Contamination-Aware Droplet Routing Algorithm for Digital Microfluidic Biochips

1. A Contamination Aware Droplet Routing Algorithm for Digital Microfluidic Biochips ACM/IEEE International Conference on Computer Aided Design 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

2. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

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

4. 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

5. Routing 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

6. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

7. 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

8. 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. 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

10. 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

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

12. 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 region globally • Increase the routability for droplet routing

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

14. 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

15. 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. 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

17. 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. 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

19. 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. 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 dropletsource waste reservoir contaminated spots

21. 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

22. 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 (vi, vk, vj), if there are edges connect and , a transitive edge also connects by assigning the

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

24. Minimum Cost Circulation Flow Technique • Construction rule 2: connection between phases • Four major phases in the MCC formulation Source Wash droplets Contaminated spots Waste reservoir I I I I O O O O W1 W2 Sink Source ... ... W3 . .. W4 L = 0 U = 1 C = 0 L = 0 U = 1 C = min-cost path L = 0 U = ∞ C = min-cost path

25. 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). Clean the contaminated spots At least one wash droplet Topology sorted order … Cn S W C1 C2 T Flow lower bound=1

26. 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. 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 si si+1 si and si+1 Intra-contamination Inter-contamination

28. 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 vi and vj (vi, vj) is the edge of flow graph Vi Consider the bounding box Inter- and Intra- contaminated spots Construction rule 1 TSP optimization Vj Inter-contaminated spots Intra-contaminated spots

29. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

30. 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] Size: Size of the microfluidic array #Sub: Number of subproblems #Net: Total input nets #Dmax: Maximum number of droplets with one subproblem #W: Number of wash droplets

31. 47.84% 12.91% 7.54% #Cintra: The number of intra-contaminations #UC: The number of used cells for routing #UC: The number of used cells for routing CPU: The CPU time (sec) Texe: The execution time for the bioassays Texe: The execution time for the bioassays 10.57% 9.19% #Cintra: The number of intra-contaminations #Ciinter: The number of inter-contaminations CPU: The CPU time (sec)

32. 27.88% 12.20% #UC: The number of used cells for routing #Cintra: The number of intra-contaminations CPU: The CPU time (sec) Texe: The execution time for the bioassays

33. Outline Introduction Problem Formulation Algorithms Experimental Results Conclusion

34. 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 (Texe) and fault tolerance (#UC) compared with the best known results

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