Hardware Reference
In-Depth Information
2X droplet will be
elongated during
transportation
(a)
(b)
Fig. 6.9
droplet to the arrow's direction, Pins B and C must be “High”, and
Pins A, D, E, and F must be “Low”; (
b
) to move the droplet in another direction, pins F and G must
be “High”, and Pins A, B, D, and E must be “Low”
(
a
) To move the 2
a
Direction 2
b
c
d
A 2x droplet
Direction 1
Fig. 6.10
(
a
)The2 droplet has two possible movement directions; (
b
) G
D
1
: graph model of
CEG corresponding to the movement in Direction 1; (
c
) G
D
2
: graph model of CEG corresponding
to the movement in Direction 2; (
d
) graph model derived by the union of G
D
1
and G
D
2
2
droplet on electrode E
x
2
E
layout
. As discussed above, when the 2
droplet is
moved in different directions, the elements in the CPG are different. Note that when
we design the pin-assignment configuration, we do not assume any knowledge of
the position of the 2
droplets or the directions in which they must be moved in
different clock cycles. Therefore, 2
droplets can be moved in any non-diagonal
direction, and these 2
droplets can be present at any position on the layout. To
derive the graph G
E
x
for any electrode, we must consider all the possible directions
in which the droplet can move, and obtain their corresponding graphs as explained
below.
The graph for the pin-assignment configuration, which is written as G
layout
,is
defined as the
union
of all the G
E
x
graphs, i.e., G
layout
D
S
E
x
G
E
x
,whereG
E
x
is defined as: G
E
x
D
S
f
G
E
x
D
1
;G
E
x
D
2
; ::: G
E
x
D
D
g
,andD
1
, D
2
;:::;D
D
are the
possible directions for the movement of the 2
droplet that stays on electrode E
x
.
We can easily prove that, for the biochips involving the transportation of 2
droplets, Lemma
6.2
can still be used as an acceptance test for feasible pin-
assignment configurations. The heuristic algorithm shown in Fig.
6.3
can be used
for the biochip with manipulations of 2
droplets. Similarly, we can determine the
upper and lower bounds for the number of control pins.
2 E
layout
