William L. Hwang † , Fei Su ‡ , Krishnendu Chakrabarty Department of Electrical & Computer Engineering Duke Universi

2. 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

3. Shrink 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

4. 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

5. 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

6. Electrowetting • Novel microfluidic platform invented at Duke University • Droplet actuation achieved through an effect called electrowetting Applied Potential The droplet’s 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.

7. 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)

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

9. 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

10. 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

11. 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., > 100 x 100 electrodes), multi-layer electrical connection structures and complicated routing solutions are needed for that many control pins

12. 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

13. 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 Dito position (1,2) and Dj to position (4,4) Di Dj

14. 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)

15. 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.

16. 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(t+1): • Di moves from Pi(t) to Pi(t+1) • Dj moves from Pj(t) to Pj(t+1)

17. 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.

18. Interference Constraints Interference constraints for two droplets moving simultaneously on a two-dimensional array

19. 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

20. Let Φ be the set of all possible pin configurations using k pins for an n x m array. For a particular pin configuration c Φ 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. Pin-ConstrainedNon-Interference Index

21. 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 Φ and k < n x m pins,

22. Examples of PCNI Layout 1 Layout 2 Layout 3

23. 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)

24. 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.

25. 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

26. Multiplexed Bioassays 15x15 array with depiction of droplet paths for multiplexed glucose and lactase assays

27. Multiplexed Bioassays With 225 control pins (i.e., fully addressable array), schedule was devised to be:

28. 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.

29. 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.

30. 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