1928 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008
BioRoute: A Network-Flow-Based Routing
Algorithm for the Synthesis of Digital
Microfluidic Biochips
Ping-Hung Yuh, Chia-Lin Yang, Member, IEEE, and Yao-Wen Chang, Member, IEEE
Abstract—Due to recent advances in microfluidics, digital
microfluidic biochips are expected to revolutionize laboratory pro-
cedures. One critical problem for biochip synthesis is the drop-
let routing problem. Unlike traditional very large scale integration
routing problems, in addition to routing path selection, the biochip
routing problem needs to address the issue of scheduling droplets
under practical constraints imposed by the fluidic property and
timing restriction of synthesis results. In this paper, we present the
first network-flow-based routing algorithm that can concurrently
route a set of noninterfering nets for the droplet routing problem
on biochips. We adopt a two-stage technique of global routing
followed by detailed routing. In global routing, we first identify
a set of noninterfering nets and then adopt the network-flow
approach to generate optimal global-routing paths for nets. In
detailed routing, we present the first polynomial-time algorithm
for simultaneous routing and scheduling using the global-routing
paths with a negotiation-based routing scheme. Our algorithm
targets at both the minimization of cells used for routing for better
fault tolerance and minimization of droplet transportation time
for better reliability and faster bioassay execution. Experimental
results show the robustness and efficiency of our algorithm.
Index Terms—Detailed routing, digital microfluidic biochips,
global routing, network-flow-based algorithm.
I. INTRODUCTION
D
UE TO the advances in microfabrication and micro-
electromechanical systems, microfluidic technology has
gained much attention recently. The composite microsystems
could perform conventional biological laboratory procedures
on a small and integrated system by manipulating microliter
or nanoliter fluids. Therefore, microfluidic biochips are used in
several common procedures in molecular biology, such as clini-
cal diagnostics and deoxyribonucleic acid sequencing analysis.
First-generation (analog) microfluidic biochips are based on
manipulating continuous liquid flow by permanently etched mi-
Manuscript received March 11, 2008; revised June 27, 2008. Current version
published October 22, 2008. This work was supported in part by the Na-
tional Science Council of Taiwan under Grants NSC 96-2752-E-002-008-PAE,
NSC 96-2628-E-002-248-MY3, NSC 96-2628-E-002-249-MY3, and NSC 96-
2221-E-002-245 and in part by the Excellent Research Projects of National
Taiwan University under Grant 96R0062-AE00-07. An earlier version of this
paper was presented at the IEEE/ACM International Conference on Computer-
Aided Design 2007 [1]. This paper was recommended by Associate Editor
K. Chakrabarty.
P.-H. Yuh and C.-L. Yang are with the Department of Computer Science
and Information Engineering, National Taiwan University, Taipei 106, Taiwan
(e-mail: r91089@csie.ntu.edu.tw; yangc@csie.ntu.edu.tw).
Y.-W. Chang is with the Department of Electrical Engineering and the
Graduate Institute of Electronics Engineering, National Taiwan University,
Taipei 106, Taiwan (e-mail: ywchang@cc.ee.ntu.edu.tw).
Digital Object Identifier 10.1109/TCAD.2008.2006140
Fig. 1. Schematic view of digital microfluidic biochips.
crochannels and external pressure sources (e.g., micropumps).
Recently, second-generation (digital) microfluidic biochips,
which are based on the manipulation of discrete microliter
or nanoliter liquid particles (the droplets), have been pro-
posed [2]. In digital microfluidic biochips, each droplet can
be independently controlled by electrohydrodynamic forces
generated by an electric field. The field can be generated by
an individually accessible electrode. Compared with the first-
generation biochips, droplets can move anywhere in a 2-D array
to perform desired chemical reactions, and electrodes can be
reprogrammed for different bioassays.
Fig. 1 shows the schematic view of a digital microflu-
idic biochip based on the principle of electrowetting on di-
electric [3]. There are three major components in a biochip:
2-D microfluidic array, dispensing ports/reservoirs, and optical
detectors. The 2-D microfluidic array contains a set of basic
cells (i.e., unit cells for droplet movement). A droplet moves
one cell in one clock cycle. Each basic cell has identical archi-
tecture and is used to perform various fundamental operations,
such as mixing of multiple droplets, droplet transportation,
droplet dilution, and droplet fission. Note that we can perform
these fundamental operations anywhere on the 2-D array. In
other words, a portion of the 2-D array can perform different
operations at different times. This property is referred to as
the reconfigurability of biochips. Moreover, we can use these
fundamental operations to build a complex bioassay. We refer
to this property as the scalability of biochips. The dispensing
ports/reservoirs are responsible for droplet generation while the
optical detectors are used for reaction detection. These three
components allow researchers to perform laboratory procedures
on a biochip, from sample preparation, reaction, to detection.
Similar to traditional very large scale integrated (VLSI) syn-
thesis methodology, a top–down synthesis approach for digital
microfluidic biochips has been proposed [2]. The synthesis
step is divided into architectural- and geometry-level syntheses.
0278-0070/$25.00 © 2008 IEEE
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YUH et al.: BIOROUTE: ROUTING ALGORITHM FOR SYNTHESIS OF DIGITAL MICROFLUIDIC BIOCHIPS 1929
The architectural-level synthesis performs scheduling with a
given bioassay and a set of design specifications [4], while the
geometry-level synthesis performs physical placement to deter-
mine the physical location of each operation as well as other
geometry details [5]. Recently, a unified synthesis and physical
placement approach has been proposed [6]–[8]. However, there
is not much work that handles the droplet routing problem
[9]–[11].
The main challenge of droplet routing is ensuring t he correct
execution of bioassays; the fluidic property that prevents un-
expected mixing among droplets needs to be satisfied. Unlike
traditional VLSI routing, in addition to routing path selection,
the biochip routing problem needs to address the issue of
scheduling droplets under practical constraints imposed by the
fluidic property and timing restriction of synthesis results.
There are two main optimization objectives for droplet rout-
ing. The first objective is to minimize the number of cells used
for routing for better fault tolerance, which is i mportant for
safety-critical applications, such as patient health monitoring
or biosensors for detecting environmental toxins. As discussed
in [5], a biochip contains primary cells for bioassay execution
and spare cells for replacing faulty primary cells to ensure t he
correctness of bioassay execution. Since droplets can only be
routed through spare cells, to maximize the number of spare
cells for fault tolerance, we need to minimize the number of
cells for droplet routing. The second objective is to shorten
droplet transportation time, i.e., minimizing the time (in cycles)
to route all droplets. Droplet transportation time is critical for
applications requiring real-time response for early warnings,
such as monitoring environmental toxins. Moreover, shorter
droplet transportation time i mproves the reliability of a biochip.
Longer transportation time implies that high actuation voltage
(up to 90 V [12]) must be maintained for a long period of
time, thereby accelerating dielectric breakdown on some cells.
Droplet transportation time is also critical for maintaining the
integrity of bioassay execution. Biological samples are sensi-
tive to environmental variations. For example, many biological
reactions require very small temperature variation (within 1
◦
C
[13]). Unfortunately, it is hard to maintain an optimal laboratory
environment on a biochip. Therefore, it is desirable to shorten
the droplet transportation time to maintain the integrity of
bioassay execution.
A. Previous Work
In the literature, there are three methods to solve the droplet
routing problem. The first one is the prioritized A
∗
-search
algorithm [9]. Each droplet is assigned a priority, and the
A
∗
-search algorithm is used to coordinate each droplet based on
its priority. The drawback of this approach is that they did not
consider the practical timing constraint for throughput consid-
eration. Moreover, they only considered two-pin nets. However,
for practical bioassays, droplet routing must be modeled as
multipin nets, since droplets connect multiple terminals for a
mix assay operation.
The second one is based on the open shortest path first
routing protocol [10]. They defined layout patterns of a biochip.
Each layout pattern has a routing table that is computed by
Dijkstra’s shortest path algorithm. We can then route each
droplet based on this routing table. However, since droplet
routing only occurs at these layout patterns, their algorithm
did not exploit the dynamic reconfiguration property of digital
microfluidic biochips.
The third one is a two-stage algorithm [11]. In the first
stage (alternative routing path generation), a set of shortest
routing paths for each droplet is generated by maze routing. In
the second stage (random selection and scheduling), a random
selection approach is used to randomly select a routing path
for each droplet. A scheduling approach is used to schedule
droplets based on the selected routing paths. The aforemen-
tioned procedure (random selection and scheduling) repeats for
an adequate number of iterations to find a feasible solution.
There are two drawbacks of this approach. First, since droplet
routing and scheduling are separated into two s tages with-
out considering the interaction between them, this approach
may not find a good solution. Second, this approach may not
be efficient, since the maze routing algorithm is performed
multiple times to generate alternative routing paths for each
droplet.
B. Our Contribution
In this paper, we propose the first network-flow-based routing
algorithm for the droplet routing problem on digital microflu-
idic biochips. The network-flow routing approach can concur-
rently route a set of noninterfering nets and obtain optimal
routing solutions in polynomial time. To tackle the complexity
issue of simultaneously considering routing and scheduling,
we adopt a two-stage technique of global routing followed by
detailed routing. In global routing, we first identify a set of non-
interfering nets and then adopt the network-flow approach to
generate optimal global-routing paths for the identified nets. In
detailed routing, we present the first polynomial-time algorithm
for simultaneous routing and scheduling with a negotiation-
based routing s cheme based on the global-routing paths in the
context of biochip routing.
In this paper, we also present how to handle three-pin
nets for practical bioassays. As discussed in [11] and [14],
for a mix operation, mixing time can be greatly reduced if
its two input droplets are mixed during their transportation.
Since mix operations are one of the fundamental operations
of a bioassay, it is important to induce the mixing of droplets
before reaching their destinations. Hence, these two input
droplets must be modeled as three-pin nets, instead of two two-
pin ones.
Experimental results demonstrate the robustness and effi-
ciency of our algorithm. Our algorithm can successfully route
all benchmarks while previous works cannot. Moreover, our
algorithm can achieve better solution quality in reasonable CPU
time. For example, for t he in vitro diagnostics, our algorithm
achieves an 11.23% fewer number of cells used for routing
(237 versus 267) with less CPU time (0.05 versus 0.15 s)
than the two-stage algorithm proposed in [11]. Our algorithm
also outperforms previous works in minimizing the number
of cycles to route all bioassays. For example, for the same
bioassay, our algorithm obtains a routing s olution requiring less
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1930 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008
Fig. 2. Side view of a 2-D microfluidic array.
routing time
1
than the two-stage algorithm proposed in [11]
(1.16 versus 2.22) with less CPU time (0.05 versus 0.17 s).
The remainder of this paper is organized as follows.
Section II describes droplet routing on biochips and formulates
the droplet routing problem. Section III details our routing
algorithm. Section IV shows the experimental results. Finally,
concluding remarks are given in Section V.
II. R
OUTING ON BIOCHIPS
In this section, we first show droplet routing on biochips.
Then, we detail the routing constraints for droplet routing.
Finally, we present the problem formulation of the droplet
routing problem.
A. Droplet Routing
Fig. 2 shows the side view of a 2-D microfluidic array. A
droplet is sandwiched by two plates. The top plate contains
one ground electrode, and the bottom plate contains a set of
control electrodes. A droplet moves to an adjacent electrode
when this electrode is activated. A droplet can stay at a cell
for a period of time if we do not activate its neighboring
electrodes. Fig. 3 shows a droplet routing example. Fig. 3(a)
shows a task graph to represent a bioassay and a 3-D module
placement with three modules to represent a synthesis result.
In a task graph, nodes represent assay operations, and edges
represent data dependences among operations. A 3-D module
placement can be divided into a set of 2-D planes at different
time steps due to the ability of dynamic reconfiguration [7].
Droplet movement among modules only occurs at these 2-D
planes. For example, the 3-D placement shown in Fig. 3(a) can
be divided into two 2-D planes, one representing the time t1
before the execution of the two dilute operations a and c and
the other one representing the time t2 when dilute a is finished.
Fig. 3(b) shows the corresponding two 2-D planes. Note that
each module is wrapped with segregation cells for functional
isolation.
The droplet routing problem is to route all droplets from a
reservoir/dispensing port to a target pin [such as the solid lines
shown in Fig. 3(b)], from a source pin to a target pin [such as
the dashed lines shown in Fig. 3(b)], or from a source pin to
a waste reservoir [such as the dotted lines shown in Fig. 3(b)].
A pin is defined as a fluidic port on the boundary of a module.
1
Routing time is measured as the maximum droplet transportation time over
the maximum Manhattan distance of all nets.
Since droplets are generated before routing, the source pin of a
droplet generated by a reservoir is the cell next to this reservoir.
To satisfy the fluidic property for correct droplet movement,
2
a
droplet may stay at a basic cell for a period of time. Therefore,
in addition to determining the routing path for each droplet, we
need to schedule each droplet to satisfy the fluidic property, i.e.,
to determine the arrival and departure times of each droplet on
each basic cell. Only modules (and the surrounding segregation
cells) that are active during droplet routing on one 2-D plane
are considered as obstacles. For example, dilute c is considered
as an obstacle at time t2 since this operation is active at t2.To
obtain a complete routing solution, we can sequentially route
each 2-D plane to determine the routing path and schedule of
each droplet.
The fluidic route of a droplet can be modeled either as a two-
or three-pin net. For a dilute operation, we model each input
droplet as a two-pin net with only one droplet. For example,
the two input droplets from the reservoirs to dilute a at time
t1 can be modeled as two two-pin nets. However, for a mix
operation, we need to model two input droplets as a three-pin
net due to the preference of merging two droplets during their
transportation for an efficient mix assay operation [11].
3
With
this modeling, the two input droplets will be merged before
reaching their sink. For example, in Fig. 3(b), the two droplets
of the mix b operation form a three-pin net. A droplet routing
algorithm must be capable of handling both two- and three-pin
nets. We use d
a
j
to denote t he jth droplet of net n
a
.Ifn
a
is a
two-pin net, j is always 1; otherwise, j =1or 2. For a two-pin
net n
a
,wealsoused
a
to denote the droplet of n
a
.
B. Routing Constraints
There are two routing constraints in droplet routing: fluidic
and timing constraints. The fluidic constraints are used to avoid
an unexpected mixing between two droplets of different nets
during t heir transportation, while the timing constraint states
the maximum allowed transportation time of a droplet.
The fluidic constraints can be further divided into the static
and dynamic fluidic constraints [11]. The static fluidic con-
straint states that the minimum spacing between two droplets
is two cells if the Cartesian coordinate system is used. In other
words, if a droplet is located at cell c at time t, then there does
not exist any droplet at the neighboring cells of c at time t.The
dynamic fluidic constraint is related to two moving droplets:
If a droplet d
p
moves to cell c at time t +1, then there must
not be any other droplet d
q
that moves to cell c
at time t +1
and locates at one of the neighboring cells of c at time t.
The reason is that since both cells c and c
are activated, d
q
may stay at its original location due to these two opposing
electrohydrodynamic forces. As a result, an unexpected droplet
mixing may occur.
Besides the fluidic constraints, there exists the timing con-
straint. The timing constraint specifies the maximum allowed
transportation time of a droplet from its source to its target.
Since droplet movement is relatively fast compared to assay
2
The fluidic property will be formally described in Section II-B.
3
Droplets of the same net have the same target pin.
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YUH et al.: BIOROUTE: ROUTING ALGORITHM FOR SYNTHESIS OF DIGITAL MICROFLUIDIC BIOCHIPS 1931
Fig. 3. Example of droplet routing on biochip. (a) A task graph and a 3-D module placement, i.e., a synthesis result. (b) The corresponding two 2-D planes.
Droplet routing only occurs at these 2-D planes.
Fig. 4. Example of fluidic constraints. (a) The static fluidic constraint. (b) The dynamic fluidic constraint when a droplet d
q
moves to one of the neighboring
cells of cell (x
p
,y
p
) at time t
p
. (c) The dynamic fluidic constraint when a droplet d
p
moves to cell (x
p
,y
p
) at time t
p
. (d) The 3-D modeling of d
p
,whered
p
is
located at the center of this 3-D cube.
operations, the existing synthesis algorithms of biochips [6], [7]
usually ignore droplet transportation time. To ensure that the
aforementioned assumption is valid for complex bioassays, the
droplet transportation time must be within a maximum value.
Note that we need to account for a droplet’s idle time when
calculating the transportation time of this droplet.
C. Modeling the Routing Constraints
We first detail how to model the fluidic constraints. The flu-
idic constraints can be illustrated in three scenarios as shown in
Fig. 4. The X(Y ) dimension represents the width (height) of a
biochip, and the T dimension represents the droplet transporta-
tion time. Let (x
p
,y
p
,t
p
) be the coordinate of droplet d
p
in this
3-D space to represent the location of d
p
at time t
p
. To satisfy
the static fluidic constraint, there exist no other droplets in the
2-D rectangle defined by the two coordinates (x
p
− 1,y
p
−
1,t
p
) and (x
p
+1,y
p
+1,t
p
) in the 3-D space, as shown in
Fig. 4(a). For the dynamic fluidic constraint, we need to con-
sider two cases. First, when d
q
moves to one of the neighboring
cells of (x
p
,y
p
) at time t
p
, to satisfy the dynamic fluidic con-
straint, no other droplets can be in the 2-D rectangle defined by
the two coordinates (x
p
− 1,y
p
− 1,t
p
+1)and (x
p
+1,y
p
+
1,t
p
+1)in the 3-D space, as shown in Fig. 4(b). Second, when
d
p
moves to cell (x
p
,y
p
) at time t
p
, to satisfy the dynamic
fluidic constraint, there exist no other droplets in the 2-D rectan-
gle defined by the two coordinates (x
p
− 1,y
p
− 1,t
p
− 1) and
(x
p
+1,y
p
+1,t
p
− 1) in the 3-D space, as shown in Fig. 4(c).
Therefore, the three rectangles identified in the aforementioned
three scenarios form a 3 × 3 × 3 3-D cube in the 3-D space as
shown in Fig. 4(d), where d
p
is located at the center of this
3-D cube. Given a routing solution, the fluidic constraints are
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1932 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008
satisfied if, for each droplet d
p
located at cell c at time t, there
exist no other droplets in the 3-D cube defined by d
p
.
Now, we present how the timing constraint is modeled.
The notations and definitions used in modeling the timing
constraint will be used in the droplet routing algorithm de-
scribed in Section III. Given the timing constraint T
max
,
we define T
m
s
(c, d
i
j
)(T
M
s
(c, d
i
j
)) as the earliest (latest) time
that the droplet d
i
j
of net n
i
can reach (stay at) a cell c
without violating the timing constraint, where T
m
s
(c, d
i
j
)=
m
d
(c, s
i
j
)(T
M
s
(c, d
i
j
)=T
max
− m
d
(c,
ˆ
t
i
)), s
i
j
represents the
source cell of the droplet d
i
j
,
ˆ
t
i
represents the target cell of net
n
i
, and m
d
(c
1
,c
2
) represents the Manhattan distance between
two cells c
1
and c
2
. We say that a cell c is available to a droplet
d
i
j
if T
M
s
(c, d
i
j
) ≥ T
m
s
(c, d
i
j
) and no obstacle is located at c.
Moreover, c is available t o d
i
j
at time t if T
M
s
(c, d
i
j
) ≥ t ≥
T
m
s
(c, d
i
j
). Similarly, c is available to a net n
i
if c is available
to at least one droplet of n
i
, and c is available to n
i
at time
t if c is available to at least one droplet of n
i
at time t.The
time interval that a droplet can stay at a cell without violating
the timing constraint is referred to as the idle interval.Weuse
di
c
ij
to denote the idle interval of droplet d
i
j
at cell c, where
di
c
ij
is defined as [T
m
s
(c, d
i
j
),T
M
s
(c, d
i
j
)] if c is available to
d
i
j
. We also define the violation interval vi
c
ij
of d
i
j
at cell c
as the time interval [T
m
s
(c, d
i
j
) − 1,T
M
s
(c, d
i
j
)+1]. If another
droplet is scheduled in c or c’s neighboring cells during the
violation interval of c and d
i
j
is scheduled at c in its idle
interval, then the fluidic constraints may be violated. We say
that a cell c is used for routing if at least one droplet uses c for
routing.
D. Problem Formulation
Since we can sequentially route each 2-D plane to form a
complete droplet routing solution, we only show the problem
formulation of one 2-D plane. Other 2-D planes can be handled
similarly. In this paper, we consider two problems. The first one
is to minimize the number of cells used for routing for better
fault tolerance. The problem formulation is given as follows.
Input) A netlist of m nets N = {n
1
,n
2
,...,n
m
},
where each net n
a
is a two- (one droplet) or
three-pin net (two droplets), the locations of pins
and obstacles, and the timing constraint T
max
.
Objective) Minimize the number of cells used for routing for
better fault tolerance.
Constraint) Both fluidic and timing constraints must be sat-
isfied. The second problem is to minimize the
maximum droplet transportation time for fast
bioassay execution or better reliability. The prob-
lem formulation is given as follows.
Input) A netlist of m nets N = {n
1
,n
2
,...,n
m
},
where each net n
a
is a two- (one droplet) or
three-pin net (two droplets), and the locations of
pins and obstacles.
Objective) Minimize the maximum droplet transportation
time for better reliability.
Constraint) The fluidic constraints must be satisfied.
Fig. 5. Droplet routing algorithm overview.
III. BIOCHIP ROUTING ALGORITHM
In this section, we present our biochip routing algorithm.
We first give the overview of the proposed routing algorithm.
Then, we detail each phase of our algorithm in subsequent
sections with the optimization objective of minimizing the
number of cells used for routing. Finally, we show how
to extend our algorithm to handle the timing-aware routing
problem.
A. Routing Algorithm Overview
Fig. 5 shows the overview of the proposed routing algorithm.
There are three phases in our routing algorithm: 1) net criticality
calculation; 2) global routing based on the min-cost max-flow
(MCMF) algorithm [15]; and 3) detailed routing based on a
negotiation-based routing algorithm.
In net criticality calculation, we determine the criticality of
each net. A net is said to be critical if it is difficult to route this
net, due to the severe interferences with other nets or a tight
timing constraint. This criticality information will be used in
both global and detailed routing.
In global routing, the goal is to determine a rough routing
path of each droplet. We divide a biochip into a set of global
cells. We first select a set of independent nets
4
that do not inter-
fere with each other. Based on these global cells, we construct
the flow network. We then apply the MCMF algorithm to route
the selected nets with the constructed flow network.
In detailed routing, the goal is to simultaneously perform
routing and scheduling based on the result of global routing.
Scheduling a droplet is equivalent to determining the arrival
and departure times of this droplet on each cell. We propose
a negotiation-based routing algorithm to handle the detailed
routing. The negotiation-based routing algorithm terminates
when a feasible solution is found or a specified maximum
number of iterations is reached.
4
The formal definition of independent nets will be given in Section III-C.
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