Hardware Reference
In-Depth Information
be calculated; then the decision needs to be made on whether to discard the biochip
and run the bioassay on a new chip, or recover from the error and continue the
experiment.
While generating entries for the error dictionary, an evaluation process can be
performed for determining whether an error is “worth being recovered”. Thresholds
for the number of droplets consumed can be set before generating the error dictio-
nary. Consider the following example. Assume that when there is no error in the
bioassay, the number of droplets consumed is N
f
, and the maximum number of
additional droplets needed for error recovery (N
max
) is set as 15 %
N
f
.Whenwe
generate the dictionary entry for operation O
E
, if the simulation result indicates
that the number of additional droplets needed for error recovery is more than
N
max
, then the entry for recovering the error in O
E
will not be added into the
dictionary. Therefore, only cost-efficient entries are recorded by the dictionary.
These dictionary entries are referred to as “effective entries” of the error dictionary.
3.3
Actuation Matrix
In order to execute the bioassay on a digital microfluidic biochip, the information
of droplet routes and the schedules of operations must be programmed into the
controller of the biochip [
11
]. The synthesis results of the bioassay are mapped
to electrode actuation sequences, in which each element represents the status of
the electrode at a specific time moment. For an M
N array, we can number the
electrodes on the array as E
1
, E
2
; :::; E
MN
. If the completion time of the synthesis
result is T clock cycles, the actuation sequences for all electrodes can be written in
the form of an .M
N/
T matrix, referred to as the
actuation matrix
and denoted
by
. The status of electrode E
i
at time j is represented by the element in the i th
column and j th row of
A
.
For an arbitrarily chosen operation
opt
i
, suppose it is performed on electrodes
E
e
1
, E
e
2
;:::E
e
k
at clock cycles T
t
1
;T
t
2
;:::T
t
l
, respectively. If we write the set of
the indices of these electrodes as I
Df
e
1
;e
2
; :::e
k
g
and the indices of clock cycles
as J
Df
t
1
;t
2
; :::t
l
g
,thenI is a subset of
f
1; 2; ::: MN
g
and J is a subset of
f
1; 2; ::: T
g
. Thus the actuation sequence for
opt
i
, (which is referred as M
op t
i
),
can be written as
A
that corresponds to the rows
with index in set I and the columns with index in set J . According to the constraints
of biochemical synthesis, no two operations can occupy the same electrode at the
same time, thus for operations
opt
i
and
opt
k
, their corresponding sub-matrices M
op t
i
and M
op t
k
do not overlap with each other.
Next, we show how the values of elements in the actuation matrices are
determined. We also estimate the percentage of non-zero elements in an actuation
matrix. During the implementation of fluid-handing operations, the status of the
electrodes can be “activated”, “deactivated”, or “don't-care”. A “don't-care” status
is assigned to an electrode when it is not required to be either active or inactive.
It is important to note that for various operations, the typical control voltages for
A
I;J
.Itisak
l sub-matrix of
A
