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Placement of Digital Microfluidic Biochips Using the T-tree Formulation Ping-Hung Yuh 1, Chia-Lin Yang 1, and Yao-Wen Chang 2 1 Dept. of Computer Science & Information Engineering 2 Graduate Institute of Electronics Engineering and Dept. of Electrical Engineering National Taiwan University, Taiwan

3 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

4 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

5 Digital Microfluidic Biochips Perform laboratory procedures based on liquid particles (droplets) The two main components:  Reconfigurable devices (electrodes) Droplets can move freely on the reconfigurable device  Non-reconfigurable devices (detectors and reservoirs) Only one functionality Reservoirs/Dispensing ports Optical detectorDroplets Electrodes Mixing two droplets The schematic view of a biochip (Duke Univ.) Storage

6 Digital Microfluidic Biochips (cont’d) Time: 1~4 Time: 4~5 Storage Dilution Time: 5~7 Mix Dilution a Mix b Dilution Mix c Task graph

7 Placement Problem of Biochips Inputs:  Sequencing graph  Microfluidic module library  Design specification: Fixed architecture (ex: 5x5-array) and maximum assay completion time (ex: 400 sec) Limited number of non-reconfigurable devices Output: the schedule and placement of tasks a b c d e f Dispense Mix Detection A sequencing graph 301x1 cellOpt. N/A1x1 cellStorage 42x3-array 72x2-arrayMixing TimeAreaResource Microfluidic Module Library

8 Previous Work Architecture-level synthesis (scheduling and binding)  Deng et al, TCAD’01 Architecture-level model and ILP-based method  Su and Chakrabarty, ICCAD’04 Sequencing graph model and two heuristics Physical placement  Su and Chakrabarty, DATE’05 Simulated annealing based algorithm with given scheduled tasks Unified synthesis and placement  Su and Chakrabarty, DAC’05 Parallel recombinative simulated annealing List scheduling and greedy placement method

9 Our Contribution Formulate the execution of a bioassay as a 3D floorplan Apply a tree-based representation (T-tree) to solve the floorplanning/placement problem Time t 1 Mix Storage Mix Dilute Mix Time t 2 Time t 3 Mix Dilute Storage T Y X Mix Storage Dilute

10 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

11 Bioassay Execution to 3D floorplan Model each task and storage as a 3D box Model the execution of a bioassay as a 3D floorplan Biochip placement problem to 3D temporal floorplanning problem Time t 1 Mix Storage Mix Dilute Mix Time t 2 Time t 3 Mix Dilute Storage T Y X Mix

12 Review of T-tree A 3-ary tree representation for temporal floorplanning/placement problem A 3D compacted floorlpan The corresponding T-tree Mix b Dilute c Storages s T Y X Mix a Mix b Mix a Storages s Dilute c

13 Review of T-tree (cont’d) The T-tree keeps the geometric relation as follows:  Left child: adjacent in the T + direction  Middle child: in the Y + direction with the same t- coordinate  Right child: in the X + direction with the same t- and y- coordinates T i : duration of i t i : starting time of i Mix b Dilute c Storage s Mix a Mix b Mix a Storage s Dilute c left child middle child right child t j =t i +T i t k = t i t l = t i i j kl The structure of T-tree

14 Modeling Tasks in a T-tree Model each task as a node in a T-tree Dispense d a b c e f Mix Detection A sequencing graph The corresponding T-tree f ce a b d

15 Modeling Storages Model each storage as a node in a T-tree  Each edge in a sequencing graph represents a storage Dispense d a b c e f Mix Detection A sequencing graph The corresponding T-tree f ce a b d s1s1 s2s2 s3s3 s4s4 s5s5 Storage s1s1 s2s2 s3s3 s4s4 s5s5

16 Modeling Storages (cont’d) The storage constraint: the duration of one storage covers the time gap between two data-dependent tasks Insert a storage node in one of the feasible locations in a T-tree  Ensure that t s = t b + T b Example of feasible locations feasible location b c s t tbtb TbTb left child middle child right child t j =t i +T i t k = t i t l = t i i j kl The structure of T-tree b e a dc s t a =t b +T b t d =t e =t a

17 Modeling the Design Specification The fixed-cube constraint:  Model the fixed architecture and max. completion time as a 3D cube  A feasible floorplan must be within this 3D cube The resource constraint:  # of non-reconfigurable tasks is limited at any time  Add the virtual edges in the sequencing graph Max. completion time Fixed architecture A feasible floorplan a b c d e f Dispense Mix Detection Virtual edge

18 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

19 Floorplanning Algorithm Based on simulated annealing (SA) The modified SA flow:  Detect the violation of the storage constraints  Delete unused storages in a T-tree for packing efficiency Data Dependency Storage Constraint Number of storages Adjustment Feasibility Detection & Tree Reconstruction Perturbation Termination? Yes No Packing

20 Floorplanning Algorithm (cont’d) Cost function:  Volume  # of storages  Penalty term for fixed-cube constraint

21 Two Methods for Fixed-cube Constraint Guide the tree perturbation based on cube violation probability p w, p h, and p t  p w = k/n, where k is the # of floorplans whose width exceeds the 3D cube in the last n iterations  If p w is large, increase the probability of placing tasks along the Y or T direction Add the excessive length into the cost function Excessive length Max. completion time Fixed architecture An infeasible floorplan

22 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

23 Experimental Settings Implemented our algorithm in C++ language on a 1.2 GHz SUN Blade-2000 machine with 8GB memory Implemented the algorithm of [Su and Chakrabarty, DAC’05] on the same machine Tested two bioassays:  Colorimetric protein assay from [Su and Chakrabarty, DAC’05]  Multiplexed in-virto diagnostics from [Su and Chakrabarty, ICCAD’04] Assigned three different design specifications (fixed- cube constraints) to each bioassay

24 Experimental Result Bioassay Design Spec. [Su et al, DAC’05]T-tree Volume CPU time (seconds) Volume CPU time (seconds) Protein [Su et al, DAC’05] 10x10x4009x10x x10x x10x36010x10x x10x x11x3208x13x x11x23866 Avg In vitro [Su et al, ICCAD’04] 10x10x1009x11x99649x8x666 8x8x1209x9x x7x6812 7x7x1409x10x105926x7x8915 Avg T-tree based algorithm is more efficient and effective Result that cannot satisfy the fixed-cube constraint volume = area × assay completion time

25 Resulting Placement of the Protein Bioassay Volume = 10x10x270 (10x10x400 fixed-cube constraint)

26 Outline Introduction T-tree Based Placement Formulation Floorplanning Algorithm Experimental Result Conclusion

27 Conclusion Formulated the placement problem of biochips as the temporal floorplanning problem First work to apply a topological representation to the placement problem of biochips Demonstrated the effectiveness and efficiency of our algorithm Future work:  Consider fault and defect tolerance during floorplanning

Thank you for your attention

Q & A

30 Question # 1 Q: Why choose the T-tree representation over other 3D representations (3D-subTCG, ST, 3D-slicing tree) ? A: Three reasons:  1. T-tree models the compacted floorplan, thus it has the advantage of volume optimization  2. T-tree is more efficient for large-scale circuits than 3D-subTCG, ST  3. T-tree is more effective in handling the storages T-tree can determine the # of storages and duration of each storage before packing with only O(n) time 3D-subTCG and ST needs O(n^2) time before packing 3D-slicing tree cannot obtain this information before packing It is difficult for 3D-slicing tree to satisfy the storage constraint

31 Question # 2 Q: Why add the # of storages in the cost function? A: Two reasons:  1. Generally, the smaller # of storages, the more compact 3D floorplan we can have  2. Release the volume occupied by storages for reconfigurable task to use

32 Question # 3 Q: Why your algorithm is better than previous work? A: There are two reasons:  1. T-tree is better in volume optimization than previous greedy placement method  2. Smoother optimization process by minimizing volume instead of area plus completion time