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 dicult to measure.
erefore, the cell area-specic membrane capacitance C
mem
=
ε
mem
and the cell area-specic 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[ ]
m
CM
. (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