2010 ACM International Symposium on Physical Design (ISPD’10) Tsung-Wei Huang and Tsung-Yi Ho http://eda.csie.ncku.edu.tw Department of Computer Science and Information Engineering National Cheng Kung University Tainan, Taiwan NCKU CSIE EDALAB
Outline ․ Introduction ․ Problem formulation ․ Our contribution ․ Basic ILP formulation ․ Deterministic ILP formulation ․ Experimental results ․ Conclusion NCKU CSIE EDALAB
Outline ․ Introduction Digital microfluidic biochips Pin-constrained digital microfluidic biochips Previous work and limitations ․ Our contribution ․ Problem formulation ․ Basic ILP formulation ․ Deterministic ILP formulation ․ Experimental results ․ Conclusion NCKU CSIE EDALAB
Digital Microfluidic Biochips (DMFBs) (1/2) ․ Three main components: 2D microfluidic array: set of basic cells for biological reactions Reservoirs/dispensing ports: for droplet generation Optical detectors: detection of reaction result ․ Perform laboratory procedures based on dro roplet s Droplet: biological sample carrier Droplets Optical detector 2D microfluidic array Electrodes Reservoirs/Dispensing ports The schematic view of a biochip (Duke Univ.) 4 NCKU CSIE EDALAB
Digital Microfluidic Biochips (DMFBs) (2/2) ․ Movement control of a droplet Ground Hydrophobic Control electrode insulation electrodes Top plate Optical detector Droplet Droplets Bottom plate Side view Spacing Droplet Control electrodes Top view Generated electrical force NCKU CSIE EDALAB
Pin-Constrained Digital Microfluidic Biochips ․ Direct-addressing biochips Dedicated pin to identify the control signal Dedicated control pin for each electrode Maximum freedom of droplets 1 2 3 4 5 6 High demanded control pins 7 8 9 10 11 12 Control pins: 24 13 14 15 16 17 18 19 20 21 22 23 24 ․ Broadcast-addressing biochips * A control pin can be shared by multiple electrodes Flexible for pin-constrained DMFBs 1 1 2 3 4 2 Control pin sharing 7 8 9 10 14 12 13 14 15 13 8 7 Control pins: 15 2 1 4 3 2 1 * [T. Xu and K. Chakrabarty, DAC’08] NCKU CSIE EDALAB
Previous Work and Limitation (1/2) Droplet routing algorithms Droplet routing in the synthesis of digital micro fluidic biochips [Su et al, DATE’06] Modeling and controlling parallel tasks in droplet based micro fluidic systems [K. F. B Ö hringer, TCAD’06] A network- flow based routing algorithm for digital micro fluidic biochips [Yuh et al, ICCAD’07] Integrated droplet routing in the synthesis of micro fluidic biochips [T. Xu and K. Chakrabarty, DAC’07] A high-performance droplet routing algorithm for digital micro fluidic biochips [Cho and Pan, ISPD’08] Pin-constrained digital microfluidic biochips Droplet-trace-based array partition and a pin assignment algorithm for the automated design of digital microfluidic biochips [T. Xu and K. Chakrabarty, CODES+ISSS’06] Broadcast electrode-addressing for pin-constrained multi-functional digital microfluidic biochips [T. Xu and K. Chakrabarty, DAC’08] NCKU CSIE EDALAB
Previous Work and Limitation (2/2) ․ Limitations Scheduled operations Separately consider the routing Droplet routing stage stage and the pin-assignment stage The solution quality is limited Pin-assignment stage # of Control pins # of Used cells Biochip design Execution time Scheduled operations Ours integrated method simultaneously Integrate pin assignment minimizes the # of control pins, # of used with droplet routing cells, and execution time for pin-constrained DMFBs. Biochip design NCKU CSIE EDALAB
Outline ․ Introduction ․ Our contribution ․ Problem formulation ․ Basic ILP formulation ․ Deterministic ILP formulation ․ Experimental results ․ Conclusion NCKU CSIE EDALAB
Previous Method – Direct Addressing ․ Apply the direct addressing to a routing result Separate pin assignment stage and routing stage 15 T 3 1 2 3 4 14 d 1 T 1 26 Control Pins: 13 Used Cell: 26 execution time: 18 12 d 2 5 6 7 8 9 11 10 16 # of control pins = # of used cells 17 22 26 20 21 23 24 25 d 3 18 19 T 2 NCKU CSIE EDALAB
Previous Method (1/2) – Broadcast Addressing ․ Apply the broadcast addressing to a routing result Separate pin assignment stage and routing stage 15 Control Pins: 15 Used Cell: T 3 26 18 execution time: 1 2 3 1 14 d 1 T 1 13 12 d 2 4 5 6 4 5 7 8 11 10 6 4 4 5 4 5 6 d 3 9 11 T 2 NCKU CSIE EDALAB
Previous Method (2/2) – Broadcast Addressing ․ Simply int ntegr grat ate the broadcast addressing with droplet routing 15 Control Pins: 12 Used Cell: 26 T 3 execution time: 18 1 2 3 1 11 d 1 T 1 Control Pins: 13 10 Used Cell: 29 execution time: 20 d 2 4 5 6 4 5 7 8 9 13 11 May increase the # of used cells and execution time 5 10 9 6 4 4 5 4 5 6 d 3 13 8 T 2 NCKU CSIE EDALAB
Ours (1/2) ․ Integrate broadcast addressing with droplet routing while simultaneously minimizing the # of control pins, # of used cells, and execution time 15 Control Pins: 4 Used Cell: 26 T 3 execution time: 18 1 2 3 1 6 d 1 T 1 Control Pins: 13 9 Used Cell: 29 execution time: 20 d 2 4 5 3 7 2 4 9 6 8 6 9 Control Pins: Used Cell: 23 7 7 execution time: 15 2 5 5 d 3 Minimized # of control pins 2 T 2 Minimized # of used cells Minimized execution time NCKU CSIE EDALAB
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, # of used cells, and execution time A basic ILP formulation is introduced to obtain an optimal solution A two-stage ILP-based algorithm is presented to tackle the complexity of the basic ILP formulation NCKU CSIE EDALAB
Outline ․ Introduction ․ Our contribution ․ Problem formulation ․ Basic ILP formulation ․ Deterministic ILP formulation ․ Experimental results ․ Conclusion NCKU CSIE EDALAB
Problem Formulation ․ Input: A netlist of n droplets D = { d 1 , d 2 ,…, d n } , the locations of modules ․ Objective: Route all droplets from their source cells to their target cells while minimizing the # of control pins, # of used cells, and execution time for high throughput designs ․ Constraint: Fluidic and timing constraints should be satisfied. • Fluidic constraint Minimum 2D microfluidic array Droplets spacing Static fluidic constraint Dynamic fluidic constraint • Timing constraint - Maximum available executed time Target NCKU CSIE EDALAB
Outline ․ Introduction ․ Problem formulation ․ Our contribution ․ Basic ILP formulation Objective function Basic constraints Electrode constraints Broadcast-addressing constraints Limitations ․ Deterministic ILP formulation ․ Experimental results ․ Conclusion NCKU CSIE EDALAB
Objective Function ․ Objective function Minimize the # of control pins (product cost) Minimize the # of used cells (fault-tolerance) Minimize the execution time (reliability) ∑ ∑ α + β + γ : ( ) ( , ) Minimize up p uc x y T l # of control pins # of used cells execution time where α , β , and γ are user-defined parameters NCKU CSIE EDALAB
Basic Constraints ․ Source/target requirement All droplets locate at their sources at time zero A droplet stays at its target once reaching it ․ Exclusive constraint Each droplet has only one location at a time step ․ Droplet movement constraint 1 A droplet can move to four adjacent cells or stall ․ Static/dynamic fluidic constraint No other droplets are in the 3x3 region centered by a droplet at time t / within t ~ t+1 Static fluidic Dynamic fluidic constraint constraint 1 2 1 2 NCKU CSIE EDALAB
Electrode Constraints (1/2) ․ Electrode constraints To model the control of droplets by turning on/off the actuation voltage of electrodes ․ Activation type “1” represents the activated electrode (turn on) “0” represents the deactivated electrode (turn off) “X” represents the don’t care (both “1” and “0” are legal) ․ Formulation technique Extract the cells that “must-be-activated” Extract the cells that “must-be-deactivated” NCKU CSIE EDALAB
Electrode Constraints (2/2) ․ Illustration Must be deactivated(0) Must be activated (1) Blockage Don’t care (X) Droplet # of activated cells: 1 # of deactivated cells: 11 activated 0 0 0 0 X 0 0 1 0 X # of activated cells: 1 0 0 0 0 X X # of deactivated cells: 8 X X X 0 0 0 deactivated X X X 0 1 0 X X X 0 0 0 NCKU CSIE EDALAB
Broadcast-Addressing Constraints ․ Broadcast-addressing constraints Model the pin assignment by “compatible” activation sequences Electrode E 1 E 2 E 3 E 4 E 5 E 6 E 7 E 8 E 9 E 10 E 11 E 12 1 1 0 0 0 X X 0 X X X X 0 0 1 1 1 0 0 1 X X X X Activation sequence 0 0 0 0 0 1 1 0 0 0 X X X X 0 0 0 0 0 0 1 1 0 0 X X X X 1 0 0 1 X X 1 1 0100X+01001 01001 Merge: E 4 and E 5 Pin-assignment result Pin-assignment result Merged activation Merged activation Pin Electrodes Pin Electrodes sequence sequence or 0 1 0 0 1 1 E 4 , E 5 0 1 0 0 X 1 E 4 2 E 5 0 1 0 0 1 01001+X0100 Invalid Merge: E 5 and E 6 NCKU CSIE EDALAB
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