bottom electrode edge cone area cell rotation state.
After escaping from the conical zone, between the bottom electrode and the thick electrode
(as shown in Figure 2.25), the cells will resume rotation about the X-axis. ere would be two ro-
tation modes, depending on pDEP or nDEP signals applied. Under pDEP, the cell is adsorbed on
the surface of the thick electrode and rotate about the X-axis. Figure 2.28(a) is the force model of
single cell under pDEP force. Figure 2.28(b) shows that a HeLa cell adsorbed on the surface of the
electrode (Vp-p = 6 V, f = 1 MHz) and rotating about the X-axis at speed of ~ 120°/s. Switching
the phase shift sequence of the electrode signals, the cell rotation direction was switched to reverse
rotation about the X-axis.
CPDMS
140
120
100
80
60
40
20
0
3
2.5
2
1.5
1
0.5
×10
5
Surface: Electric Field (V/m)
-100 -50 0
(a) (b)
Figure 2.28: e rotation of cells between the bottom electrode and the thick electrode under pDEP
force: (a) simulated force analysis; and (b) HeLa cells rotation around the X-axis under pDEP force.
45
Under nDEP, the cell between the two electrodes is repelled. Figure 2.29(a,b) is the force
model and simulation.
e horizontal force analysis yields
F
ITO
∙ sin θ
1
= F
C-PDMS
∙ sin θ
2
. (2-2)
e DEP force generated by ITO and C-PDMS is calculated by Equation (1-10):
2πR
cell
3
ε
m
Re[K
CM
]∇E
2
I
TO
sin θ
1
= 2πR
cell
3
ε
m
Re[K
CM
]∇E
2
C-PDMS
sin θ
2
. (2-3)
∇E
2
I
TO
x – ∇E
2
C-PDMS
x = 0. (2-4)
e left side of the equation is actually the component ∇E
2
in the horizontal direction:
∇E
2
∙ x = 0. (2-5)
Also in the vertical direction, the cell is balanced:
F
ITO
∙cos θ
1
+ F
C-PDMS
∙ cos θ
2
+ F
buoyancy
= G, (2-6)
where G is the cell gravity and F
buoyancy
is the buoyancy of the cells. Simplifying the above formula
produces
∇E
2
I
TO
∙ z + ∇E
2
C-PDMS
∙ z =
2(ρ
cell
– ρ
med
)g
, (2-7)
∇E
2
∙ z =
2(ρ
cell
– ρ
med
)g
. (2-8)
Substituting Vp-p = 10 V f = 1 MHz, Re[K
CM
] = –0.06, ε
m
= 60ε
0
, ρ
cell
= 1.077 × 10
3
kg/m
3
, ρ
med
= 1.017 × 10
3
kg/m
3
into Equation (2-8) yields
∇E
2
∙ z = 1.35 × 10
13
V
2
/m
3
.
e distribution of the DEP force in X axis and Z axis direction is plotted through simula-
tion analysis, and the distribution curves satisfying Equations (2-3) and (2-7) are shown in Figures
2.29(c) and 2.29(d). e intersection of the two curves in Figure 2.29(e) is the nal equilibrium
position of the cell. e simulation results show that the cell equilibrium point is located at coor-
dinates (36.3 µm, 59.5 µm).
3ε
m
Re[K
CM
]
3ε
m
Re[K
CM
]
2.6 SINGLECELL 3D ROTATION EXPERIMENT
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