何宗易 Tsung -Yi Ho eda.csie.ncku.tw

1. Droplet Routing Algorithms for Digital Microfluidic Biochips IEEE International Conference on Computer Design,2009 ACM/IEEE International Conference on Computer Aided Design, 2009 何宗易Tsung-Yi Hohttp://eda.csie.ncku.edu.tw Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan

2. Outline of Work in ICCD 2009 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. Microfluidic Biochips • Continuous-flow biochips: • Permanently etched microchannels, micropumps, and microvalves • Digital microfluidic biochips: • Manipulation of liquids as discrete droplets

8. Unified Synthesis Methodology(Su and Chakrabarty, DAC 2005)

9. Droplet Routing on Digital MicrofluidicBiochips 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

10. 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

11. Droplet Routing vs. VLSI Routing • Droplet routing • Droplets transportation from one location to another for reaction • Similar to Motion Planning in Robotics • NP-hard even for only two robots! • 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

12. 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

13. 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

14. A High-Performance Droplet Routing Algorithm for Digital Microfluidic Biochips＊ • Route one droplet movement at a time • Reduced routing search time • Bypassibility • To route a droplet with minimal impact on feasibility • Concession • To resolve a deadlock • Compaction • To satisfy timing constraint and improve fault-tolerance ＊M. Cho and D. Z. Pan, “A high-performance droplet routing algorithm for digital microfluidic biochips,” IEEE Trans. on CAD, vol. 27, no. 10, pp. 1714–1724, Oct. 2008.

15. One Droplet at a Time

16. Routing by Bypassibility • Three categories • Full: both horizontal and vertical bypasses are available. • Half: only either horizontal or vertical bypasses is available. • No: no bypass is available.

17. 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

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

19. Preferred Routing Track Construction Moving vector

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

21. 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.

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

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

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

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

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

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

28. Routing Compaction by Dynamic Programming • Illustration of dynamic programming • Decode the 2D routing path into the1D moving string (u, d, l, r) • Incremental compaction strategy MS1:rrrrrr d2 d2 d2 d2 d2 d2 d2 d2 d2 d2 MS2: dddddrrrr S2 Compaction d1 d1 d1 d1 d1 d1 d1 S1 T1 Used time = 9 T2 … P3 P1 P2 P4 Pn Pn-1 compaction compaction compaction compaction compaction

29. 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%.

30. 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.

31. 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)

32. 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%.

33. 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.

34. 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.

35. Outline of Work in ICCAD 2009 Introduction Problem Formulation Algorithms Experimental Results Conclusion

36. Contamination Constraints • Contamination problem 2D microfluidic array Contamination problem d2 d2 d2 S2 d1 d1 d2 Disjoint routes M d1 Routing with the wash droplet (1) separately S1 T1 d1 (2) simultaneously T2 W W Reservoir port Dispensing port

37. Droplet Routing on Digital Microfluidic Biochips (DMFBs) • Input: A netlist of n droplets D = {d1, d2,…, dn}, the locations of blockages, and the timing constraint Tmax • Objective: Route all droplets from their source cells to their target cells while minimizing the number of used cells and execution time for better fault tolerance and reliability • Constraint: Fluidic, timing and contamination constraints should be satisfied. • Fluidic constraint Droplets 2D microfluidic array • Contamination constraint • Timing constraint Target

38. Related Work • Droplet Routing Algorithm • Droplet routing in the synthesis of digital microfluidic biochips [Su et al, DATE’06] • Modeling and controlling parallel tasks in droplet based microfluidic systems [K. F. B hringer, TCAD’06] • A network-flow based routing algorithm for digital microfluidic biochips [Yuh et al, ICCAD’07] • Integrated droplet routing in the synthesis of microfluidic biochips [T. Xu and K. Chakrabarty, DAC’07] • A high-performance droplet routing algorithm for digital microfluidic biochips [Cho and Pan, ISPD’08] • Contamination-Aware Droplet Routing Algorithm • Cross-contamination avoidance for droplet routing in digital microfluidic biochips [Y. Zhao and K. Chakrabarty, DATE’09] • Disjoint routes • Wash operation insertion strategy o:

39. DATE’09 Wash operation between subproblems Subproblem of bioassay Wash operation within one subproblem Sequencing relationship Execution time of bioassay (time cycle) SP1 Subproblem SP1 W1 Biological reaction order W1,2 SP2 Subproblem SP2 W2 W2,3 … … SPn-1 Subproblem SPn-1 Wn-1 Wn-1,n SPn Subproblem SPn Wn I(n-1,n) I(1,2) I(2,3) Total execution time for bioassay

40. Ours Wash operation between subproblems Subproblem of bioassay Wash operation within one subproblem Sequencing relationship Execution time of bioassay (time cycle) SP1 SP1 Subproblem SP1 W1 W1 W1,2 Biological reaction order W1,2 SP2 W2 SP2 Subproblem SP2 W2,3 W2 W2,3 SPn-1 … … Wn-1 Wn-1,n SPn-1 Subproblem SPn-1 Wn-1 Wn-1,n SPn Subproblem SPn Wn I(n-1,n) I(1,2) I(2,3) Total execution time for bioassay Reduced time Total execution time for bioassay

41. Outline Introduction Problem Formulation Preprocessing Stage Intra-Contamination Aware Routing Stage Algorithms Inter-Contamination Aware Routing Stage Experimental Results Conclusion

42. Preprocessing Stage • Preferred routing tracks construction • Reduce the design complexity for droplet routing • Minimize the used cellsfor better fault-tolerance • Increase the routability by concession control • Routing priority calculation • Routing-resource-based equation that considers the interference between droplets inside the routing regionglobally • Increase the routability for droplet routing

43. Preprocessing Stage • Example Moving vector analysis Routing tracks construction d2 T3 S2 T2 S1 d1 T1 d3

44. Preprocessing Stage • Example Concession Control Route d2to the A-cell of T2 by min-cost path Moving vector analysis Routing tracks construction d2 S2 T3 T2 Routing priority calculation Res1eq=((16+0)-(2))/16 = 14/16 Res1eq=((16+0)-(2+3))/16 = 11/16 Res2eq=((15+3)-(0))/18 = 1 Res3eq=((18+10)-(2+3))/28 =23/28 Res3eq=((18+10)-(2+6))/28 =20/28 S1 d1 T1 d3 S3 Minimum cost path

45. Intra-Contamination Aware Routing Stage • Routing path modification by k-shortest path • Minimize the intra-contaminated spots by slightly modifying the routing path • Routing compaction by dynamic programming • Minimize the completion time for bioassays (series 2D routing paths to 3D routing paths) • Minimum cost circulation flow technique • Schedule the wash operation for wash droplets • Solve the intra-contaminated spots optimally under our flow construction

46. Routing Path Modification by k-shortest Path • A k-shortest based algorithm† • Modify the original routing path slightly • Minimize the contaminated spots Routing path Contamination spots Si Source location Ti Target location S2 T3 Original routing path S1 T1 Select a highly-contaminated path Find the first shortest path T2 Find the second shortest path S3 Contaminated spots: 6 -> 6 -> 2 †D. Eppstein, “Finding the k shortest paths,” Proc. IEEE FOCS, pp. 154-165, Feb. 1994.

47. Routing Compaction by Dynamic Programming • Major goals: • Transform series 2D routing into 3D routing considering the timing issue and preserve the original routing path • Estimate the contaminated time of each contaminated spot • Optimal substructure • Optimally solution for a pair of droplets • Find the solution by dynamic programming incrementally

48. Minimum Cost Circulation Flow Technique • Minimum Cost Circulation (MCC) problem • A generalization of network flow problems • Constraints: • Bounded constraint: - each flow arc has a lower bound and a upper bound • Conservation constraint: - the net flow of each node is zero • Objective: • Minimize the cost:

49. Minimum Cost Circulation Flow Technique • Circulation flow formulation • Schedule an optimal solution for correct wash operation • Four main phases of formulation • Two basic assignments • Node capacity assignment • Edge cost assignment • Two construction rules • Timing-based transitive topology • Connection strategy between phases wash droplets dummysource waste reservoir contaminated spots

50. Minimum Cost Circulation Flow Technique • Assignment 1: Node capacity assignment • Guarantee that the contaminated spot should be cleaned by the wash droplets • Node split • Assignment 2: Edge cost assignment • Minimize the used cells and routing time of wash droplets • The same routing cost model between two points O I V assign the 3-tuple (l, u, c)of this arc node split into input node and output node node v