Biomedical Engineering Reference
In-Depth Information
By definition, the modulation resolution can be determined using the
equation
Modulation resolution
Concentrationofstock so
lution
×
greservoir
volume of aunitdroplet
=
(6.1)
Capacity of mixin
In one iteration of mixing and dispensing, concentrations of the dispensed
droplet from the mixed large droplet can only be multiples of the modula-
tion resolution. For other concentrations, extra dilution steps are needed to
obtain intermediate stock solutions with reduced concentration, which in
turn yields a finer module resolution, according to Equation 6.1.
6.2.1.2 Solution-Preparation Algorithm
In this subsection, we focus on the problem of generating target solutions
with required sample concentrations using the basic dispense-mix-dispense
operation as described earlier. We refer to this process as “solution-
preparation planning.”
Given a set of target solutions, the solution-preparation-planning algo-
rithm determines
1. The types of stock solutions that are needed
2. The concentration of each stock solution
3. The number of dispensed droplets of the stock solutions
4. How these droplets must be mixed so that we can derive the target
solutions using the smallest number of droplet manipulation steps
(routing, mixing, and dilutions)
Next, we use an example to illustrate the algorithm. In this example, we plan
to generate a set of 24 target solutions from a protein crystallization assay, as
shown in Table 6.1. To start, the algorithm first determines the types of stock
solutions needed. Here we use one stock solution for each type of reagent
included in the set of target solutions. Therefore, the number of stock solu-
tions is the same as the total types of reagents included in the target solu-
tions. For the example in Table 6.1, 17 different types of reagents are included
in the target solutions. Thus, 17 types of stock solutions are needed, as listed
in Table 6.2. These stock solutions are stored in on-chip reservoirs.
Next, the algorithm determines the concentration of each type of stock
solution, identifying all the target solutions that contain the correspond-
ing reagent in the stock solution. For the example shown in Tables 6.1
and 6.2, stock solution
S
5
contains the reagent
polyethylene glycol 4000
. There
