Biomedical Engineering Reference
In-Depth Information
D
2
D
3
5
1
2
3
4
5
1
2
3
4
5
2
4
2
4
2
Reservoir
4
3
4
3
4
Well
Well
1
2
1
2
1
3
1
3
3
D
1
5
1
2
3
4
5
1
2
3
4
5
2
4
2
4
2
4
3
4
3
4
Well
Well
1
2
1
2
1
3
1
3
1
3
5
1
2
3
4
5
1
2
3
4
5
Figure 6.9
Loading of three droplets using the shuttle-passenger-like method.
D
1
dispensed
D
2
dispensed
D
3
dispensed
Step
12345678910
11
Activated
pin
52413543215
Figure 6.10
Activation sequence and dispensing time instances for routing droplets to corresponding
starting point in Figure 6.9.
Therefore, the described well-loading method contains two steps. In the
first step, droplets to be routed are transported to the corresponding start
points in their destination well units. This step is carried out as follows:
a. Calculate the electrode activation sequence to route the droplet to
the farthest starting point away from the source reservoir. This step
takes O(
N
) time for an
N
×
N
array.
b. Select a subsequence from the sequence from step (a) for each drop-
let that can be routed to its starting point. Assume that the selec-
tion is carried out using brute-force searching; this step takes
O(
NM
) time, where
M
is the number of droplets. Note that, in
the shuttle-passenger-like well-loading algorithm, the number of
droplets is no more than the number of well units, that is,
M
<
N
2
.
Therefore, this selection step takes O(
N
3
) time.
c. Applying the electrode-activation sequence from step (a), dispense each
droplet at a specific time corresponding to the start of its subsequence.
This step takes O(
N
) time, which makes the computation complexity of
the entire well-loading method to be O(
N
3
) for an
N
×
N
array.
