Hardware Reference
In-Depth Information
For example, when multiple fluid-handling operations are scheduled to be
executed concurrently, their control signals may conflict with each other. In order to
solve this problem, we must decide the order in which the fluid-handling operations
will be implemented and determine the appropriate voltages to be applied to the
electrodes.
Suppose we have a given initial schedule. Then at each time slot t , the positions
and scheduled fluid-handling operations of all the droplets are already known.
Therefore, the corresponding actuation signals that need to be applied on the pins
can be easily derived. Based on the actuation signals, the set of pins that must be
applied “High” signal (S H .t /), and the set of pins that must be applied “Low” signal
(S L .t /) can be determined. Conflicts in the actuation of the pins can occur if and
only if C.t/ D S H .t / \ S L .t / ¤
, i.e., the operation schedule requires some
control pins to be set to “High” and “Low” at the same time. In this situation, the
operation schedule needs to be adjusted.
An example is shown in Fig. 6.14 a. Assume at time t D t 0 , droplets D 1 , D 2 ,and
D 3 are scheduled to be moved in the directions indicated by the arrows, and D 4 is
scheduled to be split. To implement the fluid-handing operation for droplets D 3 ,we
have the following set of pins that must be applied “High” voltage: S D H .t 0 / Df 11 g ;
to implement the fluid-handing operation for droplets D 4 , we have the following
set of pins that need to be applied “Low” voltage: S D 4
L
¿
.t 0 / Df 2; 11; 14 g . Hence
we have S D 3
H
.t 0 / \ S D 4
L
, i.e., the fluid-handling operations scheduled for
droplets D 3 and D 4 cannot be implemented concurrently, otherwise the actuation
signals for D 3 may lead to unintended movement of D 4 . Note that the moving and
splitting of droplets are the basic operations implemented on the biochip, and other
operations such as droplet mixing and dispensing can be considered as a sequence
of these basic operations.
To determine the actuation signals that must be applied to the electrodes and
the order in which to implement the fluid-handling operations, we map the conflict
relationships of multiple droplets to a directed graph, and each droplet is mapped to
a node. For two droplets D A and D B , if the fluid-handling operation of D A may lead
to unintended splitting or movement of D B , then in the conflict graph, there will be
a directed edge starting from the node D A to node D B . The operations for droplets
that correspond to the nodes with zero out-degrees in the conflict graph must be first
.t 0 / ¤
¿
a
7
2
D 1
D 2
Fig. 6.14 ( a ) Droplets D 1 ,
D 2 ,andD 3 are scheduled to
be moved in the directions
indicated by the arrows, and
D 4 is scheduled to be split;
( b ) conflict graph derived
from the pin-assignment
configuration and scheduled
fluid-handling operations of
droplets D 1 4
3
1
5
8
6
5
4
9
b
11
13
D 1
D 2
D 3
D 4
12
10
8
2
14
11
D 3
D 4
1
9
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