Optimization of On-Chip Polymerase Chain Reaction - Hardware/Software Co-Design and Optimization for Cyberphysical Integration in Digital Microfluidic Biochips - page 138

As an instance, for 1 4 mixers for which the projections on the y-axis overlap with
each other, by setting different initial positions and moving directions, we can deter-
mine that the maximum number of droplets that can be observed in parallel is six.
When scheduling fluid-handling operations on a microfluidic biochip, this
constraint on the visibility of droplets must be considered. The simulation program
projects the movements of the droplets to the x-axis or the y-axis in order to check
the visibility for each droplet. If there is an invisible droplet, the initial positions of
droplets will be adjusted by the control software of the biochip.

5.6 Experimental Results

In this section, we first present simulation results to evaluate the proposed methodol-
ogy of designing a cyberphysical and layout-aware PCR biochip. Then experimental
results on three benchmarks for mixing protocols are presented.

5.6.1 Probabilistic Control of DNA Amplification

During the amplification of DNA strands, the statistical model proposed in
Sect. 5.2.1 can be used for on-line decision making. It is important to note that
the fluorescence signal from the amplified DNA may not be detected immediately
when the target DNA strands are amplified. This is due to the fact that each sensing
system has a minimum detectable signal (MDS) [ 32 ]. The fluorescence signal of the
amplified DNA cannot be detected if its strength is lower than the MDS. Therefore,
we assume that the probability of detecting a fluorescence signal from the amplified
DNA strands is zero before the N th thermal cycle. At the i th (i N ) thermal cycle,
the probability of detecting the fluorescence signal (i.e., the DNA is amplified) is p i .
If we assume that N D 20, P.G/ D 0:8,andp i D 0:3 ( 8 i 20), the
relationship between i (i.e., the number of thermal cycles that are carried out) and
P.G c j A i / (i.e., the probability that “this droplet is empty”) is shown in Fig. 5.12 a.
From Fig. 5.12 a, we observe that, if there is no sensor signal at the 25th, 27th, or
28th thermal cycles, the value of P.G c j A i / is 85 %, 90 %, or 95 %, respectively.
The relationship between i and P.G c j A i / for different p i and P.G/ are shown in
Fig. 5.12 a.
When the PCR is performed successively, there is an exponential increase in
the number of target DNA strands. We can assume that the probability p i increases
exponentially. For example, we can set N D 20, P.G/ D 0:8,andsetp i as follows:

8
<

0; if i<N
p 2 i N ; if N i N log 2 p
1;

p i D

:

if N log 2 p <i