Error-Recovery in Cyberphysical Biochips - Hardware/Software Co-Design and Optimization for Cyberphysical Integration in Digital Microfluidic Biochips - page 45

which implies that operations opt w and opt v are implemented concurrently.
It is important to note that multiple operations cannot share on-chip resources
(including dispensing ports and electrodes) at the same time. Thus opt w and opt v
must satisfy following constraint:

.M opt w .3/; M opt w .3/ C M opt w .5// \ .M opt v .3/; M opt v .3/ C M opt v .5// D; ;
[

.M opt w .4/; M opt w .4/ C M opt w .6// \ .M opt v .4/; M opt v .4/ C M opt v .6// D; ;

i.e., their corresponding modules cannot overlap with each other.
2. For any pair of operations opt w and opt v ,if opt w is the predecessor of opt v ,
then opt w must be completed earlier than the start time of opt v ,i.e.M opt v .1/
M opt w (2).
The completion time of the bioassay can be written as:

f M opt i .2/ g C p D Max

opt i 2 P

Thus the synthesis of the biochip can be viewed as an optimization problem. The
inputs are the set of operations P and the set of constraints C . The target is:

f M opt i .2/ g minimize: Max

opt i 2 P

Previously published computer-aided design methods for digital microfluidic
biochips have several proposed algorithms to solve this optimization problem.
For example, the PRSA-based synthesis algorithms can be used to quickly derive
optimized synthesis results [ 23 ].
After the optimized synthesis results are derived, the off-line data preparation
step is completed. The bioassay is next executed according to the initial synthesis
result, and the next step is the on-line monitoring of droplets.

2.4.2 On-Line Monitoring of Droplets and Re-synthesis

of the Bioassay

During the execution of the bioassay, the control software must implement the
following steps.