Hardware Reference
In-Depth Information
24
C
28
f
.8
8/
.5
C
18
f/
100 %:
P
nz
D
As the frequency range is 1
f
100 [
25
], we conclude that 2:45 %
P
nz
3:69 %. This implies that
A
is a sparse matrix. In Sect.
3.4
, we will illustrate that
actuation matrices are sparse in general cases.
3.4
Estimation for the Percentage of Non-zero Elements
in Actuation Matrices
According to the underlying physical principle of droplet operations, the number
of actuated electrodes on the array can be estimated on the basis of the number of
droplets that are currently being manipulated on the biochip. The discussion for all
the possible fluid-handling operations is as follows.
1. For the droplets that are scheduled to stay at its current position, the electrode
under the droplet will be actuated to “anchor” the droplet, while all other
electrodes that are in contact with the droplet will be deactivated.
2. For the droplets that are scheduled to be moved from one electrode to another
electrode, the target electrodes need to be actuated while all the other electrodes
that are in contact with the droplet need to be deactivated.
3. Dilution/mixing operations can be considered as moving two droplets in a
module. At each time moment, there are two droplets in a mixing/dilution module
and the number of actuated electrodes inside is one or two.
4. Dispensing operations can be considered as “pulling” droplets out of the
reservoir. At each time moment, the number of actuated electrodes on the output
of the dispensing port is one.
5. For splitting operations, we can consider the 2
droplet before splitting as two
1
droplets. In order to split the 2
droplet, two electrodes need to be actuated.
Therefore, the number of actuated electrodes in the splitter is equal to the number
of “equivalent” 1
droplets.
Therefore, by calculating the number of maximum number of droplets that can
be concurrently manipulated on the biochip, we can find an upper bound on the
percentage of non-zero elements in each actuation sub-matrix. Here a sub-matrix
represents the set of actuation signals applied on the electrode array at one time
moment. For a 10
10 electrode array, each actuation sub-matrix is a 10
10 vector.
Next we calculate the maximum degree of parallelism for fluid-handling operations
in the exponential dilution of a protein sample. The sequencing graph of the bioassay
can be found in Fig.
2.20
b[
16
,
34
].
Here we first define the concept of “interdependency operations”. If the output
of an operation A is the input of operation B, then operations A and B are
interdependency operations. It is clear that two interdependency operations cannot
