Hardware Reference
In-Depth Information
Tabl e 4. 2
Probabilities
of
bioassays
being
successfully
implemented
without unfinished operations
P success , T i listed
No. of dilution/
Bioassay
mixing operations
i
i
C
i
i
C
2 i
PCR
7
0:01
0:30
0.85
Interpolating dilution
35
0
0
0.45
Exponential dilution
47
0
0
0.34
completed before the next operation starts. Based on the characteristics of the
Gaussian distribution, if we set the time spent on operation O i as T i D i C i ,then
P i D 0:84;ifwesetT i D i C 2 i ,thenP D 0:98.Table 4.2 lists the probabilities
that bioassays are successfully completed (i.e., with no unfinished operations) when
no cyberphysical adaptation is used. When we conservatively set T i D i C 2 i
(and increase the operation times considerably) and obtain P i D 0:98, it leads to
low probability (0:34) of implementing the exponential mixing of protein bioassay
successfully. We can further calculate that, in order to improve the yield of the
exponential dilution bioassay to 0:90 and above, we need to set T i D i C 4 i .
We therefore conclude that the bioassay execution on conventional biochip
platforms without a sensing system, closed-loop control, or uncertainly-aware
synthesis, will lead to unacceptably low bioassay yield and low confidence in
reaction outcomes.
From Table 4.2 , we also find that P success can be increased by increasing T i .
However, on the other hand, increasing T i will elongate the reaction completion
time, and increase the risks of excessive heating and evaporation of droplets [ 23 ].
Therefore, T i should be set within in a reasonable range. Due to the lack of sufficient
data thus far from real experiments on fabricated chips, the additional probability of
bioassay failure caused by excessive heating and evaporation is not considered here.
In this way, we do not quantify this important shortcoming of the baseline methods
that we use for comparison.
Next we compare the bioassay completion time of the proposed operation-
interdependency-aware synthesis algorithm with the parallel recombinative simu-
lated annealing (PRSA)-based synthesis algorithm [ 6 , 24 ]. Here the module library
shown in Table 4.1 is used [ 6 ], and simulations are executed by considering timing
uncertainty. We assume that for each operation, its average execution time i is the
time defined in the library, and i is 0.1 i . For example, for a dilution operation
executed on a 2 3 array, i D 6 s, and i D 0:6 s.
In order to increase the yield for the baseline design, when running the PRSA-
based algorithm, extra execution time T i is added for each operation. In the
simulations, we assume that the PCR bioassay, the exponential dilution bioassay,
and the interpolation dilution bioassay are all executed on an 8 8 direct-addressing
array.
The simulation results with T i , which are set to 0, i ,2 i ,and4 i ,areshownin
Tab le 4.3 . The completion time of the bioassays derived by PRSA-based algorithm
 
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