Biomedical Engineering Reference
In-Depth Information
predetermined requirements, only a fragment of the bioassay is reexecuted.
Here we refer to monitoring and control mechanisms as a “control path” for
the digital microfluidic biochip. We next outline an automated design tool for
the synthesis of control paths.
7.2.2.1 Control-Path Design Based on Error Propagation
The synthesis of a control path consists of two segments—control-path
design and control-path synthesis. Given a bioassay-sequencing graph,
control-path design determines which operations need to be monitored
and, thereby, where the checkpoints are needed. For each checkpoint, the
control-path design determines which part of the assay must be reexecuted if
an error is detected. However, checkpoint monitoring and reexecutions lead
to increased completion times. Therefore, careful design is needed to limit
the number of checkpoints and the size of the reexecution segment for each
checkpoint. We propose an efficient control-path design method based on
the concept of error-propagation estimates.
In a digital microfluidic biochip platform, each fluidic operation works
within a specific error limit, which is defined as the worst-case percentage
offset of the actual output value from the nominal value. For example, a dis-
pensing operation with an error limit of 10% implies that the reservoir, in the
worst case, can dispense a droplet with a volume of 1.1 or 0.9 times the normal
value. In practice, the error limit can be obtained using experiments.
Given a target bioassay protocol, we can collect the error-limit information
for every fluidic operation in the protocol. Using error analysis [74], the error
limit of the output of an operation can be derived from the error limit of the
input of the operation and the operation's intrinsic error limit. From the start
of operations of the protocol, we apply the error-propagation theory and cal-
culate the error limit for the output of each operation. The value of the error
limit is increased as more operations are considered in the protocol. At some
point, the derived output error limit will exceed a predetermined threshold,
which is obtained from the precision requirement of the protocol. At this
point, a checkpoint must be added. In this way, the error-propagation-based
checkpoint-allocation method minimizes the number of checkpoints while
maintaining coverage for all the possible failures during assay operation.
After a checkpoint C
1
is determined, a reexecution subroutine needs to
be assigned to it. Here we do a “backtrace” operation along the sequencing
graph until another checkpoint C
2
is reached. We define the fragment of the
bioassay from the upstream checkpoint C2 to the current checkpoint C
1
as
execution, a checkpoint can only be reached when no failure is detected in
all its upstream checkpoints. This implies that the error is localized among
the operations between C
1
and C
2
. Therefore, by reexecuting the subroutine,
that is, operations O
1
and O
2
, the error can be corrected. Note also that there
may be multiple backtrace paths from C
1
to C
2
. In this case, it is a challenge
