Biomedical Engineering Reference
In-Depth Information
Figure 5.14
Diffusion of macromolecules initially concentrated in the middle of the detection mi-
crochamber (the macromolecules are released from the aggregate of magnetic beads). The right side
of the chamber is considered an exit towards the inlet channel.
obtained by discretization of the diffusion equation by using a Crank-Nicholson
formulation [6]. The 2D diffusion equation may be written under the form
n
1
n
1
n
1
n
1
n
1
n
1
é
+
+
+
+
+
+
ù
n
+
1
n
c
2
c
c
c
2
c
c
-
+
-
+
c
-
c
D
i j
,
i j
,
i j
,
i j
,
i
+
1,
j
i
-
1,
j
i j
, 1
+
i j
, 1
-
ê
ú
=
+
2
2
D
t
2
(
D
x
)
(
D
y
)
ê
ú
ë
û
(5.33)
n
n
n
n
n
n
é
ù
c
-
2
c
+
c
c
-
2
c
+
c
D
i j
,
i j
,
i
+
1,
j
i
-
1,
j
i j
, 1
+
i j
, 1
-
+
ê
+
ú
2
2
2
(
D
x
)
(
D
y
)
ê
ú
ë
û
where
i
and
j
are the indices corresponding to the space location and
n
is the time
index. Equation (5.33) can be written in a matrix form and inverted to obtain the
solution for the concentration at each time step
t
n
at every point of the computa-
tional grid.
An analysis of the results shows that it is necessary to block back diffusion
inside the inlet channel. This is done by injecting air in secondary reservoirs—by
thermal expansion, for example (Figure 5.15).
5.3.8 Diffusion Inside a Capillary: The Example of Simultaneous PCRs
5.3.8.1 Introduction
In order to parallelize some biological operations [like polymerase chain reaction
(PCR)] it has been thought to perform these operations at the same time at different
