48
2. THICK-ELECTRODE DEP FOR SINGLE-CELL 3D ROTATION
1,500
1,000
500
0
1,000
800
600
400
200
0
(a) (b)
575.5 6.56
Log 10 (f)
5 5.5 6
Log 10 (f)
6.5
Experiment
Fitting Curve
Experiment
Fitting Curve
Rotation Speed (°/sec)
Rotation Speed (°/sec)
Figure 2.32: Relationship between rotation speed and frequency:; (a) in-plane rotation; and (b) out-
of-plane rotation.
2.7 CELLULAR ELECTRICAL PROPERTY ANALYSIS
2.7.1 PRINCIPLES OF CELLULAR ELECTRICAL PARAMETER
MEASUREMENT
Cellular electrical properties are often used to describe cell viability, growth, and identication of
dierent cell types. Electrical parameters are closely related to the structure and chemical composi-
tion of cells, and their physiological functions can be explored by studying the electrical properties.
Quantitative analysis of cellular electrical parameters can reect the dielectric properties of cells and
can serve as cell markers. Commonly used cell electrical parameters include the permittivity and
conductivity of cell membrane, the permittivity and conductivity of cytoplasm.
Generally, a cell is considered as a single-shell model [168, 169]. e cell is mainly composed
of cell membrane and cytoplasm. Assuming that the internal structure of the cytoplasm is uniform,
the cell can be equivalent to a single-shell model, as shown in Figure 2.33.
d
R
cell
ε
mem,
σ
mem
ε
c,
σ
c
ε
cyto,
σ
cyto
Figure 2.33: Single-shell model and equivalent model.
49
e equivalent cell complex permittivity is
ε
c
*
= ε
*
m
em
(2-9)
where R is the radius of the cell and d is the thickness of cell membrane. ε
*
c yto
and ε
*
m e m
are the
complex permittivity of the cytoplasm and membrane, respectively. ε
*
c yto
= ε
cyto
j
σ
cyto
, ε
*
mem
= ε
mem
j
σ
mem
; ε
cyto
and σ
cyto
are the permittivity and conductivity of the cytoplasm, ε
mem
and σ
mem
are
the permittivity and conductivity of the membrane, respectively, and ω are the angular frequencies
of the signals.
However, the thickness of cell membrane is generally 8‒20 nm, which is dicult to measure.
erefore, the cell area-specic membrane capacitance C
mem
=
ε
mem
and the cell area-specic mem-
brane conductivity G
mem
=
σ
mem
are used instead for cell membrane permittivity and conductivity.
For most mammalian cells, the thickness of the cell membrane is generally much smaller
than the cell radius, and its complex permittivity. Equation (2-9) can be equivalent to
ε
*
c
= C
*
m em
R
cell
ε
*
c yto
. (2-10)
When the cell does rotation motion in solution, Stokes torque can be expressed as
Γ
f
= 8πηΩR
cell
3
, (2-11)
where Ω is the angular velocity of rotation and η is the viscosity of the solution.
When the DEP torque and the Stokes torque are balanced, the cell does uniform rotation
ROT f

. (2-12)
e angular velocity can be expressed as:
2
Im[ ]
2
m
CM
KE

. (2-13)
e typical electro-rotation method of measuring cell dielectric parameters (ε
*
m e m
and ε
*
c
yto
)
is to measure cell rotation spectrum and then t the dielectric parameters of the cell model so that
the theoretical electro-rotation spectrum (Ω
theory
(ω
i
)) is as close as possible to the experimental
electro-rotation spectrum Ω
exp
(ω
i
):
min
i
[Ω
exp
(ω
i
) – Ω
theory
(ω
i
)]
2
. (2-14)
R
cell
R
cell
-d
3
+2
R
cell
R
cell
-d
3
ε
c
*
yto
ε
*
m
em
ε
c
*
yto
+ 2ε
*
m
em
ε
c
*
yto
ε
*
m
em
ε
c
*
yto
+ 2ε
*
m
em
ω
ω
d
d
R
cell
C
*
m em
+ ε
*
c yto
2.7 CELLULAR ELECTRICAL PROPERTY ANALYSIS
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