Biomedical Engineering Reference
In-Depth Information
TAble 3.1
Time-Span Table with Detailed Scheduling
Results for the Overlapping Region
Partition
Time Span
1
1-7
2
5-12
3
7-23
4
17-20
23
10-14
required for independent addressing in overlap partitions. The concept of
TDPS can also be applied in the spatial dimension to the operations inside
the overlapping region to further reduce the number of control pins.
Once a spatially overlapping region is found, we determine if there are
temporally overlapping droplets in this region. Depending on the outcome of
this procedure, a spatial overlap region can then be divided into two groups:
a spatially overlapping but temporally nonoverlapping (SOTN) region, and
a spatially overlapping as well as temporal overlapping (SOTO) region. For
SOTO regions, direct addressing is used. For SOTN regions, even though
droplets traces cross each other, different droplets are sequenced in time
(one after the other); that is, at any point in time, there is at most one droplet
inside the region. In this case, a pin set with the minimum size (
k
= 5) for
single-droplet manipulation is assigned to this SOTN region.
Again, we use the previous example of Figure 3.5 for illustration. Table 3.1
shows the schedule information needed for carrying out the temporal check
for the overlapping region. Partitions 23.2 and 23.3 represent the manipula-
tion of Droplet 2 and Droplet 3 in Partition 23, respectively. Table 3.1 shows
that the time spans for these partitions do not overlap; thus, five pins (in
contrast to the nine pins needed for direct addressing) are adequate for the
overlapping partition.
3.1.3 Pin-Assignment Algorithm
In this subsection, we address the problem of how to map control pins to
the electrodes in a partition. An efficient algorithm that can be easily imple-
mented using a 3-layer PCB is presented. The algorithm is based on a strat-
egy of the Connect-5 (Gomoku) board game [61]; thus, it is referred to as the
Connect-5 algorithm.
The sets of pins assigned to the partitions belong to two groups according
to their cardinality, that is, the minimum for single-droplet manipulation
(
k =
5) or the number of pins required for direct addressing. Here, we focus
on the pin assignment problem for the first case, since pin assignment for
direct addressing is straightforward (there exists a simple one-to-one map-
ping between pins and electrodes).
