Biomedical Engineering Reference
In-Depth Information
Note that even though in each step of the previous algorithm, the largest
clique and the associated destination cells are deleted, the absence of the
corresponding destination cells does not lead to any added complexity for
droplet movement. This is because the droplet movements involving these
destination cells are incorporated in the clique determined at this step.
Therefore, when the algorithm terminates with an empty graph, all droplet
movements have been processed without any electrode interference.
The steps of the complete procedure to determine the order of droplet
movements can be stated as follows:
1. Obtain the required droplet movements (from a synthesis tool such
as [15]), and organize these movements in the form of snapshots cor-
responding to different time steps.
2. Compare consecutive snapshots to determine the destination cells
for the droplets.
3. Scan each row and each column to find the row/column with the
largest set of destination cells. The destination cells thus determined
form a group of droplets that can be simultaneously moved. If no
row/column contains more than one destination cells, set the flag
END to 1.
4. If END = 1, process the remaining movements in multiple steps, but
with two droplets at each step, or else carry out the droplet move-
ments indicated by Step 3.
5. Check if all the movements in the snapshot have been processed.
If the check yields a negative outcome, repeat Step 3.
6. Check whether all the snapshots are processed. If not, get the next
snapshot and repeat Step 2, else terminate the procedure.
3.2.3 Scheduling of routing for efficient grouping
The column- and row-scan methods described earlier enable the simulta-
neous manipulation of multiple droplets on the cross-referencing chip.
However, the efficiency of this approach depends on the prealignment of
the destination cells corresponding to the droplet movements in the target
droplet-routing snapshot. The better aligned the destination cells are (i.e., they
share the same column/row), the larger the number of droplets that can be
moved simultaneously. Therefore, to increase efficiency, it is important to
generate routing snapshots with well-aligned destination cells.
Note that routing snapshots are obtained from the schedule of droplet move-
ments corresponding to the droplet-routing plan. Typically, several sched-
ules are feasible for a given droplet-routing plan. For example, the routing
