Biomedical Engineering Reference
In-Depth Information
M
M
∑∑
1
simply (
MMM
++
)
L
=
O
(
ML
).
Note that L i ≤ 2 N , where 1 ≤ i M .
i
i
M
i
=
i
=
1
1
Thus,
L
2. We therefore conclude that the worst-case time com-
N
i
i
=
NM 2
plexity for Steps 2-5 is O(
).
The time complexity of Step 1 is O( N ). For
NM 2
Steps 7-8, we also have O(
)
; therefore, the overall time complexity of the
NM 2
scheduling algorithm is O(
).
3.2.4 Variant of Droplet-Manipulation Method for
High-Throughput Power-Oblivious Applications
For applications in which power consumption is not critical, the method
proposed in the previous section can be modified to achieve even higher
throughput.
Note that when we use the low-power manipulation method of Subsection
3.2.3 to implement the “aligned” droplet manipulations, in each step, only
droplet manipulations corresponding to a single row or column are carried
out. Note, however, that there may be other droplet manipulations that can
also be implemented without introducing electrode interference. For example,
for the droplet-manipulation pattern shown in Figure 3.15, manipulation of
D 7 and D 8 can also be carried out at the same time when we concurrently
move D 4 and D 9 .
The implementation of these “compatible” droplet manipulations will result
in higher power consumption, with the associated benefit of higher through-
put. Based on this observation, we present a modified droplet-manipulation
method that relies on the method from [63] to carry out the droplet manipu-
lation for the routing plans generated from the proposed routing-scheduling
method. Note that the straightforward application of [63] to the droplet routes
derived from the routing-scheduling algorithm leads to undesirable conse-
quences. The alignment of the droplet movements will be broken, thereby
leading to lower throughout. Therefore, we limit the use of [63] for handling
droplet movements in Step 7 of the routing-scheduling method, that is, the
ones that correspond to the reverse of the starting direction. Instead of being
carried out using additional steps, these droplet manipulations are carried
out concurrently with the ones from Steps 1-6. This approach results in
higher throughput and reduced assay completion time.
3.2.5 Simulation results
In this subsection, we use random synthetic benchmarks and a set of multi-
plexed bioassays to evaluate the proposed method.
3.2.5.1 Random Synthetic Benchmarks
We first use random synthetic benchmarks to evaluate the effectiveness of
the grouping-based droplet-movement approach. Digital microfluidic arrays
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