Optimization of On-Chip Polymerase Chain Reaction - Hardware/Software Co-Design and Optimization for Cyberphysical Integration in Digital Microfluidic Biochips - page 124

5.3.1 Device-Proximity Constraints on a PCR Biochip

On the PCR biochip, there are three categories of devices: reservoirs, detection
electrodes (DEs), and one thermal unit (e.g., a heater). In order to avoid interferences
among the on-chip devices, we assume that the following constraints must be
satisfied: which enforce minimum (threshold) intra-pair and inter-pair separation
distances between the respective device pairs, must be satisfied. These constants are
provided as inputs to biochip designers.

5.3.1.1 Separation Constraints

1. Reservoir to reservoir separation: In order to avoid fluidic leakage between two
reservoirs, the distance between them should be no less than a threshold L RR
[ 22 ]. A typical value of L RR is four times of the length of electrodes on the
DMFB [ 23 ].
2. DE to DE separation: The stationary droplets on the DEs may have undesirable
cross-contamination if they are too close together [ 11 ]. Therefore, the distance
between two DEs should be no less than a minimum value of L DD . A typical
value of L DD is four times the length of electrodes on the DMFB [ 11 ].
3. Reservoir to DE separation: Fluids loaded in the reservoirs may contain fluores-
cent labels and thus they may influence the accuracy of the microscope when
measuring the fluorescent intensity of the DE [ 11 ]. Furthermore, when a DE and
a reservoir are placed close to each other, droplets dispensed from the reservoir
may lead to contamination on the surface of the DE. Therefore, the spacing
between them should be no less than a threshold L RD . A typical value of L RD
is five times the length of electrodes on the DMFB [ 18 ].
4. Reservoir to heater separation: Since the biological samples and reagents loaded
in the reservoirs may undergo degeneration under heating [ 16 ], the distance
between a reservoir and a heater should be no less than a threshold L RH . A typical
value of L RH equals five times the length of electrodes on the DMFB [ 3 ].
5. DE to heater separation: Due to the limitation of fabrication process, the heater on
the biochip cannot overlap with any DE on the biochip [ 24 ]. Hence the distance
between a DE and a heater should be no less than the length of electrodes on the
DMFB. The spacing condition between a DE and a heater is written as L DH 1.
For simplicity, we define an operator

, which is a mapping from a pair of
arbitrarily chosen devices (written as d a and d b ) to the required minimum distance
between them:

C

C W .d a ;d b / ! Minimum distance between d a and d b :

For example, if DE is represented by d a , and a heater is represented by d b ,then
C .d a ;d b / D L DH .