Biomedical Engineering Reference
In-Depth Information
5.6 GRADIENT GENERATOR BASED ON DIFFUSIVE MIXING
Awell-defined concentration gradient is a reproduceable experimental platform to study the response
of cells to molecular gradients, which is important for many pathological and physiological
phenomena such as immune response, cancer metastasis, and stem cell differentiation. Gradient
sensing is the main path leading to these phenomena. In living organisms, cells respond and migrate
along gradients of biochemical cues. Microtechnology allows the design and implementation of
platforms for the generation of concentration gradient with precise control over spatial and temporal
resolution. The objective of designing a gradient generator is a well-defined concentration distribution
and not a homogenous concentration field as in a micromixer. These platforms can mimic cellular
environment. Drug screening and detailed investigations of disease processes can be carried out in
a controlled manner.
The design of gradient generator follows the same principles of designing micromixers based
on molecular diffusion. By controlling the diffusion/convection process in microchannels, a
desired spatial and temporal concentration distribution can be achieved. Based on their working
principles, gradient generators can be classified as parallel lamination and free-diffusion gradient
generators.
Parallel lamination gradient generators provide a stable gradient and can be tuned quickly by flow
control. However, the constant flow is not suitable for cells which do not adhere to the substrate. Even
for cells that can adhere to the substrate, the shear stress caused by the flow does not represent the real
physiological condition. For cell assays with parallel lamination gradient generator, special designs to
minimize the shear stress should be considered.
Free-diffusion gradient generator can solve the problem with shear stress. However, the shapes of
the concentration gradients are limited by the diffusion process. The gradient takes a long time to
establish and is difficult to control dynamically.
5.6.1 Parallel lamination gradient generator
As analyzed in the previous sections, parallel lamination at high Peclet numbers can maintain the
concentration of each stream due to the dominant convective transport. A desired concentration
distribution can be designed by generating streams with a given concentration and subsequent lami-
nating them with flow at high Peclet number. At a relatively low Peclet number, the concentration
distribution is dominated by diffusion and can be predicted by a simple analytical model discussed in
the previous sections on designing parallel lamination micromixers.
Jeon et al. proposed a pyramid design for a parallel lamination gradient generator ( Fig. 5.18 (a))
[31] . The original three inlets at the top of the pyramid are split and recombine to form many branches.
The solute and the solvent are mixed in the branches to form a given concentration. At the bottom of
the pyramid, the branches are merged to form the desired concentration distribution. The microfluidic
pyramid network was modeled as a resistive network with left-right symmetry. The network is
modeled by connecting the horizontal channel with a resistance of R H and the vertical branches with
a resistance of R V . The vertical branches are much longer than the connecting horizontal channels; thus
their corresponding resistances are also much larger ( R V >>
R H ). Due to the symmetry, the flow rate in
each vertical branch is the same throughout the same order B . With the total number of branches B and
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