1. NCKU CSIE EDALAB Tsung-Wei Huang, Chun-Hsien Lin, and Tsung-Yi Ho http://eda.csie.ncku.edu.tw Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan ACM/IEEE International Conference on Computer Aided Design

2. NCKU CSIE EDALAB Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

3. NCKU CSIE EDALAB Digital MicroFluidic Biochip (DMFB) Side view Top view Droplet Bottom plate Top plate Ground electrode Control electrodes (cells) Hydrophobic insulation Droplet Spacing High voltage to generate an electric field The schematic view of a biochip (Duke Univ.) Reservoir/Dispensing port Droplets Control electrodes

4. NCKU CSIE EDALAB 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 Static fluidic constraint Minimum spacing Dynamic fluidic constraint X Y T

5. NCKU CSIE EDALAB Contamination problem Disjoint routes Routing with the wash droplet S1S1 S2S2 T1T1 T2T2 2D microfluidic array M d1d1 d2d2 d1d1 d2d2 d1d1 d2d2 Dispensing port Reservoir port W Routing Constraints ․ Contamination problem d1d1 d2d2 W (1) separately (2) simultaneously

6. NCKU CSIE EDALAB Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

7. NCKU CSIE EDALAB Droplet Routing on Digital Microfluidic Biochips (DMFBs) ․ Input: A netlist of n droplets D = {d 1, d 2,…, d n }, the locations of blockages, and the timing constraint T max minimizing the number of used cells and execution time ․ 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. 2D microfluidic array Droplets Target Fluidic constraint Timing constraint Contamination constraint

8. NCKU CSIE EDALAB 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:

9. NCKU CSIE EDALAB DATE’09 Total execution time for bioassay Subproblem SP 1 Subproblem SP 2 Subproblem SP n Subproblem SP n-1 Execution time of bioassay (time cycle) Biological reaction order … I(1,2) I(2,3) I(n-1,n) SP 2 W2W2 SP 1 W1W1 W 1,2 W 2,3 W n-1,n SP n WnWn SP n-1 W n-1 … Sequencing relationship Wash operation between subproblems Subproblem of bioassay Wash operation within one subproblem

10. NCKU CSIE EDALAB Ours Total execution time for bioassay Subproblem SP 1 Subproblem SP 2 Subproblem SP n Subproblem SP n-1 Execution time of bioassay (time cycle) Biological reaction order I(1,2) SP 1 W1W1 W 1,2 … I(2,3) I(n-1,n) SP 2 W2W2 W 2,3 W n-1,n SP n WnWn SP n-1 W n-1 … Sequencing relationship Wash operation between subproblems Subproblem of bioassay Wash operation within one subproblem SP 1 W 1,2 W1W1 SP 2 W 2,3 W2W2 SP n-1 W n-1,n W n-1 Reduced time Total execution time for bioassay

11. NCKU CSIE EDALAB Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion Preprocessing Stage Intra-Contamination Aware Routing Stage Intra-Contamination Aware Routing Stage Inter-Contamination Aware Routing Stage Inter-Contamination Aware Routing Stage

12. NCKU CSIE EDALAB Preprocessing Stage ․ Preferred routing tracks construction  Reduce the design complexity for droplet routing  Minimize the used cells for 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 region globally  Increase the routability for droplet routing

13. NCKU CSIE EDALAB Preprocessing Stage S1S1 S2S2 T1T1 T3T3 T2T2 d3d3 d1d1 d2d2 ․ Example Moving vector analysis Routing tracks construction

14. NCKU CSIE EDALAB Preprocessing Stage S1S1 S2S2 T1T1 T3T3 T2T2 Res 1 eq =((16+0)-(2+3))/16 = 11/16 Res 2 eq =((15+3)-(0))/18 = 1 Res 3 eq =((18+10)-(2+3))/28 =23/28 Route d 2 to the A-cell of T 2 by min-cost path d1d1 S3S3 Concession Control d2d2 d3d3 Res 3 eq =((18+10)-(2+6))/28 =20/28 Res 1 eq =((16+0)-(2))/16 = 14/16 ․ Example Moving vector analysis Routing tracks construction Routing priority calculation Minimum cost path

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

16. NCKU CSIE EDALAB Routing Path Modification by k-shortest Path ․ A k-shortest based algorithm  Modify the original routing path slightly  Minimize the contaminated spots S1S1 T1T1 S2S2 T2T2 S3S3 T3T3 Contaminated spots: 6 -> 6 -> 2 Original routing path Select a highly contaminated path Find the first shortest path Find the second shortest path Contamination spots Routing path SiSi Source location TiTi Target location

17. NCKU CSIE EDALAB Routing Compaction by Dynamic Programming ․ Major goals:  Transform the 2D routing into 3D routing considering the timing issue and maintain the original routing path  Estimate an initial timing slot of each contaminated spot ․ Optimal substructure  Optimally solution for a pair of droplets  Find the solution by dynamic programming incrementally

18. NCKU CSIE EDALAB ․ Illustration of dynamic programming  Decode the 2D routing path into the1D moving string (u, d, l, r) ․ Incremental compaction strategy P1P1 P2P2 P3P3 P4P4 P n-1 PnPn compaction compaction compaction … compactioncompaction Routing Compaction by Dynamic Programming S1S1 T1T1 S2S2 T2T2 MS 1 : rrrrrr MS 2 : dddddrrrr dddddrrrr 0123456789 rXXXX456789 rXXXXX56789 rXXXXXX6789 rXXXXXXX789 rXXXXXXXX89 rXXXXXXXXX9 Compaction d1d1 d2d2 d2d2 d2d2 d2d2 d2d2 d2d2 d2d2 d2d2 d2d2 d2d2 d1d1 d1d1 d1d1 d1d1 d1d1 d1d1 Used time = 9

19. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Introduction to 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:

20. NCKU CSIE EDALAB 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 phaseswashdropletswastereservoir contaminated spots droplet source

21. NCKU CSIE EDALAB 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 node split into input node and output node V IO node v assign the 3-tuple (l, u, c) of this arc

22. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Construction rule 1: Timing-based transitive topology  Timing-based topology The timing slot of each contaminated spot can be estimate by dynamic programming Connect a early contaminated spot to a later one by the 3- tuple  Transitive closure Allows the multiple wash droplets to perform the wash operation, while satisfying the timing-based topology For any triple contaminated spot (v i, v k, v j ), if there are edges connect and, a transitive edge also connects by assigning the

23. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Illustration V I O V I O V I O V I O … Contaminated spots Assignment 1 Assignment 2 Timing-based topology Transitive closure Transitive edge

24. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Construction rule 2: connection between phases  Four major phases in the MCC formulation W3W3 W1W1 W2W2 W4W4 L = 0 U = 1 C = 0 L = 0 U = 1 C = min-cost path L = 0 U = ∞ C = min-cost path Source Sink... I O I O I O I O SourceWash dropletsContaminated spotsWaste reservoir

25. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Theorem 1: There exists a feasible solution under the two basic assignments and two flow construction rules  Proof The construction enhances at least one flow from the sink back to the source, meaning that one flow from the source to the wash droplet set. There also exists one possible path to travel all the contaminated node set (topology sorted order). STW Flow lower bound=1 C1C1 C2C2 CnCn Topology sorted order … At least one wash droplet Clean the contaminated spots

26. NCKU CSIE EDALAB Minimum Cost Circulation Flow Technique ․ Theorem 2: Under the proposed flow construction, we can adopt the MCC algorithm to schedule correct and optimal wash operations  Proof Theorem 1 shows there is a feasible solution, that is, the contaminated spots are correctly cleaned by the wash droplets. The MCC algorithm will obtain a feasible flow with minimum cost that represents the optimal scheduling of wash operations.

27. NCKU CSIE EDALAB Inter-Contamination Aware routing Stage ․ Look-Ahead routing scheme  Contaminated spots also occur between subproblems  Predicting the inter-contaminations for the next subproblem and clean the intra- and inter-contaminations simultaneously to reduce the completion time Inter-contamination Intra-contamination sisi s i+1 s i and s i+1

28. NCKU CSIE EDALAB Inter-Contamination Aware routing Stage ․ Travelling salesman problem optimization  Utilize the wash droplets while minimize the total used cells and completion time  Clean the set of non-washed look-ahead contaminated spots in the bounding box of node v i and v j ViVi VjVj (v i, v j ) is the edge of flow graph Consider the bounding box Inter- and Intra- contaminated spots Construction rule 1 TSP optimization Inter-contaminated spots Intra-contaminated spots

29. NCKU CSIE EDALAB Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

30. NCKU CSIE EDALAB Experimental Settings ․ Implement our algorithm in C++ language on a 2 GHz 64-bit Linux machine with 8GB memory ․ Comparison  Disjoint-route algorithm [Y. Zhao and K. Chakrabarty, DATE’09] ․ Tested on three benchmark suites  Benchmark [Su and Chakrabarty, DAC’05] CircuitSize#Sub#Net#D max #W in-vitro_116 x 16112854 in-vitro_214 x 14153564 protein_121 x 216418164 protein_213 x 137817864 Size: Size of the microfluidic array #Sub: Number of subproblems #Net: Total input nets #D max : Maximum number of droplets with one subproblem #W: Number of wash droplets

31. NCKU CSIE EDALAB Bioassay Ours (non k-SP)Ours (k-SP) #C intra #UCT exe CPU#C intra #UCT exe CPU in-vitro_1 533882250.18213511930.58 in-vitro_2 272912170.1352811910.39 protein_1 138241815921.4782221313942.58 protein_2 106145312800.7161136211081.49 Total 324455033142.49169420728865.04 #C intra : The number of intra-contaminations CPU: The CPU time (sec) T exe : The execution time for the bioassays Bioassay ContaminationsOurs (non look-ahead)Ours (look-ahead) #C intra #C inter #C intra #UCT exe CPU#UCT exe CPU in-vitro_1 2119214462270.323511930.58 in-vitro_2 5852672100.242811910.39 protein_1 8219082249315692.11221313942.58 protein_2 6114161149811720.47136211081.49 Total 169358169470431783.14420728865.04 #UC: The number of used cells for routing #C intra : The number of intra-contaminations #C iinter : The number of inter-contaminations CPU: The CPU time (sec) #UC: The number of used cells for routing T exe : The execution time for the bioassays 7.54% 12.91% 10.57%9.19% 47.84%

32. NCKU CSIE EDALAB Circuit Disjoint route (Y. Zhao and K. Chakrabarty)Ours (k-SP + look-ahead) #CS#UCT exe CPU#CS#UCT exe CPU in-vitro_1 46212680.06213511930.58 in-vitro_2 04232240.0352811910.39 protein_1 18321515080.2382221313942.58 protein_2 11157412870.1461136211081.49 Total 33583332870.46169420728865.04 #C intra : The number of intra-contaminations CPU: The CPU time (sec) #UC: The number of used cells for routing T exe : The execution time for the bioassays 27.88%12.20%

33. NCKU CSIE EDALAB Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

34. NCKU CSIE EDALAB Conclusion ․ We proposed a contamination aware droplet router for DMFBs ․ We can optimally solve the wash droplets routing for the intra-contamination problem ․ Furthermore, the experimental results shown that our algorithm can achieve better timing result (T exe ) and fault tolerance (#UC) compared with the best known results

35. NCKU CSIE EDALAB