Biomedical Engineering Reference
In-Depth Information
a
C(x) = x
5
A
1.0
0.8
0.6
0.4
0.2
0.0
A'
b
e
2x
-1
e
2
-1
1.0
C(x) =
0.8
0.6
0.4
0.2
0.0
C(x) =
erf
(x)
erf
(1)
c
1.0
0.8
0.6
0.4
0.2
0.0
3
C(x) = √x
1.0
0.8
0.6
0.4
0.2
0.0
d
500 µm
0.00.20.40.60.81.0
Normalized distance
FIGURE 3.74
Universal.gradient.generator..(From.Daniel.Irimia,.Dan.A..Geba,.and.Mehmet.Toner,.
“Universal. microluidic. gradient. generator,”.
Anal. Chem.
. 78,. 3472-3477,. 2006.. Reprinted. with.
permission.of.the.American.Chemical.Society..Figure.contributed.by.Mehmet.Toner.)
difusion. his principle can be exploited in virtually unlimited combinations, of which we will
highlight only a few here. Minoru Seki and coworkers at the Osaka Prefecture University in
Japan, for example, have shown an elegant low distributor that splits the low from two distri-
bution channels into many outlet channels (
Figure 3.76
). he amount of low received by each
outlet channel is a function of the ratio of distances between the outlet channel and the distri-
bution channels, so the performance of the mixer is easy to predict. Note that the conceptual
simplicity comes at a price: the outlets must cross over the distribution channels and, therefore,
the device requires 3-D multilayer fabrication/assembly.
Similarly, Mengsu Yang's group at the City University of Hong Kong have presented a device
in which a channel containing constant low communicates through “microtunnels” with the
area in which the gradient is desired (
Figure 3.77
). he shape of the gradient is determined sim-
ply by the length of the microtunnel.
Both the Dertinger and the universal gradient generators shown previously allow for exqui-
site spatial control of the gradients but are highly low rate-dependent. Adrian O'Neill's group at
North Carolina State University has presented a clever design that produces linear dilutions and
preserves the linearity over a wide range of low rates (0.5-16 μL/min). he ratio of the dilutions
is controlled by the volumetric low rate of the solution of interest and the diluent, which mix in
a two-layer network (
Figure 3.78
). he low rate is modulated by making use of the fact that the
channel resistance varies linearly with length (see
Equation 3.12
).
Because of its simplicity, the Dertinger device has been used by several groups to gener-
ate gradients for cell culture applications. Indeed, it can generate quantiiable, steady-state gra-
dients, but with several limitations: (1) it can only generate gradients under luid low, which
induces shear and drag forces that can alter intracellular signaling or cause changes in cell shape
and attachment that may lead to migrational bias; (2) the gradient evolves as the luid lows
downstream such that no two cells in the microchannel experience the same concentration
