A Network-Flow Based Optimal Sample Preparation Algorithm for Digital Microfluidic Biochips

Transcription

1 A Network-Flow Based Optimal Sample Preparation Algorithm for Digital Microfluidic Biochips Trung Anh Dinh Shigeru Yamashita Tsung-Yi Ho 2 Ritsumeikan University, Japan 2 National Cheng-Kung University, Taiwan

2 Agenda Introduction Problem Formulation Proposed Method Experimental Results Conclusion 2

3 Agenda Introduction Problem Formulation Digital Microfluidic Biochips Sample Preparation Illustrative Example Proposed Method Experimental Results Conclusion 3

4 Digital Microfluidic Biochips (DMFBs) Architecture of a DMFB: 2D microfluidic array: Basic cells for biological reactions Droplets: Biological samples (picoliter unit) I/O ports, peripheral devices (detector, ) Optical detector Droplet Electrodes Dispensing port Applications: Immunoassay, DNA sequencing, protein crystallization, etc. 4

5 Sample Preparation (/4) To produce droplets of the required concentrations A crucial preprocessing step in every application 90% of the cost and 95% of the analysis time single-target target droplet 75 % Processing time, reliability!!! Expensive cost!!! $$$ Sample preparation Sample droplets (c = 00%) Buffer droplets (c = 0%) Waste droplets 5

6 Sample Preparation (2/4) To produce droplets of the required concentrations A crucial preprocessing step in every application 90% of the cost and 95% of the analysis time multi-target 0 % 75 % 75 % 75 % 20 % 50 % Processing time, reliability!!! Expensive cost!!! $$$ Sample preparation Sample droplets (c = 00%) Optimization needed!!! Buffer droplets (c = 0%) Waste droplets 6

7 Sample Preparation (3/4) Dilution method in DMFBs Samples are diluted using : mixing/splitting ratio E.g., produce a droplet of concentration 25% ( 4 ) Sample port Waste 2 0 Buffer port 2 0 7

8 Sample Preparation (3/4) Dilution method in DMFBs Samples are diluted using : mixing/splitting ratio E.g., produce a droplet of concentration 25% ( 4 ) Sample port Waste Waste 2 sample droplet buffer droplet Buffer port waste droplet dilution operation 2 0

9 Sample Preparation (3/4) Dilution method in DMFBs Samples are diluted using : mixing/splitting ratio E.g., produce a droplet of concentration 25% ( 4 ) Sample port Waste Waste sample droplet 2 buffer droplets Buffer 0 port waste droplet dilution operation

10 Sample Preparation (3/4) Dilution method in DMFBs Samples are diluted using : mixing/splitting ratio E.g., produce a droplet of concentration 25% ( 4 ) Sample port Waste Waste 4 4 sample droplet 2 buffer droplets Buffer port waste droplet 2 dilution operations

11 Sample Preparation (4/4) In general: C i + C j 2 n 2n n C i C j A concentration value is always expressed by c i 2 d d: precision level of concentration d is given in each problem

12 Example: Same targets, but different cost d = 6 Targets: 2, #sample #buffer 7 7 #waste #ops T #sample #buffer 3 4 #waste #ops T

13 Agenda Introduction Problem Formulation Problem Formulation Previous Works Proposed Method Experimental Results Conclusion 3

14 Problem Formulation (/2) Given: Cost of sample droplet: cost s Cost of buffer droplet: cost b Precision level of concentration: d A set of N target concentrations: TC = {c, c 2,, c N } A set of the required number of droplets for each target N concentration: S = s, s 2,, s N ; S R = s i i= Output: A valid sample preparation process Objective: Minimize cost of sample and buffer usage F = u s cost s + u b cost b u s, u b : The numbers of used sample/buffer droplets 4

15 Problem Formulation (2/2) Example: cost s = 2 cost b = d = 3 TC = {3, 5}( 3 & 5 ) S = 4, 6 ; S R = Output: A valid sample preparation process Objective: Minimize cost function F = u s 2 + u b 5

16 Previous Works All the previous works are based on heuristics All the previous works focus on only one objective optimization Proposed Methods method: that deal Minimize with single-target the cost function problem (N = ) F = u [S. Roy et al., TCAD s cost 200] : Minimizes s + u b cost #waste b droplets Optimal solution for multiple-target problem [S. Roy et al., DATE 20]: Minimizes #waste droplets Flexible to change objective optimization Methods that deal with multi-target problem (N > ) [W. Thies et al., Natural Computing 200]: Minimize #operations By varying the values of cost s and cost b E.g., cost s = & cost b = 0 F = u s (#sample droplets) [Y.-L Hsieh et al., TCAD 202] : Minimizes #sample droplets [J.-D Huang et al., ICCAD 202] : Minimizes #sample droplets (more [D. Mitra on et this al., ISVLSI later ) 202]: Minimizes #operations 6

17 Agenda Introduction Problem Formulation Proposed Method Experimental Results Conclusion 7

18 Overview Input Min-cost max-flow (MCMF) network model construction Integer equal flows problem transformation ILP solver Output

19 MCMF Network Model Set of Vertices V Source, Sink, Waste Vertices that represent concentration values Constructed bottom-up from level 0 to level d (e.g., 3) Vertices at level l represent the set of concentration values that can be generated at this level Level 3 Level 2 Level Waste Sink Level 0 0 Source 9

20 MCMF Network Model Set of Arcs A Waste Sink cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level Minimize 0 F = f buffer 2 cost 4 b + f sample 6 cost s Level 2 Level 0 4 Level 0 0 f buffer cost = cost b = capacity = Source f sample cost = cost s = 2 capacity = 20

21 MCMF Network Model Set of Arcs A Waste Sink cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level 3 Level 2 Level Level cost = 0 capacity = Source 2

22 MCMF Network Model Set of Arcs A Waste Sink cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level 3 Level Level Level cost = 0 capacity = Source Integer equal flows constraints: f a i = f a j 22

23 MCMF Network Model Set of Arcs A Level 3 Level 2 Level Waste cost = 0 capacity = s 2 = 4 Sink cost = 0 capacity = s 2 = 6 cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level 0 0 Source Target concentration constraints: f target, Sink = s i 23

24 MCMF Network Model Set of Arcs A Waste Sink cost = 0 capacity = cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level 3 Level 2 Level Level 0 0 Source 24

25 ILP Model Minimize F = f Source, sample cost s + f Source, buffer cost b Subject to Capacity constraints: f v x, v y capacity v x, v y v x, v y A Network-flow conservation: v i :(v i,v x ) A f v i, v x = v o :(v x,v o ) A Integer equal flow constraints Target concentrations constraints f v x, v o 25

26 Agenda Introduction Problem Formulation Proposed Method Experimental Results Conclusion 26

27 Comparative Studies Single-target sample preparation problem [W. Thies et al., Natural Computing 0] [BS] [S. Roy et al., IEEE/ACM DATE ] [DMRW] [J.-D Huang et al., IEEE/ACM ICCAD 2] [REMIA] Multiple-target sample preparation problem [J.-D Huang et al., IEEE/ACM ICCAD 2] [REMIA] 27

28 Parameters Settings Cost Function F = u s cost s + u b cost b Waste droplets: [u s + u b S R ] S R : The total number of target droplets cost s cost b F Optimization Objective 0 u s #sample droplets (ours S ) u s + u b #waste droplets (ours W ) 2

29 Single-Target Sample Preparation ILP solver: CPLEX d = 0 Target concentrations: Take average values of all 023 cases BS DMRW REMIA ours S ours W # sample droplets # buffer droplets # waste droplets # operations

30 Multiple-Target Sample Preparation d =, 9, 0 N = 0, 20, 50, 00 For each pair (d, N), generate 00 random test cases d = 9 N = 0 N = 00 REMIA ours s ours W REMIA ours s ours W # sample droplets # buffer droplets # waste droplets # operations d = 0 N = 0 N = 00 REMIA ours s ours W REMIA ours s ours W # sample droplets # buffer droplets # waste droplets # operations

31 Conclusion Sample preparation Pivotal role in every assay, laboratory, and application in biomedical engineering and life science The first optimal sample preparation algorithm is proposed Based on a minimum-cost maximum-flow model Reduce the numbers of sample/buffer/waste droplets & dilution operations significantly (~60%/70%/5% & 60%, respectively) Thank you for your attention!!! 3

32 Appendix 32

33 MCMF Network Model Set of Arcs A cost = 0 capacity = Waste Sink cost = 0 capacity = s 2 = 6 cost s = 2 cost b = d = 3 TC = {3, 5} S = 4, 6 Level 3 Level Level Level 0 cost = 0 capacity = cost = cost b = capacity = cost = 0 capacity = Source cost = cost s = 2 capacity = 33

34 d = 3 Waste 4 Sink 6 Level 3 Level 2 Level Level Source

35 Problem Formulation Hybrid cost function: F = u s cost s + u b cost b The number of waste droplets: u s + u b S R cost s cost b F Minimization 0 u s #sample droplets u s + u b #waste droplets practical values u s cost s + u b cost b practical cost The cost function F is flexible 35

36 Experiment Environment Implemented by C++ ILP Solver: CPLEX Linux server Intel Core(TM) i7 CPU GHz 24 GB Memory Largest test case (d = 0, N = 00) 352,60 variables 75,374 constraints Computation time: ~30 minutes 36

37 Digital Microfluidic Biochips (DMFBs) (2/2) Advantages: High portability High throughput Low sample volume consumption Less human intervention errors Applications: immunoassay, DNA sequencing, protein crystallization, etc. 37