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Automated Design of Pin-Constrained Digital
Microfluidic Arrays forLab-on-a-Chip
Applications
William L. Hwang, Fei Su, Krishnendu
Chakrabarty Department of Electrical Computer
Engineering Duke University, Durham, NC 27708, USA
Department of Physics, University Of Oxford
Intel Corporation
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Motivation for Biochips

• Transfer conventional biochemical laboratory
  methods to lab-on-a-chip (LoC), or microfluidic
  biochips
• Potential to revolutionize biosensing, clinical
  diagnostics, drug discovery
• Small size and sample volumes, O(nL)
• Lower cost
• Higher sensitivity

Digital Microfluidic Biochip
Conventional Biochemical Analyzer
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Microfluidic Biochips

• Based on precise control of very small volumesof
  liquids
• Integrate various fluid-handling functions such
  as sample prep, analysis, separation, and
  detection
• Most commercially available microfluidic devices
  are continuous-flow
• Permanently etched microchannels, pumps, and
  valves

(Duke University) 2002
(University of Michigan) 1998
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Microfluidic Biochips

• Digital microfluidic biochips (DMBs)
• Manipulate discrete droplets (smaller volumes)
• Electrical actuation
• No need for cumbersome micropumps and microvalves
• Dynamic reconfigurability (virtual routes)
• Architectural scalability and greater automation
• System clock controls droplet motion similar in
  operationto digital microprocessor

(Duke University) 2002
(University of Michigan) 1998
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Electrowetting

• Novel microfluidic platform invented at Duke
  University
• Droplet actuation achieved through an effect
  called electrowetting

Applied Potential The droplets surface energy
increases, which results in a reduced contact
angle. The droplet now wets the surface.
No Potential A droplet on a hydrophobic surface
originally has a large contact angle.
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Actuation Principle

• Droplets containing samples travel inside filler
  medium (e.g., silicone oil), sandwiched in
  between glass plates
• Bottom plate patterned array of control
  electrodes
• Top plate continuous ground electrode
• Surfaces are insluated (Parylene) and hydrophobic
  (Teflon AF)

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Actuation Principle

• Droplet transport occurs by removing potentialon
  current electrode, applying potential on an
  adjacent electrode
• Interfacial tensiongradient created

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PCB Microfluidic Biochips

• Rapid prototyping and inexpensive
  mass-fabrication
• Copper layer for electrodes (coplanar grounding
  rails)
• Solder mask for insulator
• Teflon AF coating for hydrophobicity

• Disposable PCB biochip plugged into controller
  circuit board, programmed and powered with USB
  port

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OUTLINE

• What are digital microfluidic biochips (DMBs)?
• Pin-Constrained Digital Microfluidic Biochips
• Background
• Pin Assignment Problem
• Minimum Number of Pins for Single Droplet
• Pin-Assignment Problem for Two Droplets
• Virtual Partitioning Scheme
• Impact of Partitioning on PCNI
• Evaluation Example Multiplexed Bioassays
• Summary and future outlook

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Direct Addressing

• Most design and CAD research for DMBs has been
  focused on directly-addressable chips
• Suitable for small/medium-scale microfluidic
  electrode arrays (e.g., with fewer than 10 x 10
  electrodes)
• For large-scale DMBs (e.g., gt 100 x 100
  electrodes), multi-layer electrical connection
  structures and complicated routing solutions are
  needed for that many control pins

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Pin-Constrained DMBs

• Product cost is major marketability driver due to
  disposable nature of most emerging devices
• Multiple metal layers for PCB design may lead to
  reliability problems and increase fabrication
  cost
• Reduce number of independent control
  pins(pin-constrained DMBs)
• Reduce input bandwidth between electronic
  controller and microfluidic array while
  minimizing any decrease in performance

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Pin-Constrained DMBs

• Pin-constrained array
• Advantage Reduce number of independent pins for
  n x m array from n x m to k n x m
• k 5 is fewest of control pins to control
  single droplet
• Disadvantage Potential for unintentional
  interference when multiple droplets are present
• Example There is no way to concurrently move Di
  to position (1,2) and Dj to position (4,4)

Di
Dj
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Pin-Constraint Problem

• First, examine interference for two droplets
• For multiple droplets, the interference problem
  reduces to two droplet problem by examining all
  possible pairs of droplets
• Assumptions
• Any sequence of movements for multiple droplets
  can occur in parallel, controlled by a clock
• In a single clock cycle a droplet can move a
  maximum of one edge length
• Assume no diagonal adjacent effect
  (experimentally verified for smaller electrode
  sizes)

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Pin-Constraint Problem

• In some situations, we would like both droplets
  to move to another cell at the next clock edge.
• If this is not possible without interference,
  then a contingency plan would be to have one
  droplet undergo a stall cycle (stay on its
  current cell) and only move a single droplet at a
  time.

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Pin-Constraint Problem

• Notation
• Droplets i and j are denoted Di and Dj
• The position of droplet i at the time t is given
  by Pi(t)
• The directly adjacent neighbors of a droplet as a
  function of time is denoted Ni(t), where Ni(t) is
  a set of cells
• The operator is the set of pins (no
  redundancies) that control the set of cells
• Formulation
• We examine the general problem of two droplets
  moving concurrently, which reduces to the problem
  of one droplet moving and one droplet waiting if
  we set Pj(t) Pj(t1)
• Di moves from Pi(t) to Pi(t1)
• Dj moves from Pj(t) to Pj(t1)

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Interference vs. Mixing

• Interference constraints are designed to prevent
  long-range interference between the desired
  paths of droplets
• Fluidic constraints are necessary to avoid
  short-range interference in the form of
  inadvertent mixing
• Interference is a manifestation of the sharingof
  control pins between cells anywhere on the array
  while mixing (i.e., when fluidic constraints are
  violated) is a result of physical contact between
  droplets.

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Interference Constraints

• Interference constraints for two droplets moving
  simultaneously on a two-dimensional array

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Fluidic Constraints

• Fluidic constraints for two droplets on the same
  two-dimensional array

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Pin-ConstrainedNon-Interference Index

• Objective Given k independent pins, maximize the
  number of independent movements that a droplet
  can undertake from each position of the array
  while not interfering with another droplet on the
  same array.
• Need useful, application-independent index
  representing the independence of movement for two
  droplets on an array
• Easily extended to multiple droplets

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Pin-ConstrainedNon-Interference Index

• Let F be the set of all possible pin
  configurations using k pins for an n x m array.
  For a particular pin configuration c F using
  k-pins in our 2-droplet system, can develop
  algorithm to obtain a pin-constrained
  non-interference index (PCNI)
• The situation of one droplet moving and one
  droplet waiting is the safe contingency plan if
  two droplets moving concurrently cause
  interference. We therefore examine this case
  here.

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Pin-ConstrainedNon-Interference Index

• The output value, index, is a value between 0 and
  1 that is the fraction of legal moves for two
  droplets (one moving, one waiting) on a n x m
  array with each cell having its own dedicated
  control pin that are still legal with pin layout
  c F and k lt n x m pins,

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Examples of PCNI
Layout 1
Layout 2
Layout 3
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Maximizing PCNI

• Qualitatively speaking, better layouts seem to
  loosely obey two principles
• Spread out placement of pins used multiple times
• Place multiply-used pins on cells that have fewer
  neighbors (e.g. sides and corners)
• Most assays cannot even be completed as scheduled
  on pin-constrained arrays (functionality problem,
  not just throughput)

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Virtual Partitioning

• Alternative partition array into regions
  inwhich only one droplet will be present atany
  given time
• With partitioned array, of droplets that can be
  transported simultaneously without interference
  is equal to the number of partitions since
  partitions do not share any control pins (no
  interference between partitions possible)
• Fluidic constraints still must be satisfied so
  that inadvertent mixing does not occur.

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Virtual Partitioning

• When would droplets in each partition need to be
  near each other? When they need to be mixed!
• It would be a relatively simple matter to create
  central partition(s) of the array for mixing
  purposes. Sometimes not necessary.
• When mixing is complete, the merged droplet can
  be moved to the appropriate partition for further
  processing without fear of interference with
  other droplets.

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Virtual Partitioning
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Examples of Partitioned Arrays
Dynamically divide the array into two partitions
such that two droplets will never have the
potential to interfere - Only the fluidic
constraints need to be considered
Yellow Partition pins 1-5 Green Partition pins
6-10 I(10,5,5) 0.4041
Non-partitioned I(10,5,5) 0.2626
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Multiple Partitions
I(20,10,10) 0.7331
Four partitions can accommodate up to four
droplets simultaneously.
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Multiplexed Bioassays
15x15 array with depiction of droplet paths for
multiplexed glucose and lactase assays
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Multiplexed Bioassays
With 225 control pins (i.e., fully addressable
array), schedule was devised to be
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Multiplexed Bioassays
Can reduce input bandwidth while maintaining same
throughput (true of most assays). Only need 5
partitions and 25 pins (11.11 of original input
bandwidth).
Throughput would be significantly reduced with a
non-partitioned array with k 25 and in many
instances, assay cannot be finished. In many
instances, substantial rerouting and rescheduling
is required to finish the assay.
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Partitioning Advantage
For pin-constrained arrays, virtual partitioning
reduces interference when arrays are used
randomly, and removes interference when one
droplet per partition rule is followed.
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Summary

• Addressed an important problems in automating
  design of DMBs
• New design method for pin-constrained digital
  microfluidics involving virtual partitioning to
  reduce input bandwidth without sacrificing
  schedule functionality and throughput