Eric J. Griffith∗Srinivas AkellaDepartment of Computer ScienceRensselaer Polytechnic InstituteTroy, NewYork 12180, [email protected]@cs.rpi.edu (corresponding author)Coordinating MultipleDroplets in PlanarArray DigitalMicrofluidic SystemsAbstractIn this paper we present an approach to coordinate the motions ofdroplets in digital microfluidic systems, a new class of lab-on-a-chipsystems for biochemical analysis. A digital microfluidic system typ-ically consists of a planar array of cells with electrodes that controlthe droplets. The primary challenge in using droplet-based systems isthat they require the simultaneous coordination of a potentially largenumber of droplets on the array as the droplets move, mix, and split.In this paper we describe a general-purpose system that uses simplealgorithms and yet is versatile. First, we present a semi-automatedapproach to generate the array layout in terms of components. Next,we discuss simple algorithms to select destination components forthe droplets and a decentralized scheme for components to route thedroplets on the array. These are then combined into a reconfigurablesystem that has been simulated in software to perform analyses suchas the DNA polymerase chain reaction. The algorithms have beenable to successfully coordinate hundreds of droplets simultaneouslyand perform one or more chemical analyses in parallel. Because itis challenging to analytically characterize the behavior of such sys-tems, simulation methods to detect potential system instability areproposed.KEY WORDS—digital microfluidic system, lab-on-a-chip,droplet coordination, layout design, routing1. IntroductionThe field of biochemical analysis systems has been revolu-tionized recently by the creation of miniature biochemicalanalysis systems using microfabrication technology. Thesesystems are often termed “micro total analysis systems” or∗Eric Griffith is currently in the Computer Graphics Group at the Delft Uni-versity of Technology, the Netherlands.The International Journal of Robotics ResearchVol. 24, No. 11, November 2005, pp. 933-949,DOI: 10.1177/0278364905059067©2005 SAGE PublicationsFigures 2–6 and 10 appear in color online: http://ijr.sagepub.com“lab-on-a-chip” systems. These systems offer a number ofadvantages, including size reduction, power reduction, andincreased reliability. However, current systems are typicallytailored to a specific task. Therefore, an important goal is tocreate reconfigurable and reprogrammable systems capableof handling a variety of analysis tasks.Digital microfluidic systems (DMFS) that use techniquessuch as electrowetting and dielectrophoresis are promisingcandidates for reconfigurable systems (Pollack, Fair, andShenderov 2000; Jones et al. 2001; Cho, Moon, and Kim2003; Paik, Pamula, and Fair 2003). We focus on microfluidicsystems that manipulate discrete droplets by electrowetting,where the interfacial tension of the droplets is modulated witha voltage (Paik, Pamula, and Fair 2003). Droplets are micro-liters in volume, and have been moved at 12–25 cm s−1onplanar arrays of 0.15 cm wide electrodes (see Cho, Moon,and Kim 2003 and Fair et al. 2003 for details). The ability tocontrol individual droplets on a planar array enables complexanalysis operations to be performed in biochemical “lab-on-a-chip” systems (Figure 1). For example, they can be used toperform polymerase chain reactions for DNA sequence anal-ysis. For simple biochemical analysis operations, no specialpurpose devices are required aside from the array itself. Thearray may additionally contain cells that can perform spe-cialized operations, such as heating or optical sensing. Thesesystems have the potential to process hundreds of samplesquickly. While there are important engineering challenges infabricating and demonstrating the feasibility of these systems,the primarycomputational challengewith using droplet-basedsystems is developing algorithms for the simultaneous coor-dination of a potentially large number of droplets. Planningoptimal paths through the array for each droplet would becomputationally intractable for a large number of droplets.In this paper we describe an approach to creating a general-purpose DMFS. First, we explain a semi-automated approachto design the array layout in terms of modular components,along with the motivating design choices. Next, we discusssimple algorithms to select destination components for the933934 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / November 2005Droplet DropletControl ElectrodesTop ViewSide ViewHydrophobic InsulationTop PlateBottom PlateGround ElectrodeFiller FluidFig. 1. Droplets on an electrowetting array (side and top views). The droplets are in a medium (usually oil or air) between twoglass plates. The gray and white droplets represent the same droplet in two different positions. The gray droplet representsthe droplet’s initial position. Over a period of three clock cycles, the droplet is moved into the position represented by thewhite droplet. A droplet moves to a neighboring electrode when that electrode is activated; the electrode is turned off whenthe droplet has completed its motion. Based on Paik, Pamula, and Fair (2003).droplets and a decentralized scheme for components to routethe droplets. These are then combined into a reconfigurablesystem that has been simulated in software to perform DNApolymerase chain reaction and other analyses. The algorithmshave been able tosuccessfully coordinate hundredsof dropletssimultaneously and perform one or more chemical analyses inparallel. Because it is challenging to analytically characterizethe behavior of such systems, methods to detect potential in-stabilities due to congestion are proposed. An earlier versionof this work was presented in Griffith and Akella (2005).2. Related WorkDigital Microfluidic Systems. Pollack, Fair, and Shen-derov (2000) demonstrated rapid manipulation of dis-crete microdroplets by electrowetting-based actuation. Ding,Chakrabarty, andFair(2001) describedan architecturaldesignand optimization methodologyfor scheduling biochemical re-actions using electrowetting arrays. They identified a basic setof droplet operations and used an integer linear programmingformulation to minimize completion time. Droplet paths andareas on the array for storage, mixing and splitting operationsare predefined by a human. Fair et al. (2003) describe exper-iments on injection, dispensing, dilution, and mixing of sam-ples in an
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