Hardware Reference
In-Depth Information
time instance during mixing, there is only one electrode in the mixer that must be
activated. Voltages applied to other electrodes are either “0” or “X”, and all the “X”
terms can be replaced by “0”.
Next we write the actuation sequences of operation Mix 1 as an actuation matrix
M
Mix
1
.Thei th-row vector in M
Mix
1
indicates the status of E
1
to E
6
at the i th clock
cycle of Mix 1. Suppose the completion time for operation Mix 1 is 5 clock cycles
and at the 6th clock cycle the mixed droplet will be split. Then M
Mix
1
has 6
6
elements. It can be written as:
2
4
3
5
v
1
00000
0
v
1
0000
00
v
1
000
000
v
1
00
0000
v
1
0
000
v
2
0
v
2
M
Mix
1
D
:
We see that each row in M
Mix
1
has one or two non-zero elements, which is a general
case in fluid-handling operations.
Figure
3.3
c shows the steps involved in dispensing a droplet from an on-
chip reservoir. In order to pull a droplet out from the reservoir, the electrodes in
the transportation path are activated in sequence, as shown from Steps A to D
in Fig.
3.3
c[
24
]. This dispensing procedure is completed in four clock cycles.
The droplet is formed by activating the electrodes on the outlet of the dispensing
port. In this process shown in Fig.
3.3
c, the liquid drop in the reservoir is deformed
under the electrical force.
Based on the steps shown in Fig.
3.3
c, we derive corresponding actuation matrix
M
Dis
for a dispensing operation. The matrix M
Dis
has four rows and it includes a
total of five non-zero elements.
Since for any two operations
opt
i
and
opt
k
, the corresponding sub-matrices M
op t
i
and M
op t
k
are non-overlapping, we can estimate the number of non-zero elements
in the actuation matrix
on the basis of the sub-matrices corresponding to all the
operations in the bioassay. If we assume that the working frequency of the biochip
is f Hz (f usually varies from 1 to 100 [
25
]), then an operation that is completed
in N seconds includes N
f clock cycles. For the synthesis result shown in the first
entry of Table
3.1
, the number of non-zero elements corresponding to the sequence
matrix of each operation can be calculated accordingly according to their execution
time. Apart from the mixing operations, there are six dispensing operations that
are not shown in Table
3.1
, and each of them corresponds to a sub-matrix with 4
non-zero elements. Thus the total number of non-zero elements in the actuation
matrix for the entire bioassay can be estimated by adding the number of non-zero
elements for each operation. The resulting number is 24
C
28f . On the other hand,
since the completion time of the bioassay is 4
C
18f clock cycles, the size of
A
A
is
.8
8/
.4
C
18
f/. Thus the percentage of non-zero elements (P
nz
)inmatrix
A
can be calculated as:
