Hardware Reference
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faults, test stimuli droplets will stick to them at intermediate points during the
transportation. However, if all of the test stimuli droplets reach the droplet sink,
there is no catastrophic fault on the biochip.
In order to minimize the total testing time for a given biochip, the test scheme
must be optimized. Researchers in [ 46 ] found that the test planning problem can be
formulated in terms of graph partitioning and the Hamiltonian path problem from
graph theory. The two-dimensional microfluidic array is modeled as a direct graph,
which is then divided into non-overlapping sub-graphs. Each sub-graph represents a
sub-array on the biochip, and all of these sub-arrays are concurrently tested. In this
way, the total time required for the test is reduced.
Researchers have also proposed an on-line error testing method that enables
checking the correctness of the assay without hampering the normal operations in
the bioassay [ 47 ]. Compared with the structural test introduced above, the online
test procedure requires no extra test stimuli droplets, and it is finished when the
bioassay is completed or sooner. The working principle of the proposed method is
explained as follows.
First, “one time frame” was defined as the time required to perform a basic
fluidic operation, such as dispensing a droplet, transporting a droplet to an adjacent
electrode, merging two droplets in a mixer, and splitting a droplet. Hence, if a
bioassay has n successive basic fluidic operations, the entire duration of the bioassay
can be divided into n time frames, which are written as f 1 ;f 2 ;:::;f n . Assume that
the first droplet of the bioassay is dispensed into the biochip at the beginning of the
bioassay and that the last droplet reaches the desired sink reservoir at the end of the
bioassay.
At any time moment, the presence or absence of a droplet at a particular sink
reservoir can be represented by 1 or 0, respectively. Assume that the bioassay is run-
ning on a biochip with s sink reservoirs, which are represented as S R 1 ;S R 2 ;:::;S R s .
At time frame f i , the expected “signature” of the bioassay can be written as an s-bit
vector (r i ). If the droplet is supposed to reach the sink reservoir S R j at time f i ,then
the j bit of r i is 1, otherwise the j bit of r i is 0.
Then, the expected signatures r 1 , r 2 ,...,r n can be derived based on the synthesis
results of the bioassay. During the execution of the bioassay, the actual signature
r 1 , r 2 , ..., r n of the bioassay at each time frame can be captured by the integrated
detectors on the bioassay.
By comparing the expected signatures and the actual signatures, researchers can
tell whether there is a fault or error on the biochip. An error has occurred in the
bioassay if there exists an integer i.1 i n/, such that r i ¤ r i . The assay is
supposed to be executed without any error, and the outcome is accepted if for any
integer i.1 i n/; r i D r i . In this way, the method can check the functionality
of the biochip without any extra testing time or test stimuli droplets.
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