Biomedical Engineering Reference
In-Depth Information
This is particularly useful because after the magnetic beads have done their job
carrying target molecules, they must be separated from them (by thermal heat-
ing for example) before being removed out of the reaction chamber. A com-
pact aggregate of magnetic beads cannot “free” the targets in the detection
chamber.
The weak magnetic traction that can exert a small magnetic bead is not an im-
portant drawback: if the target is small (like a 32-bp. DNA strand), the magnetic
force need not be very important, and if the target is larger (a cell for instance),
more than one bead can be attached to the target and the magnetic traction is the
result of all the forces exerted by each bead.
9.2 Characterization of Magnetic Beads
The mechanical behavior of magnetic beads depends on their magnetic properties.
Characterization of magnetic beads consists of determining the average magnetic
properties of the beads. On a general point of view, Maxwell's equations determine
the electromagnetic behavior of any material. The magnetic induction in Maxwell's
equation is related to the magnetic field by [3]
�
� �
B
=
µ
0
(
H M
+
)
(9.1)
where the magnetization is given by
� � �
M
=
χ
H M
+
(9.2)
r
�
M
where
is the remanent magnetization,so that
�
�
�
B
=
µ µ
H
+
µ
M
0
r
0
r
with
μ
r
= 1 +
c
This shows that the information we need is contained in the relation between
the magnetization
M
�
�
of the bead and the applied external magnetic field
H
. This
relation is usually determined experimentally by making use of a superconducting
quantum interference device (SQUID) or a Hall probe.
9.2.1 Paramagnetic Beads
Magnetic micro- and nanoparticles used in biotechnology are nearly always para-
magnetic—even superparamagnetic—because the magnetic force should vanish
when the external field is switched off. If not, the beads would agglomerate and it
would be impossible to have them dispersed in the carrier fluid.
Paramagnetic media follows Langevin's law [4]
M
æ
3
χ
H
ö
1
=
coth
-
(9.3)
ç
÷
3
χ
H
M
è
M
ø
s
s
M
s
