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Hybrimune Hybridoma Production System
Publication 015-1010191 Rev 4.0 • www.btxonline.com
As
a / b
gets small, the gap gets large and
∇
E
2
gets small and
V
o
must increase to compensate. As
a / b
approaches 1 the gap gets
smaller and
∇
E
2
gets large and less voltage is required. However,
as the gap decreases so does the volume. Increasing the chamber
height to hold volume constant has practical limits. It becomes
more difficult to maintain a homogeneous cell suspension.
A simulation of
∇
E
2
and the complete force equation and has
been used to define the optimum radius of the inner electrode
and the outer electrode in the BTX Fusion chamber to provide the
optimum combination of parameters to:
1. Have a quasi-uniform force on the cells in the gap
2. Maximize volume
3. Minimize voltage required
Figure 14: Chamber Definitions
∇
E
2
is the characteristic of the chamber used
The character
∇
is the mathematical operator to differentiate with
respect to spatial volume. It is important to note that the E is the
electric field vector and the electric field intensity is squared. Thus
the force on the cell is always in one direction; the force does not
reverse direction when a sine wave voltage waveform goes from
plus to minus. If the electric field is uniform then:
∇
E
2
=
0
Thus with uniform electric fields, such as those produced in
a cuvette (parallel plate), the force is zero. There have been
publications claiming to have fused cells in a cuvette.
The geometry of the chamber and the cell radius are the two major
elements that determine the force on the cells. Non-uniform fields
can be produced in a number of ways: by two parallel wires, by a
wire and a plate, etc. The optimum chamber is two coaxial cylinders
called a coaxial chamber. The mathematical model of a coaxial
chamber is given by the following (see Pohl). Chamber dimension
definitions are given in Figure 14:
V
o
= The voltage applied from the inner electrode to
the outer electrode
a
= The radius of the outside of inner electrode
b
= The radius of the inside of the outer electrode
a / b
= Always less than 1
r
g
= The variable radial distance in between a and b.
V = V
o
ln [
r
g
/ b
]
ln [
a / b
]
E
r
=
V
o
r
g
ln [
a / b
]
V
varies with
r
g
the radial
position from a to b in the
chamber gap
E
field varies with
r
g
and is
non-linear
∇
E
2
=
– 2
V
o
2
r
g
3
ln [
a / b
]
2
∇
E
2
varies with
r
g
, and force
is from the outer to inner
electrode
Cell Electrofusion Tutorial