Tsung-Wei Huang and Tsung-Yi Ho eda.csie.ncku.tw

1. A Fast Routability- and Performance-Driven Droplet Routing Algorithm for Digital Microfluidic Biochip IEEE International Conference on Computer Design Tsung-Wei Huang and Tsung-Yi Ho http://eda.csie.ncku.edu.tw Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan

2. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

3. Introduction to Biochips • General definition • A chip with a small solid platform made of glass, plastic, or membrane • Functionality • Analysis, reaction, or detection of biological samples (DNA or human blood) • Application • Clinical diagnostics • Environmental monitoring • Massive parallel DNA analysis • Automated drug discovery • Protein crystallization Biochip (Agilent Technologies)

4. Biochip Miniaturization • Smaller sample consumption • Lower cost • Higher throughput • Higher sensitivity • Higher productivity Shrink Conventional Biochemical Analyzer DNA microarray (Infineon AG)

5. The Need of CAD Support • Design complexity is increased • Large-scale bioassays • Multiple and concurrent assay operations on a biochip • Electro-biological devices integration • System-level design challenges beyond 2009 • International Technology Roadmap of Semiconductors (ITRS) Heterogeneous SOCs -Mixed-signal -Mixed-technology Digital blocks Analog blocks MEMScomponents Microfluidiccomponents

6. Classification of Biochips Biochips Microfluidic biochips Microarray DNA chip Protein chip Continuous-flow Droplet-based Chemical method Thermal method Electrical method Acoustical method Digital Microfluidic Biochips (DMFBs)

7. DMFB Architecture Control electrodes (cells) Ground electrode Hydrophobic insulation 2D microfluidic array Top plate Photodiode Droplet Droplets Bottom plate Side view Spacing Droplet Reservoirs/Dispensing ports Control electrodes The schematic view of a biochip (Duke Univ.) Top view High voltage to generate an electric field

8. Routing Constraints • Fluidic constraint • For the correctness of droplet transportation • No unexpected mixing among droplets of different nets • Static and dynamic fluidic constraints • Timing constraint • Maximum transportation time of droplets T Y Minimum spacing X Dynamic fluidic constraint Static fluidic constraint

9. Droplet Routing vs. VLSI Routing • Droplet routing • Droplets transportation from one location to another for reaction • Difference from traditional VLSI routing • Cells can be temporally shared by droplets - no permanent wires on a biochip • Droplet routing and scheduling; scheduling is to determine droplets’ locations at each time step • Unique fluidic properties for correct droplet movement Di Droplet Routing VLSI Routing

10. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

11. Droplet Routing on Digital Microfluidic Biochips (DMFBs) • Input: A netlist of n droplets D = {d1, d2,…, dn}, the locations of m blockages B = {b1, b2,…, bm}, and the timing constraint Tmax. • Objective: Route all droplets from their source cells to their target cells while minimizing the number of unit cells for better fault tolerance. • Constraint: Both fluidic and timing constraints are satisfied. • Fluidic constraint • Timing constraint Blockage Source of droplet i Target of droplet i Ti Si

12. Related Work • Prioritized A*-search algorithm [K. Böhringer, TCAD’06] • A*-search for each droplet based on its priority • High-priority droplets may block low-priority droplets • Open shortest path first algorithm [Griffith et al, TCAD’06] • Layout patterns with routing table • No dynamic reconfiguration • Two-stage algorithm [Su et al, DATE’06] • Alternative routing path generation and droplet scheduling • Random selection • Network flow-based approach [Yuh et al, ICCAD’07] • Maximize the number of nets routed • Min-cost Max-flow formulation + prioritized A* search • High-performance approach [Cho and Pan, ISPD’08] • Capable of handing routing obstacles • Routing order decided by bypassibility of targets

13. Problems with Bypassibility S1 S2 S3 S2 S3 S1 S4 T5 ? S5 S8 T2 T2 T1 T3 S6 T7 S5 T3 T9 T4 T1 S4 T4 T5 T6 S7 T8 S9 (b) Test d (a) Test b Blockage Source of droplet i Target of droplet i Ti Si

14. Outline Introduction Problem Formulation Preferred Routing Track Construction Routing Ordering by Entropy Equation Algorithms Routing Compaction by Dynamic Programming Experimental Results Conclusion

15. Preferred Routing Track Construction Moving vector

16. Preferred Routing Track Construction A* maze searching T2 S2

17. Routing Ordering by Entropy Equation • Entropy where ΔBEdi : the variant of entropy of each droplet ΔQdi: the energy variant for this energy system ESdi: the energy system for the droplet.

18. Routing Ordering by Entropy Equation 5 S5 9 7 9 T5 6 4 ΔBEd5 = (9-(4+5)-(6)+(9+7))/9 = 10/9

19. Routing Ordering by Entropy Equation S5 Find a min-cost path for S5

20. Routing Ordering by Entropy Equation S5 Route S5 to the A-cell of T5

21. Enhance Routability by Concession Control Dynamic Fluidic Constraint S5 S6 Concession control

22. Routing Compaction by Dynamic Programming duplicate movement Delete the duplicate movement

23. Routing Compaction by Dynamic Programming D2 = rruuuuuulllluuruu D4 = llldddddddddd Ex:

24. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

25. Experimental Settings • Implemented our algorithm in C++ language on a 2 GHz 64-bit Linux machine w/ 8GB memory • Compared with three state-of-the-art algorithms • Prioritized A* search [K. Böhringer, TCAD’06] • Network-flow algorithm [Yuh et al, ICCAD’07] • High-performance algorithm [Cho and Pan, ISPD’08] • Tested on three benchmark suites • Benchmark I [30] [Cho and Pan, ISPD’08] • Benchmark II [10] [Self generated] • Benchmark III [4][Su and Chakrabarty, DAC’05] ※Benchmark II: (1) bounding boxes of droplets are overlapped; (2) nx1 or 1xn narrow routing regions are used for routing; (3) the density of blockage area is over 30%.

26. Experimental Results on Benchmark Suite I ■ Size: Size of microfluidic array. ■ #Net: Number of droplets. ■ Tmax: Timing constraints. ■ #Blk: Number of blockage cells. ■ #Fail: Number of failed droplets. ■ Tla: latest arrival time among all droplets. ■ Tcell: Total number of cells used for routing.

27. Experimental Results on Benchmark Suite I ■ Tla: latest arrival time among all droplets. ■ Tcell: Total number of cells used for routing. ■ CPU: CPU time (sec)

28. Experimental Results on Benchmark Suite II ■ Size: Size of microfluidic array. ■ #Net: Number of droplets. ■ Tmax: Timing constraints. ■ #Blk: Number of blockage cells. ■ #Fail: Number of failed droplets. ■ Tla: latest arrival time among all droplets. ■ Tcell: Total number of cells used for routing. (1) bounding boxes of droplets are overlapped; (2) nx1 or 1xn narrow routing regions are used for routing; (3) the density of blockage area is over 30%.

29. Experimental Results on Benchmark Suite III ■ Size: Size of microfluidic array. ■ #Sub: Number of subproblems. ■ #Net: Number of droplets. ■ Tmax: Timing constraints. ■ #Dmax: Maximum number of droplets among subproblems. ■ Tcell: Total number of cells used for routing.

30. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

31. Conclusion • We proposed a fast routability- and performance-driven droplet router for DMFBs. • Experimental results demonstrated that our algorithm achieves 100% routing completion for all test cases in three Benchmark Suites while the previous algorithms are not. • Furthermore, the experimental results shown that our algorithm can achieve better timing result (Tla) and fault tolerance (Tcell) and faster runtime (CPU) with the best known results.

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