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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
51. 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
52. 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
53. 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
54. 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
55. 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.
56. 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
57. 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-contaminated spots Construction rule 1 TSP optimization Inter-contaminated spots Intra-contaminated spots Vj † R. Bellman, “Dynamic programming treatment of the travelling salesman problem,” J. ACM, pp. 61-63, Jan. 1962.
58. 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
59. 13% 48% 8% #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 11% 9% #Cintra: The number of intra-contaminations #Ciinter: The number of inter-contaminations CPU: The CPU time (sec)
60. 28% 12% #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
61. Conclusion We proposed a contamination aware droplet routing algorithm for DMFBs We can optimally solve the wash droplets routing for the intra-contamination problem Experimental results show that our algorithm can achieve better timing result (Texe) and fault tolerance (#UC) compared with the best known results
62. A Two-Stage ILP-Based Droplet Routing Algorithm For Pin-Constrained Digital Microfluidic Biochips ACM International Symposium on Physical Design, 2010 Tsung-Yi Ho http://eda.csie.ncku.edu.tw Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan
63. Pin-Constrained Digital Microfluidic Biochips Dedicated pin to identify the control signal Direct-addressing biochips Dedicated control pin for each electrode Maximum freedom of droplets High demanded control pins Broadcast-addressing biochips * A control pin can be shared by multiple electrodes Flexible for pin-constrained DMFBs Control pin sharing 1 1 1 2 2 3 3 4 4 5 6 2 Control pins: 24 7 7 8 8 9 9 10 10 14 11 12 12 13 13 14 14 15 15 16 13 17 8 7 18 2 19 20 1 4 21 22 3 23 2 1 24 Control pins: 15 *[T. Xu and K. Chakrabarty, DAC’08]
64. Previous Method – Direct Addressing 15 T3 14 d1 T1 13 26 Control Pins: Used Cell: execution time: d2 12 11 2 3 1 8 4 9 5 6 7 10 16 26 18 22 26 24 25 23 20 21 17 18 # of control pins = # of used cells d3 19 T2 Apply the direct-addressing scheme to a routing result
65. Previous Method (1/2) – Broadcast Addressing 15 T3 14 15 Control Pins: Used Cell: execution time: d1 T1 26 13 18 d2 12 8 2 3 7 1 4 1 5 4 5 6 11 6 4 5 6 4 4 5 10 9 d3 11 T2 Apply the broadcast-addressing schemeto a routing result
66. Previous Method (2/2) – Broadcast Addressing 12 T3 11 15 Control Pins: Used Cell: execution time: d1 T1 26 10 18 d2 Control Pins: Used Cell: execution time: 13 8 9 2 3 7 1 4 1 5 13 4 5 6 11 29 20 9 6 4 5 6 4 4 5 10 5 May increase the # of used cells and execution time d3 13 8 T2 Integrate the broadcast-addressing scheme with droplet routing
67. Ours (1/2) 4 8 T3 7 6 15 Control Pins: Used Cell: execution time: d1 T1 26 5 9 18 d2 Control Pins: Used Cell: execution time: 13 2 7 2 3 3 1 4 1 5 4 9 6 6 29 20 7 9 Control Pins: Used Cell: execution time: 2 5 23 d3 2 15 T2 Minimized # of control pins Minimized # of used cells Minimized execution time Integrate broadcast-addressing scheme with droplet routing while simultaneously minimizing the # of control pins, # of used cells, and execution time
68. Ours (2/2) Contributions: We propose the first algorithm that integrates the broadcast-addressing with droplet routing problem, while simultaneously minimizing the # of control pins, the # of used cells, and the execution time A Basic ILP formulation is introduced to optimally solve the droplet routing problem A two-stage ILP-based algorithm is presented to tackle the complexity of the basic ILP formulation
69. Thank You for Your Attention!