Hardware Reference
In-Depth Information
As discussed in Sect.
3.7
, if the ratio of electrowetting forces are out of the
acceptable range, abnormal droplets will be generated. It is important to note that,
in the bioassay protocols, there is an underlying assumption that the splitting of a
droplet is the last step in the mixing/dilution procedure, i.e., splitting operations are
executed at the end of each mixing/dilution operation. If droplets with abnormal
volumes are generated when splitting the droplet at the end of operation O
M/D
,this
situation is defined as “an error occurs in O
M/D
”.
In the fault simulation setup considered here, we set the distribution function of
the Gaussian random variable R
c
D
.t
h
"
rd
C
t
d
"
rh
/ as r
c
N.1; 0:03
2
/,wherer
c
is
a nominal value, and N.1; 0:03
2
/ is the Gaussian distribution function with mean 1
and variance 0:03
2
.
For a typical biochip, t
d
"
rh
t
h
"
rd
for R
c
[
8
]; the distribution function for R
c
is
estimated according to the process variance of t
d
. For a typical biochip fabrication
process, the average spread in t
d
is 11 nm [
37
], while the value of t
d
usually is
450
800 nm [
8
,
37
]. Therefore, it is reasonable to set the normalized variance for
R
d
as 3 %.
When a droplet is split by electrowetting forces F
1
and F
2
,and
k
F
1
k
k
1:10
F
2
k
(alternatively,
k
F
2
k
kF
1
k
1:10), we assume that an error occurs. We run the fault
simulation procedure a total of 1,000 times. Among the simulation results for the
1,000 runs, one error occurs 233 times and none of these 1,000 runs include more
than one error.
For the 233 runs with errors, the distributions for the number of extra droplets
consumed in error recovery and the total completion time of bioassay derived by the
proposed error recovery method are shown in Fig.
3.8
a, b, respectively. As shown
in Fig.
3.8
, for these 233 runs, the maximum number of droplets consumed in error
recovery is 5; the maximum total completion time for the bioassay is 237 s.
Part of the simulation results for the 233 runs with errors can be found in
Tab le
3.8
. After the error is detected, the biochip can derive the re-synthesis results
either by the Online Synthesis Strategy (ONS) [
12
], Fast Online Synthesis [
36
],
or by looking up the prepared error dictionary. The response time in Table
3.8
is
defined as the time spent in deriving the actuation sequences to recover the error.
Here we assume that both ONS and Fast Online Synthesis are using the hardware
setup presented in Fig.
2.5
, i.e., the biochip and the computer are connected via
an FPGA/signle board controller. The response times of ONS and Fast Online
Synthesis include the time spent on writing the new actuation matrices into the
memory initialization files of the FPGA (Table
3.8
).
Note that during on-line re-synthesis, all fluid-handling operations for the
bioassay are suspended. The execution time in Table
3.8
is calculated from the
beginning to the end of the bioassay, without considering the CPU time spent in
re-synthesis. Thus the total completion time for the bioassay is the sum of the
response time and the execution time.
As shown in Table
3.8
, the CPU time needed for performing on-line re-synthesis
by both ONS and Fast Online Synthesis are longer than the proposed method.
It is important to note that for the laboratorial experiments in biochemistry, the
