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Journal ArticleDOI

A Droplet-Manipulation Method for Achieving High-Throughput in Cross-Referencing-Based Digital Microfluidic Biochips

TL;DR: The proposed design-automation method facilitates high-throughput applications on a pin-constrained biochip, and it is evaluated using random synthetic benchmarks and a set of multiplexed bioassays.
Abstract: Digital microfluidic biochips are revolutionizing high-throughput DNA, immunoassays, and clinical diagnostics. As high-throughput bioassays are mapped to digital microfluidic platforms, the need for design automation techniques for pin-constrained biochips is being increasingly felt. However, most prior work on biochips computer-aided design has assumed independent control of the underlying electrodes using a large number of (electrical) input pins. We propose a droplet-manipulation method based on a ldquocross-referencingrdquo addressing method that uses ldquorowrdquo and ldquocolumnsrdquo to access electrodes. By mapping the droplet-movement problem on a cross-referenced chip to the clique-partitioning problem from graph theory, the proposed method allows simultaneous movement of a large number of droplets on a microfluidic array. Concurrency is enhanced through the use of an efficient scheduling algorithm that determines the order in which groups of droplets are moved. The proposed design-automation method facilitates high-throughput applications on a pin-constrained biochip, and it is evaluated using random synthetic benchmarks and a set of multiplexed bioassays.

Summary (3 min read)

Introduction

  • A number of prototypes of such biochips use a direct-addressing scheme for the control of electrodes [6].
  • The method includes a power-efficient high-throughput droplet manipulation scheme which allows concurrent transportation of multiple droplets.
  • Section II provides an overview of digital microfluidic biochips.

II. DIGITAL MICROFLUIDIC BIOCHIPS

  • The authors consider digital microfluidic biochips that rely on the principle of electrowetting on dielectric.
  • In most prototype digital microfluidic biochips based on the direct-addressing scheme, the bottom plate contains a patterned array of individually controlled electrodes, and the top plate is coated with a continuous ground electrode.
  • A unit cell can be activated by selecting orthogonally positioned pins on the top and bottom plate that cross at this cell.
  • Fluidhandling operations such as droplet merging, splitting, mixing, and dispensing can be executed in a similar manner.

IV. POWER-EFFICIENT INTERFERENCE-FREE DROPLET MANIPULATION BASED ON DESTINATION-CELL CATEGORIZATION

  • The authors focus on the problem of manipulating multiple droplets based on digital microfluidic biochips that use cross-referencing to address the electrodes.
  • Authorized licensed use limited to: IEEE Xplore.

A. Electrode Interference

  • For the concurrent manipulation of multiple droplets on a cross-referencing-based biochip, multiple row and column pins must be selected to activate the destination cells, i.e., cells to which the droplets are supposed to move.
  • The selected row and column pins may also result in the activation of cells other than the intended droplet destinations.
  • The goal here is to route Droplets 1–3 simultaneously to their destination cells.
  • Two additional cells are activated unintentionally when the activation voltage is applied to the row and column pins corresponding to the destination cells.
  • The authors refer to this phenomenon as electrode interference.

B. Fluidic Constraints

  • Droplet manipulations must also conform to rules referred to as the fluidic constraints [23].
  • These constraints are given by the following set of inequalities:.
  • The fluidic constraints specify the minimum distance between droplets needed to avoid unintentional fluidic operations that arise due to the overlapping of droplets over adjacent electrodes.
  • These constraints apply to both direct-addressing-based and crossreferencing-based biochips.

C. Destination-Cell Categorization

  • As shown in Fig. 3, the concurrent manipulation of multiple droplets must be carried out without introducing any electrode interference.
  • The authors propose a solution based on destination-cell categorization.
  • Note that if these two droplets are concurrently moved, as determined by the grouping procedure, by the activation of (Column 2, Row 2) and (Column 3, Row 2), they mix at (3, 2).
  • This approach provides more concurrence than the baseline method of moving one droplet at a time.
  • Simulation results in Section VII show that there is only a small increase in the bioassay processing time compared to direct addressing.

D. Graph-Theoretic Model and Clique Partitioning

  • The authors have thus far introduced the basic idea of multiple droplet manipulations based on destination-cell categorization, and shown that the droplets in each group can simultaneously be moved.
  • Note however that the grouping need not be unique.
  • Nodes 1 and 2, which represent the Droplet 1 and Droplet 2, respectively, are connected by an edge because the destination cells for these droplets are accessed using Column 3 in the array.
  • Clique partitioning refers to the problem of dividing the nodes into overlapping subsets such that the subgraph induced by each subset of nodes is a clique.
  • The categorization of destination cells using the grouping of droplets is equivalent to the problem of determining a minimal clique partition.

E. Algorithm for Droplet Grouping

  • Next, the authors describe a greedy algorithm to determine a clique partition for the DMG.
  • The largest clique is first determined and then nodes and edges corresponding to this clique are deleted form the graph.
  • The steps of the complete procedure to determine the order of droplet movements can be stated as follows.
  • 3) Scan each row and each column to find the row/column with the largest set of destination cells.
  • 5) Check if all the movements in the snapshot have been processed.

V. SCHEDULING OF ROUTING FOR EFFICIENT GROUPING

  • The column- and row-scan methods described above enable the simultaneous manipulation of multiple droplets on the cross-referencing chip.
  • The efficiency of this approach depends on the prealignment of the destination cells corresponding to the droplet movements in the target dropletrouting snapshot.
  • The better aligned the destination cells are, i.e., they share the same column/row, the larger the number is of droplets that can simultaneously be moved.
  • Therefore, to increase efficiency, it is important to generate routing snapshots with well-aligned destination cells.

A. Routing Plan Decomposition

  • Note that routing snapshots are obtained from the schedule of droplet movements corresponding to the droplet-routing plan.
  • Next, the algorithm moves them one electrode downwards and one electrode to the right when they meet D4.
  • The authors therefore conclude that the worst case time complexity for Steps 2)–5) is O(NM2).
  • Therefore, the authors limit the use of [29] for handling droplet movements in Step 7) of the routing scheduling method, i.e., the ones that correspond to the reverse of the starting direction.

A. Random Synthetic Benchmarks

  • The authors first use random synthetic benchmarks to evaluate the effectiveness of the grouping-based droplet-movement approach.
  • Each droplet-movement plan is provided as input to the grouping-based method, and the number of steps required for droplet movement is calculated.
  • As shown Table I, regardless of DIP value, the NSR decreases with array size.
  • This shows that the grouping-based Authorized licensed use limited to: IEEE Xplore.
  • Method is more efficient for concurrent droplet manipulation on large-scale digital microfluidic arrays.

B. Multiplexed Bioassay Example

  • Next, the authors evaluate the proposed scheduling and groupingbased droplet-manipulation methods by using them to implement the routing plan for a set of real-life bioassays, namely multiplexed in vitro diagnostics on human physiological fluids.
  • The computation time for the routing scheduling and the manipulation method for the entire assay is 173 s, on a Intel Core Duo 2-GHz PC with 2G of RAM.
  • If no grouping method is used, droplet movements are carried out one per cycle.
  • Using the grouping-based manipulation method, the number of cycles is reduced to 53 cycles.
  • Next, the authors apply a combination of the proposed cross-based scheduling method and grouping-based droplet-based manipulation to the routing plan.

VIII. CONCLUSION

  • The authors have proposed a power-efficient high-throughput droplet manipulation method for a “cross-referencing” addressing method that uses “rows” and “columns” to access electrodes in digital microfluidic arrays.
  • Comput.-Aided Design Integr. Circuits Syst., vol. 25, no.
  • S. Fei and K. Chakrabarty, “Architectural-level synthesis of digital microfluidics-based biochips,” in Proc. IEEE/ACM Int. Conf. Comput.
  • M. G. Pollack, “Electrowetting-based microactuation of droplets for digital microfluidics,” Ph.D. dissertation, Duke Univ., Durham, NC, 2001. [31].
  • He is currently a Professor of electrical and computer engineering with Duke University, Durham, NC.

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Content maybe subject to copyright    Report

IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008 1905
A Droplet-Manipulation Method for Achieving
High-Throughput in Cross-Referencing-Based
Digital Microfluidic Biochips
Tao Xu, Student Member, IEEE, and Krishnendu Chakrabarty, Fellow, IEEE
Abstract—Digital microfluidic biochips are revolutionizing
high-throughput DNA, immunoassays, and clinical diagnostics.
As high-throughput bioassays are mapped to digital microflu-
idic platforms, the need for design automation techniques for
pin-constrained biochips is being increasingly felt. However,
most prior work on biochips computer-aided design has as-
sumed independent control of the underlying electrodes using a
large number of (electrical) input pins. We propose a droplet-
manipulation method based on a “cross-referencing” addressing
method that uses “row” and “columns” to access electrodes.
By mapping the droplet-movement problem on a cross-
referenced chip to the clique-partitioning problem from graph
theory, the proposed method allows simultaneous movement of a
large number of droplets on a microfluidic array. Concurrency is
enhanced through the use of an efficient scheduling algorithm that
determines the order in which groups of droplets are moved. The
proposed design-automation method facilitates high-throughput
applications on a pin-constrained biochip, and it is evaluated using
random synthetic benchmarks and a set of multiplexed bioassays.
Index Terms—Bioassays, droplet-based microfluidics, droplet
routing, lab-on-chip, physical design.
I. INTRODUCTION
M
ICROFLUIDICS technology has made great strides in
recent years [1]–[3]. Promising applications of this
emerging technology include high-throughput deoxyribonu-
cleic acid (DNA) sequencing, immunoassays, environmental
toxicity monitoring, and point-of-care diagnosis of diseases
[4]. Microfluidics-based miniaturized devices, often referred to
in the literature as biochips, are being increasingly used for
laboratory procedures involving molecular biology.
Currently, most commercially available biochips rely on
continuous fluid flow in etched microchannels. Fluid flow is
controlled either using micropumps and microvalves [2] or us-
ing electrokinetics [5]. An alternative category of microfluidic
biochips relies on the principle of electrowetting on dielectric.
Discrete droplets of nanoliter volumes can be manipulated
Manuscript received December 29, 2007; revised May 12, 2008. Current
version published October 22, 2008. This work was supported by the National
Science Foundation under Grant CCF-0541055. An earlier version of this
paper was published in Proc. IEEE Design Automation and Test in Europe
Conference, pp. 552–557, 2007. This paper was recommended by Associate
Editor D. Z. Pan.
The authors are with the Department of Electrical and Computer Engi-
neering, Duke University, Durham, NC 27708 USA (e-mail: tx@ee.duke.edu;
krish@ee.duke.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCAD.2008.2006086
in a “digital” manner on a 2-D electrode array. Hence, this
technology is referred to as “digital microfluidics” [1].
A digital microfluidic biochip typically consists of a pat-
terned metal electrode array (e.g., chrome or indium tin oxide),
on which fluid-handling operations such as merging, split-
ting, mixing, and dispensing of nanoliter droplets containing
biological samples are executed. Electrodes are connected to
control pins for electrical activation. A number of prototypes
of such biochips use a direct-addressing scheme for the control
of electrodes [6]. Each electrode is connected to a dedicated
control pin; it can therefore be activated independently. This
method allows the maximum freedom of droplet manipulation,
but it necessitates an excessive number of control pins for prac-
tical biochips. As more bioassays are concurrently executed on
digital microfluidic platforms [7], [8], system complexity and
the number of electrodes are expected to steadily increase. A
large number of control pins and the associated interconnect
routing problem significantly add to product cost. Thus, the
design of pin-constrained digital microfluidic arrays is of great
practical importance for the emerging marketplace.
Electrode addressing methods that allow the control of dig-
ital microfluidic arrays with a small number of pins are now
receiving attention. The method presented in [9] uses array
partitioning and careful pin assignment to reduce the number of
control pins. However, this method leads to a mapping of pins
to electrodes that is specific to a target biofluidic application.
An improved design method based on array partitioning is
presented in [10], but it is also specific to a given bioassay. A
more promising design uses row and column addressing, which
is referred to as “cross referencing.” An electrode is connected
to two pins, corresponding to a row and a column, respectively
[11]. However, due to the problem of electrode interference, a
cross-referencing method is particularly prone to unintentional
droplet movement when it attempts to simultaneously move
more than two arbitrarily positioned droplets. This limitation
is a major drawback for high-throughput applications, such as
DNA sequencing and large-scale proteomic analysis [12].
In this paper, we propose an automated droplet-manipulation
method based on the cross-referencing design for high-
throughput applications. The method includes a power-efficient
high-throughput droplet manipulation scheme which allows
concurrent transportation of multiple droplets. The graph-
theoretic concept of clique partitioning is used to determine
groups of droplet that can simultaneously be moved on the
microfluidic array. To enhance the efficiency of the grouping
method, a routing-scheduling algorithm is introduced to
0278-0070/$25.00 © 2008 IEEE
Authorized licensed use limited to: IEEE Xplore. Downloaded on October 30, 2008 at 08:54 from IEEE Xplore. Restrictions apply.

1906 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008
Fig. 1. Schematic diagram of a digital microfluidic biochip.
generate well-aligned manipulation snapshots from the target
droplet-routing plan, thereby facilitating high throughput oper-
ations on cross-referencing-based chips.
The proposed method provides the means for carrying out
high-throughput bioassays on a cross-referencing-based chip
through the activation of a small number of electrodes. There-
fore, this approach is particularly useful for low-power ap-
plications such as battery-operated sensors for environmental
monitoring and hand-held devices for point-of-care diagnosis.
For other applications where power consumption is not a sig-
nificant concern, a variant of the proposed method is presented
to further enhance droplet-manipulation throughput.
The rest of this paper is organized as follows. Section II
provides an overview of digital microfluidic biochips. In
Section III, we discuss related prior work on pin-constrained
biochip design for high-throughput applications. Section IV
maps the droplet manipulation problem to graph theory and
presents the proposed power-efficient high-throughput droplet
manipulation method. Section V describes the route scheduling
algorithm for droplet routing, which leads to enhanced con-
currence of droplet movement. Section VI presents a power-
oblivious version of the design technique, which leads to higher
throughout. The proposed methods are evaluated using random
synthetic benchmarks in Section VII. A multiplexed bioassay
is also used as a case study. Finally, conclusions are drawn in
Section VIII.
II. D
IGITAL MICROFLUIDIC BIOCHIPS
In this paper, we consider digital microfluidic biochips that
rely on the principle of electrowetting on dielectric. Droplets
of nanoliter volumes, which contain biological samples, are
manipulated on a 2-D electrode array [1]. A unit cell in the
array includes a pair of electrodes that acts as two parallel
plates. In most prototype digital microfluidic biochips based
on the direct-addressing scheme, the bottom plate contains a
patterned array of individually controlled electrodes, and the
top plate is coated with a continuous ground electrode. A
droplet rests on a hydrophobic surface over an electrode, as
shown in Fig. 1. Recently, coplanar microfluidic devices, i.e.,
arrays without a top plate, have also been demonstrated [13].
Using the electrowetting phenomenon, droplets can be moved
to any location on a 2-D array. An alternative category of digital
microfluidic biochips utilizes orthogonally placed rows of pins
on the top and bottom plates. A unit cell can be activated by
selecting orthogonally positioned pins on the top and bottom
plate that cross at this cell.
Both designs move droplets by applying a control voltage
to a unit cell adjacent to the droplet and, at the s ame time,
deactivating the one just under the droplet. This electronic
method of wettability control creates interfacial tension gra-
dients that move the droplets to the charged electrode. Fluid-
handling operations such as droplet merging, splitting, mixing,
and dispensing can be executed in a similar manner. For ex-
ample, mixing can be performed by routing two droplets to the
same location and then turning them about some pivot points
[14]. The digital microfluidic platform offers the additional
advantage of flexibility, referred to as reconfigurability, since
fluidic operations can be performed anywhere on the array.
Droplet routes and operation scheduling result are programmed
into a microcontroller that drives electrodes in the array. In
addition to electrodes, optical detectors such as LEDs and
photodiodes are also integrated in digital microfluidic arrays to
monitor colorimetric bioassays [7].
Demonstrated applications of digital microfluidics include
the on-chip detection of explosives such as commercial-grade
2,4,6-trinitrotoluene (TNT) and pure 2,4-dinitrotoluene [6],
automated on-chip measurement of airborne particulate mat-
ter [ 15], [16], and colorimetric assays [7]. Digital microflu-
idic biochips are being designed for on-chip gene sequencing
through synthesis [15], and integrated hematology, pathology,
molecular diagnostics, cytology, microbiology, and serology on
the same platform [17]. A prototype has been developed for
pyrosequencing [17], which targets the simultaneous execution
of 10
6
fluidic operations and the processing of billions of
droplets. Other lab-on-chip systems are being designed for pro-
tein crystallization, which requires the concurrent execution of
hundreds of operations [18]. A commercially available droplet-
based (using dielectrophoresis) lab-on-chip embeds more than
600 000 20 µmby20µm electrodes with integrated optical
detectors [19].
In a recent review paper on the use of microfluidics for pro-
tein crystallization [20], the following question was posed: can
we purchase identical crystallization devices, produced under
adequate quality control? The authors go on to say, “Drawing
upon integrated circuits as an analogy, microfluidics devices
may be reducible to a standard set of discrete operations which
can then be custom assembled to form more complex operations
as needed. With this approach, the success of manufacturing
investment does not have to rest upon a single application.”
Authorized licensed use limited to: IEEE Xplore. Downloaded on October 30, 2008 at 08:54 from IEEE Xplore. Restrictions apply.

XU AND CHAKRABARTY: DROPLET-MANIPULATION METHOD FOR ACHIEVING HIGH-THROUGHPUT 1907
The discrete droplet-based biochip being considered in this
paper is perfectly suited as a platform technology, since it
avoids the common pitfall of custom devices offered by other
continuous-flow microfluidic technologies.
III. R
ELATED PRIOR WORK
Recent years have seen a steady increase in the level of inte-
gration and system complexity of digital microfluidic biochips
[15]. These advances in technology serve as a powerful driver
for research on computer-aided design tools for biochip design.
Classical architectural and geometric-level synthesis method
can be adapted for the automated design of biochips that
can execute laboratory protocols [21]–[25]. A unified synthe-
sis method, which combines operation scheduling, resource
binding, and module placement, has been proposed in [22].
Systematic droplet routing strategies have also been developed
[23], [26]–[28]. These early design automation techniques are
useful for biochip design and rapid prototyping, but they all rely
on the availability of a direct-addressing scheme.
Pin-constrained design of digital microfluidic biochips was
recently proposed in [9]. This method uses array partitioning
and careful pin assignment to reduce the number of con-
trol pins. However, it requires detailed information about the
scheduling of assay operations, microfluidic module placement,
and droplet routing pathways. Thus, the array design in such
cases is specific to a target biofluidic application. An improved
design method based on array partitioning is presented in [10]
but i t is also specific to a given bioassay.
In another method proposed in [7], the number of control
pins for a fabricated electrowetting-based biochip is minimized
by using a multiphase bus for the fluidic pathways. Every nth
electrode in an n-phase bus is electrically connected, where n
is small number (typically n =4). Thus, only n control pins
are needed for a transport bus, irrespective of the number of
electrodes that it contains. Although the multiphase bus method
is useful for reducing the number of control pins, it is only
applicable to a 1-D (linear) array.
An alternative method based on a cross-reference driving
scheme is presented in [11]. This method allows control of
an N × M grid array with only N + M control pins. The
electrode rows are patterned on both the top and bottom plates,
and orthogonally placed. In order to drive a droplet along
the X-direction, electrode rows on the bottom plate serve
as driving electrodes, while electrode rows on the top serve
as reference ground electrodes. The roles are reversed for
movement along the Y -direction, as shown in Fig. 2. This
cross-reference method facilitates the reduction of control pins.
However, due to electrode interference, this design is partic-
ularly prone to unintentional droplet manipulation; the simul-
taneous movement of more than two droplets is attempted.
The resulting serialization of droplet movement is a serious
drawback for high-throughput applications.
The minimization of the assay completion time, i.e., the max-
imization of throughput, is essential for environmental moni-
toring applications where sensors can provide early warning.
Real-time response is also necessary for surgery and neonatal
clinical diagnostics. Finally, biological samples are sensitive to
Fig. 2. Cross sections of a cross-referencing microfluidic device that uses
single-layer driving electrodes on both top and bottom plates.
the environment and to temperature variations, and it is difficult
to maintain an optimal clinical or laboratory environment on
chip. To ensure the integrity of assay r esults, it is therefore
desirable to minimize the time that samples spend on-chip
before assay results are obtained.
Increased throughput also improves operational reliability.
Long assay durations imply that high actuation voltages need
to be maintained on some electrodes, which accelerate insulator
degradation and dielectric breakdown, reducing the number of
assays that can be performed on a chip during its lifetime.
Recently, Griffith et al. [29] proposed a droplet-manipulation
method that can ensure concurrent manipulation of multiple
droplets without unintentional droplet movements. While this
method leads to higher throughput for cross-referencing-based
biochips, the increase in throughput is limited by the precom-
puted droplet routing pathways. To overcome this bottleneck,
efficient algorithms are needed to generate efficient routing
pathways that facilitate high-throughput droplet manipulation.
Moreover, the droplet-manipulation method of [29] is in-
efficient in terms of power consumption. Power consumption
is typically neglected in direct-addressing-based chips because
it has been found to be negligible for small prototypes (the
activation of one cell typically requires 1 2 µWpower)
[30]. However, in a cross-referencing-based design, to activate
a single unit cell, two pins (a column pin and a row pin)
must be activated. For an N × N array, the current drawn by
a pin is N times that for a direct-addressing chip, since all
electrodes on the corresponding row or column are activated.
Therefore, the power consumption for activating a cell i n a
cross-referencing-based chip is also N times higher than that
for a direct-addressing chip. The method in [29] relies on the
activation of multiple column and row pins simultaneously
to carry out concurrent droplet manipulations. Therefore, this
scheme can potentially lead to a sharp increase in biochip power
consumption. High power consumption is a serious problem for
battery-driven chemical/biosensors and hand-held lab-on-chip
devices. High power consumption (and the resulting on-chip
heat generation) is also detrimental for thermal-sensitive sam-
ples such as proteins, which are commonly used in bioassays
[31]. Therefore, a power-efficient droplet-manipulation method
is needed for cross-referencing biochips.
IV. P
OW E R -EFFICIENT INTERFERENCE-FREE
DROPLET MANIPULATION BASED ON
DESTINATION-CELL CATEGORIZATION
In this section, we focus on the problem of manipulating
multiple droplets based on digital microfluidic biochips that use
cross-referencing to address the electrodes.
Authorized licensed use limited to: IEEE Xplore. Downloaded on October 30, 2008 at 08:54 from IEEE Xplore. Restrictions apply.

1908 IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 27, NO. 11, NOVEMBER 2008
Fig. 3. Example to illustrate the problem of electrode interference. H/L stands
for high/low voltage pairs to activate the cells, and unselected row/column pins
are left floating (F).
A. Electrode Interference
For the concurrent manipulation of multiple droplets on a
cross-referencing-based biochip, multiple row and column pins
must be selected to activate the destination cells, i.e., cells to
which the droplets are supposed to move. However, the selected
row and column pins may also result in the activation of cells
other than the intended droplet destinations. An example is
shown in Fig. 3. The goal here is to route Droplets 1–3 simul-
taneously to their destination cells. Droplet 4 is supposed to
remain in its current location. However, two additional cells are
activated unintentionally when the activation voltage is applied
to the row and column pins corresponding to the destination
cells. As a result, Droplet 4 is unintentionally moved one cell
up (along the Y -direction). We refer to this phenomenon as
electrode interference.
B. Fluidic Constraints
Droplet manipulations must also conform to rules referred to
as the fluidic constraints [23]. These constraints are given by the
following set of inequalities: 1) |P
i
(t) P
j
(t)|≥2;2)|P
i
(t +
1) P
j
(t)|≥2;3)|P
i
(t) P
j
(t +1)|≥2;4)|P
i
(t +1)
P
j
(t +1)|≥2, where P
i
(t) is the position of droplet i at time
t and P
j
(t) is the position of droplet j at time t. The fluidic
constraints specify the minimum distance between droplets
needed to avoid unintentional fluidic operations that arise due
to the overlapping of droplets over adjacent electrodes. These
constraints apply to both direct-addressing-based and cross-
referencing-based biochips.
C. Destination-Cell Categorization
As shown in Fig. 3, the concurrent manipulation of multiple
droplets must be carried out without introducing any electrode
interference. For simplicity, here we only focus on the imple-
mentation of a set of multiple droplet manipulations that can be
carried out concurrently (in a single routing step) on a direct-
addressing-based chip, without violating any fluidic constraints.
We refer to such a set of droplet manipulations as a droplet-
manipulation snapshot.
We propose a solution based on destination-cell categoriza-
tion. Note that the problem highlighted in Fig. 3 can be avoided
if the destination cells of the droplets being simultaneously
moved reside on the same column or row. However, electrode
interference may still occur within the same column or r ow, as
Fig. 4. Example of electrode interference within the same row.
Fig. 5. Example to illustrate destination-cell-based categorization.
shown in Fig. 4. Suppose Droplet 1 and Droplet 2 are both
moved one cell to the left at the same time. Although no
additional cells are unintentionally activated, Droplet 1 under-
goes unintentional splitting in this situation. Fortunately, further
scrutiny reveals that the situation in Fig. 4 is only a false alarm.
The intended multiple droplet manipulation violates the con-
straint |P
i
(t +1) P
j
(t)|≥2. Such manipulations cannot be
carried out concurrently even on a direct-addressing-based chip.
Thus, they will never appear in a single droplet-manipulation
snapshot. Therefore, it is safe to carry out concurrent manipu-
lation of multiple droplets whose destination cells are accessed
by the same column or row.
On the basis of the above observations, we consider the
droplets that can simultaneously be moved as part of the bioas-
say, and place them in different groups. A group consists of
droplets whose destination cells share the same column or row.
An example is shown in Fig. 5. A total of nine droplets are
needed to be moved on a 10 × 10 array. As discussed above,
we group the droplet movements according to their destination
cells. For example, Droplets 4 and 9 form a group since the
destination cells, in both cases, resides on Row 2. Similarly,
Droplets 1, 2, and 3 are placed in the same group since they are
all moving to Column 3. Following this grouping process, we
finally get four groups of droplets, i.e., {4, 9}, {1, 2, 3}, {5, 6},
{7, 8}.
In this way, the manipulation of multiple droplets is ordered
in time; droplets in the same group can simultaneously be
moved without electrode interference, but the movements for
the different groups must be sequential. For example, droplet
movements for the group {4, 9} in Fig. 5 can simultaneously
be carried, as shown in Fig. 6. Droplet movements are carried
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XU AND CHAKRABARTY: DROPLET-MANIPULATION METHOD FOR ACHIEVING HIGH-THROUGHPUT 1909
Fig. 6. Example to illustrate the concurrent movement of a group of droplets.
Fig. 7. Example of potential electrode interference due to asynchronous
processing of multiple droplet manipulations.
out one group after another until all the droplet movements are
completed.
Note that the ordering of droplet movements based only on
the above grouping strategy can cause electrode interference
and inadvertent mixing. An example is shown in Fig. 7. The
movement of Droplet 2 alone to the left by activating Column 3
will not influence Droplet 1. Similarly, the movement of
Droplet 1 alone to the right by activating Column 2 will not
influence Droplet 2. Note that if these two droplets are concur-
rently moved, as determined by the grouping procedure, by the
activation of (Column 2, Row 2) and (Column 3, Row 2), they
mix at (3, 2). However, manipulations of this type violate the
fluidic constraint given by |P
i
(t +1) P
j
(t +1)|≥2. Thus,
they cannot exist in a single droplet-manipulation snapshot.
Therefore, it is safe to carry out the droplet manipulations in
a single manipulation snapshot with an arbitrary ordering.
Although the grouping of droplets based on destination
cells reduces the number of droplets that can simultaneously
be moved, this approach provides more concurrence than the
baseline method of moving one droplet at a time. Compared
to direct addressing, an order of magnitude reduction in the
number of control pins is obtained. Simulation results in
Section VII show that there is only a small increase in the bio-
assay processing time compared to direct addressing. The above
droplet-manipulation method is focused on minimizing power
consumption because, in each step, only droplet manipulations
that involve a single column or row are carried out. Additional
droplet movements are typically possible, but concurrence is
traded off for power in this method. An extension to allow
higher concurrence is described in Section VI.
D. Graph-Theoretic Model and Clique Partitioning
We have thus far introduced the basic idea of multiple
droplet manipulations based on destination-cell categorization,
and shown that the droplets in each group can simultaneously
be moved. Assuming that each step takes constant processing
time, the total completion time for a set of droplet movement
operations is determined by the number of groups derived from
Fig. 8. Mapping of destination-cell layout to an undirected graph.
the categorization of destination cells. Note however that the
grouping need not be unique. For instance, in the example of
Fig. 5, we can form four groups, i.e., {4, 9}, {1, 2, 3}, {5, 6},
and {7, 8}. However, {1, 2, 3, 4}, {5, 6}, {7, 8, 9} is also a
valid grouping of the droplets. The latter grouping is preferable
because three groups allow more concurrence and, therefore,
lower bioassay completion time.
The problem of finding the minimum number of groups can
directly be mapped to the clique-partitioning problem from
graph theory [32]. To illustrate this mapping, we use the droplet
manipulation problem defined in Fig. 5. Based on the destina-
tions of the droplets, an undirected graph, referred to as the
droplet-movement graph (DMG), is constructed for each time-
step (see Fig. 8). Each node in the DMG represents a droplet.
An edge in the graph between a pair of nodes indicates that
the destination cells for the two droplets either share a row or
a column. For example, Nodes 1 and 2, which represent the
Droplet 1 and Droplet 2, respectively, are connected by an edge
because the destination cells for these droplets are accessed
using Column 3 in the array. Similarly, Nodes 4 and 9 are
connected by an edge because the corresponding destination
cells are addressed using the same row.
A clique in a graph is defined as a complete subgraph, i.e.,
any two nodes in this subgraph are connected by an edge [32].
Clique partitioning refers to the problem of dividing the nodes
into overlapping subsets such that the subgraph induced by each
subset of nodes is a clique. A minimal clique partition is one
that covers the nodes in the graph with a minimum number
of nonoverlapping cliques. The grouping of droplets as dis-
cussed above is equivalent to the clique-partitioning problem.
The categorization of destination cells using the grouping of
droplets is equivalent to the problem of determining a minimal
clique partition. Cliques of different sizes for a given DMG are
shown in Fig. 8. A minimal clique partition here is given by
{1, 2, 3, 4}, {5, 6}, {7, 8, 9}, which corresponds to the groups
derived above. Although the general clique-partitioning prob-
lem is known to be NP-hard [33], a number of heuristics are
available in the literature to solve it in an efficient manner.
E. Algorithm for Droplet Grouping
Next, we describe a greedy algorithm to determine a (min-
imal) clique partition for the DMG. The algorithm determines
cliques for the DMG in an iterative manner.
The largest clique is first determined and then nodes and
edges corresponding to this clique are deleted form the graph.
Next, the clique searching procedure is applied to the reduced
graph. The algorithm terminates when all the nodes in the DMG
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Citations
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Journal ArticleDOI
Suresh Neethirajan1, Xuan Weng1, A. Tah1, J.O. Cordero1, K.V. Ragavan1 
TL;DR: Major challenges to allergen monitoring include the introduction of new allergens into modern diets, the rising incidence hypersensitivities, lack of clinical understanding of the types and causes of food allergies, limited commercial availability of biosensors, and the lack of international standards or agreement on threshold detection levels.
Abstract: Food allergies are a type I hypersensitivity immune responses that can be life threatening. While exposure therapy and urgent care interventions can limit the damage of an allergic episode, there is currently no cure for food hypersensitivities. Many patients will experience an accidental exposure to a known allergen due to the complexity of food preparation methods in the modern diet. One method of avoidance is to monitor food with point of care (POC) biosensors that can detect known allergens. These detectors are categorized according to their sensor mechanism, such as optical, electromechanical, and electrochemical biosensors. More innovations that are recent combine biosensors with genosensors and cell assays. Major challenges to allergen monitoring include the introduction of new allergens into modern diets, the rising incidence hypersensitivities, lack of clinical understanding of the types and causes of food allergies, limited commercial availability of biosensors, and the lack of international standards or agreement on threshold detection levels. Public health leaders are taking on these challenges, and their efforts will reduce the incidence of preventable exposures and improve overall food safety management.

81 citations

Journal ArticleDOI
TL;DR: This paper presents the first design automation flow that considers the cross-contamination problems on pin-constrained biochips, and proposes early crossing minimization algorithms during placement and systematic wash droplet scheduling and routing that require only one extra control pin and zero assay completion time overhead for practical bioassays.
Abstract: Digital microfluidic biochips have emerged as a popular alternative for laboratory experiments. Pin-count reduction and cross-contamination avoidance are key design considerations for practical applications with different droplets being transported and manipulated on highly integrated biochips. This paper presents the first design automation flow that considers the cross-contamination problems on pin-constrained biochips. The factors that make the problems harder on pin-constrained biochips are explored. To cope with these cross contaminations, this paper proposes: 1) early crossing minimization algorithms during placement, and 2) systematic wash droplet scheduling and routing that require only one extra control pin and zero assay completion time overhead for practical bioassays. Experimental results show the effectiveness and scalability of our algorithms for practical bioassays.

61 citations


Cites background from "A Droplet-Manipulation Method for A..."

  • ...Some of these considerations are now addressed as in [ 22 ] and [24] but not combined with those considered in this paper....

    [...]

Proceedings ArticleDOI
13 Jun 2010
TL;DR: This paper presents the first design automation flow that considers the cross-contamination problems on pin-constrained biochips, and proposes early crossing minimization algorithms during placement and systematic wash droplet scheduling and routing that require only one extra control pin and zero assay completion time overhead for practical bioassays.
Abstract: Digital microfluidic biochips have emerged as a popular alternative for laboratory experiments. Pin-count reduction and cross-contamination avoidance are key design considerations for practical applications with different droplets being transported and manipulated on highly integrated biochips. We present in this paper the first design automation flow that considers the cross-contamination problems on pin-constrained biochips. We explore the factors that make the problems harder on pin-constrained biochips. To cope with these cross contaminations, we propose (1) early crossing minimization algorithms during placement, and (2) systematic wash droplet scheduling and routing that require only one extra control pin and zero assay completion time overhead for practical bioassays. Experimental results show the effectiveness and scalability of our algorithms for practical bioassays.

44 citations

Journal ArticleDOI
TL;DR: This paper presents a comprehensive pin-constrained biochip design flow that addresses the pin-count issue at all design stages and shows the efficiency and a 55-57% pin- count reduction over the state-of-the-art algorithms/flow.
Abstract: Digital microfluidic biochips have emerged as a popular alternative for laboratory experiments. To make the biochip feasible for practical applications, pin-count reduction is a key problem to higher-level integration of reactions on a biochip. Most previous works approach the problem by post-processing the placement and routing solutions to share compatible control signals; however, the quality of such sharing algorithms is inevitably limited by the placement and routing solutions. We present in this paper a comprehensive pin-constrained biochip design flow that addresses the pin-count issue at all design stages. The proposed flow consists of three major stages: 1) pin-count aware stage assignment that partitions the reactions in the given bioassay into execution stages; 2) pin-count aware device assignment that determines a specific device used for each reaction; and 3) guided placement, routing, and pin assignment that utilize the pin-count saving properties from the stage and device assignments to optimize the assay time and pin-count. For both the stage and device assignments, basic integer linear programming formulations and effective solution-space reduction schemes are proposed to minimize the assay time and pin-count. Experimental results show the efficiency of our methods and a 55-57% pin-count reduction over the state-of-the-art algorithms/flow.

43 citations


Cites background from "A Droplet-Manipulation Method for A..."

  • ...The issue of power consumption has been addressed in the routing problem on cross-referencing microfluidic biochips [ 21 ]....

    [...]

  • ...Thus, the activation power of a single control pin is higher [ 21 ]....

    [...]

  • ...Interested readers may find more discussions about the design of cross-referencing biochips in [8], [ 21 ], and [22]....

    [...]

Journal ArticleDOI
TL;DR: This paper proposes the first droplet routing algorithm for PDMFBs that can integrate pin-count reduction with droplets routing stage, and is capable of minimizing the number of control pins, the numbers of used cells, and the routing time.
Abstract: With the increasing design complexities, the design of pin-constrained digital microfluidic biochips (PDMFBs) is of practical importance for the emerging marketplace. However, solutions of current pin-count reduction are inevitably limited by simply adopting it after the droplet routing stage. In this paper, we propose the first droplet routing algorithm for PDMFBs that can integrate pin-count reduction with droplet routing stage. Furthermore, our algorithm is capable of minimizing the number of control pins, the number of used cells, and the droplet routing time. We first present a basic integer linear programming (ILP) formulation to optimally solve the droplet routing problem for PDMFBs with simultaneous multiobjective optimization. Due to the complexity of this ILP formulation, we also propose a two-stage technique of global routing followed by incremental ILP-based routing to reduce the solution space. To further reduce the runtime, we present a deterministic ILP formulation that casts the original routing optimization problem into a decision problem, and solve it by a binary solution search method that searches in logarithmic time. Extensive experiments demonstrate that in terms of the number of the control pins, the number of the used cells, and the routing time, we obtain much better achievement than all the state-of-the-art algorithms in any aspect.

41 citations


Cites background from "A Droplet-Manipulation Method for A..."

  • ...In other words, multiple electrodes are controlled by a single control signal and are thus driven simultaneously....

    [...]

References
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Book
01 Jan 1979
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Abstract: This is the second edition of a quarterly column the purpose of which is to provide a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed. Readers having results they would like mentioned (NP-hardness, PSPACE-hardness, polynomial-time-solvability, etc.), or open problems they would like publicized, should send them to David S. Johnson, Room 2C355, Bell Laboratories, Murray Hill, NJ 07974, including details, or at least sketches, of any new proofs (full papers are preferred). In the case of unpublished results, please state explicitly that you would like the results mentioned in the column. Comments and corrections are also welcome. For more details on the nature of the column and the form of desired submissions, see the December 1981 issue of this journal.

40,020 citations

Journal ArticleDOI
TL;DR: It was found that the system of phenol and 4-amino phenazone is well suited to the determination of glucose and the development of phosphatase is described.
Abstract: the oxygen acceptors originally used were 0 tolidine, benzidine and o-dianisidine. It has since been established that these three substances are carcinogens and many alternative oxygen acceptors have been suggested. Any dye showing oxidation-reduction properties or any dye formed by oxidation, such as those used in colour photography, are potentially useful but it is obviously advantageous to use reagents which have high stability. For manual work on blood a two-solution technique is desirable, one solution being used to precipitate the protein and the other to develop the colour. The development of such a method will now be described. In the determination of phosphatase, use is made of the fact that phenol in the presence of an oxidising reagent gives a purple colour with 4-amino phenazone. The possibility that the H.Oz released in the reaction of glucose oxidase with glucose could act as the oxidising agent was investigated and it was found that the system of phenol and 4-amino phenazone is well suited to the determination of glucose. By suitable adjustment of conditions the colour develops completely in 10 minutes, being stable thereafter for at least 30 minutes. Using a single-solution phosphotungstic acid precipitant containing phenol to precipitate blood protein the only other solution required is one containing glucose oxidase, peroxidase and 4-amino phenazone. These solutions contain azide as preservative; azide has no effect on the rate of colour development. In the micro and macro automated methods, the two solutions required are a diluent containing 4-amino phenazone and a colour reagent containing glucose oxidase, peroxidase and phenol.

4,548 citations


"A Droplet-Manipulation Method for A..." refers background in this paper

  • ...11 only require three manipulation steps (one step for each)....

    [...]

Book
30 Dec 1998
TL;DR: In this article, the authors present a model for drawing graphs and digraphs based on the topology of low dimensions Higher-Order Surfaces and a model of a graph.
Abstract: INTRODUCTION TO GRAPH MODELS Graphs and Digraphs Common Families of Graphs Graph Modeling Applications Walks and Distance Paths, Cycles, and Trees Vertex and Edge Attributes: More Applications STRUCTURE AND REPRESENTATION Graph Isomorphism Revised! Automorphisms and Symmetry Moved and revised! Subgraphs Some Graph Operations Tests for Non-Isomorphism Matrix Representation More Graph Operations TREES Reorganized and revised! Characterizations and Properties of Trees Rooted Trees, Ordered Trees, and Binary Trees Binary-Tree Traversals Binary-Search Trees Huffman Trees and Optimal Prefix Codes Priority Trees Counting Labeled Trees: Prufer Encoding Counting Binary Trees: Catalan Recursion SPANNING TREES Reorganized and revised! Tree-Growing Depth-First and Breadth-First Search Minimum Spanning Trees and Shortest Paths Applications of Depth-First Search Cycles, Edge Cuts, and Spanning Trees Graphs and Vector Spaces Matroids and the Greedy Algorithm CONNECTIVITY Revised! Vertex- and Edge-Connectivity Constructing Reliable Networks Max-Min Duality and Menger's Theorems Block Decompositions OPTIMAL GRAPH TRAVERSALS Eulerian Trails and Tours DeBruijn Sequences and Postman Problems Hamiltonian Paths and Cycles Gray Codes and Traveling Salesman Problems PLANARITY AND KURATOWSKI'S THEOREM Reorganized and revised! Planar Drawings and Some Basic Surfaces Subdivision and Homeomorphism Extending Planar Drawings Kuratowski's Theorem Algebraic Tests for Planarity Planarity Algorithm Crossing Numbers and Thickness DRAWING GRAPHS AND MAPS Reorganized and revised! The Topology of Low Dimensions Higher-Order Surfaces Mathematical Model for Drawing Graphs Regular Maps on a Sphere Imbeddings on Higher-Order Surfaces Geometric Drawings of Graphs New! GRAPH COLORINGS Vertex-Colorings Map-Colorings Edge-Colorings Factorization New! MEASUREMENT AND MAPPINGS New Chapter! Distance in Graphs New! Domination in Graphs New! Bandwidth New! Intersection Graphs New! Linear Graph Mappings Moved and revised! Modeling Network Emulation Moved and revised! ANALYTIC GRAPH THEORY New Chapter! Ramsey Graph Theory New! Extremal Graph Theory New! Random Graphs New! SPECIAL DIGRAPH MODELS Reorganized and revised! Directed Paths and Mutual Reachability Digraphs as Models for Relations Tournaments Project Scheduling and Critical Paths Finding the Strong Components of a Digraph NETWORK FLOWS AND APPLICATIONS Flows and Cuts in Networks Solving the Maximum-Flow Problem Flows and Connectivity Matchings, Transversals, and Vertex Covers GRAPHICAL ENUMERATION Reorganized and revised! Automorphisms of Simple Graphs Graph Colorings and Symmetry Burnside's Lemma Cycle-Index Polynomial of a Permutation Group More Counting, Including Simple Graphs Polya-Burnside Enumeration ALGEBRAIC SPECIFICATION OF GRAPHS Cyclic Voltages Cayley Graphs and Regular Voltages Permutation Voltages Symmetric Graphs and Parallel Architectures Interconnection-Network Performance NON-PLANAR LAYOUTS Reorganized and revised! Representing Imbeddings by Rotations Genus Distribution of a Graph Voltage-Graph Specification of Graph Layouts Non KVL Imbedded Voltage Graphs Heawood Map-Coloring Problem APPENDIX Logic Fundamentals Relations and Functions Some Basic Combinatorics Algebraic Structures Algorithmic Complexity Supplementary Reading BIBLIOGRAPHY General Reading References SOLUTIONS AND HINTS New! INDEXES Index of Applications Index of Algorithms Index of Notations General Index

1,407 citations

Journal ArticleDOI
TL;DR: This work presents an alternative paradigm--a fully integrated and reconfigurable droplet-based "digital" microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids, and demonstrates reliable and repeatable high-speed transport of microdroplets.
Abstract: Clinical diagnostics is one of the most promising applications for microfluidic lab-on-a-chip systems, especially in a point-of-care setting. Conventional microfluidic devices are usually based on continuous-flow in microchannels, and offer little flexibility in terms of reconfigurability and scalability. Handling of real physiological samples has also been a major challenge in these devices. We present an alternative paradigm—a fully integrated and reconfigurable droplet-based “digital” microfluidic lab-on-a-chip for clinical diagnostics on human physiological fluids. The microdroplets, which act as solution-phase reaction chambers, are manipulated using the electrowetting effect. Reliable and repeatable high-speed transport of microdroplets of human whole blood, serum, plasma, urine, saliva, sweat and tear, is demonstrated to establish the basic compatibility of these physiological fluids with the electrowetting platform. We further performed a colorimetric enzymatic glucose assay on serum, plasma, urine, and saliva, to show the feasibility of performing bioassays on real samples in our system. The concentrations obtained compare well with those obtained using a reference method, except for urine, where there is a significant difference due to interference by uric acid. A lab-on-a-chip architecture, integrating previously developed digital microfluidic components, is proposed for integrated and automated analysis of multiple analytes on a monolithic device. The lab-on-a-chip integrates sample injection, on-chip reservoirs, droplet formation structures, fluidic pathways, mixing areas and optical detection sites, on the same substrate. The pipelined operation of two glucose assays is shown on a prototype digital microfluidic lab-on-chip, as a proof-of-concept.

1,124 citations


"A Droplet-Manipulation Method for A..." refers background or methods in this paper

  • ...This method allows the maximum freedom of droplet manipulation, but it necessitates an excessive number of control pins for practical biochips....

    [...]

  • ...This electronic method of wettability control creates interfacial tension gradients that move the droplets to the charged electrode....

    [...]

  • ...A number of prototypes of such biochips use a direct-addressing scheme for the control of electrodes [6]....

    [...]

Frequently Asked Questions (12)
Q1. What are the contributions in "A droplet-manipulation method for achieving high-throughput in cross-referencing-based digital microfluidic biochips" ?

The authors propose a dropletmanipulation method based on a “ cross-referencing ” addressing method that uses “ row ” and “ columns ” to access electrodes. 

Although the multiphase bus method is useful for reducing the number of control pins, it is only applicable to a 1-D (linear) array. 

the proposed method requires only 32 (16+16) control pins while 256 (16×16) pins are required for the directaddressing method. 

Power consumption is typically neglected in direct-addressing-based chips because it has been found to be negligible for small prototypes (the activation of one cell typically requires 1 ∼ 2 µW power) [30]. 

He has contributed over a dozen invited chapters to book volumes, published 280 papers in archival journals and refereed conference proceedings, and delivered over 110 keynote, plenary, and invited talks. 

The computation time for the power-oblivious routing scheduling and manipulation method for the entire assay is 288 s, on an Intel Core Duo 2-GHz PC with 2G of RAM. 

As a result, only 34 cycles are required for this routing plan, which is only 57% of the time required for one-at-a-time droplet, and 64% of the time required if droplet grouping is carried out without route scheduling. 

The above droplet-manipulation method is focused on minimizing power consumption because, in each step, only droplet manipulations that involve a single column or row are carried out. 

The column- and row-scan methods described above enable the simultaneous manipulation of multiple droplets on the cross-referencing chip. 

the power consumption for activating a cell in a cross-referencing-based chip is also N times higher than that for a direct-addressing chip. 

To overcome this bottleneck, efficient algorithms are needed to generate efficient routing pathways that facilitate high-throughput droplet manipulation. 

Although the general clique-partitioning problem is known to be NP-hard [33], a number of heuristics are available in the literature to solve it in an efficient manner.